Session JP11: Poster Session IV: BEAMS: Laser- and beam-plasma interactions Fundamental: Measurements and analysis in fundamental plasma physics; Plasma Sheaths, Sources, and Shocks MFE: Turbulence and transport in fusion plasmas; High Field Tokamaks 2:00 PM - 5:00 PM

Acceleration of heavy ions and muons by wakefields driven by non-relativistic short pulse proton beams

We investigate the possibility of generating non-relativistic wakefields with mono-energetic proton beams in both magnetized and un-magnetized plasma. The generation of short pulse mono-energetic proton beams in the energy range 1-10MeV has been demonstrated theoretically and experimentally in intense short pulse laser driven shock waves. This has led to the idea of using these non-relativistic proton beams to generate plasma waves and wakefields in plasma to provide a fast, compact and controllable acceleration of sub-relativistic heavy ions and muons. Relativistic proton beams have been demonstrated to self-modulate generating relativistic electron plasma waves that produce relativistic electrons. Non-relativistic proton beams propagating across magnetic fields generate lower hybrid waves through the modified two stream instability and commonly invoked to explain ion heating and electron acceleration in collisionless magnetized shock waves. With short intense proton beams, where the pulse length is comparable to the electron skin depth, there is the possibility of generating non-relativistic electrostatic wakes that can accelerate heavy ions or muons. We will present theory and simulations.   

High-Density Helicon Studies on the Madison AWAKE Prototype

The AWAKE project at CERN opens up the frontier of next generation electron colliders using beam-plasma wakefield acceleration. Acceleration gradients exceeding 1 GV/m have been demonstrated using a laser-ionized plasma. However a full scale accelerator will need a reliable, high-density plasma source that scales to kilometer lengths with a high degree of axial density uniformity. The Madison AWAKE Prototype (MAP) is utilizing 30 kW of RF power to generate a helicon plasma with expected densities reaching 10²⁰ m^-3 in a multi-antenna setup. In order to optimize the density profile in MAP, an understanding of wave propagation and power deposition is essential. To this end we have developed a finite element model that solves for the quasi-3D wavefields and power deposition for a given temperature, density and neutral distribution. Using this model alongside experimental measurements and analytics we have for the first time revealed the mechanism responsible for the directionality of helicon discharges and the preference of right- over left-handed whistler modes. In addition to this discovery, we will further present current results for measured plasma density and ion temperature along with our progress towards enabling high-power steady-state operation.   

Derivation of the Helicon Particle Balance by Laser Induced Fluorescence in MAP

A moderately high plasma density (10²¹ m^-3) with very high axial uniformity is needed to achieve wakefield acceleration of electrons in the GV/m range in AWAKE plasmas. While pulsed helicon plasmas are capable of reaching sufficient densities transiently, it is not known if steady state helicon plasmas can sustain these densities. Using laser induced fluorescence (LIF) it is possible to infer plasma density in steady state and pulsed helicon plasmas. Initial results in a steady state plasma in the Madison AWAKE Prototype (MAP) indicate a peaked axial and hollow radial density profile at low power of 1.3 kW in a 5.2 cm diameter chamber. Radial and axial flow velocities of ions and neutrals are also measured by LIF, and these velocities are used to derive the particle source rates and particle balance in the plasma. Previous work on helicons indicated a dominant axial flux, but we measure a radial flux of the same order of magnitude as the axial flux, much stronger than merely Bohm. The radial flux suggests a different fueling mechanism for the plasma compared to devices with larger diameter. The 2D particle balance indicates how helicon plasmas are formed and sustained. This information about helicons can provide insight into how to adapt these plasmas for more uniform and higher densities on axis, so that they may approach the AWAKE parameter requirements.   

Underdense Passive Plasma Lens for Focusing Relativistic Electron Beams

The utility and application of an accelerated particle beam is limited significantly by its emittance. When exposed to the strong transverse focusing forces of a plasma wakefield accelerator over large distances, the projected emittance of a beam can grow significantly due to chromatic phase spreading. This emittance growth can be mitigated by if the beam is initially matched to the plasma, which generally requires it to have a very small spot size. Conventional quadrupole electromagnet focusing devices struggle to focus the beam to a sufficiently small spot size at the entrance of a plasma wakefield accelerator. A plasma lens may be more appropriate for this task, as it can focus an electron beam with hundreds-to-thousands of times greater strength than magnetic focusing devices. When an electron beam travels through the plasma lens, an attractive force is exerted radially inward, which focuses the electrons of the beam in the same way that a converging lens focuses light. If the plasma is less dense than the electron beam, a nonlinear blowout wake will form, which exerts a linear focusing force whose strength scales with the plasma density. We call this the underdense, passive plasma lens.

The plasma lens offers several advantages over conventional magnetic focusing devices: it is significantly stronger, ultra-compact, and it is axisymmetric, focusing in both the vertical and horizontal dimensions simultaneously. Through simulation, this project examines the interaction between an accelerated electron beam and a passive, underdense plasma lens using realistic parameters for upcoming experiments planned at SLAC’s FACET-II facility.

    

Optically-Generated Plasma Lens for Focusing Relativistic Electron Beams

To maintain beam emittance and quality, particle beams in plasma wakefield accelerators (PWFAs) need to be focused to extremely small sizes upon entering the accelerator. Conventional methods that achieve this involve large quadrupole electromagnets, which can occupy a considerable amount of space, often spanning several meters. The plasma lens, however, represents a compact, strong alternative means of focusing high-energy electron beams.

We present an experimental infrastructure designed to generate this plasma lens. The plasma lens is formed by the laser-ionization of gas in the outflow of a gas jet positioned along the electron beam line. By using cylindrical lenses to focus an ultrashort, 10 mJ, Ti:sapphire laser pulse, a pancake-like region of plasma is created prior to the arrival of the electron beam. To avoid undesired ionization from the Coulomb field of the electron beam, a high ionization threshold gas, like helium, is used. Results of experiments testing the optical setup at the University of Colorado Boulder will be presented, demonstrating the feasibility and tolerance of the system.   

Experimental Analysis of a Pilot Lithium Charge Stripper Using a Magnetohydrodynamic Pump

 The pilot lithium charge-stripper for the uranium charge removal of the Rare isotope Accelerator complex for ON-line experiences (RAON) was optimally designed and experimentally characterized. The liquid lithium thin film was formed by colliding a liquid lithium jet with a planar deflector of the charge-stripper, where a helical type of DC MHD pump was used to generate the liquid lithium flow. The MHD pump with a nominal flowrate of 6 cm³/s and a developed pressure of 14.6 bar in the operating temperature of 200℃ was designed and fabricated from the COMSOL Multiphysics code based-optimum analysis of its electromagnetic and hydraulic variables. The analysis of the geometrical arrangement of the permanent magnet of the MHD pump revealed that the input current for the nominal flow rate and developed pressure were 500 A. The lithium injection nozzle of the charge stripper was optimized through simulation analysis and water similarity experiments in terms of formation of the required liquid lithium film thickness of 22 µm. The fabricated nozzle diameter and angle of the lithium charge stripper was 0.7 mm and 34°, respectively. The formation of a 22-µm thick liquid lithium thin film required to obtain the 79+ charge state of uranium was confirmed at the flow rate of 5.93 cm³/s and input current of 107 A   

Ion Motion in Resonantly-Driven Plasma Wakefield Accelerators

Plasma-based accelerators can sustain electric fields orders of magnitude higher than accelerators based on radio-frequency cavities. The AWAKE experiment at CERN drives plasma wakefields over long distances using highly relativistic proton bunches with 10s of kilo-Joules stored energy. This may allow for TeV energy gain in a single acceleration stage. To establish high accelerating fields, the currently available long proton bunch must be self-modulated to resonantly drive a plasma wave and its associated wakefield.

The charged drive bunch deflects plasma electrons, which then oscillate due to the restoring force of the ions. Resonant excitation using equally spaced bunches relies on the restoring force being uniform along the bunch, which may not be the case if the bunch is long enough for ions to respond to the fields. Recent experiments used ion species with different mass to investigate the impact of ion motion on such resonantly driven systems. Lighter ions were found to reduce wakefield amplitudes towards the proton bunch tail. This work utilizes particle-in-cell simulations to study the effect ion motion on the wakefield development and compares them to experimental results. We show and explain the physics of how ion motion can detune the self-modulation resonance. These findings allow limits to be placed on the choice of plasma gas in resonantly driven wakefield accelerators.   

Generalized description of the efficient electron acceleration in ion channels by multi-PW lasers

Direct laser acceleration (DLA) is a mechanism of electron acceleration by relativistic laser pulses propagating through underdense plasmas. It is based on the so-called betatron resonance between the simultaneous electron oscillations in the background field of an ion channel and in the field of the laser pulse. This mechanism provides a high total charge of accelerated electrons (100s of nC was already achieved in experiments). Plasma interaction with 10 PW laser pulses has the potential to provide electrons with energies up to 10 GeV through DLA. Apart from being a source of high-energy electrons, it also can provide high flux gamma-ray radiation. This mechanism of electron acceleration is naturally present and affects the electron heating in the interaction of lasers with preplasma of solid targets, which is important to study for high- intensity pulses of next generation.

We present analytical scaling laws for electron energies as a function of the plasma density and the laser intensity. Furthermore, we discuss the effects of varying plasma density on acceleration. We derive conserved quantities that allow to predict scaling laws for arbitrary slowly varying profiles. Analytical predictions are in good agreement with the simplified test-particle model as well as with Quasi-3D PIC simulations performed with the code OSIRIS. Furthermore, we provide guide for laser focusing in order to optimize future DLA-based electron and radiation sources that can be directly verified at multi-PW laser facilities [1].   

Computational Studies on Low Intensity Near Critical Density Laser Wakefield Acceleration for Medical Applications

Conventional laser wakefield acceleration requires high intensity lasers and plasma densities much lower than the laser critical density in order to both be stable against thermal plasma instabilities and to achieve electron trapping and acceleration. Here, we use particle-in-cell simulations to study laser wakefield acceleration near the critical density. We show that even at low intensities (<10¹⁵ W/cm²) nonlinear laser-plasma interactions excite both high and low phase velocity electron plasma waves through multi-wave coupling. The low phase velocity waves are able to initially trap and accelerate electron bunches so that higher phase velocity waves can further accelerate this bunch to energies of approximately 10 keV or greater. Theoretical studies using nonlinear optics formulations are also used to show the wave-wave excitation in the low intensity regime. These electron bunches of 10 keV are suitable for many applications, particularly medical and radiation therapy where doses of > 1 Gy are possible with improving fiber laser technology.   

Staging of high-efficiency and high-quality laser-plasma accelerators for collider applications

The viability of next generation, compact, TeV-class electron-positron colliders based on staging of independently-powered plasma-based accelerators relies on the possibility of accelerating high-charge bunches to high energy with high efficiency and high accelerating gradient, while maintaining a small energy spread and emittance. Achieving a small energy spread with high efficiency requires employing witness bunches with optimally tailored current profiles (optimal beamloading). Such profiles are analytically known in the case of plasma-wakefield accelerators operating in the blowout regime, while in the case of laser-plasma accelerators (LPAs) can only by computed numerically, and their determination requires, among other things, taking into account the laser driver evolution. A small bunch energy spread is a necessary condition to enable staging and minimize emittance degradation from chromaticity when bunches are transported from one plasma accelerator stage to the following one. In this contribution we will discuss examples of LPA stages operating in different regimes, namely a self-guided stage in the nonlinear regime and a quasi-linear stage in a hollow plasma channel, providing high-gradient, high-efficiency, and quality-preserving acceleration of bunches for collider applications. We will present, for each example, the current profile distribution for optimal beamloading, and we will analyze bunch emittance degradation when staging of such LPAs is considered.   

Electron Beam Transport from Laser Plasma Accelerator to Undulator with Quadrupole FODO Lattice

Laser Plasma Accelerators (LPAs) provide a means for producing electron beams (e-beams) of GeV energy levels through the mm-scale acceleration of charged particles via laser-driven plasma wakefields. In this work, we present on the transport of e-beams generated from an LPA to a unique undulator that was built with an embedded permanent magnet based FODO lattice. The 16 cell FODO lattice which spans the full length of the 4m undulator is designed to maintain small transverse beam sizes over the full undulator length and thereby increase the FEL rho parameter averaged over the length of the undulator. This focusing channel is beneficial for FEL applications but simultaneously imposes stringent requirements on the transverse stability of the LPA source. We have developed diagnostic techniques that enable precise measurement and characterization of these fluctuations. By understanding the root causes of these variations, we implement stabilization methods to minimize their impact on the electron beam before it enters the FODO lattice and undulator [1]. This work highlights the significance of efficient beam transport and stabilization techniques in bridging the gap between LPAs and their adoption in high impact applications like compact FEL systems.   

Hydrodynamically shaping plasmas for enhanced Laser Plasma Acceleration

Laser Wakefield Acceleration (LWFA) is a compact, plasma-based accelerator technique that can generate accelerating fields up to GeV/cm, ~1000 times greater than conventional RF accelerators. These compact accelerators can help further the study of fundamental physics and improve applications in other fields, such as functioning as a compact x-ray source for medical applications. We are improving the LWFA process by producing Helium waveguides via optical field ionization using 60mJ, 40 fs pulses that can extend the propagation of the 800 nm, 700 mJ, 40 fs wakefield accelerating pulse by many Rayleigh ranges. We also introduce another 10 mJ, 40 fs plasma ionizing beam to facilitate downramp injection at the beginning of the plasma waveguide, and study its structure and effectiveness at inducing electron injection in a guided plasma channel.   

"Isomer population control via direct irradiation of solid-density targets using a laser-plasma accelerator"

A small component of spent nuclear fuel is both highly radioactive and long-enough lived to require costly long-term storage. Efforts to accelerate the decay of these species through excitation into the multi-MeV nuclear “quasicontinuum” via nuclear-plasma interactions are underway. In this work we present results using a hundred terawatt laser-plasma accelerator to excite Bromine nuclei through pulsed ultra-fast (<10 fs) direct irradiation of solid-density active LaBr targets. These targets absorb real and virtual 5-30 MeV photons and then immediately de-excite to states with different lifetimes. The population of these excited states provides a sensitive probe of gamma strength and level densities in the nuclear quasicontinuum. Further probing of these nuclear-plasma interactions could have far-reaching impact including decreased storage of long-term nuclear waste and an improved understanding of heavy element formation in astrophysical settings.   

Using an on-shot pulse duration diagnostic in an LPA driven FEL system to directly measure correlations between drive laser and electron beam properties

Laser-plasma-accelerators (LPAs) have emerged as a promising technology to overcome the gradient limitations in conventional accelerators. LPAs are being developed for a broad range of applications, including as a compact source of electrons for free-electron-lasers (FELs), which benefit from their inherently large peak currents and high transverse beam brightness. One of the challenges towards reliable LPA-driven FEL operation are the strict limitations imposed on the bunch properties by the undulator acceptance, which requires high shot-to-shot stability and precise tunability. In this work, we report on implementation of an on-shot diagnostic on the Hundred Terawatt Undulator (HTU) beamline at the BELLA center to directly correlate laser pulse temporal profile and spectral phase, important parameters impacting bunch generation, and stability with electron beam properties, transport, and the undulator performance. Thus, we are able to gain important insights into the underlying dynamics, bringing us closer to effectively matching the electron bunches to the FEL acceptance and thereby towards realizing an application ready LPA driven FEL.    

Electromagnetic pulses from high intensity laser experiments with gas-density plasma

Radio frequency (RF) electromagnetic radiation in the form of an electromagnetic pulse (EMP) resulting from high intensity laser plasma experiments has the potential to damage scientific diagnostics in experiments. Although solid-target laser EMP has been thoroughly studied, there is a dearth of published research with respect to to gas-density targets, even though EMP can still be catastrophic in such cases. Here we compare the EMP generated in a direct laser acceleration (DLA) experiment at the Texas Petawatt laser facility to that in a laser-wakefield acceleration (LWFA) experiment at the HERCULES laser facility at the University of Michigan, elucidating the mechanisms for the purpose of understanding the physics and developing mitigation strategies. In the Texas Petawatt, a 150-fs, 100 J laser pulse focused with a f/40 parabola on a supersonic hydrogen gas jet target with density from 10^18 cm^-3 to 10^19 cm^-3. In HERCULES, a 39 fs, 9 J laser pulse was focused with an f/40 parabola into a gas cell of nitrogen-doped helium with a measured electron density of about 4 x 10^18 cm^-3. The relative contribution of beam-electrons and non-beam electrons to the EMP will be discussed for both cases, as well as PIC simulations with experiment-relevant parameters   

Measurement and hydrodynamic modeling of meter-scale plasma waveguides for multi-GeV electron accelerators

In recent experiments, low density, hydrodynamic plasma waveguides from Bessel beam-induced optical field ionization were employed to achieve multi-GeV laser wakefield acceleration (LWFA)  [1]. Improving the electron energy and beam quality requires fine control of electron injection and acceleration inside the waveguide.  A full experimental characterization of the plasma waveguide evolution in 3 dimensions, along with an accurate hydrodynamic model, are therefore indispensable for channel-guided LWFAs. We present time resolved two-color interferometry-based measurements of the plasma and neutral density profiles during plasma expansion in various gases, including hydrogen, nitrogen, and argon via under various conditions. Complementary to the measurements, we present hydrodynamic simulations using the SPARC module of TurboWAVE  [2,3], which uses as the initial condition the Bessel beam heated plasma modeled by our code YAPPE [4].

1.    B. Miao, et al., Multi-GeV Electron Bunches from an All-Optical Laser Wakefield Accelerator, Phys. Rev. X 12, 31038 (2022).

2.    D. Gordon, et al., SPARC—A Simulation Model for Electrical Charges, Nav. Res. Lab., Washington, DC, USA, NRL Memo. Rep 6706 (2006).

3.    D. F. Gordon, et al., A Ponderomotive Guiding Center Particle-in-Cell Code for Efficient Modeling of Laser-Plasma Interactions, IEEE Trans. Plasma Sci. 28, 1135 (2000).

4.    L. Feder, et al., Self-Waveguiding of Relativistic Laser Pulses in Neutral Gas Channels, Phys. Rev. Res. 2, 043173 (2020).   

Propagation of Texas Petawatt laser through high density gas jet targets

We report on a recent experimental campaign funded by LaserNetUS investigating the propagation of the Texas Petawatt laser through high density (~ 10¹⁹ cm^-3) gas jet targets of hydrogen and deuterium in the direct laser acceleration (DLA) regime. Nominal laser parameters are 140 J delivered in 140 fs pulses. Primary objectives of this campaign included investigation of laser propagation instabilities, ion dynamics, electromagnetic pulse production, shock wave generation, plasma heating, optical observation of ion filamentation, and the effects of apodizing the laser beam. Various sizes and geometries of apertures were employed in the laser near field to improve the spatial quality of the laser on target. Diagnostics used included neutron time of flight detectors, an electron spectrometer, radiochromic film, optical probing (shadowgraphy, schlieren, interferometry), bubble detectors, NaI gamma detectors, and electromagnetic pulse detectors. Initial data analysis indicates the existence of an annular electron beam with a divergence of a few degrees surrounding the on axis electron beam. The structure and quality of this annular beam is correlated to the type of aperture used.   

Laser-wakefield-accelerated electron bunch interactions with matter

Laser-wakefield accelerators (LWFAs) have attracted intense research attention in recent years as compact sources of relativistic electron bunches. Additionally, laser-wakefield-accelerated electron bunches have unique properties, such as femtosecond durations and micron-scale dimensions, due to their mechanism of generation. This poster reviews AFRL research on the interaction of LWFA electron bunches with matter.   

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For the past two decades, intense lasers have supported new schemes for generating high-energy particle beams in university-scale laboratories. With the direct laser acceleration (DLA) method, the leading part of the laser pulse ionizes the target material and forms a positively charged ion plasma channel into which electrons are injected and accelerated. DLA has been realized over a wide range of laser parameters, using low-atomic-number target materials. A striking result is the extremely high conversion efficiency from laser energy to MeV electrons, with reported values as high as 23%, which makes this mechanism ideal for generating large numbers of photo- nuclear reactions. DLA is well understood and reproduced in numeric simulations. Specifically, the electron beam energy has been confirmed to scale with the normalized laser intensity up to values of a0~1.5. However, the electron energies obtained with the highest laser intensities available nowadays, fail to meet the prediction of these scaling laws. Here we reveal that at these higher laser intensities, the leading edge of the laser pulse depletes the target material of its ionization electrons prematurely. We demonstrate that for efficient DLA to prevail, a target material of sufficiently high atomic number is required to maintain the injection of ionization electrons at the peak intensity of the pulse when the DLA channel is already formed. Applying this new understanding to experiments on petawatt laser facilities, within the LaserNetUS network is expected to increase the electron energy overlap with the neutron production cross-sections of any material. These increased neutron yields are required to enable a wide range of research and applications, such as investigation of nucleosynthesis in the laboratory, performing non-destructive material analysis, and industrial applications.   

Plasma-accelerator-based linear beam cooling systems

Plasma-based accelerators enable compact acceleration of beams to high energy and are being explored as a potential technology for future linear colliders. Conventional linear colliders require damping rings to generate the required beam emittance for particle physics applications.  We present and discuss a plasma-based linear radiation damping system that allows cooling of ultrashort bunches compatible with plasma-based accelerators. The plasma accelerating gradients enable relatively compact linear damping systems, and there is a trade-off between system length and the achievable emittance reduction. Final asymptotic normalized transverse beam emittance is shown to be independent of beam energy.  The impact of coherent radiation emission is considered.   

Guiding of 400 TW laser pulses at the BELLA Center using hydrodynamic optical-field-ionized plasma channels

Laser-plasma accelerators (LPAs) have large acceleration gradients, orders of magnitude greater than conventional accelerators. Plasma channels can guide high intensity laser pulses, increasing the acceleration length and final beam energy by maintaining the laser pulse intensity over distances greater than the diffraction length. Single stage acceleration to the 10 GeV level using the petawatt (PW) laser at the Berkeley Lab Laser Accelerator (BELLA) Center requires plasma channels with density ~1E17/cc and matched spot size tens of micron. Hydrodynamic optical-field-ionized channels (HOFI) can meet these requirements. Recently, a second beamline was commissioned at the BELLA PW facility that allows for two independently adjustable high intensity laser pulses in one target chamber with up to ~40J total energy. We present guiding results with HOFI plasma channels formed using the BELLA PW second beamline.   

Generation of Highly-Collimated Pair-Plasma Electron, Positron, and Gamma-Ray Beams by Longitudinal Laser Fields

An 'all-optical' set up for the acceleration of electron-positron (e^- e⁺) beams in pair plasma is investigated using 3D particle-in-cell (PIC) simulations.  By irradiating a pair plasma target with a highly focused ultra-relativistic laser, electrons and positrons are accelerated into beams in a similar mechanism to Linear Direct Acceleration (LDA) of electron-ion plasma.  Here, a pre-fabricated hollow micro-channel target acts as a wave-guide and stabilizes the acceleration process of electrons pulled into the channel.  Though, the set up can be sensitive to issues such as laser-channel alignment and pre-expansion of plasma into the vacuum channel.  These are largely avoided in the pair plasma set up where the vacuum channel is formed pondermotively by the laser as it propagates through the target.  Regardless, the LDA mechanism is similar in both; the vacuum channel acts as a wave-guide for the powerful laser, pulling bunches of particles from the walls and propelling them into the longitudinal laser electric field.  Their near speed-of-light forward motion, free of transverse oscillations, enables prolonged interaction with the accelerating region of the longitudinal electric laser fields.  The result, in our pair plasma simulation, are highly relativistic and collimated bunches of electrons and positrons that generate energetic and similarly directed beams of gamma-rays through synchrotron emission.     

Plasma waveguide generation with diffractive logarithmic axicon

 

The use of plasma waveguides in Laser Wakefield Acceleration (LWFA) offers a compelling approach for achieving enhanced electron acceleration by enabling extended laser-plasma interaction lengths [1,2]. This poster explores the utilization of a logarithmic diffractive axicon in order to improve the longitudinal uniformity of the plasma and regularize the guiding and acceleration processes in LWFA.

Logarithmic axicons have logarithmically varying radial phase function, engineered based on radial to axial mapping of energy [3]. The spot size of the Bessel-like beam generated through this type of axicon stays nearly constant in an extended focal range but maintains a much more constant intensity than the Bessel beams formed with a classical axicon. We demonstrate fabrication and characterization of a diffractive logarithmic axicon as well as generation of a meter-scale plasma waveguide structure.

References:

1. Feder, L. et al. (2020). Self-waveguiding of relativistic laser pulses in neutral gas channels. Physical Review Research, 2(4).

2. Miao, B. et al. (2022). Multi-GeV Electron Bunches from an All-Optical Laser Wakefield Accelerator. Physical Review X, 12(3).

3. Sochacki, J. et al. (1992). Nonparaxial design of generalized axicons. Applied Optics, 31(25), 5326.   

Design and Operation of Cross Polarization Wave Generation in a Double Crystal Setup for Seeding a 100 TW Laser System

We present a compact and energy-efficient setup for femtosecond pulse cleaning, utilizing a double crystal arrangement to generate highly efficient cross-polarization wave (XPW) pulses. By employing 1.4 mJ, 35 fs input pulses, we achieve the production of a 150 µJ, 30 fs XPW pulse with a contrast ratio 10^7 at kHz repetition rate. To maintain stability and prevent white light generation, we ensure the internal efficiencies of XPW generation are approximately 12%. This poster outlines the design parameters, layout configuration, and measurements conducted for assessing contrast ratio, pulse duration, and spectral width. Moreover, we present and discuss the results of implementing XPW in the BELLA Hundred TW laser system, specifically focusing on applications in laser-plasma acceleration (LPA) and Thomson scattering generation. The utilization of XPW in these systems demonstrates its potential for enhancing the performance of the advanced LPA beams. The findings of this study contribute to the understanding and optimization of XPW generation, providing valuable insights for the design and operation of highly efficient XPW generation in laser systems. The compact nature and energy efficiency of our setup make it a promising candidate for various applications that require precise spatial and temporal filtering of femtosecond pulses.   

Measuring Coulomb Explosion Ions from OMEGA EP Interactions

Direct laser acceleration (DLA) can generate electron beams with high charge to produce secondary radiation sources. Experiments at the OMEGA EP laser facility were designed to optimize the direct laser acceleration of electrons in an underdense plasma created from a helium gas target. In these experiments, the ponderomotive force expels electrons from the regions of highest laser intensity to form a channel. The charge separation creates a strong transverse electric field that accelerates ions radially through a Coulomb explosion; it is the same radial channel field, along with the electron beam-generated azimuthal magnetic field, that facilitates DLA. Since the channel formation is key to understanding electron acceleration, the accelerated helium ions, measured with a Thomson Parabola Ion Energy (TPIE) spectrometer, provide an interesting complementary measurement for understanding the field strengths inside the channel.   

Collimation of Laser-Driven Proton Beams for in vivo radiobiological investigation of FLASH Radiotherapy

Laser-driven ion acceleration (LDA) promises a more compact and cost-effective alternative to conventional proton therapy. Ultra-high dose rates have been shown to differentially spare healthy tissue relative to tumor tissue (FLASH effect). LDA beams can achieve these dose rates with the use of a beam transport system to compensate for the substantial divergence and energy spread of the beams following the laser-target interaction. Presented here is the implementation of a compact, permanent magnet-based beam transport to deliver 10 MeV protons to in vivo biological samples to investigate the FLASH effect. Dosimetry was performed by a suite of diagnostics including multiple online integrating current transformers to indirectly estimate the dose, a scintillating screen for dose profile monitoring, and radiochromic films for the on-target dose profile. This work further establishes the practicality of employing compact LDA proton sources for FLASH studies and showcases the capability of the BELLA Center iP2 beamline to accommodate additional radiobiological experiments.   

The impacts of downstream heating on ion reflection for collisionless electrostatic shock

Collisionless electrostatic shock (CES) can accelerate ions efficiently with a narrow energy spread, making it one of the most prominent ion acceleration mechanisms using intense lasers. In CES, ions can be reflected at the shock front due to the presence of electrostatic potential, resulting in an ion beam accelerated to velocity up to twice that of the shock velocity. While the reflection plays the main role in the ion acceleration scheme and can also impact the overall shock structure, the detailed mechanism remains unknown. For instance, it is not clear how partial reflection (0 < reflection fraction < 1) is achieved when we have cold ions upstream. Contrary to previous studies attributing ion reflection to the temperature of the upstream (pre-shock) region, we argue that the reflection can be explained by the downstream heating by evidence in particle-in-cell simulation. In our proposed model, all ions travel to the downstream region, where they gain thermal energy by various kinetic instabilities. Consequently, ions show a wide velocity dispersion, and those with velocities larger than the shock velocity are "kicked" back to the upstream, constituting the reflected fraction.   

BELLA iP2: High-Intensity Laser Beamline with Double Plasma Mirror

The high-intensity laser beamline at BELLA PW facility, iP2, enables frontier capabilities in High Energy Density Science (HEDS), including accessing exciting new regimes of ion acceleration. This system provides a focal spot of ~3 μm diameter, resulting in on-target peak intensities of > 5×10²¹ W/cm². The high laser pulse repetition rate capability (up to 1 Hz), if paired with innovative, replenishable target systems, will increase the particle flux for applications and allows for the collection of large data sets, enabling adequate statistical analysis of the results. In this presentation, we report updates of the capabilities such as pulse contrast enhancement system based on a double plasma mirror. The iP2 beamline is accessible to users through LaserNetUS.   

Laser-driven proton-boron reaction for alpha particles production

The fusion reaction P + ¹¹B generates 3 alpha-particles with a total energy of 8.7 MeV. It opens the possibility of developing a novel generation of high brightness alpha-particle source, with potential interest in astrophysics, fusion energy [1] and medical in particular for the production of radioisotopes for diagnostics or medical treatment [2].

This work aims at studying different schemes of laser-driven p-¹¹B reaction exploiting the high-power and the high repetition rate of VEGAIII laser to improve the alpha production detection and Scandium radioisotope production. Different setups are proposed: (i) Pitcher-catcher configuration: TNSA proton produced from thin aluminium foil target (Pitcher) interact on a solid B type target (catcher) and (ii) Directly irradiation of solid samples of Boron-nitride (BN) target.

We present in this work the experimental setup and the diagnostics used during the campaign, as well as the first preliminary results of the experiment.

[1] H. Hora, et al. Laser and Particle Beams (2015), 33, 607–619

[2] K. Szkliniarz, et al. Applied Radiation and Isotopes 118, 182 (2016)   

A mid-beta booster for proton beams

Acceleration of ion beams in laser-driven plasma waves is challenging, owing to the difficulty of trapping the slow velocity ions in the relativistic plasma wave. In a laser-plasma accelerator, the phase velocity of the plasma wave is approximately the group velocity of the laser driver propagating in the underdense plasma. Due to their high rest mass, protons only reach comparable velocities with multi-GeV kinetic energies. However, the typical proton energy obtained from a compact laser-solid source is tens of MeV. Here, we explore the possibility of post-accelerating an ion beam produced in a compact laser-based source using the “snow-plow” field of an intense laser pulse propagating in a near-critical density target [B. Liu, et al., PRL 129, 274801 (2022)]. The electron sheet that accumulates in front of the laser pulse generates an electric field on the order of 10 TV/m, that yields GeV energy gains within a 100 μm target, eventually reaching an energy sufficient for a subsequent beam injection into a laser-plasma accelerator.   

Application of Azimuthal Doppler Shifts for Transverse Flow Velocity Measurements

We have developed a novel method, Optical Vortex Laser Absorption Spectroscopy (OVLAS), specifically for measuring transverse flow velocities in plasma. Conventional Tunable Diode Laser Absorption Spectroscopy (TDLAS) has a limitation in the measurement direction, with sensitivity restricted to the laser's propagation direction. This limitation is particularly problematic when attempting to observe particles moving perpendicular to the material surface during plasma-material interactions. We overcome this limitation by replacing the probe beam with an optical vortex beam, thus introducing the concept of the azimuthal Doppler shift for transverse flow velocity measurement. In our setup, an optical vortex beam was introduced into a flowing inductively coupled plasma (ICP) and derived the azimuthal Doppler shift distribution from the absorption spectra. These spectra are constructed based on the intensity variation in the beam cross-section. The results confirm that the azimuthal Doppler shift varies sinusoidally in the azimuthal direction, allowing the calculation of transverse flow velocities. For flow velocities exceeding 70 m/s, we observed measurement errors of less than 15%, with a mean absolute percentage error (MAPE) below 8%.   

Measuring the Ion Temperature of a Plasma Jet Using a Two-Dimensional Optical Fiber Array for an Improved Spectroscopic Analysis to Study the Possibility of Pre-heating During Plasma Compression

Outlined is our arrangement to measure the ion temperature of a plasma jet via Doppler-broadening spectroscopy to investigate the possibility of pre-heating plasma during plasma compression. The jet, formed by puffing a controlled amount of Argon gas into Embry-Riddle’s cylindrical vacuum chamber and then ionizing it via high-voltage electronically switched capacitor banks, is regulated to undergo magnetohydrodynamic (MHD) current-driven instabilities and magnetic reconnection, and is ultimately terminally collided with a gas cloud [1]. Ion temperature measurement of plasma is inferred by spectroscopic analysis [2] [3]. To improve the fidelity of our spectroscopy, the presented method implements a unique assemblage of 54 optical fiber cables into a systematic two-dimensional array, broadening the area of observation. With this, we aim to develop our analysis of instability-induced ion heating and its contribution to collisional plasma heating, thus shedding light on the possibility of pre-heating the plasma during plasma compression.   

Filterscope Analysis Techniques for Nearby Tungsten Impurity Line Screening

Antennas in fusion reactors generate radio frequency (RF) fields and plasma sheaths that interact with the local plasma which can result in increased erosion of the antenna structure. The RF Plasma Interaction Experiment (RF PIE) at Oak Ridge National Lab (ORNL) is used to simulate this RF antenna structure. RF PIE is an Electron Cyclotron Resonance microwave-based plasma source (2.45 GHz, <5 kW) with an RF biased electrode. RF PIE can provide relatively clean spectral plasmas and a simplified viewing geometry with a large solid angle making spectral measurements easier to capture. The filterscope diagnostic, developed at ORNL, uses band-pass filters and photomultiplier tubes to detect specific spectral emission lines.

Filterscopes are being used to measure the W line emission at 400.88 nm as a function of ion energy on RF PIE. Different filter techniques are being explored and compared. The effectiveness of these techniques to screen out nearby impurity lines, like the Ar II 401.39 nm line expected on the fully-tungsten wall WEST experiment, is being determined by comparing the measurements to a high-resolution 1.0 m Czerny-Turner spectrometer with 40 um spatial resolution and 0.012 nm spectral resolution. The ability to filter out nearby impurity emissions is useful when imaging divertor and antenna guard limiters. Initial results with a helium plasma show little difference between the techniques at higher bias voltages. At lower DC bias voltages, a difference can be seen. Further results will be presented.   

Considerations for Uncertainty Within Absolute Temperature and Emissivity Measurements Accessible Though the Application of Two-Color Infrared Pyrometry

Two-color pyrometry has been demonstrated utilizing non-contact, high temporal-resolution multispectral infrared imaging data for the retrieval of absolute temperature and material emissivity of both high-temperature and actively combusting materials. This is particularly useful within Tokamak reactors and other plasma containment vessels, within which extreme conditions limit opportunities for direct measurement techniques. Telops’ multispectral imaging systems are well suited for this task as narrowly spaced spectral bandpass filters can be selected strategically to omit radiation expected from known combustion gasses. This allows the collected imagery to observe thermal emissions originating solely at the surface of interest.

Pyros, a two-band ratio pyrometry algorithm developed by Telops and Polytechnique Montreal has proven effective in conducting such analysis, and uniquely, does so on a pixel-by-pixel basis within sequential frame images, though error considerations remain broad and further development is needed. This work will address key sources of uncertainty within the Pyros algorithm, including differences observed when imaging combusting and non-combusting surfaces, the critical nature of temporal resolution, and spectral bandpass considerations. As a further development, an ongoing measurement campaign will be discussed which aims to utilize multiple multispectral systems simultaneously, with cameras synchronously imaging both the combusting and non-combusting surface of a single sample.   

Use of Thomson Scattering for Plasma Characterization in the Embry Riddle Plasma Jet Experiment

Plasma diagnostics play a crucial role in understanding the behavior and properties of plasmas, especially in high-energy applications such as fusion research. Thomson scattering, a widely used diagnostic technique, provides valuable insights into electron density and temperature. We present the setup and utilization of a laser system for Thomson scattering measurements in a MHD driven plasma jet experiment. The experimental setup consists of a high-energy laser system, a plasma jet generator, and a collection optics system. The 10 Hz, 400 mJ YAG laser generates a 10 ns pulse width beam that is carefully focused onto the center of the plasma jet inside the chamber. The scattered light from the electrons is collected into a 1-D optical fiber and a 1-m spectrometer for analysis. The spectrum is expected to show a collective Thomson scattering signal as the parameter ranges are within the collective regime. The collective Thomson spectrum allows us to extract valuable information about the plasma's electron density and temperature. We discuss the key components of the laser system, including the laser source, optics, and detectors, highlighting their roles in achieving accurate and reliable Thomson scattering measurements.   

First Ion Velocity Distribution Function Measurements In A Room Temperature Calcium Plasma With Laser Induced Fluorescence

Measurements with laser-induced fluorescence (LIF) techniques on metastable states are not always indicative of the bulk ion dynamics and signal-to-noise ratio (SNR) is limited by photon counting proportional to metastable state density. Calcium ions provide access to ground state, single-photon LIF transitions with affordable diode lasers which are favorable to typically employed argon ion metastable states. Ground state LIF provides a large increase in SNR due to the larger state density and is more indicative of bulk ion behavior. A novel plasma source has been developed for production of room temperature calcium plasma. The mass of calcium (40.078 au) is very similar to that of argon (39.95 au) and the ground state transition of Ca-II (396.96 nm) is very close to a metastable transition in Ar-II (394.95 nm). The Ar-II transition shares an upper state with the commonly employed 668 nm LIF scheme, allowing calcium to act as a convenient test particle in argon plasmas with similar dynamics and diagnostic access. Calcium plasma is produced by first vaporizing solid calcium, then passing a collimated neutral beam of calcium through an ionization source developed at the University of Iowa. The ionized beam of calcium is then interrogated with LIF and provides demonstration of the increased SNR LIF technique. Also presented are axially and radially scanned LIF measurements obtained through a confocal telescope focused into the plasma production region to characterize the source.   

Mapping the Local Electron Density of a Laboratory Hydrogen Plasma via the Investigation of Stark Broadening

The Caltech MHD Plasma Jet experiment generates a relatively low temperature plasma of approximately 2eV and density of approximately 10^21m-3, and yet has been observed to emit X-rays with energies averaging around 7keV. How a modest temperature plasma generates electrons energetic enough to produce these X-rays is an open question. The local electron density is to be investigated with the use of a two-color optical diagnostic tool which allows for the capture of side-by-side monochromatic images at different wavelengths. Using two ultra-narrowband optical filters placed at 484.7nm and 485.6nm, the Stark broadening of the Hβ spectral line can be investigated. Using a fast framing camera, measurements of this broadening may be resolved with a higher degree of spatial and temporal resolution than simple spectrometry, which has already been used to demonstrate significant stark broadening. Specific attention will be given to a hydrogen plasma undergoing the kink instability and a secondary Rayleigh-Taylor instability (RTI), for which temperature and density maps are to be generated. A preliminary goal is to measure the correlation between local electron density reduction, temperature fluctuation, and overall dimming of the plasma in the region of the RTI.  This measurement is expected to provide information relevant to how a low temperature plasma can generate electrons greatly exceeding the average thermal velocity.   

Modulating Plasma Parameters using a Hollow Cylindrical Electrode in ALEXIS

The Auburn Linear Experiment for Instability Studies (ALEXIS) is a 2m long, 10 cm diameter, inductively coupled, rf, linear plasma device that is designed to support a variety of plasma instabilities and waves. Recent studies in ALEXIS have focused on the production and detection of both electrostatic and electromagnetic waves in the ion cyclotron to low hybrid frequency regimes and then using a biased cylindrical electrode to change local plasma conditions to modify wave propagation. Experiments have been performed in which the cylindrical electrode has been demonstrated to systematically vary the local plasma parameters. It has also been observed that, at certain plasma conditions and electrode bias voltages, light emission from the plasma near the hollow electrode dramatically decreases. Plasma measurements were made in the “dark” regions caused by the electrode biasing. At low RF power input and large negative bias voltages (<-60V) electron density decreased by over an order of magnitude when compared to measurements made with no bias voltage applied to the cylindrical electrode. Spectroscopic measurements were also made in the “dark” regions to fully characterize the decrease in visible light emission. The results of these measurements are presented.   

Quantum entangled two-photon absorption for selective, localized, and low intensity pumping of excited state populations in plasma

Entangled two-photon absorption (ETPA) has the potential to pump a fluorescing excited state population with low incident intensity and high state selectivity for innovative quantum-enhanced plasma spectroscopy measurements. The time-frequency entanglement of entangled photon pairs allows for the simultaneous arrival of entangled pairs at the target location and a narrow bandwidth for the sum frequency. The simultaneous arrival gives a linear scaling of the ETPA cross section with the incident photon flux compared to a quadratic scaling for two-photon absorption (TPA) with classical light. ETPA reduces incident flux requirements for chemical sensing and biological microscopy by up to seven orders of magnitude compared to classical TPA [1], and we are hopeful to realize a similar quantum enhancement for ETPA in plasma. The lower incident flux for ETPA can be compatible with a low-intensity continuous laser, in contrast to classical TPA which requires a high-intensity, pulsed laser. Finally, the narrow bandwidth of the sum frequency can precisely target an excited state with minimal contamination into non-target states, and the two-photon process is inherently compatible with cross-beam spatial localization. Potential diagnostic schemes include pumping low-n states for low-Z impurities, high-n Rydberg states for high-Z impurities, and charge-exchange populations.

[1] M. Raymer et al., J. Chem. Phys. 155, 081501 (2021); A. Eshun et al., Acc. Chem. Res. 55, 991 (2022)   

Neutral Krypton Three-photon Laser Induced Fluorescence and 3+1 Photoionization Spectroscopy Measurements on Allowed and Forbidden Transitions

Remotely situated diagnostics are desirable for fusion devices since electromagnetic interference (EMI) and radiation are becoming more of an issue as the field moves into an era of burning plasmas. Specifically, diagnostics capable of measuring absolute neutral densities are critical to controlling fueling rates and maintaining transport barriers in the plasma edge. Two-photon absorption laser induced fluorescence (TALIF) non-perturbatively measures spatially resolved neutral velocity distribution functions (NVDF) to determine absolute, ground state neutral densities of hydrogenic species if the measurements are calibrated with a noble gas, commonly krypton or xenon. However, TALIF injects deep ultraviolet light (<!--[if gte msEquation 12]> style='mso-bidi-font-style:normal'>∼205  nm) that is easily absorbed in air and difficult to couple into vacuum chambers. These limitations restrict the location of the TALIF systems to regions of potentially high EMI and eliminate use of fibers and common optical materials. A three-photon laser induced fluorescence (3pLIF) technique has the potential to provide similar measurements, while injecting a more near-visible wavelength, <!--[if gte msEquation 12]>300-308  nm, alleviating the requirements for special optics, allowing the use of high-power fibers, and allowing the laser system to be situated further from EMI. In this work, a Quantel Qscan pulsed dye laser excites ground state krypton through three-photon excitation or photoionizes krypton through a 3+1 photon process. Light is generated over 6<!--[if gte msEquation 12]> style='mso-bidi-font-style:normal'>∼6 ns pulses at 10 Hz. Fluorescence is either fiber coupled, or free space coupled to detecting electronics. Here, ground state neutral krypton spectral and photoionization current lineshapes are presented for allowed and forbidden transitions.   

Collective Thomson Scattering Feasibility Study for the LArge Plasma Device (LAPD)

Collective Thomson Scattering (CTS) is a powerful diagnostic tool that provides information about ion and electron temperatures, flow/drift velocities, and electron density. By utilizing an adequate source, measurements are obtained from the scattered radiation spectrum of electron density fluctuations in the plasma. In HED plasmas, CTS has been used extensively with laser based sources, typically in the visible spectrum. CTS has been implemented in fusion plasmas with RF sources for fast ion distribution and density fluctuation measurements. At the Basic Plasma Science Facility (BaPSF), the diagnostic will be used for ion temperature measurements in hydrogen minority heating experiments, including energetic ion interaction with fast waves. The LAPD, an 18 m long and 1 m diameter cylindrical device, produces a magnetized plasma (n = 10¹¹-10¹³ cm^-3, Te= 0.1-15 eV)¹ that is challenging to diagnose with CTS due to the unconventional source required in the far infrared. This study will evaluate laser and non-laser based sources and their requirements to develop CTS for LAPD, including diagnostic setup and measurement techniques. 

¹W. Gekelman, et al., Rev. Sci. Instr., 87, 025105 (2016)   

Asymmetric optical vortex laser-induced fluorescence (aOVLIF) method

We have been developing a novel method for flow-velocity measurement using optical vortex beams. When an optical vortex beam with azimuthally symmetric intensity distribution is applied to the laser-induced fluorescence (LIF) method, it is possible to measure the velocity of flow traversing the beam, which is, in principle, impossible with conventional plane-wave-like beams. However, information on the direction is lost because the additional azimuthal Doppler shift is observed as the broadening of the LIF spectrum [1]. Recently, we have found that asymmetry in the azimuthal intensity distribution of optical vortex beams enables the flow measurement that includes the direction. In this case, the azimuthal Doppler shift gives a frequency shift to the LIF spectrum. On the other hand, asymmetric optical vortex beams are known to rotate their intensity distribution while propagating. The effect of the rotation on the aOVLIF measurement was evaluated numerically and found to be practically negligible. Details, including preliminary experimental results, will be reported at the meeting.

[1] S. Yoshimura et al., Jpn. J. Appl. Phys. 59, SHHB04 (2020).   

Research and Development of Wideband Ferrite Waveguide Circulators for Industrial Applications: Realistic Magnetic Field Integrated with Electromagnetic Modeling

Circulators are used to safeguard microwave sources in plasma processing systems and separate electromagnetic (EM) signals in radar and communication systems. Despite introductory materials on the fundamental principles of circulators being available in the literature, research and development (R&D) in some specific companies and research labs have been confidential, limiting public access to advanced technologies and know-how. This study examines nine configurations of WR340 waveguide circulators using the finite element method (FEM), assuming a saturated magnetization with a uniform magnetic bias as considered by other R&D groups in the literature survey for comparison and optimization purposes. A T-shape geometry employing circular metal stages and partial height cylindrical ferrite disks with a bandwidth of 190 MHz, insertion loss less than 0.21 dB, reflection, and isolation better than -20 dB was selected for industrial prototyping and optimized with ten types of ferrites. However, during prototype testing, the transmission was lower than expected, and the loss was high. To overcome these issues a methodology involving a magnetic circuit design using a magnetostatic solver coupled with an EM solver was done. The simulations revealed that the magnetic field inside the ferrite disks was non-uniform, and two strategies were proposed to mitigate non-saturated magnetization. The proposed methodology can achieve a bandwidth of over 100 MHz, isolation better than -20 dB, and transmission up to 95%. The study highlights the importance of considering a realistic magnetic field and magnetization inside the ferrite disks and its relevance to advancing the research and development of ferrite circulators.   

Novel Semi-Classical Cross Section Solver of Particle-Particle and Particle-Cluster Interactions for the inclusion of Heavy Ion Impacts and Cluster Formation in Plasma Simulations

A main problem in cluster formation models is the lack of fundamental data describing particle-particle and particle-cluster interactions, such as interatomic potentials, differential scattering cross-sections and total cross-sections. Calculation of the classical differential scattering cross section with analytical calculations are practical only for the simplest cases, and experiments measuring cross-sections are seldomly performed for large molecules or clusters due to their complexity of interpretation. In this work, a new software tool is presented for the solution of the semi-classical scattering problem, and then verification studies are performed. The code is implemented in Python, with non-dimensionalization, and Chebyshev Polynomial root finding. Chebyshev polynomial root finding is used to calculate roots of the distance of closest approach equation for attractive-repulsive potentials, since Newton solvers frequently fail for potentials with multiple real roots. This allows the solving of a wide variety of attractive-repulsive potentials. Numerical explorations are run for reactive plasmas containing metals, such as uranium-oxygen and aluminum-oxygen plasmas, which lack theoretical or experimental cross-sections.   

Average trajectory method for computing magnetohydrodynamic transport coefficients

A simple method to compute the transport coefficients of magnetohydrodyamics from kinetic theory is developed. It is based on the average trajectory of test particles computed from moments of a kinetic equation, which are applied to an approximate form of the Green-Kubo relations for weakly correlated systems. Results agree with those of the Chapman-Enskog, or Grad, methods which are obtained by computationally laborious expansions of the phase-space distribution function. The new method trades the need to solve the distribution function iteratively as a perturbation from equilibrium (as in the Chapman-Enskog or Grad methods) for the need to solve time integrals of correlation functions. Results are compared to the expected Braginskii transport equations in the weakly magnetized regime. The model is also used to derive transport coefficients in strongly magnetized plasmas were an MHD theory has not yet been developed. Results are benchmarked by comparison with molecular dynamics simulations of the one-component plasma.    

A Hamiltonian structure preserving discretization of Maxwell's equations driven by a ponderomotive current

In the presence of an inhomogeneous oscillatory electric field, charged particles experience a net force, averaged over the oscillatory timescale, known as the ponderomotive force. We first derive a simple one-dimensional Hamiltonian model which self-consistently couples the electromagnetic field to a plasma which experiences the ponderomotive force. We then derive a Hamiltonian structure preserving discretization of this system using a finite element exterior calculus spectral element method. The method is found to conserve the Casimir invariants of the continuous model to machine precision and the energy to the order of the splitting method used.   

Hybrid particle-spectral method for kinetic plasma simulations

A hybrid model for numerical solutions of the Vlasov-Maxwell equations is presented which blends spectral and particle approaches. 

The model splits the distribution function in the velocity space for plasma species in both spectral and particle representations with the goal of taking advantage of both. 

The spectral approach leverages asymmetrically-weighted Hermite basis, and the particle-in-cell (PIC) method is used for the particle method. Configuration phase space is decomposed with the Fourier method which is well suited for periodic problems. The method's conservation properties for mass, momentum, and energy are derived. It is shown that the coupling error between spectral and particle representation is absent in the semi-discrete setting (not taking into account time discretization). Finally, numerical test cases are presented simulating a weak electron beam interaction with plasma, leading to beam-plasma instability. The initially localized electron beam evolved into a highly non-equilibrium distribution function in the velocity space. A small growth rate and resonance nature of instability makes it difficult to obtain accurate solutions for purely particle methods due to present noise which falls as ∽1/√N_p with a number of particles. At the same time, purely spectral methods may require a large number of modes to capture the highly non-equilibrium state of the evolved beam. We show that the hybrid method is well suited for such problems, it reproduces the linear stage with sufficient accuracy as well as nonlinear dynamics with a highly non-equilibrium distribution function.   

High-Order accurate relativistic Vlasov simulations in up to 3D+3P

The cost of direct simulation of solutions to kinetic equations has meant that dimensionally reduced systems are often considered. For example, the LOKI code has previously been employed for Vlasov simulation in 2D+2P (2 physical and 2 momentum dimensions). In the present work, we present new capabilities in LOKI to allow configurations for all plausible dimensionalities ranging from 1D+1P to 3D+3P. In continuation from previous work, this includes relativistic capabilities. The code is verified by showing the expected 4^th and 6^th order convergence using the method of manufactured solutions. Finally, a comparison is made to analytic damping rates and frequencies for relativistic Landau damping in up to three momentum dimensions where the results show excellent agreement between theory and simulation.   

Extended MHD equilibrium having boundary layer at plasma-vacuum interface

The conventional MHD equations are known to be invalid when plasma density decreases to a certain level. Since the ion's and electron's inertial lengths are inversely proportional to the square root of density, the Hall and electron-inertia effects should be no longer negligible especially around plasma-vacuum interface. In this study, the cylindrical Z pinch equilibrium is considered as a simplest solution with plasma-vacuum interface and the extended MHD (XMHD) equations, which legitimately include the Hall and electron-inertia terms, are solved. If the collisional effects (resistivity, viscosity and collision with neutrals) are dominant, the solution can be close to the MHD equilibrium. However, at low collisionality, the electron-inertia effect becomes dominant and plays the role of singular perturbation. Namely, the solution of XMHD has a boundary layer that connects the inner MHD solution and the outer vacuum solution, inside of which surface current is generated. The solution is, therefore, different from that of MHD even in the limit of small electron inertia. By considering matching conditions, the equilibrium position of the plasma-vacuum interface can be predicted theoretically.   

A Conservative Dynamical Low-rank Method for the Vlasov Equation

Dynamical low-rank method has recently arisen as a popular dimension-reduction technique to solve the high dimensional kinetic equations. When it is applied to the Vlasov equation for plasmas, the overall computational cost can be greatly reduced compared to the full 6d simulation. However, the important physical quantities such as mass, momentum and energy are not guaranteed to be conserved in this framework. We propose a conservative dynamical low-rank method based on a novel macro-micro decomposition of the probability density function. Several benchmark tests will be presented to demonstrate the effectiveness of the proposed approach.   

Combination of Hermite-Legendre bases for kinetic plasma equations

Kinetic plasma simulations allow for modeling of effects associated with non-equilibrium distribution functions in velocity space. In contrast to fluid models, kinetic approaches have to deal with the higher dimensionality associated with resolving velocity space, which can make it challenging or impossible for numerous physical configurations. Thus, decreasing the number of degrees of freedoms (DOFs) is critical for large-scale simulations with kinetic effects. Spectral, particle, and finite difference/element methods are often used to discretize distribution functions in velocity space.

Spectral methods offer many advantages, such as fast global convergence, i.e., allowing fewer DOFs to represent functions behaviour.

We propose a spectral method that combines two bases, Hermite and Legendre, to split the distribution function in velocity space for efficient representation of equilibrium bulk plasma and non-equilibrium complex structures such as shocks, beams, etc. The Hermite basis with tuned parameters may require only a few degrees of freedom (DOF) to represent near-equilibrium (Maxwellian) plasma, while Legendre basis are parameter-free and generally better suited for non-equilibrium distributions. We have implemented a model that combines the two approaches in velocity space while using the discontinuous-Galerkin method for configuration space, with the main emphasis on velocity space. A dynamical scheme is implemented that projects higher Hermite coefficients into Legendre basis to minimize the total number of DOFs. We have performed numerical tests that are based on the evolution of beam-plasma instability with electron beam evolution into a highly non-Maxwellian state. Our initial tests reveal that the dynamical reprojection allows us to achieve better accuracy for the same number of DOFs in the range of a relatively low number of DOFs.   

Development of a charge- and energy-conserving implicit moment-acceleration method for the Vlasov-Darwin Particle-in-Cell System

The coupled set of Vlasov-Maxwell equations describes the dynamic evolution of a collisionless plasma. Explicit particle-in-cell (PIC) approaches are attractive because they are simple to implement, highly parallelizable, and inexpensive per timestep. However, explicit PIC schemes are subject to numerical instabilities when the Debye length is not resolved or the Courant–Friedrichs–Lewy (CFL) condition is not met. This becomes a significant challenge when the dynamics of interest occur on large spatial and temporal scales compared to these parameters. Conversely, implicit schemes can bypass both of these limitations at the cost of being more expensive per timestep by solving the evolution iteratively. Previous work by Taitano et al. [1] developed a method that uses an auxiliary but self-consistent set of moment-field equations, called the lower order (LO) equations, which act as an algorithmic accelerator for an underlying iterative nonlinear solver for the electrostatic, one-dimensional (1D) implicit PIC, i.e., the higher order (HO) system. In the present work, we discuss preliminary results of extending the HOLO framework to a 1D electromagnetic Darwin system. The solver performance sensitivity to different choices of LO equations is studied on various test cases, such as the electron/ion Weibel instabilities.   

A Novel Method for Solving the Linearized 1D Vlasov–Poisson Equation Using Cauchy-type Integrals

We describe a new method for solving the linearized 1D Vlasov-Poisson equation by using properties of Cauchy-type integrals. Our method remedies critical flaws of the two standard methods and reveals previously unrecognized time evolutions. The Landau approximation involves deforming the Laplace inversion contour around the poles closest to the real axis due to the analytically-continued dielectric function to find the long-time behavior for a stable system, which is known as Landau damping. Jackson, in an attempt to fully solve the initial value problem, generalized this to encircle all poles while sending the contour to infinity, assuming its contribution vanishes in the limit, which is not true in general. This gives incorrect solutions for physically reasonable configurations and in some cases of infinite sums does not result in an asymptotic form; an error widely reproduced in standard textbooks. We show examples clearly revealing the error, simultaneously obtaining time evolutions that are not simply exponentials with arguments linear in time. The van Kampen method, which expresses the solution to the initial value problem for a stable system as a continuous superposition of waves, results in an opaque integral. Case generalized this to include unstable systems and predicts a decaying discrete mode for each growing discrete mode, resulting in an apparent contradiction to both the Jackson solution and ours. We show the decaying modes are not present in the time evolution due to an unconditional cancellation with part of the continuum. Our solution is free of integral expressions, is obtained using algebra and Laurent series expansions, does not rely on an analytic continuation of the dielectric function, and naturally results in a correct asymptotic form in the case of infinite sums. The analysis used can be readily applied in higher-dimensional, electromagnetic systems and also provides a new technique for evaluating certain inverse Laplace transforms.   

Hybrid fluid-particle simulations of plasma plume evolution following photoablation events

In computational plasma physics, fluid solvers can be used to model collisional plasmas more efficiently than particle-based simulation methods. However, fluid solvers make assumptions on the shape of the plasma's velocity distribution, rendering them less widely applicable than particle-based methods. We have implemented a hybrid modeling capability in the hPIC2 plasma simulation software, which combines fluid and particle methods in the same code. This allows us to simultaneously model highly collisional plasma species with a fluid solver and far-from-equilibrium species using particles. Its utility is demonstrated on a simulation of the photoablation of a material surface, which shows good agreement with previous results.   

Metriplectic 4-bracket dynamics: A curvature-like framework for describing dissipation

An inclusive framework  [1] for joined Hamiltonian and dissipative dynamical systems, which builds on early work [2,3,4], will be described.  The framework describes dynamical systems that preserve energy and produce entropy. The dissipative dynamics of the framework is based on the metriplectic 4-bracket, a quantity like the Poisson bracket defined on phase space functions, but unlike the Poisson bracket has four slots with symmetries and properties motivated by Riemannian curvature. Metriplectic 4-bracket dynamics is generating using two generators, the Hamiltonian and the entropy, with the entropy being a Casimir of the Hamiltonian part of the system. The formalism includes all known previous binary bracket theories for dissipation or relaxation as special cases. Rich geometrical significance of the formalism and methods for constructing metriplectic 4-brackets are explored. Examples of both finite and infinite dimensions will  be discussed including  plasma, fluid,  and kinetic descriptions.

[1] P. J. Morrison and  M. H. Updike, An inclusive curvature-like framework for describing dissipation: metriplectic 4-bracket dynamics, arXiv:2306.06787v1 [math-ph] 11 Jun 2023.

[2] P. J. Morrison, Bracket formulation for irreversible classical fields, Phys. Lett. A 100, 423 (1984).

[3] P. J. Morrison, Some Observations Regarding Brackets and Dissipation, Tech. Rep. PAM--228, Univ.  Cal.  Berkeley (1984).

[4] P. J. Morrison, A Paradigm for joined Hamiltonian and dissipative systems, Physica D 18, 410 (1986).   

The PlasmaPy project: growing an open source software ecosystem for plasma science

The mission of the PlasmaPy project is to foster the creation of a fully open source Python ecosystem for plasma research and education. The PlasmaPy package is being developed to include core functionality needed by plasma physicists across disciplines. PlasmaPy is a platform for the plasma community to collaborate and openly share commonly needed software functionality. PlasmaPy prioritizes code readability, consistency, and maintainability while using best practices for scientific computing such as open development, version control, continuous integration testing, and code review. We will describe enhancements to the particles and formulary subpackages, as well as capabilities related to charged particle radiography, Thomson scattering, time series analysis, and MHD equilibria. We will describe how to contribute to PlasmaPy, as well as how to join PlasmaPy's working groups.   

Building an Open-Source Collaborative Software Ecosystem for Space and Laboratory Plasma Simulations

From the plasma environment around planets and black-holes, to confined plasmas in fusion machines, plasmas are ubiquitous in the visible universe. Computer simulations are critical to understand, and in the case of laboratory plasmas, design, such complex systems. Supported by the National Science Foundation (NSF) Cyberinfrastructure for Sustained Scientific Innovation (CSSI) program we are building an open-source, collaborative software ecosystem to provide advanced simulation capabilities to the whole plasma physics community. This ecosystem consists of two major parts: a core simulation engine with several advanced solvers, and a Plasma Science Virtual Laboratory to allow access to these tools via an easy-to-use web interace. The simulation engine is built on top of the open-source Gkeyll framework and provides solvers for multifluid, multimoment equations and the Vlasov-Maxwell equations in its various manifestations. The Plasma Science Virtual Laboratory is designed to broaden researcher and educator access to plasma science and space weather analysis on high performance computing platforms. It supports creation and execution of automated workflows that run on multiple NSF ACCESS compute systems without burdening users with execution, storage, and access details of each system. Our project aims to be community driven and welcomes enhancements via new solvers, improvements to existing code, updates to documentation via github pull-requests or issue creation.   

Analytical Approach to the Galactic Radial Migration Induced by Overlapping Perturbations

Many galaxies, including our Milky Way, exhibit a bar-like structure at their center. Within these galactic bars, millions of stars rotate and collectively spin as a solid body. Besides, there are a multitude of revolving galactic bodies with spiral (density) waves that exist in the galactic disk. Through resonant interactions, these bodies can effectively absorb energy from the bar and cause stars within the bar to migrate radially. The aim of this work is to establish a transport equation for the resonant relaxation of a distribution of galactic bodies due to the simultaneous action of multiple overlapping perturbing sources. The limiting case of dominant stochasticity, in which the effective background diffusion frequency ν_eff is faster than the libration (bounce) frequency Ω_b, is shown to lead to considerable analytic simplification. In this regime, the relaxation of the angle-averaged distribution can be cast as a quasilinear diffusion equation that can be analytically integrated to all orders in the small parameter 1/Δ ≡ ω_b²/ν_eff². This framework, which is a non-trivial extension of a previously treated case of single perturbations (Hamilton et al. Astrophys. J. 2022, in press, arxiv.org/abs/2208.03855), is relevant to formulating reduced models for the radial migration problem of the bar-spiral coupling as well as to galaxies with two bar structures. Analytical insights and simulation are then applied to better understand the N-body simulations of Minchev & Famaey [Astrophys. J. 722 112 (2010)].   

Noise and error analysis and optimization in particle-based kinetic plasma simulations

We revisit a meshfree particle model for kinetics of a 1D

electrostatic plasma, using kernel density estimation and a similar

method for the electric field E. The kernel K(x − y) represents the

macroparticle charge distribution. Two length scales enter, the width

w of K and the interparticle spacing λ. This model conserves momentum

and energy. Similarly, continuity is satisfied exactly, and the

Gauss’s law and Ampere’s law formulations are exactly equivalent. A

unified analysis is used for numerical stability and noise

properties. The force can be computed directly using the correlation

K2 = K ∗ K, and K2 is symmetric and positive definite. We discuss the

analogy in the presence of a grid. We can specify a single kernel Kp ,

related to the `kernel trick’ of machine learning. Numerical

instability can occur unless Kp is positive definite, related to a

breakdown in energy conservation. For the noise analysis, the

covariance matrix for the electric field shows a plasma dispersion

function modified by w and λ. The number of particles per cell does

not enter, and the noise is characterized by the number of particles

per kernel width, i.e. w/λ. We present the bias-variance optimization

(BVO) for the electric field, and compare it to the density BVO[1].   

Modeling Multiscale Phenomena in Magnetized Plasmas

Capturing multiscale phenomena in magnetized plasmas is complicated by interactions that connect across the various spatiotemporal scales. For example, the magnetized Kelvin-Helmholtz instability (KHI) is known to develop macroscale plasma structures whose details depend on microscale physics [Vogman et al PoP 27 (2020)]. Kinetic models accurately describe the microscale, but solving kinetic models is often impractical for capturing macroscale dynamics. Hybridizing kinetic and moment models across spatial domains [Datta & Shumlak JCP 483 (2023)] offers an approach to strategically combine computationally efficient reduced models with higher fidelity models, which is facilitated using the finite-element continuum WARPXM framework [Shumlak et al CPC 182 (2011)]. Applications of the domain-decomposed hybrid method include the magnetized KHI and plasma photonic crystals [Thomas & Shumlak PoP 30 (2023)]. Developments in the dynamical low-rank approximation (DLRA) of high-dimensional PDEs suggest an additional promising avenue for the efficient solution of the kinetic plasma model. In particular, the Vlasov equation and the Dougherty-Fokker-Planck collision operator have the structure necessary for DLRA. The applicability of DLRA to this kinetic plasma model is demonstrated on several benchmark problems. The suitability of DLRA to the nonlinear evolution of magnetized plasma instabilities such as the KHI is investigated, with a focus on how collisions impact the rank of the solution manifold.   

A BBGKY-like Heirachy for Quantum Field Theories

We present a general method for constructing BBGKY-like hierarchies of arbitrary quantum field theories. Further, we show that our hierarchy has a natural Hamiltonian structure directly analogous to the classical case. Under suitable choices, we show how our method creates a system of BBGKY-like evolution equations for the k-th order reduced density matrices. These equations can be closed at finite order to give non-perturbative, semi-classical, and structure-preserving approximation schemes for quantum field theories, particularly quantum electrodynamics.   

Computational and theoretical study of nonlinear kinetic transport properties of lower hybrid drift instabilities in low-beta plasmas

Collisionless low-beta plasmas limit the performance of pulsed power inertial confinement fusion experiments. These plasmas, which are governed by nonlinear kinetic physics, lead to breakdown of magnetic insulation and give rise to parasitic currents that affect load dynamics. The plasmas are subject to acceleration-driven and gradient-driven microinstabilities that strongly influence transport properties. To characterize the nonlinear plasma state, a self-consistent quasilinear model is developed for a current-carrying two-species magnetized plasma undergoing the lower hybrid drift instability. The model fully captures gyromotion, encapsulates velocity-space diffusion for both ions and electrons, and self-consistently tracks electric field energy density. The coupled nonlinear velocity-space diffusion model is solved numerically and is validated using fourth-order continuum kinetic Vlasov-Poisson simulations facilitated by the code VCK. The computational study sheds light on nonlinear transport properties and on the degree to which they can be captured by weak turbulence theory.   

Finite-particle instability in the gyrokinetic delta-f PIC algorithm

The mathematical form of the gyrokinetic delta-f particle-in-cell algorithm (GK-δf-PIC), as distinct from traditional PIC analysis (Ref. 1), was performed in Ref. 2. There, in addition to a finite-particle instability, an unconditional numerical instability was highlighted and its properties discussed. Additional analyses in Refs. [3] and [4] clarified that the instability, as converged in time step and particle number, is an aliasing (finite-mesh) instability with peculiar properties due to spatial anisotropy in gyrokinetics. These latter two analyses were in the infinite particle limit, where it was assumed that a sufficient number of particles are used to approximate the continuous distribution function arbitrarily closely, albeit with fields defined on a discrete mesh.

Here a complementary analysis is presented to illuminate the remaining instability studied in Ref. 2: that due to insufficient particles. In this analysis, the mesh is eliminated, but finite-particle effects are maintained. It is found that Fourier modes are linearly coupled to each other via particle weights. The diagonal terms are physical and remain in the limit of infinite particle number, and in this case the physical dispersion relation is recovered. With finite number of particles, off-diagonal coupling terms are nonzero. With sufficiently low number of particles (which can still be quite large for some systems), it is shown that this coupled system is unstable. Properties of this finite-particle instability, implications for more complicated systems, and mitigation methods will be discussed.

[1] Birdsall and Langdon. Plasma Physics via Computer Simulation (2004)

[2] Wilkie and Dorland. PoP 23:052111 (2016)

[3] Sturdevant and Parker. J. Comp. Phys. 305:647 (2016)

[4] McMillan. PoP 27:052106 (2020)   

Classification of extended MHD models for special relativistic plasmas using scale analysis

 Relativistic magnetohydrodynamics (RMHD) has been widely used to analyze and simulate various cosmic phenomena. MHD conventionally represents a model that neglects certain terms of the two-fluid equations, such as the electron-inertia and Hall effects. On the other hand, when dealing with non-relativistic plasmas, extended MHD (XMHD) has been derived from the two-fluid equations by enforcing the quasi-neutrality condition and retaining the electron-inertia and Hall effects. XMHD has wider applicability than MHD, since MHD becomes invalid for low-density, small-scale or collision-less situations.

 The counterpart of relativistic extended MHD (RXMHD) has been proposed by Koide (2009), in which “proper charge neutrality” is imposed. However, the precise conditions, under which this approximation holds, remain unclear. To clarify them, we start with the special relativistic two-fluid equations assuming cold and non-dissipative plasma and approximate them by means of the scale analysis. We present a hierarchical map of various approximate models, ranging from the two-fluid equations to RMHD, which are classified in terms of representative dimensionless parameters. This map includes RXMHD as well as relativistic Hall MHD, and the applicable ranges of these models are elucidated.   

Continuum-kinetic studies modeling the impact of secondary electron emission on sheath structure and dynamics

Plasma-material interactions, such as those which occur in fusion and propulsion applications involving the flow of plasma through a channel, drive the emission of secondary electrons from the material wall. Such emission can alter the fundamental sheath structure and behavior, understanding of which is vital to support the success of multiple fusion and propulsion concepts. The emission spectrum is characterized by two regions, a peak of elastically backscattered primary electrons, and cold secondary electrons inelastically emitted directly from the material. Novel implementation of semi-empirical models allows the full range of emission to be captured at the boundary of continuum-kinetic simulations. Simulations are performed using the Gkeyll code examining the dependence of the emission on model and plasma parameters. Results are shown of high and low emission cases in the classical and space-charge limited sheath modes, with particular attention given to the regime where the yield ratio of emitted to impacting particles exceeds unity and theory predicts transition to an inverse sheath. We discuss the relationship between emission mechanisms and how they drive the overall trend in yield, as well as the resulting sheath structure.   

Initiation and termination of a hydrogen dc-glow discharge plasma sheath

Understanding the formation and structure of sheaths is critical to the understanding of plasma physics. In recent decades researchers have begun to make detailed, time-resolved measurements of plasma sheaths as diagnostic technology has improved. In this work, an investigation of a dc-glow discharge sheath for a hydrogen plasma will be presented. Imaging of the plasma is performed using a gated ICCD camera to capture photographs of the plasma emission during the initiation of the sheath, as well as the termination and afterglow of the plasma, on the order of tens of nanoseconds time resolution. Studies of the plasma sheath dynamics are made for a range of rise- and fall-times of the electrode voltage, as well as a range of electrode voltages. Using an image doubler, images of H-α and H-β emission are captured simultaneously providing spatial maps of the emission intensity and spectral line ratios. To provide more quantitative measurements from the plasma emission, Langmuir probe measurements are made during the plasma steady state to ascertain plasma densities and electron temperatures at various electrode voltages and correlate those measurements to H-α and H-β intensities and spectral-line ratios.   

A Continuum Kinetic Investigation into the Role of Transport Physics in the Bohm Speed formulation.

Non-oscillatory solutions to the Bohm criterion require the ion exit flow speed at the sheath entrance to be greater than or equal to the Bohm speed, which is generally equal to the sound speed in collisionless plasmas. This formulation, however, is only applicable when the sheath entrance is well defined, a condition that is not satisfied in many numerical and experimental cases of interest. Instead, a sheath transition region is found to exist. To resolve this and provide a Bohm speed formulation for the intermediate plasma regime, a new fluid sheath model that considers the effects of transport terms such as the electron heat flux, thermal force, and temperature isotropization has been proposed by [Y. Li et al., Physical Review Letters (2022)]. This work studies this model and numerically solves the Vlasov-Maxwell equations using a continuum kinetic formulation in the Gkeyll code to capture the sheath physics, which is inherently kinetic in nature, without tracking individual particles. Multiple cases ranging from a Knudsen number of 20 to 5000 have been considered in a 1X3V domain using the Lenard-Bernstein collisional operator. The results of the simulations offer insights into the formation of the sheath transition region, the Bohm speed in this region, and the role of the transport terms in the formulation of the Bohm speed. The noise-free continuum-kinetic approach is benchmarked to the particle-in-cell results.   

Development and implementation of acoustic diagnostics to measure plasma energy deposition from a laser plasma generated in air

The absorbed energy from a short pulse laser produced plasma is proportional to the magnitude of the acoustic wave the plasma launches; however, methods to resolve absolute energy from the acoustic signal are still being developed. This is the first report of quantitatively estimating the energy deposited by a femtosecond laser-induced plasma using a shock wave approximation from acoustic measurements. To further understand energy deposition mechanisms, two diagnostics, a single microphone which measures the acoustic signal propagation and an array of microphones which measure the changing acoustic signal longitudinally along the plasma were developed and implemented to measure the energy absorbed. A weak shock wave approximation model is used to fit results from the acoustic measurements to yield a quantitative energy deposition estimation. 2D Unidirectional Pulse Propagation Equation (UPPE) simulations show general agreement in experimental longitudinal energy deposition profile results and absolute total energy deposition values. These results will help to further understand the relationship between the dynamics of a laser-induced plasma and weak, broadband microwave frequencies known to radiate from them.

DISTRIBUTION A: Approved for public release; distribution is unlimited. Public Affairs release approval #AFRL20232760   

Probing the structure of multi-ion-species plasma shocks with spatially resolved spectroscopy

This presentation highlights an investigation into the structure of shock-compressed multi-ion-species plasmas, induced by the collision of a freely-expanding supersonic plasma jet with a quasi-stagnant background plasma. Previous results have shown that the piston-like action of the supersonic jet serves as a snowplow, compressing background material with a density enhancement that suggests collisional shock formation. By performing spatially resolved spectroscopy in concert with collisional radiative modeling, we report spatial distributions of ion species density, electron temperature and electron density, quantifying the transition from pre- to post- shocked flow. Of particular interest is understanding the role of diffusive mass-flux near the shock front, where it has been predicted that large gradients in plasma parameters can induce species separation. The structure of multi-ion-species plasma shocks is also relevant to the study of supernovae events where the effects of non-LTE physics within the shock remains an open topic of interest. We expect that these results will contribute to the growing database of studies meant to benchmark physics models of plasma shocks in both laboratory and astrophysical settings.   

Withdrawn

The multipole plasma trap (MPT) [1] is a three-dimensional confinement volume bounded by an envelope of radio-frequency (RF) electrodes.  In this work, plasma interaction with the boundary field of the MPT is investigated via particle-in-cell (PIC) simulations using software such as VSim 12 [2] and PlasmaPy [3].  Spherical and cylindrical electrode geometries are considered, and a static multicusp magnetic field arrangement is added as well.  Scenarios for trapping nonneutral and/or pair ion plasmas are investigated, as well as conventional plasma with quasineutrality provided by the electron species; the latter case depends particularly on optimization of the multicusp magnetic field.  Energy modification (heating) of the plasma particle distribution at the MPT boundary due to the spatially inhomogeneous RF field is investigated.  The PIC simulation work is conducted to inform experimental design of MPT configurations that reflect particle species (positive ions, negative ions, electrons) of varying incidence energy over a range of adjustable RF, magnetic field, and plasma parameters; specific experimental scenarios for electron and ion reflection and energy analysis are then identified.

[1] N. K. Hicks, A. Bowman, and K. Godden, Physics 1 (3), 392–401 (2019) doi:10.3390/physics1030028

[2] C. Nieter and J. R. Cary, J. Comput. Phys. 196, 448 (2004)

[3] PlasmaPy Community et al. (2023). PlasmaPy, version 2023.5.1, Zenodo, https://doi.org/10.5281/zenodo.8015753       

Full-fluid Moment Modeling and Theory of DC Breakdown

Plasma breakdown in DC gas discharges is primarily described by Paschen theory. The breakdown voltage required to sustain a plasma is considered a function of the gas pressure (P), the electrode gap distance (d), and the secondary electron emission (SEE) coefficient at the cathode (γ). While Paschen theory accounts for the flux balance correctly, the relation between the reduced electric field and the ionization coefficient is given empirically. In this study, DC breakdown is investigated using the full-fluid moment (FFM) model, in which the electron inertial effects are accounted for, and the electron energy is self-consistently modeled [1,2]. The results show a multivalued behavior for small values of Pd, i.e., the left branch of the Paschen curve. Additionally, the results show that the first Townsend coefficient α, often used as a constant modeling parameter in other DC breakdown studies, exhibits spatial variations and generally varies for different values of Pd. The contribution of Joule heating, reactive energy losses, and convective energy losses is also investigated, showing a gradual change between regimes where convective losses dominate reactive losses. The breakdown theory is revisited, including the electron energy equation without any empirical parameters.  

[1] R. Sahu, A. R. Mansour, and K. Hara, "Full fluid moment model for low-temperature magnetized plasmas", Physics of Plasmas 27, 113505 (2020)

[2] A. R. Mansour and K. Hara, “Full Fluid Moment Modeling of Rotating Spokes in Penning-type Configuration”, Plasma Sources Science and Technology 31, 055012 (2022)   

Improvements in ultrabroadband microwave generation by USPL filaments by using far IR wavelength laser

When focused to form a plasma, ultrashort pulse lasers (USPLs) can generate several decades of spectral content that range from above to far below the frequency of the driving laser.  The ultra broadband microwave generation is of particular interest, however when originally studied with 800nm, femtosecond laser, resulted in low signals on the order of 10 mV peak to peak.  Improvements were previously seen moving to longer pulse durations (ps) with higher energies, which allowed for more effective laser heating of the plasma.  Due to wavelength scaling of the ponderomotive force of the laser, it was predicted that increasing the wavelength to far IR would dramatically improve the amplitude of the resulting microwaves.  This was investigated at using the 9.2-micron CO₂ laser at Brookhaven National Laboratory.  Microwaves were measured from 1-70 GHz using multiple broadband horns and a Tektronix high frequency oscilloscope.  Plasma florescence was measured using a 2 ns gated ICCD camera.  Experiments demonstrated an order magnitude increase in the signal of the microwave fields measured from a filament driven with a 9.2 micron laser compared to a 1.053 micron laser of comparable energy and pulse duration.  Experimental results will be compared to computational model of the microwave generation.

Approved for public release; distribution is unlimited. Public Affairs release approval #AFRL-2023-3069.   

Role of vertical magnetic field on intermittent transport in simple magnetized torus

  Role of vertical field on intermittent transport is investigated in a simply magnetized torus (SMT) THORELLO. A SMT is a device in which plasma is confined purely by toroidal field. The main challenge in this device is the cross-field drift of particles caused by charge polarization, which leads to particle loss. Additionally, the lack of rotational transform prevents the system from reaching a magnetohydrodynamic (MHD) equilibrium. To address these issues, a quasi-stationary equilibrium is achieved by introducing a vertical magnetic field in addition to the toroidal field. This effectively reduces the connection length, meaning that the plasma is confined within finite values rather than extending to infinity. By varying the applied vertical field strength, different operational regimes is identified above and below 0.4 mT. To study the behavior of the plasma under different connection lengths or applied vertical fields, time-averaged measurements and conditional averaging techniques are employed. These techniques provide insights into the dynamics of the plasma state and allow for the analysis of intermittent turbulent fluctuations, often referred to as "blobs".

  

Intermittency in the Dimits Regime of Toroidal Ion Temperature Gradient Driven Turbulence

In toroidal ion temperature gradient (ITG) driven turbulence, it remains a challenge to understand heat flux reduction at and above the threshold of linear instability for a range of driving gradients called the Dimits regime. A known but unexplained feature of this regime is the observation of temporally intermittent turbulent fluctuations and resulting transport. Preexisting theory for the Dimits shift successfully attributed heat flux reduction to resonance in mode coupling, but this analysis was based on a cumulant-discard method which neglected intermittency and also did not produce any bifurcation demarcating variation in transport with driving gradient above and below the nonlinear critical threshold. In this work, weak turbulence closures are employed to produce dynamical equations for a fourth order cumulant as well as the heat flux itself. The former predicts conditions under which intermittent behavior may develop while the latter is a direct attempt to model said phenomenon. Preliminary analysis has found strong cumulant growth near the linear threshold which can be attributed to resonances in triplet correlation times and nonlinear coupling coefficients. This suggests possible coincidence between the mechanism responsible for heat flux suppression and the inherent non-Gaussian tendencies of the Dimits regime. Analytical work is compared against solutions of the reduced two-field fluid model for toroidal ITG driven turbulence from the numerical solver Dedalus.   

Investigating confinement and pedestal stability discrepancies between two high density H-mode DIII-D discharges

Operation at high pedestal pressure and density is a promising route to high performance in future fusion reactors. In this work, we investigate why a recent hybrid scenario experiment carried out on the DIII-D tokamak was unable to access the “peeling-limited” pedestal branch at high density, despite matching operational parameters and using more heating power than an earlier reference discharge that entered this regime. As a key difference between the experiments was slightly different combinations of electron cyclotron heating and co/counter-beam injection, a sensitivity analysis for confinement dependence on rotation and heating power was conducted. Transport modeling using TGYRO and TGLF predicts negligible impact from changes in heating power, or rotation on the electron temperature or density. However, ion temperature is found to increase as rotation is increased. These results are consistent with suppression of stiff long wavelength turbulence by increased shear flow. Based on computational analysis with the EPED code, the predicted impact of rotation-induced changes in core pressure on the pedestal stability will be analyzed and interpreted towards future experiments and fusion reactors.

This work was supported by USDoE via awards DE-SC0018287 and DE-FC02-04ER54698.   

Nonlocal effects in gyrokinetic simulations of turbulent transport in the edge pedestal

The local flux-tube formulation for gyrokinetic simulations, valid in the small rho-star limit, provides a robust and efficient method for understanding critical properties of anomalous plasma transport. However, for plasma regions where the density and temperature scale lengths are only a small fraction of the device size, the validity of the local model becomes questionable. The validity cannot be assessed by comparing local simulation with a nonlocal simulation that uses artificial sources and boundary conditions, as is done in most nonlocal gyrokinnetic simulations. We will use GEM to perform both local and nonlocal simulations for parameters representative of H-mode pedestal conditions. Preliminary results indicate that turbulence spreading, a process beyond the local model, frequently occurs in nonlocal simulations of pedestal. In order to assess the boundary effects in nonlocal simulations, we will implement arbitrary time-dependent Dirichlet boundary condition in GEM's ffield solvers to model the effects of the scrape-off layer turbulence on the pedestal. A buffer region outside the field solver boundary will be used to improve the boundary condition for the distribution function. Ad hoc particle and heat sources will be used to prevent profile relaxation and ensure steady-state transport. The effects of these sources, as well as the impact of shearing driven by a fixed Dirichlet radial boundary conditions, will be assessed.   

Global flux-driven simulations of plasma turbulence in the boundary of stellarators

We present the first 3D, global, two-fluid, flux-driven simulations of plasma turbulence in stellarator configurations [1]. We consider a 5-field period stellarator with a vacuum magnetic field constructed using the Dommaschk potentials. The simulations are carried out with the GBS code [2], which solves the two-fluid drift-reduced Braginskii equations. In contrast to tokamak simulations and experiments, but in agreement with W7-X measurements, coherent filamentary structures are essentially bound to a flux surface. The radial particle and heat transport are mainly driven by a field-aligned mode with low poloidal wavenumber, in contrast to smaller size turbulent structures observed in tokamaks. Confidence in these simulation results is increased by the first validation of a simulation of boundary turbulence in a stellarator configuration, where GBS retrieves the main turbulence properties of the TJ-K stellarator [3]. The peculiar features of stellarator turbulence are investigated through a set of turbulence simulations in magnetic configurations that smoothly transition from a tokamak to a stellarator.

[1] A. J. Coelho et al, NF 62, 074004 (2022)

[2] P. Ricci et al., PPCF 54, 124047 (2012)

[3] A. J. Coelho et al, PPCF accepted (2023)   

Modeling of tungsten transport in the WEST tokamak with the gyrokinetic code XGC

Tokamak physics in a tungsten environment is a critical topic of research, as tungsten impurities cause radiative collapses and disruptions of the plasmas. Tungsten physics is studied in WEST plasmas [1] with the XGC code [2,3]. WEST is the transformation of the Tore Supra tokamak from a limiter to a divertor configuration in a full tungsten environment relevant to the most recent ITER scenario. Neoclassical and turbulent transport of tungsten ions (and of the main plasma) will be discussed. Reduction of neoclassical tungsten peaking in presence of Nitrogen will be presented. Modeled heat load width will be compared to experimental one. Tungsten neoclassical transport will be compared to FACIT [4,5] and the turbulent transport will be compared to quasi-linear modeling by Qualikiz [6]. Finally, we will present the most recent XGC simulations of WEST plasmas in which the many ionization states of tungsten are modeled with gyrokinetic bundles [7,8] including atomic interaction based on ADAS rates. 

[1] Bourdelle et al (2015) Nuclear Fusion, 55 (6) 063017

[2] Dominski et al (2019) Journal of Plasma Physics 85 (5) 905850510

[3] Dominski et al 27th IAEA Fusion Energy Conference (FEC 2018) 22–27 October 2018, Gandhinagar India

[4] Maget et al. (2020) Plasma Physics and Controlled Fusion, 62(10):105001

[5] Fajardo et al (2022) Plasma Physics and Controlled Fusion, 64(5):055017

[6] Bourdelle  et al (2007) Physics of Plasmas, 14(11):112501

[7] Dominski et al 46th EPS Conference on Plasma Physics, 7-12 July 2019, Milan Italy.

[8] Dominski et al "Neoclassical transport of tungsten ion bundles in total-f neoclassical gyrokinetic simulations of a whole-volume JET-like plasma" submitted,  arXiv:2306.13145   

Influence of temperature gradients on drift wave turbulence through numerical simulation

In this study, we investigate the influence of temperature gradients on drift wave turbulence (DWT) in a linear device using Hermes-3 (https://github.com/bendudson/hermes-3/), a three-dimensional drift reduced fluid model built on the BOUT++ framework. According to linear theory, the stability of drift waves depends on the ratio of normalized electron temperature gradient to normalized electron density gradient (η_e), where values of η_e below 2/3 stabilize drift waves, while values above 2/3 lead to destabilization [1, 2]. Previous numerical simulations have shown overall agreement with this theory, which aligns with recent experimental findings in LAPD for η_e < 2/3 [3]. Expanding on prior research, the impact of neutrals on DWT is considered by using a fluid neutral model in Hermes-3. This is investigated both with a fixed neutral background and an evolving neutral background. Additionally, simulations with varying temperature gradients are analyzed to explore the role of turbulence spreading.

Acknowledgments:

Work supported by US DOE under DE-SC0007880, US NSF under NSF PHY 2144099 and in part under the auspices of the US DOE by LLNL under Contract DE-AC52-07NA27344.

References:

[1] Horton et al. Physics of Plasmas 11, 5(2004), 2600-2606

[2] Goldston Introduction to Plasma Physics (2020)

[3] Perks et al. Journal of Plasma Physics 88, 4(2022), 905880405   

The Unexplained Complexities of Strong SOL Interchange-Type Turbulence

The Helimak is the least complex experimental realization possible of the cylindrical slab, the minimal model of the interchange instability, a “universal” instability of confined plasmas, especially in the SOL. The development of a unique magnetically baffled probe array has enabled simultaneous, local measurements of fluctuations in density, temperature, and true plasma potential as well as the turbulent transport fluxes of particles and electron thermal energy, revealing the remarkable complexity of this turbulence. Neither the three fields nor the transport are consistently correlated with each other; there is no trace of a primary linear instability or normal mode. The PDF of transport has a strong mode at 0; net transport arises solely from skew. Changes in azimuthal flow profile, even without increasing shear, has a strong effect on both turbulence and transport. These all want explanation. An important and robust conclusion from the observations is that floating potential fluctuations are highly correlated with temperature fluctuations, but not with plasma potential. Floating potential can be used only to infer properties of T_e turbulence. The Helimak is now at Shenzhen University.   

Confinement scaling with machine size in the updated ITPA global H-mode energy confinement database

A revision of the International Tokamak Physics Activity (ITPA) global H-mode energy confinement scaling in tokamaks was carried out in 2020, using the latest version of the multi-machine ITPA database (DB5.2.3), including data from machines with fully metallic walls (ASDEX Upgrade with the full tungsten wall and JET with the ITER-like wall). This resulted in the ITPA20 scaling law for ELMy H-modes, a power law estimated both in engineering and dimensionless form, exhibiting several dependencies that are different to those seen in the IPB98(y,2) scaling. One of the notable differences is a considerably weaker dependence on major radius. The present work aims to contribute to an explanation for this reduced size scaling. Although multicollinearity between the predictor variables may play a role, various multicollinearity diagnostics and mitigation techniques suggest that it is not the sole cause of the observed reduction. Optimisation and classification techniques reveal a subset of database points exhibiting weak size dependence, whereas the majority of points lie in a region characterized by strong size scaling, reminiscent of IPB98(y,2). Both clusters are relatively well separated in the space of normalised collisionality, gyroradius and pressure, with the standard operational point for ITER lying closest to the region of strong size scaling.   

Resolving Gyrokinetic Turbulence Using the Non-Twisting Flux Tube in the Gyrokinetic Code GX

GX is a recently developed, GPU-enabled, pseudo-spectral gyrokinetic code used for simulating microturbulence in fusion relevant plasmas [1]. It uses the radially local flux-tube approximation with a field aligned coordinate system that aims to resolve the underlying structure of the turbulence [2]. At the outboard midplane, the perpendicular domain is rectangular and the normal/binormal directions are typically several gyroradii in length. However, due to both global and local magnetic shear, the perpendicular cross section shears into a parallelogram away from the outboard midplane. This perpendicular box shearing might unphysically cut off transport-relevant long-wavelength turbulence, while often unnecessarily simulating transport-irrelevant ultra-fine-structure turbulence. In this work, we present the implementation and results of a non-twisting flux tube (NTFT) in GX, which retains a rectangular cross section at all poloidal locations. Building off previous work that implemented a NTFT in the gyrokinetic code GENE [3], this presentation will focus on nonlinear implementation of the NTFT as well as linear and nonlinear results. We will also discuss benefits of the NTFT in device applications such as tokamak pedestals and stellarators.

[1] N. R. Mandell, W. D. Dorland, I. Abel, R. Gaur, P. Kim, M. Martin, and T. Qian, arXiv:2209.06731 (2022).

[2] M.A. Beer, S. C. Cowley, and G. W. Hammett, Phys. Plasmas 2, 2687 (1995).

[3] J. Ball and S. Brunner, Plasma Phys. Control. Fusion 63, 064008 (2021).   

Comparison of Saturation Rules used for Gyrokinetic Quasilinear Transport Modeling

Modeling tokamak plasmas using computer simulation can be a time-consuming and costly endeavor due to the non-linear nature of the gyrokinetic system of equations. To expedite this process, linear simulations can be employed to simplify these models. In good confinement regimes, it is reasonable to assume that the turbulent fluctuations are made up of a superposition of linear eigenmodes so that quasilinear expressions for fluxes are valid. What is more uncertain is the turbulent saturation level. Rather than choosing an ad-hoc, data-driven, or empirical saturation rule, we quickly “scan” sensitivity to the saturation rule by comparing three theory-based models capturing what is currently used in the community. The saturation rules used for this comparison are found in Bourdelle(2007), Lapillonne(2011), and Kumar(2021). In addition, we compare our three saturation rules to the widely used TGLF (Tokamak Gyro-Landau Fluid) model. The objective of this poster is to discuss and compare these saturation rules for gyrokinetic quasilinear transport modeling of linear plasma simulations conducted using GENE. Linear GENE calculations provide ion-scale eigenvalue and eigenmode information for detailed quasilinear flux estimates. A comparison of the quasilinear theory with the three saturation rules will be presented.

C. Bourdelle, X. Garbet, F. Imbeaux, A. Casati, N. Dubuit, R. Guirlet, T. Parisot 2007 Physics of Plasmas 14 112501

X Lapillonne et al 2011 Plasma Phys. Control. Fusion 53 054011

N. Kumar et al 2021 Nucl. Fusion 61 036005   

Constructing a Correlation ECE Synthetic Diagnostic forGyrokinetic Simulations with Application to HSX

Transport driven by nonlinear, turbulent interactions of ion and electron scale fluctuations play a

critical role in determining the performance of stellarators and has not been directly addressed

in turbulence optimization. As numerical modeling and simulations are the primary method by

which turbulence optimization will be advanced, it is critical the underlying physics models be

validated through rigorous comparison of numerical simulations with experimental data.

To perform microturbulence validation, density-gradient-driven trapped electron mode (TEM)

microturbulence is studied in the HSX stellarator. Using the GENE code, nonlinear flux-tube

simulations of TEM microturbulence have been performed at experimentally relevant

parameters for HSX. A synthetic correlation ECE diagnostic has been constructed using the

spatial and temporal resolutions of the experimental diagnostic. The simulation data is mapped

from the co-rotating plasma frame to the laboratory frame and integrated over Gaussian point

spread functions centered on the diagnostic channels. These results, coupled with an

understanding of the errors in synthetic diagnostic implementation, e.g. introduced through

numerical Monte Carlo integration, provide an important basis on which a thorough validation

study will be based.   

Exploring plasma turbulence with a gyrokinetic moment-based approach: from the core to the edge, from reduced fluid to full gyrokinetic modelling

We present the first detailed analysis of local delta-f nonlinear gyrokinetic (GK) simulations based on a gyromoment (GM) approach [1], which exploits the projection of the distribution functions onto a Hermite-Laguerre velocity-space space basis to solve the GK equation [2,3]. We first demonstrate that, in contrast to gyrofluid models, the GM approach reproduces the Dimits shift, i.e. the nonlinear upshift in the gradient required for the onset of significant turbulent transport with respect to the linear growth rate [4]. Notably, we report that the width of the shift can be retrieved with a coarser velocity space resolution than state-of-the-art continuum GK codes, such as GENE. The convergence properties of the GM moment further improves with the gradient strength and collisionality. In addition, we reveal that the choice of collision operator model (Dougherty, Sugama, Lorentz and Landau [5]) significantly impacts the level of turbulent transport, in particular through zonal flow damping, questioning the use of simplified collision operators [6]. The full potential of the GM approach is then shown by discussing tokamak relevant edge turbulence simulations [7]. Finally, our results demonstrate, for the first time, the unique multi-fidelity property of the GM approach, which bridges the gap between fully GK and reduced fluid models [8], retrieving fluid results at low velocity space resolution and GK results at high velocity space resolution.   

Energy exchange induced by ITG turbulence in weakly collisional plasmas

In magnetically confined plasmas, turbulence induces energy exchange between electrons and ions as well as particle and heat fluxes[1]. In a previous study [2], the effect of turbulent energy exchange on prediction of plasma density and temperature profiles was investigated under specific conditions and it was found to be negligible. However, a detailed comparison between the turbulent and collisional energy exchanges has not been shown in the case of very high-temperature plasmas such as those in ITER, where the collision frequency is very low. In this work, effects of ion temperature gradient (ITG) turbulence on the energy exchange in tokamak plasmas are quantitatively investigated by the gyrokinetic simulation code GKV[3]. As a result, different properties between collisional and turbulent energy exchanges are revealed. The turbulent energy exchange can dominate over the collisional one at high temperature (low collision frequencies). Also, the turbulent energy transfer can occur in the opposite direction to the collisional one. Coulomb collisions make energy transfer from hotter to colder species. On the other hand, in the ITG turbulence, energy can flow from colder ions to hotter electrons. In addition, to develop the quasilinear model for the turbulent energy exchange, we have found a good correlation between the linear and nonlinear simulation results. [1] H. Sugama et al., Phys. Plasmas, 1996. [2] J. Candy, Phys. Plasmas, 2013.[3] T.-H. Watanabe et al., Nucl. Fusion, 2006.   

Self-consistent saturation of plasma profile and kinetic ballooning modes in the global, total-f gyrokinetic code XGC

Kinetic ballooning modes (KBMs) could be one of the ultimate limiters of the plasma energy content and its gradient. We demonstrate saturation of the plasma profile in self-organization with the KBM turbulence, the neoclassical physics, and the sheared E×B flow in a model tokamak plasma using a global total-f gyrokinetic code XGC. XGC uses mixed-variable and pull-back transformation methods together with the total-f algorithm [1,2] and nonlinear Fokker-Planck collision operator.  The E×B shear regulates the turbulence level during the short transit time scale dynamics (<0.01 ms) and the profile relaxations are responsible for the turbulence level in the longer time scale (>0.1 ms).  Radial heat-flux due to the self-organized plasma profile and KBM turbulence is in power-balance with the plasma heating.   

Development of a 2-D impurity fluid code for a neoclassical transport of High-Z impurities in a realistic tokamak geometry and rotation.

The accumulation of tungsten in the core region of tokamak plasmas can be a serious issue for plasma operations, as it can cause radiative cooling and dilution of the main plasma species. For evaluating impurity accumulation, it is important to know whether there is an influx or outflux of particle, which can be calculated by neoclassical kinetic analysis [1-4]. There are several characteristics that are commonly considered to affect the impurity neoclassical particle flux. The first one is a collisional regime of main ions, which can change the coefficients of the temperature screening effect [5,6]. The second factor is the poloidal asymmetry of impurity density caused by high plasma rotation [5-8] or geometric effects [9,10]. We found that the rotation can make a significant impact on particle flux in the Pfirsch-Schluter regime [7]. To comprehensively study these properties and the transport time scale evolution of impurities, we are currently developing a 2-D impurity transport fluid code in a realistic tokamak geometry and toroidal rotation. The impurity density and parallel flows are evolved by the friction and viscosity using the coefficient models in FACIT [5], in which the neoclassical kinetic radial fluxes in NEO are well fitted.   

Extending Modulation Transport Studies to the Pedestal with Edge Particle Source Measurements in DIII-D

Particle transport coefficients are obtained in the pedestal region of DIII-D by utilizing absolutely calibrated source measurements in a time-dependent forward modeling framework, in order to explore transport dependence on factors such as the curvature pinch via normalized safety factor gradient. The diffusion and convection coefficients influence the shape of the density pedestal. We extract the transport coefficients through gas puff modulation. This technique is often employed for core transport, where the modulated and fixed ionization source from the gas puff and wall recycling is negligible [1]. To extend this technique to the pedestal, we require absolute edge particle source measurements from the LLAMA Lyman-alpha diagnostic [2] that are utilized in time-dependent forward modeling with Bayesian inference to optimize a diffusion and convection profile against density profile measurements. This method allows for separation of diffusion and convection terms by exploring the evolution of the density profile through dynamic events such as gas puff modulation or recent work on the inter-ELM rebuild cycle. [3]

[1] S. Mordijck 2020 Nucl. Fusion 60 082006

[2] A.M. Rosenthal et al 2021 Rev. Sci. Instrum. 92 033523

[3] A.M. Rosenthal et al 2023 Nucl. Fusion 63 042002   

Intermediate-Wavenumber Pedestal Fluctuation Measurements with Charge eXchange Imaging on DIII-D

Localized 2D measurements of low-to-intermediate wavenumber density fluctuations in the H-mode pedestal reveal a range of broadband turbulent modes during the inter-ELM cycle. These measurements are obtained with a new higher radial resolution multichannel Charge eXchange Imaging (CXI) diagnostic. CXI observes charge exchange emission between neutral beam atoms and intrinsic carbon impurity ions by detecting the n=8-7 hydrogenic  emission line. Fluctuations are measured in a 12 (radial) x 2 (poloidal) array at 2 MHz with a resolution of dR ~ 0.4 cm and dZ ~ 1.2 cm. Optimal CXI signal to noise ratios are predicted for experiments that maximize the NBI injection voltage and minimize the background neutral density content. Initial measurements include observations of broadband carbon density fluctuations in ELM’ing H-mode pedestal regions near rho=0.95-1.0. First measurements demonstrate excellent spatial resolution and signal to noise ratios at all frequencies, and strongly correlated fluctuation measurements remain coherent up to 400 kHz. Two distinct and counter-propagating modes are occasionally observed near the base of the pedestal, and EHO observations in QH-Mode are observed alongside coherent turbulence.   

Modeling of Transport-Limited, Near-Edge Tokamak Profiles Using Control Volumes

Accurately predicting temperature and density profiles in the near-edge region between the core and scrape-off layer (roughly the outer 10%-20% of closed flux surfaces) is essential for self-consistent modeling of tokamak performance. We present initial results from a new approach to predicting these profiles, building upon lessons learned from advances in core transport and stability modeling. Model forms such as “modified” tanh functions or piecewise-linear scale lengths are used to describe density and temperature profiles with only a small number of free parameters. These parameters are determined by a combination of prescribed boundary conditions and discretization of the flux-surface averaged transport equations via control volumes. For this initial work, only simple analytic expressions of neoclassical and stiff turbulent transport are used, but extensions to more complex models is straightforward. The net result is that self-consistent solutions can be determined by solving a relatively small set of equations with standard root-finding and minimization techniques. Illustrative examples of  the predictions and their key parametric dependencies will be shown, and future development directions discussed.

 

This work was supported by the US DOE under award DE-SC0018287.   

Cross Phase Modification through Drive Adjustment to Control I-mode Transport

Novel enhanced confinement regimes such as the I-mode and similar new transport regimes offer good confinement properties with reduced density limit issues and potentially better control. Few if any suggested mechanisms allow enhanced confinement in one channel but not another which is seen in the I-mode. We have proposed differential cross-phase modification as a possible mechanism for different transport in different channels and investigate control tools. In this work we present GENE simulations with various and multiple instability drives to test the plausibility of this mechanism. Included are ITG, ETG and TEM and start with linear simulation then extent to fully nonlinear simulations. Following these results, we use a simple dynamical model which has been able to capture a remarkable amount of the dynamics of core and edge transport barriers to further explore the dynamics of more continuous transitions such as the I-mode with this mechanism. We look at I-mode transitions and explore using differential electron and ion heating to control the I-mode regime in the simpler model and we demonstrate the ability to stay in the I-mode without slipping into the H-mode regime.   

The impact of magnetic islands on microtubulent transport in KSTAR

Global gyrokinetic simumlations with kinetic electrons are performed to study microturbulence in the presence of magnetic islands with self-generated ExB shear flow around islands. In this work, we use the global gyrokinetic toroidal code GTC with a drift kinetic electron model to simulate microturbulence in the KSTAR tokamak with resonant magnetic perturbation (RMP). Magnetic islands generated by RMP coils are included in the equilibrium which is obtained from M3D-C1 MHD simulations of the discharge #19118. Simulations shows microturbulence is dominated by Ion temperature gradient (ITG) turbulence. Magnetic islands have little effect on linear growth rate, frequency and spectrum of the ITG instability. However, larger transport levels are found in nonlinear simulations near the X points of the island compared to the O points. A vortex flow, an ExB flow around the islands by electrostatic potential with the same periodicity and location as the magnetic island, is nonlinearly generated and regulates the ITG turbulence across the islands.   

The role of the radial magnetic drift in toroidal ITG turbulence

It is well known that, in toroidal systems, the radial magnetic drift is important for the linear physics of zonal flow (e.g. the Rosenbluth-Hinton residual [1] or geodesic acoustic modes). We here study its role on the nonlinear saturation of zonal flows and ITG turbulence. First, we show how the upshift of the nonlinear ITG critical gradient known as Dimits shift [2], caused by zonal flow that fully suppresses ITG turbulence close to marginality, is strongly dependent on the radial magnetic drift. Secondly, for ITG turbulence far from marginality, we show that the turbulence radial correlation length set by critical balance follows a new scaling set by zonal flow physics, contrary to previous theories assuming perpendicular isotropy [3] or grand critical balance [4]. The anisotropy between the radial and binormal length scales leads to revised scalings, e.g. of the heat flux with the temperature gradient, which is verified using the codes GS2 [5], stella [6], and GX [7,8]. We will show that the radial magnetic drift affects the turbulence through its impact on the zonal flow, and not due to its effect on the non-axisymmetric turbulent fluctuations.

[1] Rosenbluth, M.N. (1998) PRL 80, 724

[2] Dimits, A.M. (2000) PoP 7, 969

[3] Barnes, M. (2011) PRL 107, 115003

[4] Ghim, Y. (2013) PRL 110, 145002

[5] Dorland, W. (2000) PRL 85, 5579

[6] Barnes, M. (2019) JCP 391, 365

[7] Mandell, N.R. (2018) JPP 84, 905840108

[8] Mandell, N.R., et al. (2022) arXiv:2209.06731   

Experimental investigation of impurity transport in the core and edge of the wide pedestal QH-mode regime on DIII-D

    Wide Pedestal Quiescent H-mode (WPQH) is a promising scenario for future fusion reactors, offering intrinsically ELM–free operation and high energy confinement [1].      We have performed a detailed investigation of impurity transport in the WPQH pedestal.  The particle confinement time τ_imp of carbon injected by impurity powder dropper and nitrogen from gas puff is 0.09 and 0.25s, respectively. In contrast, τ_imp of fluorine and calcium injected by laser blow-off system is 1.0 and 3.2s, close to the prediction from a neoclassical model. The primary cause of high τ_imp is a  low diffusion and high inward convection at the wide edge transport barrier,  comparable to inter-elm transport coefficients observed in ELMy discharges, however, without the particle sink from ELMs.  The n = 2 resonant magnetic perturbation (RMP) reduced calcium τ_imp by 40%, while H₉₈ and β_N degraded only by 5%. Nevertheless, the carbon density remained unchanged. Low carbon τ_imp and insensitivity of carbon content to the RMP indicate that the high Z_eff  is likely a consequence of a significant carbon source rather than unfavorable pedestal transport.

 [1] K.H. Burrell et al., Nucl. Fusion 60 086005 (2020).   

Comparing Hydrogen and Deuterium Plasmas in DIII-D Using Gyrokinetic Simulation

Linear growth rate and dominant-mode-frequency spectra between dimensionally similar plasmas with differing isotope mass exhibit distinct features that suggest why confinement varies strongly with ion mass. Using the CGYRO code, we run linear simulations of DIII-D plasmas based on experimental profile data. First, we compare simulations based on data of two plasmas fueled by either deuterium or hydrogen, with nearly matched kinetic profiles with the same plasma current and toroidal field. Second, we compare the deuterium simulations using an artificial hydrogen ion mass. The deuterium case shows unstable modes that peak at normalized poloidal wavenumbers k_yρ_s between 0.6 and 0.8, while for hydrogen, growth rates also peak near 0.6, but are higher and vary more with respect to minor radius. We also investigate the effects of temperature gradient and density gradient to help identify the dominant mode at a given frequency and minor radius. Results indicate modes in the electron diamagnetic direction dominate in both deuterium and hydrogen. Initial nonlinear simulations of deuterium and artificial hydrogen plasmas are compared. We also examine the effects of carbon impurities, fast ions, and normalized gyroradius. Future work will examine aspect ratio, particularly that of NSTX-U.   

Towards Efficient and Practical Models for Energetic Particle Transport in Tokamaks*

In addition to alpha particles, ICRH and NBI also heat the thermal plasma, increasing the temperature of tokamak plasmas. As fusion power surpasses input heating power in devices like ITER, alpha or energetic particles play a crucial role in plasma heating and can potentially trigger particle-driven instabilities. These instabilities may cause cross-field transport of energetic ions, leading to reduced plasma heating and altered power deposition profiles, affecting thermal plasma confinement. Understanding the physics of energetic ion-driven instabilities and associated heat and particle transport across the plasma confinement is crucial due to the significant role of energetic particles in fusion plasma. Accurate modeling of energetic particle transport is essential for comprehending and controlling these processes. However, current transport models for energetic particles in tokamaks are complex and computationally intensive, making them impractical for time-dependent plasma profile predictions and control. Hence, there is a need for physics-based fast transport models that can efficiently and accurately predict energetic particle transport while preserving the essential physics. The energetic particle transport model, which incorporates basic resonances as well as resonance broadening, is provided, as are preliminary numerical results.

  

Advances in Transport Studies in the Spherical Tokamak (ST) PI3 at General Fusion Inc

The ST PI3 is a medium-size device in operation at General Fusion Inc., aiming to study transport, equilibrium, stability, plasma-wall interaction, while developing core & edge diagnostics for the unique environment created by the lithium (Li) coating of the vacuum vessel, thus guiding the future devices where Li liners will be used for plasma compression.

The PI3 plasmas are formed exclusively via coaxial-helicity injection (CHI) and last ~30ms. They can be close-fitted or slightly detached from the aluminum spherical vacuum vessel of 1.00m inner radius and 50mm thickness, acting as a flux-conserver. This wall is regularly coated with Li using 4 heated evaporators.

Typical values of Pi3 plasmas in early phases of discharge (~3ms) are: R_o=0.67m, a=0.37m, A=1.8, k=1.7, δ~0.4, B_T(R_o)=0.23T, I_p =250-500kA, n_e(bar)=2-3x10¹⁹m^-3, T_e(0)=300eV and T_i(bar)=400eV.

Equilibrium reconstruction is performed by Flagship code using constraints from poloidal pickup coils inside of the vacuum vessel wall and polarimeter signals.

Experimental results of the thermal energy confinement time tauE and the thermal diffusivity Chi will be presented. The former is calculated from kinetics diagnostic and magnetic power balance methods. Preliminary results from kinetics method in medium plasma densities (N_G=0.5) show tauE=13ms, thus much higher than ~8ms expected from the ITER97-L-mode scaling. Analysis of tauE in new regimes at higher B_T(R_o), I_p, and T_e(0), comparison with H-modes scenario (scaling and L-H power transition), and the impact of pressure constrained equilibria, as well as few simulations with standard transport codes will also be presented.   

Quasilinear Gyrokinetic Modeling of Reduced Transport in the Presence of High Impurity Content, Large Gradients, and Large Geometric αMHD

Transport barriers in tokamak discharges are often characterized by large gradients that can destabilize electrostatic microinstabilities, thereby driving anomalous turbulent transport. However, large gradients can also lead to large geometric α_MHD, a stabilizing parameter in certain regimes. The resulting transport is inherently constrained to be ambipolar; in effect, these large gradients can make this flux constraint impossible to satisfy, resulting in stabilization and the reduction of turbulent transport. Due to the high computational cost of nonlinear gyrokinetic simulations, using a reduced turbulent transport model is ideal for predictive modeling. However, reduced models tailored for the tokamak core can become unreliable in transport barrier regimes, thus necessitating model development and improvement. We test the extent to which the gyrokinetic quasilinear code QuaLiKiz can reliably predict anomalous transport in transport barrier discharge regimes to determine parameters that lead to turbulent transport reduction. We use the gyrokinetic code GENE, based on first principles, as a point of comparison for QuaLiKiz. Unlike GENE, QuaLiKiz uses many approximations to ensure computational tractability. In particular, QuaLiKiz assumes a Gaussian eigenfunction, uses s-α_MHD geometry, and only captures electrostatic fluctuations. To ensure accurate predictions in transport barrier discharge scenarios, we improve the approximations made for trapped particles, and thus the trapped electron mode (TEM), by incorporating the bounce-averaged electrostatic eigenfunction. The Gaussian ansatz allows us to analytically estimate this bounce-averaging effect with sufficient accuracy. We also improve the approximate methods used to solve for the mode structure in order to accurately calculate bounce-averaging effects.   

Impurity transport studies in DIII-D H-mode plasmas: Experiment and Turbulence Modeling

The transport of impurities in tokamaks is anticipated to play a critical role in future fusion reactors. As a result, there is a strong desire to accurately measure and model impurity transport in current devices, to allow for extrapolation to burning plasma regimes. In this work we present a study of core impurity transport in DIII-D H-mode plasmas. The H-mode conditions have been studied in ITER baseline scenarios (IBS), and in ITER Similar Shape (ISS) plasmas. In IBS conditions, Al  impurities were studied with gyrokinetic modeling, suggesting that slightly hollow profiles may occur to strengthen TEM activity outside of r/a = 0.8. The ISS plasmas were studied by comparing Aurora modeling and direct density measurements with gyrokinetic modeling.  Low-Z impurities exhibit good agreement with experimental measurements over a wide radial range (inside ρ =0.8) while medium Z impurities (Ca) show some disagreement.  Sources of possible error, including atomic physics, and the Z scaling of impurity diffusion will be discussed.  Analysis of DIII-D low power (3-4 MW) H mode plasmas in ISS  with transition from ITG to TEM dominated turbulent regime is currently underway. Profile and power balance analysis using TRANSP will be presented along with TGLF modeling of heat and particle transport. 

This work was supported by the U.S. Department of Energy award DE-SC0014264 and DIII-D cooperative agreement DE-FC02-04ER54698. 

    

Nonlinear Selection Rules for Saturation Channels in Toroidal and Slab ITG Turbulence

The saturation of toroidal and slab ITG turbulence involves the transfer of energy from unstable modes to stable modes through different intermediary modes. Typically, the former occurs via the zonal flow, while the latter occurs through a marginally stable mode. The underlying physics governing the selection of these intermediary modes is not fully understood. To identify the selection rules, a three-field model with toroidal and slab branches is employed, allowing interactions between unstable and stable modes, with marginal or zonal modes as intermediaries. The investigation is conducted by examining nonlinear-coupling quantities, including triplet correlation times, spatial mode overlap, and coupling coefficients. The maximum triplet correlation times obtained from the two intermediary modes are similar for both branches. The number of mode-coupling triads whose triplet correlation time exceeds a nominal threshold value is higher in the slab limit than in the toroidal limit. Mode overlap is determined using mode structures represented by the Hermite function. The results indicate that the overlap involving marginal modes is significantly greater than that observed with zonal coupling in the slab limit, and vice versa in the toroidal limit. Consequently, correlation time and mode overlap serve as selection rules for saturation process. Additionally, we explore the potential significance of coupling coefficients in determining the selection of intermediary modes.    

A Subgrid Gyrokinetic Model of Electron-Temperature-Gradient Turbulence in Tokamaks

Substantial research has been conducted in validating gyrokinetic models at ion-temperature-gradient (ITG) scales for a variety of experimental magnetic confinement plasmas. Ion-scale gyrokinetic simulations are now able to accurately predict ion transport levels and flux spectra; however, they can often underestimate electron thermal transport levels. Recent multiscale simulations [Howard16, Holland17], while impractically expensive, have shown that the inclusion of electron-scale turbulence can lead to better agreement with experimental heat flux levels and that capturing cross-scale dynamics can be important as well. Therefore, a reduced model of fine-scale turbulence is of interest in modeling future burning plasma experiments such as ITER, where electron-temperature-gradient (ETG) effects can become important [Holland17]. Here we investigate a subgrid ETG model which considers spatially, and possibly temporally, averaging the electron-scale turbulence onto the ITG turbulent state. This method would result in ion-scale simulations which produce better agreement with experimental electron thermal transport levels, while also capturing how the ion-scale turbulence could be affected by finer-scale turbulent interactions. Electron-scale flux-tube simulations are carried out using GENE [Jenko00] and then input into global GEM ITG simulations [Chen04]. Various analytic radial profiles of electron-scale turbulence will also be constructed and tested against flux-tube runs at multiple radial locations in order to simplify the simulation complexity.

Howard N.T. et al 2016 Phys. Plasmas 23 056109

Holland C. et al 2017 Nucl. Fusion 57 066043

Jenko F., Dorland W., Kotschenreuther M., and Rogers B.N. 2000 Phys. Plasmas 7 1904

Y. Chen and S.E. Parker 2003 J. Comput. Phys. 189 463   

Whole Device Modelling of coupling between fixed gradient driven core delta-f and flux driven edge total-f gyrokinetic models with XGC.

A Whole Device Model (WDM) for coupling core delta-f and edge total-f gyrokinetic models is presented as a tool for understanding and predicting the H-mode of ITER and other future fusion facilities. This model, which is implemented in a single XGC simulation, lets the gradient-driven E×B turbulence of the core flow into the edge region. The edge being modeled with the usual XGC flux driven total-f model. The new core delta-f model solves the same equations than the total-f model while using a different background definition (such as corrected canonical Maxwellian), which enables to keep a small δf ≪ f0 in the core by applying coarse-graining and thermal-bath procedures. The thermal bath fixes the averaged temperature profile while leaving the flux-surface averaged density and parallel momentum free to relax. We will discuss the convergence and numerical aspects of this new numerical scheme. Preliminary results of a core-edge whole-device model simulation will be presented.   

Electron temperature barriers as Lagrangian Coherent Structures

The formation of transport barriers with impact on transport and dynamical regimes is common to the main configurations for the magnetic confinement of hot plasmas: tokamak, stellarator, and reversed-field pinch (RFP).

The aim of this work is to describe and deploy a numerical method for computing "Lagrangian Coherent Structures" (LCS) in scenarios typical of RFP helical self-organization, where magnetic stochasticity and electron temperature barriers appear together.

LCSs are coherent curves, developed and studied in the framework of dynamical systems, constructed as the most attractive or repelling of nearby magnetic field lines. As a result, LCSs have a significant impact on the transport of physical quantities. In this work, LCSs are shown to behave as barriers to magnetic field lines in chaotic regions of numerically verified 3D nonlinear MHD simulations of RFP and in experimental data from the RFX-mod experiment in Padua. In the first case, LCSs locate / divide regions with different connection length. In experiments, LCS coincide with high electron temperature gradients, showing that transport barriers are akin to simple objects of dynamical system theory called Cantori.   

Reduction of tokamak self-driven current by magnetic island perturbations

Magnetic island (MI) perturbations, likely unavoidable in long pulse discharges, may cause a reduction of plasma self-driven current in tokamaks. A novel effect on tokamak self-driven current revealed by global gyrokinetic simulations results from MI-induced electric potential islands, which have dominant mode numbers the same as that of the MI, whereas centered at both the inner and outer edge of the island. The non-resonant potential islands are shown to drive a current through an efficient nonlinear parallel acceleration of electrons. In large-aspect ratio (large-A) tokamak devices, this new effect can result in a significant global current reduction to the electron bootstrap current when the MI size is sufficient large, in addition to the local current loss across the island region due to the pressure profile flattening. It is shown that there exists a critical magnetic island width for large-A tokamaks beyond which the electron bootstrap current loss is global and increases rapidly with the island size. As such, this process may introduce a size limit for tolerable magnetic islands in large-A tokamak devices in the context of steady state operation. On the other hand, the current loss by MIs in low-A tokamaks (e.g., spherical tokamak) is minor. The reduction of the axisymmetric current by the MI scales with the square of island width. However, the loss of the current is mainly local in the island region, and the pace of the current loss as the increase of MI size is substantially slower compared to large-A tokamaks. In particular, the bootstrap current reduction MIs in STs is even smaller in the reactor-relevant high-β_p regime where NTM islands are more likely to develop. The connection of this newly revealed effect of MI on the current to some experimental observations will be also discussed.   

Withdrawn

I-mode is an important alternative operational scenario for burning plasmas. A possible theoretical understanding is presented for a unique turbulent transport phenomenon in the I-mode regime, i.e., the so-called transport decoupling between heat and particle in tokamak edge plasmas. Based on our particle simulations by running gyrokinetic toroidal code (GTC), we found that a particular instability can account for such experimental phenomenon, which makes it the major candidate for experimentally observed weakly coherent modes (WCMs) turbulence. This instability is driven by steep electron temperature gradient up to a certain value, with characteristic time scale around transit time of passing electrons while the spatial scale falling in the range of ion's poloidal gyro-radius. A crucial feature about this instability is that neither ions nor passing electrons can be treated adiabatically, which distinguishes it from the conventional drift-like instabilities such as ion temperature gradient modes (ITGs), trapped electron modes (TEMs) and normal electron temperature gradient modes (ETGs). Those non-adiabatic responses for both ions and electrons indeed excited this unique instability and could be saturated by typical flow shearing suppression mechanism including low frequency zonal flow and geodesic acoustic modes (GAMs) instead of poloidal mean flow to give rise to the considerable particle and heat transport compared with experimentally observed values. A detailed discussion about this instability and its nonlinear saturation mechanism which may account for experimentally observed WCMs and associated turbulent transport will also be presented in this talk.
Keywords: I-mode, WCMs, Transport decoupling.   

Intrinsic toroidal rotation in tokamaks from global total-f gyrokinetic simulations

Understanding intrinsic toroidal rotation is important for future tokamaks like ITER. In gyrokinetic plasmas, the ion gyrocenter toroidal angular momentum can be transported in the radial direction via three processes: turbulent transport of the parallel momentum, neoclassical transport of the parallel momentum, and turbulent transport of the E cross B momentum. Theories and conventional delta-f simulations have been mainly focused on the first process based on the ordering assumption. However, global total-f simulations have suggested that the three processes could be on the same order. Here, we study intrinsic toroidal rotation in flux-driven ion-temperature-gradient turbulence using the global total-f gyrokinetic code XGC1. After the turbulence onset, zonal flows quickly form and reach a steady value. Meanwhile, there is a persistent toroidal-rotation acceleration, whose direction correlates with the zonal-flow pattern. Simulation results showed that for the ion gyrocenter particle flux, the turbulent contribution is balanced by the neoclassical contribution, resulting in steady-state zonal flows. However, for the momentum flux, simulations suggested that the turbulent transport of E cross B momentum is not balanced by other processes and results in persistent toroidal-rotation acceleration. The correlation between zonal flows and toroidal rotation can be explained as the result of the correlation between turbulent particle and momentum flux.   

Overview of SPARC Progress: Construction, Manufacturing, and Operational Planning

Commonwealth Fusion Systems (CFS) and its partners are building SPARC, a high field (B_T = 12.2 T), compact (R₀ = 1.85 m, a = 0.57 m) tokamak designed to achieve Q~11 and P_fusion~140 MW at H₉₈ = 1.0.  SPARC is under construction in Devens, Massachusetts and has progressed significantly in the past year.  Tokamak and plant buildings are nearing completion and installation of the SPARC cryostat base is anticipated by the end of 2023.  SPARC magnets are in manufacturing at the CFS magnet factory and will be tested at temperature before assembly into SPARC. Major procured items, such as the vacuum vessel and cryoplant, are well into production at vendors and will be arriving throughout 2024.  Early SPARC operation will focus on commissioning the machine and then achieving Q > 1 in DT L-mode plasmas, which have recently been thoroughly analyzed.  SPARC will then transition to studying H-mode in deuterium, before pushing to full power DT operation.  Throughout, a primary focus of SPARC's research program will be to inform ARC design and operation.   

ARC Physics Basis Status

Commonwealth Fusion Systems plans to build ARC, a high magnetic field tokamak, as the first fusion pilot plant by the early 2030’s.  ARC will follow SPARC, now under construction, where a primary focus of the SPARC research program will be to inform ARC design and operation.  The ARC design, which has evolved from early iterations [1,2], targets production of 400 MW net electric power based on achieving H₉₈=1.0 in pulsed, inductive operation and leveraging HTS magnet technology for a compact design (R₀=4.08 m, a=1.06m, B₀=11.5 T, I_p=10.1 MA) with P_fus≈1 GW at n_G≈0.85 and β_N≈1.7; values subject to change based on ongoing design activities. A set of physics studies has been initiated to increase the fidelity of analysis for the scenario at the ARC design point and inform the SPARC research program in support of ARC, including divertor physics, pedestal and ELMs, core transport, disruptions, MHD stability, alpha physics, and ICRF heating, which will result in a set of peer-reviewed publications similar to the SPARC Physics Basis [3].  Description of the current 2023 design and planned operation will be presented, including preliminary results of the ARC Physics Basis studies.

 

[1] Sorbom et al, FED 2015

[2] Kuang et al, FED 2018

[3] Creely et al, JPP 2020   

Edge code modelling to explore divertor configurations for SPARC's Advanced Divertor Mission

SPARC is a compact high-field tokamak under construction by Commonwealth Fusion Systems and partners, with a primary mission to achieve Q>1 in magnetic confinement fusion. In addition, SPARC will also serve to test a variety of physics and technology requirements for the follow-on ARC pilot plant. The divertor and vacuum vessel designs for ARC are intended to remain flexible for as long as possible, so that results of advanced divertor experiments can inform their design. To this end, SPARC has a dedicated Advanced Divertor Mission, which focuses on developing an integrated divertor scenario that projects well to long pulse operations in ARC conditions.

Modelling is being employed to characterise operational divertor scenarios in SPARC for this purpose, utilising edge simulation codes such as SOLPS-ITER and SOLEDGE2D. A variety of divertor magnetic topologies will be explored, from a standard divertor, X-divertors, and the X-point target divertor currently conceptualised for ARC. Main ion and impurity radiator gas injection will be varied to access dissipative divertor regimes that project to low target erosion rates, with an aim to better characterise SPARC experiments that could inform the design of an ARC-class divertor. This contribution will present the status of this work.   

Power and Temperature Asymmetries in the SPARC Divertor in SOLPS-ITER Simulations

SPARC is expected to have unmitigated parallel heat fluxes equal to or exceeding the highest values observed in existing devices. To support SPARC's breakeven and advanced-divertor missions, we perform scrape-off-layer (SOL) and divertor simulations using SOLPS-ITER. We observe strong divertor power and temperature asymmetries using SPARC geometries and parameters, with drifts not enabled. In a single-null (SN) horizontal-inner/vertical-outer divertor configuration, the inner target receives ∼60% of the power instead of the outer: an unexpected result compared to experiments. More dramatically, in an up-down-symmetric double-null (DN) configuration, several simulations converge to an up-down-asymmetric steady-state, with one target completely detached (∼5 eV) and the other completely attached (∼200 eV).

As these effects could impact SPARC operation, we are investigating whether their causes are physical or numerical. A dependence on input core power is found, indicating a power threshold necessary to trigger them. Initial conditions strongly affect steady-state currents and power-sharing in connected DN. We analyze parallel current as a potential driver, and we present a method to reach balanced steady-state solutions in DN, by initially disabling current terms in SOLPS-ITER.   

Fluctuations in the near and far scrape-off layer of Alcator C-Mod

Profiles and fluctuations in the boundary region of the Alcator C-Mod device is investigated with gas puff imaging (GPI) and Langmuir probe measurements. Exceptionally long measurement time series are obtained under stationary plasma conditions by dwelling the probe at a fixed radial position in the scrape-off layer (SOL) through an entire discharge. A detailed analysis of measurement data from both the near and the far SOL regions is presented, comparing GPI and Langmuir probe measurements. The results are interpreted in a statistical framework describing the fluctuations as a super-position of uncorrelated pulses, corresponding to large-amplitude blobs moving through the SOL.

The probe measurements close to the separatrix reveal that the time scale of the duration of the fluctuations is significantly shorter than that measured in the far SOL. These near-SOL fluctuations are close to normally distributed resulting in small relative fluctuations. In the far SOL there is an order unity relative fluctuation level and the probability density for the fluctuations is a strongly skewed Gamma distribution. It is demonstrated that the fluctuations become increasingly intermittent as the line-averaged density increases. A novel time delay estimation technique applied to GPI data reveals that the large-amplitude far SOL fluctuations are associated with blob structures moving radially outwards. The radial blob velocity increases significantly with line-averaged density, leading to profile broadening and flattening.

 

The results presented here emphasizes the role of large-amplitude fluctuations for plasma-wall interactions, which is particularly strong as the empirical discharge density limit is approached.   

Preparing for Disruptions in the SPARC Q>1 Campaign

The first SPARC campaign targets Q>1 in a DT L-mode that will experience disruptions with comparable electromagnetic (EM) loads but reduced thermal loads relative to the Q~11 scenario; here preparations for these disruptions are discussed. Radiative collapses and vertical displacement events (VDEs) during flattop or ramp-down are the most likely disruption types for this campaign. Early commissioning will provide an opportunity to test mitigation actuators and prediction algorithms. Physics-based algorithms will trigger actuators to avoid and mitigate disruptions; these algorithms, as well as machine learning-based alternatives, are under development. The toroidal and poloidal distribution of a 6-valve massive gas injection (MGI) system is finalized, informed by M3D-C1 and NIMROD simulations. Co-located bolometers are optimized using 3D tomographies of simulated data. A test stand and prototype MGI valve are designed and in procurement to validate the delivery characteristics. The runaway electron mitigation coil (REMC) is predicted to prevent relativistic electron beams that could otherwise damage tungsten PFCs and will be commissioned at low plasma current. New M3D-C1 VDE simulations are in progress to inform optimal current quench mitigation and aid the development of EM load diagnostic analysis.   

Overview of SPARC disruption prediction and avoidance research

SPARC disruption prevention strategies will leverage first-principle and machine learning-based solutions to ensure that SPARC will accomplish its mission goals. This poster will provide an overview of research advances addressing disruption prediction and avoidance on SPARC. An off-normal warning (ONW) system for asynchronous control actions is under development, with a particular focus on first campaign operations. The ONW software will include physics-based thresholds beyond machine learning-driven ones, with particular focus on radiative limits and vertical instabilities. The most extreme off-normal event being a plasma disruption, the poster will present progress made in developing potential candidate algorithms for the Disruption Mitigation System trigger based on deep learning and pre-trained architectures. Typically, these algorithms provide a classification probability for the current plasma state. However, time-to-event predictions allow the control system to better prioritize actuators' responses and tailor them to the plasma trajectory and expected margin to stability. Progress will be discussed in this area leveraging deep survival analysis (C. Nagpal et al 2021 IEEE JBHI) and a more classical statistical definition of disruptivity (in units of 1/time) derived from available databases.   

Do Fusion Plasma Time-Series Have a Persistent Memory that Machine Learning May Exploit?

Numerous Machine Learning (ML) models [1–4] have been proposed which, with varying degrees of success, attempt to predict the probability of disruption throughout the shot. Here, our work here is two-fold: (1) we give a practical study of model introduction, in which we demonstrate several ML techniques for consideration, and (2) we give a scientific study of model comparison, to interpret why one model may perform better than another. We compare a GPT2-like transformer [5] to several other algorithms, including a random forest and neural nets with limited window convolutions and/or recurrence. All are rigorously tuned to ensure a fair benchmark. One aspect of the transformer sets it apart from the others: masked self-attention, i.e. the ability to explicitly use information across the entire shot (including the ramp-up) when making a decision on the disruption probability. With these model comparisons, we argue for (or against) the persistence of a “memory” throughout the plasma that ML may exploit.

[1] J. Vega et al 2014 Nucl. Fusion 54 123001

[2] J.X. Zhu et al 2021 Nucl. Fusion 61 026007

[3] C. Rea et al 2019 Nucl. Fusion 59 096016

[4] K.J. Montes et al 2019 Nucl. Fusion 59 096015

[5] A. Randord et al 2019, OpenAI blog 1.8   

Towards Tearing Onset Prediction with Physics Informed Machine Learning

Improving tearing-onset prediction in tokamaks may facilitate the discovery of robust tearing-free scenarios for reactors. To this end, we have begun development of a physics-informed machine learning (ML) tearing stability metric for time-independent magnetic equilibria. A database of equilibria in cylindrical geometry is being generated and evolved linearly in M3D-C1. Inputs to the ML predictor include: observed M3D-C1 growth rates (ML training set); Δ' in the constant-psi approximation; ratios of big and small asymptotic solutions in inner resistive-MHD and outer ideal-MHD regions about the rational surface; and growth rates from asymptotic matching. Diverging stability predictions were observed between the constant-psi, zero-pressure tearing theory and full asymptotic matching in relation to a low-pressure equilibrium. M3D-C1 was able to independently match both predictions by including/excluding pressure effects. Work is progressing towards identifying stability boundaries in a multiple parameter design-space with the ML predictor. Next steps involve investigating the hypothesis that increasing classical tearing stability can improve robustness to magnetic island seeding events, and adding finite island-width effects to the model.   

Off-normal warning threshold development on SPARC

To achieve a high fusion performance, SPARC tokamak plasmas will have large stored energies, which could lead to high heat fluxes on in-vessel components and large forces applied to conducting structures in the event of a disruption. This work explores the preliminary development of the Off-Normal Warning system for SPARC, the aim of which is to minimize the disruption rate via the detection and pacification of anomalous conditions. The detection will be facilitated via physics-based warning thresholds as well as machine learning-based Proximity-to-Instability Algorithms, and the pacification (e.g. equilibrium steering, "soft-landing" triggers, or DMS triggers) will depend on the severity and (more notably) the type of the anomaly. An emphasis is placed here on the development of physics-based warning thresholds for two of the disruption types expected for the first L-mode campaign on SPARC, radiative instabilities (i.e. UFOs and impurity accumulation) and Vertical Displacement Events. Additionally, the diagnostic requirements for detecting these anomalies based on expected physical timescales for SPARC are presented.   

Risk-aware framework development for disruption prediction: Alcator C-Mod survival analysis

Disruptions pose a significant threat to the operation of future high-performance tokamaks. Over the course of a discharge, the plasma control system must be able to predict disruption onset with enough warning such that mitigation systems can be triggered. Risk-aware frameworks allow better prioritization of actuator response, enabling not only prediction of disruptions but also performance optimization. Determining the least hazardous actions to avoid disruptions is comparable with the time-to-event predictions often used in healthcare for selecting treatments given some mortality risk. This framework is called survival analysis, and there have been many tools developed which we aim to apply to disruption prediction. Using the open-source Auton-Survival package [1] and data from Alcator C-Mod, we have benchmarked performance of the binary classifier model Disruption Prediction with Random Forests [2] against several survival analysis models including Cox Proportional Hazards, Deep Survival Machines, and Kaplan-Meier [3]. We find that while the survival analysis models have similar accuracy with respect to binary classifiers, they allow robust instability predictions at greater time horizons.

[1] C. Nagpal et al., Proceedings of Machine Learning Research 182 (2022)

[2] C. Rea et al., Nuclear Fusion 59, 096016 (2019)

[3] R. A. Tinguely et al., Plasma Physics and Controlled Fusion 61, 095009 (2019)   

A Deep Dive Into Disruptivity: Learning to Predict and Avoid Disruptions

In order to effectively operate high performance tokamaks, it is imperative to prevent disruptions either in real time control or in scenario planning. This poster will provide a deep dive into the disruptivity (disruptive frequency), a metric first introduced for the analysis of statistical properties of disruptions on JET [De Vries et al NF 2011]. The disruptivity is used to create maps that outline safe and unsafe regions of plasma parameter space that can be used for many applications. For operational planning, operators can look for dangerous plasma configurations or precursor events in disruptivity maps that can be avoided. In real time, control policies based on gradient descent can provide a restoring force that pushes the control system away from data-driven nonlinear boundaries. Disruptivity can be inverted to predict the time to disruption, further informing the control system on which emergency actions are viable. In simulations, disruptivity maps can create probabilities for which off-normal events can occur. An analysis of disruptivity hyperparameters, such as the method in which the disruptivity is calculated and the definition of the time of disruption, is presented. For new machines and exploration of parameter space, initial guesses for the disruptivity in the form of priors are introduced to the formalism. Analyses are conducted on Alcator C-Mod and TCV using the tokamak-agnostic disruptionStatistics (https://github.com/pkaloyannis-cfs/disruptionStatistics)  code base. 

Work funded by Commonwealth Fusion Systems.   

Investigating SPARC Runaway Electrons Under Various Disruption Scenarios with DREAM Simulations

In SPARC tokamak, disruptions under 'primary reference discharge' (PRD) conditions of e>~7keV and P_fusion~140MW (Creely 2020 JPP) can generate significant seed runaway electrons (REs) through various mechanisms, including hot-tail and Dreicer generation, Compton scattering, and tritium beta decay. These seeds subsequently grow exponentially via the avalanche effect that is particularly pronounced in SPARC due to its high plasma current of 8.7MA. Thus, unmitigated SPARC disruptions can have several MA of RE current (Tinguely 2021 NF). 

We use the DREAM code (Hoppe 2021 CPC) to study the RE evolution during SPARC disruptions under various parameters, including scans of pre-disruption plasma current I_p, thermal quench time t_TQ, magnetic field strength B(8T or 12.2T), and different temperature/density/current profiles. Results from both fluid and fluid-kinetic simulations, presented herein, offer a comprehensive perspective on RE dynamics. 

The REMC design, a potential RE mitigation strategy, uses disruptions' intense electric field to induce magnetic fluctuations, thus increasing RE loss (Sweeney 2020 JPP). Comparative DREAM simulation results, reflecting transport with or without REMC, will also be presented.   

A modular architecture for off-normal event models and implementation in MOSAIC for SPARC

The simulation of off-normal events (ONEs) that occur during tokamak operation is required to estimate the impact of these events on tokamak subsystems, as well as to facilitate the development of advanced controllers that aim to predict, avoid, or mitigate the effects of such events. We will present a candidate meta-data schema and framework for describing ONEs and injecting them into tokamak simulators.  This will be implemented in a simulation environment agnostic way in order to accommodate multiple stakeholder’s simulators both internal and across machines. Two simulators will initially be targeted: a lightweight python driven simulator used for magnet disruption loading and power supply modeling, and the MOSAIC simulation environment used in support of control design and qualification for the SPARC tokamak. Models of “kick” events leading to vertical displacement events (VDEs), as well as a model for impurity injection events (UFOs) leading to impurity accumulation and disruption will be presented. These examples of event chains leading to disruption will be captured and implemented in simulation to demonstrate the completeness, generality, and efficacy of this approach.   

Assessing the impact of vessel eddy currents on SPARC equilibrium reconstructions

Accurate determination of the plasma shape, position, and divertor strike points is required to ensure heat and particle loads to in-vessel components are within design limits during operation of SPARC. However, with time varying magnetic coil currents, as well as changing plasma current and shape, the eddy currents induced through various conducting structures and vacuum vessel walls can make equilibrium reconstructions of the plasma geometry challenging. These currents can be especially large during critical periods for plasma control, including plasma start-up and strike point sweeps. To assess the impact of these eddy currents on equilibrium reconstruction quality, a suite of codes including, TSC, FreeGS, ThinCurr, and MEQ were used to determine eddy currents in the conducting structures for different operational scenarios. The newest code, ThinCurr, calculates the full 3D structure of the eddy currents in a more realistic conducting structure model. This allows for comparison with the 2D eddy current structures calculated in the TSC and MEQ codes, as well as possible refinement of the 2D models. The synthetic equilibria from these codes and the corresponding eddy currents were used as inputs to the EFIT equilibrium reconstruction code. The reconstruction quality in certain key geometric parameters was found to degrade when eddy currents were not considered by EFIT, however the level of degradation was dependent on the eddy current distribution and amplitude.   

Design of Passive and Structural Conductors for Tokamaks Using Thin-Wall Eddy Current Modeling

A new three-dimensional electromagnetic modeling tool (ThinCurr) has been developed using the existing PSI-Tet finite-element code in support of conducting structure design work for both the SPARC and DIII-D tokamaks. Within this framework a 3D conducting structure model was created for both the SPARC and DIII-D tokamaks in the thin-wall limit. This model includes accurate details of the vacuum vessel and other conducting structural elements with realistic material resistivities. This model was leveraged to support the design of a passive runaway electron mitigation coil (REMC), studying the effect of various parameters, including coil resistivity, current quench duration, and plasma vertical position, on the effectiveness of the coil. The REMC is a non-axisymmetric coil designed to passively drive large non-axisymmetric fields during the plasma disruption thereby destroying flux surfaces and deconfining RE seed populations. These studies indicate that current designs should apply substantial 3D fields at the plasma surface during future plasma current disruptions as well as highlight the importance of having the REMC conductors away from the machine midplane in order to ensure they are robust to plasma vertical displacement events.   

Neutron Diagnostics Simulations for SPARC using OpenMC

This poster presents an OpenMC [1] model for neutron diagnostics simulations for the SPARC tokamak [2]. Geometries are constructed from realistic SPARC dimensions but temporarily with a simplified vessel, and the neutron emissivity profile is calculated by TRANSP [3] using SPARC's Primary Reference Discharge (PRD) parameters. The OpenMC model is verified with a CAD-based MCNP model for SPARC performed by Commonwealth Fusion Systems (CFS). The two models produce consistent tokamak hall neutron flux spectra. Three neutron diagnostics methods are modeled: neutron flux monitors (NFMs), activation foils, and neutron collimators for the neutron camera and spectrometer. U235 and B10 NFMs with appropriate shielding sleeves have flat responses with neutron energy, which makes them ideal for total neutron emission measurements, and U238 NFMs can serve as fast response detectors thanks to its insensitivity to thermal neutrons; activation foils at the front of the foil channel in the port shielding have the highest signal, and the ratio of uncollided neutron flux to total neutron flux is about 15%, which is verified by CFS's MCNP calculation; collimators perform well in filtering out scattered neutrons, and most of the scattered neutrons passing through the collimators are back-scattered by the inner surface of the vessel.   

Access to Edge Pedestals in the SPARC Tokamak

Access to a sufficiently large edge pedestal on the SPARC tokamak will be a key ingredient in the realization of high fusion gain on this compact (R=1.85m, a=0.57m) high field (reference B_T=12.2T) device. Building on available empirical results, projections of H-mode and I-mode access are made, with a goal of identifying potential scenarios of high confinement operation free of large edge localized modes (ELMs). Because L-I power thresholds scale less strongly with B_T than L-H thresholds, a significant window of I-mode access appears feasible in SPARC single null plasmas with B×∇B directed away from the active X-point. In order to refine these projections, we model the core plasma of SPARC L-modes to obtain heat flows through the edge, accounting for heating power deposition, ion-electron energy exchange, and core radiation losses. We find that L-modes with a 50:50 DT mix, and heated with up to 15MW of ICRF, typically have large ratios (~2x) of ion-to-electron heat flux at the edge. High ion power fractions may create more favorable conditions for H-mode and I-mode access than simple scalings predict.   

Full-pulse simulations for SPARC using MOSAIC

MOSAIC (Modelling framewOrk for ScenArIo and Control) is a flexible, modular simulation framework built for efficient planning and optimization of the pulse scenarios needed to achieve the target missions of the SPARC tokamak. The framework supports predictive full-pulse, time-dependent simulations with medium-fidelity plasma models at close-to-real-time computational speeds in order to enable automated optimization of actuator trajectories that satisfy the device constraints and maximize the likelihood of achieving the mission of the scenario. Control-oriented models are derived from the actuator and plasma parameter trajectories in order to support separate closed-loop calculations for control development and testing, particularly for off-normal event response. The first application of MOSAIC illustrates the integration of the Matlab EQuilibrium (MEQ) tools and the core transport solver RAPTOR with reduced models for divertor PFC sputtering and heat flux constraints in order to establish the target pulses demonstrating Q > 1 operation. MOSAIC will provide a framework for broad community participation in developing scenario and control solutions for SPARC and ARC that easily translate to the proprietary control system platforms developed at Commonwealth Fusion Systems.   

Flexible test of reduced transport models for SPARC scenarios in ASTRA

The prediction of transport and confinement is crucial in burning plasmas of nuclear fusion experiments. There are several ways to perform such predictions, mainly based on experimental trends or physics-based modeling. The former often misses physics details and precise description of the kinetic profiles. Therefore, it is necessary to perform physics-based modeling of the core transport for reliable performance predictions. An integrated transport analysis for SPARC scenarios has been obtained in a previous work [P. Rodriguez-Fernandez et al., J. Plasma Phys. (2020), vol. 86, 865860503], using the TRANSP 1.5D transport solver with TGLF as reduced transport model and validating the kinetic profiles with nonlinear gyrokinetic simulations. Preliminary results of the transport predictions within the ASTRA framework, a 1.5D highly customizable transport solver, will be compared with the previous TRANSP results for high performance scenarios in SPARC. The flexibility of ASTRA will allow the development and test of multiple transport models. Work supported by Commonwealth Fusion Systems.   

Estimates of RF induced sputtering and impurity emission from the ICRH actuators on SPARC

We present preliminary estimates of the impurity fluxes emitted by the plasma-facing components of the ICRF antennas and surrounding structures on the SPARC tokamak during burning-plasma operations. The VSim code (Tech-X) has been employed to solve the electromagnetic fields emitted by the ICRF antenna, considering dedicated RF-sheath boundary conditions and realistic 3D geometry. The output from these simulations has served as input for the hPIC2 and RustBCA codes at UIUC, enabling an accurate determination of ion impact energy-angle distributions and material surface response, including sputtering, reflection, and implantation. The calculations have been performed for a realistic plasma composition, taking into account multiple impurities, and at a millimeter-scale resolution. The approach allows a thorough exploration of areas with the highest erosion rates, and the identification of potential mitigation strategies. A detailed analysis of the RF limiters, Faraday rods, and other critical components surrounding the ICRF actuators has been performed. Analyses at different levels of RF power and far-SOL conditions allow to constrain the expected erosion rates and make preliminary considerations on core compatibility during ICRF heating. Work supported by Commonwealth Fusion Systems.   

Alpha and Runaway-electron transport in SPARC due to field perturbations

Numerical simulations of alpha orbits in the SPARC tokamak have been performed by the ASCOT (https://arxiv.org/abs/1908.02482) and SPIRAL (PPCF 55 (2013) 025013) codes to determine alpha transport and loss by static magnetic perturbations (error field correction coils) and by time-dependent perturbations (Alfven eigenmodes).  The eigenmode structure of the Alfven instability was computed by the NOVA code with its amplitude left as a free parameter.  Most of the simulations terminate the orbits at the last closed flux surface, to study internal redistribution of the alphas by the perturbed magnetic field.  But because a concentrated loss of even a small fraction of the alphas could damage the plasma-facing components (PFCs), some simulations follow the orbits to CAD models of the PFC surface.  The resulting pattern of surface heating is input to the HEAT (FST 78 (2022) 10) code along with other heating terms to compute the PFC temperature response. Results for the SPARC ‘primary reference discharge’ (Pfusion ~ 100 MW) and other scenarios will be presented.   Simulations of runaway electron (RE) transport during disruptions will also be presented, with and without the field perturbation generated by the RE mitigation coil, using RE distribution functions calculated by the DREAM code (https://doi.org/10.1016/j.cpc.2021.108098).    

Progress on the design and prototyping of SPARC diagnostics

The SPARC diagnostic system is comprised of approximately forty subsystems that will enable the demonstration of Q > 1 in the first SPARC campaign and support the de-risking of the ARC fusion pilot plant in subsequent campaigns. A high-level diagnostic design update will be presented with all subsystems having completed their preliminary designs. Prototyping and environmental testing efforts are underway to increase the likelihood that each measurement will function in the challenging thermal, structural, electromagnetic, and radiation environment presented by SPARC. One key prototyping effort that will be highlighted is a full-scale 60° mockup of the SPARC vacuum vessel (VV) where the integrated assembly of in-vessel diagnostics and plasma-facing components (PFCs) is being tested. This mockup not only ensures that diagnostics and PFCs will fit together but also that they can be assembled efficiently given the aggressive SPARC schedule. Additional environmental testing efforts include mechanical shock/vibration testing of electrical feedthroughs, magnetic field and neutron exposure of electronics, and thermal and vacuum testing of components mounted on the VV and in port plugs.   

A High-Resolution Magnetic Proton Recoil Neutron Spectrometer for Burning Plasma Diagnosis in SPARC

This poster presents the design of a high-resolution neutron spectrometer to be installed on the SPARC tokamak. SPARC will employ a suite of neutron diagnostics to accurately assess the fusion performance of the reactor. Within this suite, a Magnetic Proton Recoil (MPR) spectrometer [1][2] will provide unique insight into the kinetic physics of the fusion plasma, being capable of measuring core ion temperature, fuel concentrations, and fast particle populations. In addition, the highly collimated view of the plasma and collocation with the neutron camera enables an optical calibration strategy for interpreting flux measurements of the spectrometer, potentially giving an independent absolutely calibrated measure of the fusion rate and power gain factor, Q [3]. The MPR technique relies on 3 main components: a proton conversion and selection system, a set of magnets to focus and disperse the scattered protons, and a hodoscope in the focal plane on the ion optics. Uncertainty and efficiency of the proton conversion process is assessed using SRIM [4], and the ion optics have been optimized using COSY [5]. The system is designed for a variable energy acceptance in order to measure spectral features from 1-20MeV, with energy resolution dE/E<1% and a time resolution dt<200ms during high performance discharges.   

Progress in the Design of a Spectrometric Neutron Camera for SPARC

The SPARC tokamak is now under construction in Devens, Massachusetts and is predicted to robustly enter the burning plasma regime (Qp > 5) in DT operation [Creely et al. 2020]. Neutron cameras have been fielded on a variety of other toroidal fusion devices (JET, TFTR, LHD, MAST-U) in order to make spatially resolved measurements of neutron emission. SPARC is planning to deploy a neutron camera using spectrometric detectors in order to measure both the neutron emissivity, ion temperature profile, and possibly non-thermal spectral features. We present recent progress in the design of this camera, specifically the design of the spectrometric detector units. A combination of chemical vapor deposition single-crystal diamond detectors and deuterium-based liquid organic scintillators is being considered to cover SPARC's large dynamic range and provide reliable spectrometric information. Recent laboratory testing has included the use of DT and DD neutron generators for comparing deuterium and hydrogen based scintillators, as well as generator emission characterization using diamond detectors. We present results from neutronics simulations using OpenMC [Romano et al. 2015] of the proposed design configuration, and discuss the use of spectrum unfolding and tomography techniques being considered.   

Measuring MeV-range photons from runaway electrons and fast ion reactions in SPARC

The SPARC tokamak1 has the potential to generate runaway electrons (REs) during plasma start-up and disruptions, with energies that, if not mitigated, could rapidly reach the MeV range and possibly damage plasma facing components2. A passive mitigation system is planned for post-disruptions REs2, while the strategy for start-up REs is to ramp-down any discharge that presents signs of them. SPARC will install, in the torus hall, two hard X-ray (HXR) monitors with tangential fields of view which cover both negative and positive plasma current. They will detect photon energies in excess of 100 keV, emitted by REs during bremsstrahlung interactions with the plasma and the tokamak vessel. Their goal is to monitor start-up RE formation, together with a cadmium detector installed down a beamline, and to measure the evolution of post-disruption REs. Starting from OpenMC3 and FISAPCT4 simulations, the preliminary design for the HXR monitors is here outlined, with particular emphasis on the challenges posed by neutron-induced background, external magnetic fields, and high counting rates. SPARC will also generate gamma-rays in nuclear reactions between plasma ions, and an estimate of  this source of gamma-rays in SPARC beryllium-less plasmas is presented.

1 A. J. Creely et al., Journal of Plasma Physics 86.5 (2020)

2 R. A. Tinguely et al., Nuclear Fusion 61 (2021) 124003

3 P. Romano et al., Annals of Nuclear Energy 82 (2015) 90-97

4 J-Ch. Sublet et al., Nuclear Data Sheets 139 (2017) 77-137   

Withdrawn

Silicon diodes used for soft x-ray (SXR) detection in tokamaks are sensitive to neutron damage, making them unsuitable for use in tokamaks like SPARC. Furthermore, they are typically placed in beamlines several meters away from the plasma, limiting their field of view to a small cross-section. Presented here is the design for an array of chemical vapor deposition (CVD) single-crystal diamonds which will be placed in the upper and lower port plugs of the SPARC tokamak with a large enough view of the poloidal cross-section to enable tomographic inversion. CVD diamonds have been used successfully for the detection of both vacuum ultra-violet and SXR photons at the Frascati Tokamak Upgrade  [1], and have been shown to withstand a 14.8 MeV neutron fluence of at least 2.0×10¹⁴ n/cm²  [2], much higher than that of silicon diodes. In addition to their neutron tolerance, these diamonds are evaluated for their rise time and responsivity for the purpose of developing an array calibration method. The array design presented here is optimized to provide a wide field of view of the poloidal cross-section while maintaining its positional calibration when exposed to high temperatures during bake-in and g-forces during disruptions. Simulated plasma conditions are used to estimate the x-ray signal that this array will receive and to fine-tune the detector placement within the array.

[1]  F. Bombarda, M. Angelone, G. Apruzzese, C. Centioli, S. Cesaroni, L. Gabellieri, A. Grosso, M. Marinelli, E. Milani, S. Palomba, V. Piergotti, G. Pucella, G. Rocchi, A. Romano, A. Sibio, B. Tilia, C. Verona, and G. Verona-Rinati, Nucl. Fusion 61, 116004 (2021).

[2]  M. Pillon, M. Angelone, G. Aielli, S. Almaviva, M. Marinelli, E. Milani, G. Prestopino, A. Tucciarone, C. Verona, and G. Verona-Rinati, J. Appl. Phys. 104, 054513 (2008).   

Compact multiple x-ray spectrometers for SPARC

The main design options and characteristics of SPARC’s x-ray spectrometers are presented.

SPARC’s first campaign mission of reaching Q > 1 requires a quick learning curve of operating the tokamak in the desired regime of temperature, density and radiation losses. This requires a means of keeping track of impurities in the plasma, especially with tungsten plasma facing components. A low-resolution survey X-ray spectrometer is designed for this task, complementing grating-based vacuum ultraviolet spectroscopy.

Measuring Q > 1 with a good level of confidence, and knowing the input power, can be done using neutron and kinetic measurements. A set of 2 different high-resolution X-ray spectrometers is designed to measure ion temperature via the Doppler-broadening of extrinsically seeded high-Z impurities. One will focus on Ne-like Xe (~2.720 AA) for accessing Ti in low-temperature plasma phases, the other will focus on He-like Kr (~0.944 AA) to access it in high-temperature plasmas phases.

A tokamak operating D-T shots comes with specific constraints, like a neutron-rich environment and the need to minimize risks of tritium exposure. It will be shown how these constraints drove some key aspects of the design of the spectrometers, which are grouped by pairs or triplets on a set of < 100 mm diameter and ~20m-long beamlines granting direct views through the plasma with minimal opening for neutrons. It will be explained how cost and risks are minimized by utilizing a novel compact layout, while meeting performance requirements for spectral resolution and signal levels.   

Implementation of fast switching of the SPARC Runaway Electron Mitigation Coil

The SPARC tokamak's runaway electron mitigation coil (REMC) is an asymmetric, in-vessel coil that is passively driven due to coupling between the plasma and the coil during the current quench of a disruption. As the plasma quenches, the REMC circuit is inductively driven to high (100s of kA) current, providing a perturbing 3D field in addition to the perturbing magnetic fields already present from the disruption dynamics. Past modeling has indicated that the 3D field provided by the REMC deconfines runaway electrons and keeps the runaway electron population at low levels.Transients during the plasma flattop phase and the loop voltage during ramp-up can drive enough current in the coil to negatively impact normal operation, such as instigating locked modes. This necessitates a switch for the REMC circuit that passively actuates during the onset of the current quench. A review of the REMC switch requirements and the switch's impact on the REMC design including in-vessel insulation material requirements to stand off kilovolts of high voltage, radiation protection of sensitive circuit components in a 10^9 cm^2/s neutron environment, and ex-vessel inductance and resistance limitations will be presented.   

SPARC Laser Aided Plasma Diagnostics for Q > 1 Campaign

To help ensure SPARC achieves its operational and scientific milestones, two laser-based diagnostics are included in its early campaign diagnostic set: the Two-Color Heterodyned interferometer (INTF) and Core Thomson Scattering (CTST). The INTF system is essential for tokamak operations providing active density feedback control from day-1 via real-time streaming of line averaged core plasma density at 10 kHz to the plasma control system (PCS). Reliance on INTF for density feedback control informs the design to be as robust as possible, prompting the focus on a single plasma leg with active alignment tracking, ≥ 10 W laser power, NIR & CO₂ wavelengths to minimize optical losses, and redundant systems to maximize signal reliability & minimize downtime. SPARC CTST is built with the same principles in mind, utilizing the early stages of the first campaign to commission & validate the diagnostic performance. Initially, CTST will operate at a 100 Hz laser repetition rate with a few spatial positions over 0.0 < r/a < 0.6, before expanding to higher spatial resolution and possibly a future Edge TS. Neutron shielding requirements on SPARC preclude direct line of sight to the plasma for laser beamlines and collection optics, requiring multiple mirrors inside and outside the vacuum chamber. For INTF and CTST this means a careful consideration of optical substrates, coatings, in-vessel location, and protective structures to maintain effective diagnostic operation over the course of multiple SPARC campaigns.    

Edge Scanning Reflectometry on SPARC

Edge scanning reflectometry (ESRL) on SPARC aims to determine the ICRF evanescent layer location and thus help assess the ICRF antenna loading, and also to measure H-mode pedestal density profiles. ESRL uses a standard frequency sweep technique covering the range from 18 GHz to 120 GHz. Both O-mode and left-hand-cutoff (LHC) X-mode will be implemented. For B₀ ~ 12 T, the cutoff density ranges from ~0.4e19 m^-3 to ~6e20 m^-3. There are 2 pairs of horns for O-mode and 2 pairs for X-mode. Considering the relatively short distance (~20 m) from the diagnostic hall to the tokamak, we plan to use overmoded waveguides to minimize signal loss while allowing system flexibility. The horn antennas are optimized with COMSOL RF modeling. EM load analysis and thermal analysis will be presented. The mm-wave and IF electronics have been analyzed and optimized based on synthetic reflectometry data. The latest status of the project will be presented.    

Tearing mode detectability in the SPARC tokamak

To prepare for disruption prediction, the SPARC tokamak’s [Creely JPP 2020] magnetic sensor arrays’ ability to detect tearing modes is assessed. The instabilities are modeled in the ThinCurr code [Battey APS-DPP 2022] and the responses of the proposed sensors are evaluated. The tearing modes are modeled using three-dimensional current filaments running parallel to the magnetic field at the resonant surface. The inductive coupling between the current filaments, vacuum vessel, and modeled sensors is calculated. The sensor amplitudes are then assessed in the frequency domain assuming the tearing mode exhibits a sinusoidal current perturbation along the midplane. By scanning mode rotational frequency and width, the range of detectable tearing modes is determined. It is then determined if the sensitivity and placement of the magnetic sensors is sufficient for reliable detection of tearing modes.   

Analysis of Equilibrium Pressure and Current Dynamics in SPARC

The plasma shape of the SPARC tokamak changes as a function of pedestal height and current density distribution. The equilibrium sensitivity to these dynamics is assessed using both the “TokaMaker” time-dependent Grad-Shafranov solver [1] and the time-independent EFIT solver. This investigation informs shape control tolerances, an essential step in avoiding damage to the divertor and first-wall during plasma operation. Changes to the strike point locations as a function of pedestal height are found to be sensitive to the bootstrap current fraction and fidelity of real-time equilibrium reconstructions. This suggests potential challenges in constraining strike point sweep locations if an unexpected L-to-H transition occurs. Additionally, the sensitivity of magnetics-only equilibrium reconstructions to tearing-unstable current profiles is investigated, assessed without the benefit of Motional Stark Effect. These analyses will be further generalized using a more precise treatment of current diffusion and equilibrium time evolution, with the goal of anticipating uncertainties that may interfere with shape control and profile stability during SPARC operation. 

[1] C. Hansen et al 2017 Physics of Plasmas 24 (4): 042513   

Investigating RF Far-Field Sheath Rectification on SPARC using the STIX Finite-Element Code

The upcoming SPARC device will be able to achieve > 20 MW of ion cyclotron radio frequency (ICRF) power to reach fusion relevant temperatures. Although the ICRF frequency range is a robust method of heating tokamaks, it is prone to adverse effects such as RF sheath rectification that damage plasma-facing components. New capabilities now allow to numerically model RF sheath rectification using a finite sheath impedance boundary condition (BC) developed by [J. Myra Phys. Plasmas 2015]. Using this sheath BC, far-field sheath behavior in the poloidal cross section of SPARC is investigated using the cold plasma RF finite-element code ``Stix’’ through a non-linear iteration. Using lower order thermal corrections to the cold plasma dielectric, Stix can emulate the resonance broadening and Landau damping within the core. This research will report on the dependence of various single pass absorption regimes and plasma parameters on the strength and locations of far-field rectification within SPARC.   

Multimachine Database Study of I-Mode Core Confinement and Edge Gradients

A multi-machine database for the study of I-mode performance has been compiled, consisting of over 100 time-averaged parameters across steady-state time slices from DIII-D, ASDEX-Upgrade and Alcator C-Mod, including previously unanalyzed discharges. I-mode is an ELM-free enhanced confinement regime with L-mode-like particle transport, though no multi-machine confinement scalings such as those for L- and H-mode have yet been produced. Stemming from the 2022 DOE Joint Research Target, with some AUG and many C-Mod slices added, the database will be used to close this knowledge gap. In-device and cross-device dimensional τE scalings will be derived and compared with literature. Other key parameters for predicting I-mode performance are edge gradients and pedestal pressures. Fits for each of these will be derived in terms of dimensional parameters and compared to literature, with particular attention given to differences in edge behavior between I-modes and high power L-modes. With an improved understanding of core and edge performance we can improve confidence in projections of high-performance I-mode operation in future devices.   

Defining the Engineering Roadmap for High-Field Tokamak-Based Fusion Plants: Lessons Learned from SPARC

Developing tokamak-based fusion power plants requires an efficient and robust engineering roadmap aligned with plasma physics requirements. Drawing upon lessons learned from the SPARC project, a high-field tokamak net energy plant, this study defines a comprehensive roadmap laying out the interdependencies of key engineering decisions, parallel and interconnected work, key interface development, and more.  We discuss the major design deliverables and milestones that are key for rapid progress. This includes product breakdown of the plant, which major interfaces need to be defined to unlock further stages of the project, major cross-functional topics that need to be considered in each stage of the design, and the organization of a joint engineering and physics team for effective execution.  Lessons learned from the SPARC engineering program will guide ARC power plant development, aiming to improve efficiency, reduce development time, and enhance robustness. By leveraging these insights, the roadmap aims to inform and optimize engineering decision-making, minimize risks, and expedite progress towards realizing fusion energy as a safe, sustainable, and economically viable power source.   

Tailoring Industrial Plant Systems to Support Unique Design Aspects of High-Field Tokamak-Based Fusion Power Plants

In designing a fusion power plant, it may be tempting to entirely outsource more standard industrial systems such as cooling water, HVAC, compressed air, and standard electrical power to allow organizations to focus on direct fusion technology. However, as these systems ultimately support a tokamak fusion plant, they have unique design attributes that need to be taken into consideration. Using the SPARC design as an example, we show the distinctive design aspects of building a power plant around a high-field tokamak. This poster will focus on the top level requirements derived early in the project and how these technical concepts systematically flow to the sub-levels of the plant design. This ensures that the standard plant systems are effectively supporting the overall design functionality of the tokamak over all expected operational modes. Considerations for redundancy, pulsed operations, tritium fuel, electromagnetic field, and radiation environments create constraints on intermittent high-energy systems, actively managing tritium migration throughout the facility, supporting cryogenic facilities with multifaceted failure modes, and managing the distribution of emergency power to a complex facility.   

Identifying SPARC divertor operation space and understanding divertor asymmetry through SOLPS-ITER simulations

Density scans using the SOLPS-ITER code reveal asymmetric divertor conditions in the SPARC V2 8 T (2/3 of full field) H-mode scenario with P_SOL ~ 10 MW [1]. These conditions, characterized by sharp, cliff-like transitions in target parameters relative to particle source or upstream density, are consistent across different main particle sources. Time-dependent SOLPS-ITER simulations with OMP gas ramp up and down were conducted to map the phase space of the SPARC V2y geometry. The phase space, defined by upstream density and target electron temperature, exhibits strong non-linearity and hysteresis. The asymmetry transition event happens in both directions, with localized high density spots exchanging between two targets through the PFR. Despite the strong target electron temperature asymmetry, the thermo-electric current contribution to heat flux is negligible with heat fluxes primarily driven by electron conduction and supported by convection in the detached condition. The narrow PFR geometry is suspected to be the main driver of the non-linearity in SPARC's divertor operation space as similar behaviors were observed in KSTAR divertor upgrade. Symmetric, linear regimes can be found by injecting neon, suggesting feasible divertor operation space can be achieved using impurity seeding.

 

 

[1] Creely A J et al. Overview of the SPARC tokamak. J. Plasma Phys. 86 865860502 (2020)   

Experimental validation of the SOLPS-ITER neutral model with experimental Lyman-alpha and neutral profiles on Alcator C-Mod

Accurate modeling of neutral density and ionization profiles in future tokamaks is crucial for both fueling and profile shape predictions. We validate the ability of SOLPS-ITER, a 2D fluid plasma/kinetic Monte Carlo neutral code, to accurately model upstream neutral density profiles of an L-mode, I-mode, and H-mode discharge on Alcator C-Mod. By first matching outer midplane measurements of ne and Te through iterative tuning of the perpendicular transport coefficient profiles, it is shown that SOLPS can reproduce edge profiles of the neutral D density as inferred from Lyman-alpha measurements to within uncertainties. To further validate the SOLPS neutral model, a synthetic diagnostic is implemented in SOLPS to emulate the viewing chords of the Lyman-alpha array. Simulated Lyman-alpha emissivity profiles reveal a consistent match with experiment, mostly within uncertainties. However, modeled line-integrated brightness profiles are systematically lower than experiment by a factor of ~2, implying underestimated contributions from atomic interactions. It is demonstrated that the quality of match between model and experiment degrades significantly outside of the plasma computational domain, motivating the adoption of full-vessel plasma simulations in the future.