Session UP11: Poster Session VIII: Fundamental Plasma Physics - Analytical and Computational Techniques; Magnetic Reconnection; Antimatter Heliospheric, Magnetospheric, and Ionospheric Plasma Phenomena and Their Scaled Laboratory Experiments MFE - DIII-D Tokamak II, ITER, HBT-EP, and Other Tokamaks 2:00 PM - 5:00 PM

Progress towards the trapping and accumulation of large numbers of positrons.

The APEX collaboration aims to produce neutral pair plasmas, composed of equal quantities of electrons and positrons, magnetically confined in two different traps: a levitated dipole and a stellarator. More than $10^10$ positrons are needed to achieve a short-Debye-length plasma with a volume of 10 L and a temperature of $< 1$~eV. This necessitates new advances in positron accumulation and storage. These advances are enabled by non-neutral plasma techniques developed for the manipulation and control of single-species plasmas. Here we report on progress in developing antimatter traps to achieve the required number of positrons for the pair-plasma experiment. A multi-stage buffer-gas-trap (BGT) will be used for the efficient trapping of the high-flux positron beam from the NEPOMUC high-flux positron source in Munich, Germany. A continuous beam of positrons from NEPOMUC will be magnetically guided into a low-pressure molecular gas, where inelastic collisions enable efficient positron capture (maximum expected accumulation $< 10^9$ positrons). Accumulation of larger numbers of positrons will be achieved in a separate multicell Penning-Malmberg trap in UHV and a 5 T magnetic field that is currently under development.   

Back to the future: reviewing CNT en route to EPOS

The use of "true" (irrational) magnetic flux surfaces to confine a non-neutral plasma (NNP) is a relatively rare combination, straddling the divide between fusion energy research and basic plasma science in a significantly lower density, lower temperature regime. A likely application of this scenario is for the creation of magnetically confined electron-positron pair plasmas (for example, if the nested flux surfaces are first filled with electrons, into which one or more pulses of positrons are then injected until quasineutrality is achieved). Such plasmas are the goal of the APEX (A Positron Electron eXperiment) Collaboration, the newest branch of which is the EPOS (Electrons and Positrons in an Optimized Stellarator) project.

By far the most extensive research to date on the topic of non-neutral plasmas in flux surfaces has been done at or in connection with the Columbia Non-neutral Torus (CNT). A four-coil, low-aspect-ratio, 0.2-T stellarator optimized for a large volume of robust flux surfaces, CNT was used for non-neutral plasmas from 2004-2011 and generated numerous important theoretical and experimental results. Among the highlights were the verification of macroscopically stable single-species plasma equilibria [Kremer et al., PRL 97, 095003 (2006)], the investigation of instabilities at finite ion fraction [Marksteiner et al., PRL 100, 065002 (2008)], and systematic studies of plasmas of arbitrary neutrality [Sarasola et al, PPCF 54 124008 (2012)].

In this poster, we will first review some key findings from CNT, then relate these to non-neutral plasmas in linear devices (the most commonly employed geometry for NNPs). Then we will describe the resulting implications for the design and development of EPOS, and how these compare to more typical stellarator optimization targets for fusion devices.   

A compact high-Tc superconducting levitated dipole experiment for creation and study of positron-electron plasma

We present design and construction progress for a compact high-T_c superconducting (HTS) levitated dipole experiment to confine and study a magnetized positron-electron plasma. The confinement volume (0.01 m³) will be loaded with >10¹⁰ positrons (and electrons) to produce a low-temperature (~ 1 eV) pair plasma with a Debye length ~1 cm.  The closed floating coil (15 cm diam.) has 150 turns of HTS tape (GdBaCuO, T_c = 92 K) each with >400 A at the design magnetic field (< 2 T at the coil).  The coil is inductively charged using a (164 kA-t) HTS open-lead coil that is fixed to a coldhead and incorporates a sealable/openable chamber into which He gas (~ 1 Torr) can be introduced to control the cooling of the floating coil.  Tests of the cooling and inductive charging strategy verified the feasibility of the technique.  The feedback levitation system required to stably levitate the floating coil has been tested.  Levitation times of order an hour are anticipated with a cooled (80 K) copper radiation shield. Construction of all major components of the final system is underway; cooling, charging, and levitation tests are anticipated in 2021 with electron plasma and positron injection experiments starting in 2022.  Experiments performed in a prototype dipole, as well as simulations of the final setup, proved the feasibility of using an ExB drift technique to inject positrons.  Efficient positron injection into an electron plasma (n ~ 4x10¹² m^-3) was demonstrated.    

Annihilation detection in the APEX electron-positron plasma from volumetric and localized sources

Annihilation gamma rays promise to be a powerful diagnostic for electron-positron pair plasma. The APEX collaboration aims to magnetically confine such pair plasma in a levitated dipole geometry. Gamma rays will be detected and time stamped with FPGA processing of signals from an array of 48 Bismuth-Germanate (BGO) scintillators with photomultiplier tubes. The experiment will generate gamma rays 1) in the bulk plasma from direct annihilation and decay of radiatively recombined positronium and 2) from locally increased annihilation on insertable target probes, injected solid particles, and introduced gas jets. The volumetric signal can be related to the bulk density and the localized signal can be used to diagnose injection efficiencies and loss channels. In order to learn how to differentiate between the volumetric and localized sources, we have conducted measurements with β+ emitters placed inside a circular arrangement of detectors. We compare three methods for identifying localized sources: triangulation from coincident lines of response, single photon detection along collimated views, and distance attenuated single photon detection simultaneously observed with multiple detectors.   

How the electron frozen-in-law is broken during anti-parallel magnetic reconnection

The mechanism that breaks the electron frozen-in-law has represented a long-standing open issue in collisionless magnetic reconnection. Aided by fully kinetic simulations, a resolution to this problem for anti-parallel reconnection is presented here. We find that magnetic field aligned electron pressure anisotropy develops upstream of the electron diffusion region (EDR), imposing strong off-diagonal electron stresses within the EDR. Along the direction of the reconnection X-line, however, these stresses cancel, and the electron frozen-in law is instead broken by thermal forces related to heating of the electrons directly by the reconnection electric field itself. The reconnection rate then freely adjusts to the value imposed externally by the ion dynamics.    

Regulation of the normalized rate of driven magnetic reconnection through shocked flux pileup

Magnetic reconnection is explored on the Terrestrial Reconnection Experiment (TREX) for asymmetric inflow conditions and in a configuration where the absolute rate of reconnection is set by an external drive. Magnetic pileup enhances the upstream magnetic field of the high-density inflow, leading to an increased upstream Alfvén speed and helping to lower the normalized reconnection rate to values expected from theoretical consideration. In addition, a shock interface between the far upstream supersonic plasma inflow and the region of magnetic flux pileup is observed, important to the overall force balance of the system, thereby demonstrating the role of shock formation for configurations including a supersonically driven inflow. Despite the specialized geometry where a strong reconnection drive is applied from only one side of the reconnection layer, previous numerical and theoretical results remain robust and are shown to accurately predict the normalized rate of reconnection for the range of system sizes considered.   

Not Participating

The heating and acceleration of ions due to magnetic reconnection have been observed in space, such as in planetary magnetospheres and the solar corona, as well as in various plasma simulations and laboratory experiments. These observations help to understand the heating process and the physics of reconnection as the energized ions tend to acquire most of their energies from the release of stored energy in the magnetic fields. In a study of magnetized flux ropes on the LArge Plasma Device (LAPD), two 11 m long kink-unstable flux ropes were created within a 18 m long background plasma using separate lanthanum hexaboride (LaB₆) sources. A retarding field energy analyzer specifically constructed for the two flux rope experiment was used to determine the ion temperature at localized points within the plasma. The background ion temperature was estimated to be 4 eV. The results were also compared to broadened He II spectral lines. In addition, the time-dependent ion temperature oscillates between 4 and 8 eV and is well-correlated with the localized magnetic field, which oscillates at the rope kink frequency. The occurrence of bimodal distribution functions at the ion temperature peaks suggest that ions are being accelerated and they could be jetted along the background magnetic field.   

A new plasma experiment relevant to magnetohydrodynamics instability and magnetic reconnection at Embry-Riddle Aeronautical University

We introduce a new plasma experiment facility in the physical sciences department at Embry-Riddle Aeronautical University. A newly installed plasma gun, planned diagnostic instruments, and experimental plans will be discussed. This facility can provide students and plasma physics and engineering communities with various opportunities in the central Florida area as a new experiment relevant to the study for magnetohydrodynamics instability, magnetic reconnection, and testing diagnostic instruments. As a new experimental facility developed by a newly joined assistant professor at ERAU, invaluable discussion and input are desired.   

Scaling Theory of 3D Magnetic Reconnection Spreading

We develop a first-principles scaling theory of the spreading of three-dimensional (3D) magnetic reconnection of finite extent in the out of plane direction. This theory addresses systems with or without an out of plane (guide) magnetic field, and with or without Hall physics. The theory reproduces known spreading speeds and directions with and without guide fields, unifying previous knowledge in a single theory. New results include: (1) Reconnection spreads in a particular direction if an x-line is induced at the interface between reconnecting and non-reconnecting regions, which is controlled by the out of plane gradient of the electric field in the outflow direction. (2) The spreading mechanism for anti-parallel collisionless reconnection is convection, as is known, but for guide field reconnection it is magnetic field bending. We confirm the theory using 3D two-fluid and resistive-magnetohydrodynamics simulations. (3) The theory explains why anti-parallel reconnection in resistive-magnetohydrodynamics does not spread. The results provide a theoretical framework for understanding spreading beyond systems studied here, and are important for applications including two-ribbon solar flares and reconnection in Earth's magnetosphere.   

Not Participating

The transfer and dissipation of energy at small scales in weakly collisional systems are crucial to many important plasma processes, such as magnetic reconnection, plasma turbulence, and collisionless shocks. The plasmas in which these processes occur are often far from local thermodynamic equilibrium, where kinetic physics plays an important role in the dynamics. A number of measures have been developed to identify locations where small scale energy transfer and dissipation takes place in numerical simulations and in satellite observations. We investigate the use of kinetic entropy, the entropy within the kinetic theory description of a plasma, to identify and facilitate the study of such processes. We study a kinetic entropy-based measure of non-Maxwellianity in the context of magnetic reconnection from three viewpoints: theoretically, numerically using particle-in-cell simulations of magnetic reconnection, and observationally using the Magnetospheric Multiscale (MMS) satellites.   

Detecting Energetic Electrons from Magnetic Reconnection in the PHAse Space MApping (PHASMA) Experiment

The Phase Space Mapping experiment is designed to investigate distribution functions in magnetic reconnection events arising from the merger of two flux ropes generated by two pulsed plasma guns. This results in an opportunity to search for energetic electrons in the out-of-plane direction with the use of a compact retarding field energy analyzer (RFEA). The raw data is differentiated to provide a trace which is interpreted as a particle energy distribution function. Here we describe the instrument design and implementation as well as first results. Traces of energetic electrons in the tails are investigated as a function of magnetic guide field strength and reconnecting field strength.   

Measurements of Ion Velocity Distribution Functions in a Flux Rope

As models and simulations of magnetic reconnection become increasingly powerful, laboratory measurements at kinetic scales are vital as benchmarks. Towards this end, the PHAse Space MApping experiment (PHASMA) was constructed to study magnetic reconnection in the laboratory at the kinetic scale. In PHASMA, magnetic reconnection is achieved when flux ropes (generated by pulsed plasma guns) merge. By varying the strength of the magnetic guide field and the ion species, reconnection in PHASMA can be varied from standard to electron-only. Here we report measurements of the ion velocity distribution function (IVDF) with laser induced fluorescence (LIF) in flux rope plasmas with and without magnetic reconnection. We report measurements of ion heating and details of non-Maxwelllian features in the IVDFs.   

Particle Velocity Distribution Function, Magnetic Field, and Turbulence Measurements in the PHAse Space MApping (PHASMA) Experiment

The PHAse Space MApping (PHASMA) experiment employs non-perturbative, optical diagnostics for ion velocity distribution, electron velocity distribution, magnetic field, and turbulence measurements. Here we review the design and implementation of a pulsed laser induced fluorescence (LIF) system at 611.6616 nm for ion velocity distribution function measurements of argon ions; of a 532 nm Thomson scattering system employing an 850 mJ laser at 10 Hz for electron velocity distribution measurements; and of a 300 GHz microwave system for plasma density measurements and sub-mm wavelength plasma turbulence measurements. The same LIF system is also used to measure the Zeeman splitting of an argon neutral line at 696 nm. From the Zeeman splitting, magnetic field changes as small as 10 G are resolvable. All these diagnostic techniques are validated in a steady-state helicon plasma before being deployed in single and dual pulsed plasma gun discharges. The dual plasma gun discharges undergo magnetic reconnection as they evolve.   

The rapid destruction of toroidal magnetic surfaces

An ideal magnetic evolution can cause the development of an exponentially large variation between the distance of closest approach and greatest separation between neighboring pairs of magnetic field lines.  When this occurs, a fast magnetic reconnection naturally arises on the evolution time scale of magnetic field times a factor that depends only logarithmically on the strength of the non-ideal effects.  An obvious example arises when the magnetic evolution is driven by footpoint motion, as in the solar corona.  A similar effect can be responsible for the sudden loss of magnetic surfaces during a tokamak disruption.  In almost all magnetic surfaces in toroidal geometry, a magnetic field line never closes on itself as it is followed in the toroidal angle φ, and the line comes arbitrarily close to every point in the surface.  When an arbitrary pair of magnetic field lines are separated by an infinitesimal distance δ₀ in a surface at φ=0, then their separation can be written as δ₀ exp(Υ(φ)).  The Lyapunov exponent, which is Υ/φ as φ→∞, vanishes, but that does not preclude the variation in their exponentiation, Υ_v ≡ Υ_max - Υ_{_min}, from having an arbitrarily large value.  When Υ_v  is sufficiently large in a region of magnetic surfaces, rapid reconnection becomes inevitable.   

Example of exponentially enhanced magnetic reconnection driven by a spatially-bounded and laminar ideal flow

In plasmas of practical interest the spatial scale $\Delta_d$ at which magnetic field lines lose distinguishability differs greatly from the scale $a$ of magnetic reconnection (MR) across the field lines. In the solar corona, plasma resistivity gives $a/\Delta_{d}\sim 10^{12}$ which is the magnetic Reynold number $R_m$. The scale paradox is typically resolved by assuming the current density $j$ of the reconnecting field $B_{rec}$ concentrates by a factor of $R_{m}$ ideally, $j\sim B_{rec}/\mu_0\Delta_{d}$. A second resolution is for the ideal evolution to increase the ratio of the maximum to minimum separation between pairs of neighboring magnetic field lines $\Delta_{max}/\Delta_{min}$. MR is inevitable where $\Delta_{max}/\Delta_{min}\sim R_m$. A simple model of the solar corona is used to numerically illustrate that $j$ increases linearly in time while $\Delta_{max}/\Delta_{min}$ increases exponentially. MR occurs on a time scale and with a current density enhanced by only $\ln(a/\Delta_d)$ from the ideal evolution time and current density $B_{rec}/\mu_0 a$. In both resolutions, once a sufficiently wide region has reconnected, the magnetic field loses static force balance and evolves on an Alfvénic time scale, expanding the region in which $\Delta_{max}/\Delta_{min}$ is large.   

Reconstruction of the magnetic field configuration by use of novel MHD-EFIT model in TS-6 spherical tokamak merging experiment

We present procedures and results of the novel MHD-EFIT model to reconstruct the magnetic field configuration using the external magnetic probes and Rogowski coil data measured during the plasma formation and merging of TS-6 spherical tokamak.  In TS-6 merging experiments, it is possible to measure the magnetic field components directly right after plasma formation before plasma merging/ reconnection heating.

The current MHD-EFIT method utilizes the external plasma parameters to reconstruct the plasma shape and position at the end of merging process; however there is no information on magnetic field components during the merging process. The main goal of this work is to reconstruct the internal magnetic field values during the merging.

In order to reconstruct the internal magnetic field, a series of out of domain virtual zero size coils have been virtually installed to adjust the magnetic field to values measured at the external probes positions. To control the size of the plasma toroids, the total plasma current data obtained from the Rogowski coil are also used which leads to  4% absolute error between the numerical and experimental B_z at the mid-plane during the merging confirming the ability of MHD-EFIT to reconstruct the magnetic configuration during merging.    

Experimental Study of Reconnection Heating and Acceleration by use of Glass-Tube-Pair Type Doppler Probe Array

We had developed a glass-tube-pair type Doppler probe array for 1D profile measurement of two component ion flow vector and ion temperature. It needs just two parallel glass-tube insertion, realizing low plasma perturbation and 1D ion flow vector measurement on a single discharge. Using four mirrors and optical fibers, this system can measure ion light emissions of each measurement volume from four different directions, enabling us to measure its local ion flow vector and temperature. All set of mirrors and optical fibers are aligned in the two parallel glass tubes for 1D profile measurement on a single discharge. Using Doppler shift measurement along bi-directional viewing lines, we can significantly decrease calibration error of the Doppler shifts. By use of this system, we measured successfully ion outflow speed of two merging tokamak plasmas, about 80% of poloidal Alfvén speed in agreement with recent reconnection experiments and theories. For more precise survey of reconnection heating and acceleration mechanisms, we have been improving spatial resolution and measurement accuracy of parallel component of ion velocity to glass-tube. By making the mirror holders of the array thinner, we reduced the mirror interval to 2.5 cm which is 1/2 of the previous one. By increasing the incident angle of light to 30 degrees twice as large as the previous one, we improved the measurement accuracy of ion velocity parallel to glass-tube.   

Application study of magnetic reconnection for high temperature spherical tokamak formation

Here we present the latest report of our application/exploration of high field reconnection heating in ST40 and TS-6 merging spherical tokamak formation experiments. MAST-like high performance scenario has successfully been reproduced in ST40, and TS-6 explores further investigation of heating/transport process using the full-2D Dopploer tomography diagnostics. Based on the experimental scaling ΔT_i ∝ B_rec² by outflow heating mechanism and the saturation of guide field dependence on reconnection heating in high guide field regime B_t (guide field)/B_rec (reconnecting field) > 3, both projects selected high B_rec for more heating and high B_t /B_rec to suppress perpendicular heat conduction with the weight of κⁱ_∥/κⁱ_⊥ ~ 2(ω_ciτ_ii)² >>1 as a standard plasma scenario. The sustainment of the high temperature plasma in τ_duration >> τ_merging has successfully been demonstrated in both projects and it was found that the characteristic double-peak T_i structure is sustained after the end of outflow acceleration/heating for longer time scale than the merging process. The propagation process of high T_i area is affected by guide field polarity and it was found that the positive potential side of guide field reconnection has higher T_i through parallel acceleration and globally gyrating heat transport.   

"Multistage ion heating during high guide field reconnection associated with plasmoid formation"

 The series of experiments of the torus plasma merging have made clear the following high guide field reconnection characteristics such as, (i)significant ion heating in the downstream area, (ii) quadrupole electrostatic potential structure formation for ion heating and ion acceleration. Here, in this report, several ion heating events are observed in the early reconnection phase during our torus plasma merging experiment, TS-6. The novel 288CH extensive/high-resolution ( Δr = 1.5cm, Δz = 1.0cm) ion doppler spectroscopy system and newly developed high resolution magnetic probe array ( Δz = 1.1cm ) clearly detected the process of pull-type plasmoid production and ion heating synchronizing with plasmoid's movements. As the two initial torus plasmas are formed, magnetic flux surface which is close to X-point ( z = 0) starts to expand, ejecting mass of plasmas continuously. Subsequently, several X-points are formed, and the ion heating occurs downstream. When the plasmoid vanishes, ions are heated intensively, and finally significant heating occurs during the main toroidal plasmas merging. This series of ion heating in early reconnection phase should be suppressed to achieve effective energy conversion through magnetic reconnection.   

Particle Injection and Nonthermal Particle Acceleration in Relativistic Magnetic Reconnection

Magnetic reconnection in the relativistic regime has been proposed as an important process for efficiently accelerating particles and producing high-energy emission. Using fully kinetic particle-in-cell (PIC) simulations, we study particle injection and nonthermal particle acceleration during relativistic magnetic reconnection in an electron-positron plasma. While several different mechanisms contribute to particle injection, the mechanism primarily responsible for the high-energy power-law spectrum is a Fermi mechanism. We evaluate quantities relating to the injection and power-law acceleration over a range of guide field strengths and spatial domains. In the weak guide field regime, particle injection is dominated by mechanisms related to the electric field perpendicular to the magnetic field (Wperp), and their importance increases for larger domains. A strong guide field limits the role of Wperp, but Wperp is nevertheless increasingly important for larger domains. We also find that the power-law index p increases with the guide field strength and domain size of the simulation. These findings will help us understand the nonthermal acceleration and emissions in high-energy astrophysics, including black hole jets and pulsar wind nebulae.   

Experimental study of Ion Energization During Guide Field Reconnection in the Magnetic Reconnection Experiment (MRX)

Magnetic Reconnection is a fundamental plasma process in which magnetic energy is converted to particle energy during a global change in magnetic topology. Most reconnection events in space and fusion plasmas occur in the presence of a finite magnetic field component perpendicular to the reconnection plane, known as a guide field. A new campaign on the Magnetic Reconnection eXperiment (MRX) at Princeton Plasma Physics Laboratory (PPPL) aims to elucidate the role of the guide field in the conversion of magnetic energy to particle energy of ions. A new ion Doppler diagnostic [Goodman et al. RSI (2021)], utilizing tomographic inversion of line-of-sight emission measurements, is used for the first time on MRX to measure the ion temperature and flows parallel to the guide field. Existing Ion Doppler Spectroscopy Probes (IDSP) are used to calibrate ion temperature measurements, while Mach and Langmuir probes are used for floating potential measurements and flows in the reconnection plane. Data  is collected across the reconnection region for four guide field strengths, ranging from zero to 2.1 times the strength of the reconnecting field and used to quantify the changes in ion energization. Detailed results will be presented, discussed, and compared with relevant theoretical predictions.

    

2D Kinetic Simulations of Electron Acceleration during Magnetic Reconnection with ad-hoc Pitch Angle Scattering to Mimic 3D Effects

Particle acceleration during magnetic reconnection is a long-standing topic in space physics and astrophysics. Recent 3D magnetic reconnection simulations show that particles can leave flux ropes due to 3D field-line chaos, allowing particles to access additional acceleration sites, gain energy through Fermi acceleration, and develop a power-law energy distribution. This 3D effect does not exist in traditional 2D simulations, where particles are artificially confined to magnetic islands due to their restricted motion across field lines. Full 3D simulations, however, are prohibitively expensive for most studies. Here, we attempt to reproduce and further extend 3D results in 2D simulations by introducing ad-hoc pitch-angle scattering to a small fraction of the electrons. We show that scattered particles are able to transport out of 2D islands and achieve more efficient Fermi acceleration, leading to a significant increase of energetic electron flux. We also study how the scattering frequency influences the nonthermal particle spectra.   

Signatures of Phase Space Energy Transfer in 2-D Strong Guide Field Collisionless Magnetic Reconnection using Field-Particle Correlations

Magnetic reconnection plays an important role in the energization of particles in collisionless plasmas. We apply an established field-particle correlation technique to explore the energization of ions and electrons in collisionless magnetic reconnection simulations. The goal is to determine the characteristic velocity-space signatures of energy transfer in a collisionless plasma due to magnetic reconnection using single-point measurements of the electromagnetic fields and particle velocity distributions. We compare signatures of kinetic energization in phase space to density and field profiles at specific spatial locations. The comparisons and characterization of energy outflows due to magnetic reconnection will help in understanding the impact of this phenomena on collisionless plasma energization. This work utilizes a diagnostic suite developed to analyze field-particle correlations from the gyrokinetic simulation code AstroGK. Understanding the phase-space energy budget and phenomenological signatures in single point measurements may provide novel insight into kinetic plasma energy transfer. These signatures offer new ways to guide design of spacecraft measurement techniques to identify particle energization due to magnetic reconnection.   

Phase space eigenmodes for cyclotron waves and instabilities in ring-distributed plasmas

Collisionless electrostatic modes in a spatially homogeneous magnetized plasma are considered through linear Vlasov-Poisson analysis. The function known as Gordeyev's integral for Maxwellian velocity distributions is extended to loss-cone, or ring, distributions with representations as trigonometric integrals and hypergeometric functions. Eigenmodes of perpendicular-propagating cyclotron waves are shown to be helical waveforms in phase space. Eulerian phase-space simulation of unstable propagating modes reveal fine structures and particle trapping.   

High-fidelity plasma simulations using a domain-hybridized model

High-fidelity simulations of plasma dynamics can involve various mathematical formulations, including the multi-species (electrons, ions, and neutrals) 5$N$-moment fluid model and the continuum kinetic model.  This work combines these models in a single domain-decomposed hybrid model where multiple formulations are used in a single simulation.  Special attention is given to the development of interface boundary conditions between formulations and determination of the parameter regimes most appropriate for each to maintain sufficient physical fidelity over the whole domain while minimizing computational expense.  The WARPXM framework developed at the University of Washington which implements these formulations using a discontinuous Galerkin spatial discretization on unstructured meshes is being used to develop the domain-decomposed hybrid model.  Simulations involving a double rarefaction wave, a plasma sheath, and the magnetized Kelvin-Helmholtz instability are presented, showing the viability of the domain-hybridized model.  In addition, linear analysis and kinetic simulations of the Dory-Guest-Harris instability are presented for the Vlasov-Maxwell continuum kinetic model, highlighting a method for benchmarking of kinetic codes for electromagnetic problems.   

Mixed potential formulations and electrode boundary conditions

Electrode interactions are a critical part of many plasma devices.

Applying electrode boundary conditions directly on the electric and magnetic fields generally requires path integrals between the electrodes, which are not spatially localized.

Using a mixed potential formulation of Maxwell's equations eliminates the need for path integrals entirely and may provide a way to the direct impose electrode boundary conditions on the potential fields.

This research investigates methods for applying electrode boundary conditions on a mixed potential formulation of Maxwell's equations coupled with the two fluid plasma model to study electrode interactions in planar and pinch-like plasma configurations.   

Multiscale Phenomena in the Magnetized Kelvin-Helmholtz Instability

The magnetized Kelvin-Helmholtz instability (KHI) is known to develop macroscale plasma structures whose details depend on microscale physics. The magnetized KHI is simulated with two-species kinetic and fluid plasma models. Deviations between the simulations demonstrate the development of multiscale phenomena. Local plasma parameters are investigated as a means to identify the onset of multiscale effects and to characterize the relevant physics driving the phenomena. Insights from the localization suggest a method to strategically combine computationally efficient reduced models with higher fidelity models, which is facilitated using the finite-element continuum WARPXM framework. Initial applications of this domain-decomposed hybrid method include the magnetized KHI and plasma photonic crystals.   

An efficient, fully implicit electrostatic full-PIC algorithm for strongly magnetized plasmas

We introduce a new fully implicit, strictly charge- and energy-conserving, asymptotic-preserving electrostatic particle-in-cell algorithm for strongly magnetized plasmas. The algorithm extends earlier electrostatic fully implicit particle-in-cell (PIC) implementations\footnote{Chen, Chac\'on, and Barnes, \textit{JCP,} \textbf{230} p.7018 (2011)} with a new asymptotic-preserving particle-push scheme\footnote{Ricketson and Chacon, \textit{JCP,}  \textbf{418} 109639 (2020) } that allows timesteps much larger than particle gyroperiods. In the large-timestep limit, the integrator preserves all the averaged particle drifts, while recovering the standard CN scheme for small timesteps. The scheme allows for a seamless, efficient treatment of particles in coexisting magnetized and unmagnetized regions, conserves energy and charge exactly, and is compatible with arbitrary boundary conditions, all the while without spoiling implicit solver performance. We demonstrate by numerical experiment with several strongly magnetized problems (e.g., diocotron instability, modified two-stream instability, drift instability, etc.) that orders of magnitude wall-clock time speedups vs the standard fully implicit electrostatic PIC algorithm are possible without sacrificing solution quality. We will also discuss possible extensions to the electromagnetic context.   

VPIC 2.0: High-Performance Particle-in-Cell on Modern Hardware Architectures

VPIC is a general purpose particle-in-cell simulation code for modeling plasma phenomena such as magnetic reconnection, fusion, solar weather, and laser-plasma interaction in three dimensions using large numbers of particles. Utilizing the Kokkos performance-portable framework, VPIC 2.0 achieves high performance on multiple CPU and GPU architectures and is scheduled for public, open-source release in 2021. In this poster, we report performance results and highlight features and areas of active development. Our performance-portability study includes weak-scaling runs on three of the top ten TOP500 supercomputers, as well as a comparison of low-level system performance of hardware from four different vendors. Compared with VPIC 1.0, VPIC 2.0 will include higher-order particle shapes, HDF5 output, more standardized visualization and analysis methods, and better documentation   

Analysis of noise in particle codes and the development of a meshless kinetic particle code

Recent work [JCP 440 (2021) 110394] is extended to include time dependent results on the noise and correlations in the density and electric field in particle-based kinetic codes. A meshfree particle code in 1D with electrostatic dynamics is under development. The estimated density is obtained by kernel density estimation (KDE), which does not require a mesh. In this meshfree setting, bias-variance optimization of the density error shows that the number of particles per cell does not have any relevance; instead, the number of particles-per-kernel-width is the relevant quantity. The electric field interpolation is discussed in terms of a partition of unity principle. The conservation properties of such a code are discussed and the relationship with statistical errors is explored. A comparison of Vlasov-Gauss (Vlasov-Poisson) methods and the Vlasov-Ampere approach is shown. Results on the covariance matrix of the electric field, obtained from the density by Gauss's law, also in a meshfree context, are presented and the analogy with the Ornstein-Uhlenbeck bridge of stochastic processes is explained. Comparison and interpretation of the meshfree results is made with a standard PIC code.   

A relativistic fluid model for magnetically insulated transmission line flow

Numerical modeling of magnetically insulated transmission line (MITL) electron flow is traditionally accomplished with a particle-in-cell (PIC) method. A PIC method can efficiently solve the collisionless Vlasov model for MITL flow. Additionally, space charge limited (SCL) emission boundary conditions have been well developed for PIC methods [1]. However, a cold electron fluid model may have utility for studying MITL flow. To this end, we have formulated an approximate SCL emission boundary condition for a relativistic charged fluid model. We show the results of a benchmarking activity which compares computed solutions to the relativistic electron fluid equations against corresponding solutions for canonical, cold electron fluid benchmark problems. We consider a one-dimensional Child-Langmuir diode, a canonical two-dimensional diode problem [2] and magnetically insulated planar flow which is representative of MITL flow.

[1] Stoltz, P. H., Luginsland, J. W., Chap, A., Smithe, D. N., & Cary, J. R. (2020). A new simple algorithm for space charge limited emission. Physics of Plasmas, 27(9), 093103.

[2] Luginsland, J. W., Lau, Y. Y., Umstattd, R. J., & Watrous, J. J. (2002). Beyond the Child–Langmuir law: A review of recent results on multidimensional space-charge-limited flow. Physics of Plasmas, 9(5), 2371-2376.   

Progress toward finite Larmor radius effects in an implicit, asymptotic preserving full-orbit integrator for particle-in-cell schemes

While the gyrokinetic approximation has been extremely successful in accelerating simulations of strongly magnetized plasmas, there is growing interest in full-orbit simulation in key cases where the gyrokinetic ordering breaks down.  As such, we present an implicit time-stepping scheme for charged particles that recovers the gyrokinetic limit when stepping over the gyration scale while converging to the exact, full-orbit dynamics in the small time-step limit. The scheme preserves the exact total energy conservation enjoyed by recently-developed implicit PIC schemes. Development proceeds in two stages. First, we summarize prior work in which Crank-Nicolson is modified to capture the drift-kinetic limit by introducing an effective force to capture the magnetic drift.  Next, to handle finite Larmor radius effects, we alternate large and small time-steps to sample equispaced gyrophases.  The numerical time-scales introduced by the scheme are analyzed and resulting time-step bounds derived. Tests on single particle motion in complex field configurations are shown.  The ability to step over the gyration time-scale and recover correct dynamics is demonstrated - even in configurations featuring structure on the gyroradius scale - along with the scheme’s conservation properties.     

High-fidelity kinetic modeling of instabilities in nonuniform low-beta finite-gyromotion plasmas

Performance and scalability of pulsed power inertial confinement fusion experiments are strongly influenced by the kinetic physics of low-beta collisionless plasmas.  Such plasmas are produced at electrode surfaces of power feeds, which deliver mega-amps of current to a Z-pinch load and which feature an ExB environment.  Through unexplained transport mechanisms, these plasmas lead to parasitic currents and can contaminate the load.  To shed light on how kinetic processes influence macroscopic transport properties, a high-fidelity kinetic modeling approach is employed.  The methodology is based on a fourth-order finite-volume continuum kinetic Vlasov solver and a systematic method for constructing customizable two-species kinetic equilibria.  The quiet-start noise-free approach is applied to investigate Kelvin-Helmholtz and lower hybrid drift instabilities in 4D (x,y,v_x,v_y) phase space.  Configurations where ion gyroradii are comparable to gradient scale lengths are investigated.  Distribution function structures, energy partitioning, and finite Larmor radius effects are explored in detail.  The methodology opens the way for targeted high-accuracy computational studies of plasma configurations where gyromotion plays an important role.  LLNL-ABS-824101   

Terahertz radiation generation by a soliton in a laser-plasma system

In recent years, there has been considerable interest in exploiting intense laser-plasma interactions for generating terahertz (THz) radiation[1,2]. In the present study, we propose a novel mechanism that is based on the creation of a localized `soliton’ structure due to the interaction of the laser pulse with the plasma [3]. A population of oscillating electrons trapped inside this localized cavity then acts as a dipole antenna to emit radiation whose frequency lies in the THz range. We demonstrate this mechanism through detailed particle-in-cell simulations. The configuration of the laser-plasma system can be suitably arranged to form the localized structure near the plasma vacuum boundary so that the radiation can propagate to the vacuum without getting fully absorbed within the plasma. THz generation through such a mechanism has advantages over other conventional schemes on account of its compact size and high damage threshold limit.   

Towards quantum simulation of extreme plasmas

Quantum Simulation is a new computing paradigm that promises significant speedups over classical simulation. The quantum algorithms can natively be applied to only certain kind of problems, which are described through the Schrödinger equation. Recently, some new solutions have been proposed that map non-Hermitian and non-linear problems to quantum circuits, which could potentially boost plasma physics research in this area.

Current quantum hardware is too noisy to perform standard simulations over more than ~15 qubits and ~100 gates, leading current research to focus on toy problems. A possible way forward for the near-term quantum computers is to use the Variational algorithms, which present three main advantages: their circuits are shorter than in regular Hamiltonian simulation, they allow for reconstruction of the wavefunction at each timestep and they can be extended to nonlinear dynamics. In this work we apply this variational approach to simulate an extreme plasma physics problem, which is inherently non-linear in its nature.   

Hybrid fluid-kinetic Hall Magnetohydrodynamics: Hamiltonian structure and equilibrium equations

We present two hybrid kinetic-Hall MHD models describing the interaction of a two-fluid plasma consisting of thermal ions and massless electrons with energetic ion populations described by Vlasov dynamics. The coupling of the bulk plasma with the energetic particle component is accomplished through the current density (Current Coupling Scheme-CCS) and the ion pressure tensor appearing in the momentum equation (Pressure Coupling Scheme-PCS) in the first and the second model, respectively. The noncanonical Hamiltonian structures of the aforementioned models,  which can be employed  to study equilibrium and stability properties via the energy-Casimir variational principle, are identified. As a first application here, we derive a generalized Hall MHD Grad-Shafranov-Bernoulli system that governs translationally symmetric equilibria with anisotropic electron pressure and energetic particle contributions in the PCS.   

Quantum Algorithms for Plasma Physics Simulations

The nonlinearity of plasma physics makes its numerical simulations resource-expensive. It is natural to seek alternative computational platforms that may offer speedups of such simulations. Quantum computers are an attractive option, as they have the potential to solve certain problems exponentially or polynomially faster than classical computers (Grover 1996, Shor 1999). We investigate two approaches to simulating plasma physics on quantum computers. First, we consider the linearized Vlasov equation with collisions. Using a Fourier expansion in real space and Hermite expansion in velocity space, we obtain a system of differential equations (Kanekar et al. 2014) that can be solved using Hamiltonian simulation and operator splitting (i.e., Trotterization) techniques on a quantum computer (e.g., Childs and Wiebe 2012). The second approach considers discrete time quantum walks, which are analogous to classical random walks. In the continuous limit, such quantum walks can converge to Schrodinger's equation (Hatifi et al. 2019), which can be mapped to the MHD equations using the Madelung transform (Dodin and Startsev 2020). Thus, by implementing these quantum walks on a quantum computer, we can simulate certain classes of MHD problems.   

Preserving Hamiltonian structure for discretized Maxwell equations with sources

In the past few decades (e.g. Bossavit) differential forms have been used in computational electromagnetism. We build on the mimetic discretization framework of Bochev and Hyman to construct a mimetic Petrov-Galerkin method for Maxwell equations with general nonlinear polarization and magnetization. Two de Rham complexes are used: one complex represents orientation independent straight forms, the other orientation dependent twisted forms. These complexes are related to each other through the Hodge star operator, which plays a crucial role in modeling the constitutive relations. We found that the Petrov-Galerkin mass matrix is a discrete approximation to the Hodge star operator closely related to existing discrete Hodge star operators in the literature. The two complexes are discretized on staggered cell complexes, yielding a method reminiscent of the Yee scheme but with significant flexibility to prescribe general geometries. The use of mimetic discretization facilitates a strategy for projecting the Hamiltonian structure of the continuous model to that of the discretization,  allowing for exact enforcement of the electromagnetism constaint relations.    

On the Hamiltonian structure of the BBGKY hierarchy

It is now well known that the Vlasov-Poisson system is a noncanonical Hamiltonian field theory [P. Morrison, Phys. Lett. A 80, 383, (1980)]; however, it is less well known that there exists families of Hamiltonian closures , Vlasov-like Hamiltonian field theories for the coupled dynamics of 1-point and 2-point functions, coupled 1-point, 2-point, and 3-point functions, and so on up the chain [J. Marsden, P. Morrison, & A. Weinstein, Cont. Math. 28, 115 (1984)]. We will review this structure and analyze the system for the coupled 1-point and 2-point functions, a system that can produce the Lenard-Balescu collision operator following a natural procedure.   

Exact conservation laws for gauge-free electromagnetic gyrokinetic equations

The exact energy and angular-momentum conservation laws are derived by Noether method for the Hamiltonian and symplectic representations of the gauge-free electromagnetic gyrokinetic Vlasov-Maxwell equations. These gyrokinetic equations, which are solely expressed in terms of electromagnetic fields, describe the low-frequency turbulent fluctuations  that perturb a time-independent toroidally-axisymmetric magnetized plasma. The explicit proofs presented here provide a complete picture of the transfer of energy and angular momentum between the gyrocenters and the perturbed electromagnetic fields, in which the crucial roles played by gyrocenter polarization and magnetization effects are highlighted. In addition to yielding an exact angular-momentum conservation law, the gyrokinetic Noether equation yields an exact momentum transport equation, which might be useful in more general equilibrium magnetic geometries.   

On the outstanding problem of energy confinement in a controlled nuclear fusion system

The single most important scientific question in fusion research is confinement in a fusion plasma. A recently-developed theoretical model [1] is reviewed for the confinement time of ion kinetic energy in a material where fusion reactions occur. In the theoretical model where ion stopping was considered as a key mechanism for ion kinetic energy loss, an estimate was obtained for the confinement time of ion kinetic energy in a D-T plasma - and found to be orders of magnitude lower than required in the Lawson criterion. As ions transfer their kinetic energies to electrons via ion stopping, electron cyclotron radiation is identified as a key mechanism for electron kinetic energy loss in a magnetically confined plasma. These theoretical results are compared with measurements from TFTR, JET and Wendelstein 7-X.

1. C. Chen, J.R. Becker, and J.J. Farrell, "Confinement time of ion kinetic energy in a controlled nuclear fusion system," Proc. of 47th European Physical Socieity Conf. on Plasma Physics, P1.4006 (2021).    

Optimal symplectic integrators for molecular dynamics

The second-order velocity Verlet integrator is the most widely used symplectic integrator for molecular dynamics. We examine higher order symplectic integrators and access their performance with Lennard-Jones, and Yukawa potentials. We find that the optimized Verlet integrator which requires two force calculations per time step is the most efficient in most cases. In addition, we find that the performance of the integrators strongly depends on the accuracy of force calculation itself. We also discuss the performance of adaptive time steps.   

A data-driven analysis of non-equilibrium transport in the magnetized Kelvin-Helmholtz instability

Collisional kinetic equations such as the Boltzmann equation provide a detailed

description of plasma physics, but their numerical solution can present a

challenge. Particle methods suffer from stochastic noise, and the direct

solution of kinetic equations in 6D phase space is out of reach computationally.

A common class of reduced models are the moment methods, which

integrate the kinetic equation over velocity space to obtain an infinite coupled

hierarchy of unknowns, requiring an ansatz for the distribution function to

close the hierarchy. Near local thermodynamic equilibrium (LTE), the Boltzmann

H-Theorem indicates that the natural choice of ansatz is a Maxwellian. However,

in regimes far from LTE, the available choices of ansatz are less satisfactory.

This work applies a data-driven approach to the analysis of the moment closure

problem. Full particle distribution data from a continuum kinetic simulation of

the magnetized Kelvin-Helmholtz instability are analyzed using the Sparse

Identification of Nonlinear Dynamics (SINDy) method. It is verified that mass,

momentum and energy conservation are witnessed by the SINDy analysis. SINDy is

then applied to derive approximate higher-order transport relations, and the

regimes of applicability of these relations are discussed. Finally, we explore

the departure from LTE, as measured by the dynamics of the 1-norm of deviation

from the local Maxwellian, χ.   

Prospects for a Quantum Speedup of Classical Nonlinear Plasma Simulations

Large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, are important in both fluid and kinetic computational plasma physics. The simulation of these systems can be extremely computationally demanding, which motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. Quantum computers are expected to provide a dramatic speedup for many linear computations, e.g. through the application of quantum linear systems algorithms, but obtaining any large speedup for nonlinear computations is made difficult by the linearity of quantum mechanics. We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system, which can then be approximated with finite linear systems if the nonlinearity is sufficiently weak [1]. Using this approach, a quantum computer could approximate the simulation of weakly nonlinear dynamical systems using a number of qubits only logarithmic in the size of the nonlinear system.

[1] "Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms," A. Engel, G. Smith, S. E. Parker, Phys. Plasmas 28, 062305 (2021).   

Carleman Embedding of the Driven Pendulum

Carleman embedding is a linearization technique that allows writing a finite system of nonlinear (NL) first-order initial-value ordinary differential equations (ODEs) as an infinite linear system of first-order ODEs.  Most challenging computational plasma problems can be cast as such a first-order NL dynamical system.  Hence, it is worthwhile to explore the Carleman linearization (CL) technique.  Additionally, quantum circuits can be represented as a linear system, and there is much recent work in the development of quantum linear systems algorithms (QLSAs).  Therefore, CL may provide a tool to solve nonlinear problems on a quantum computer [1].  Efficient QLSAs will have a computational complexity that is logarithmic with system dimension.  Here, we examine the driven pendulum problem as a test for applying CL to NL Hamiltonian dynamics.  The pendulum problem is seemingly elementary and is also a classic example of Hamiltonian chaos.  It is fundamental for the understanding of island overlap and other aspects of Hamiltonian dynamics. We show that the exact solution can be expressed as an infinite linear system by a change of variables.  We truncate the linear system and explore numerical convergence properties.  Using the eigenvalue solution of the truncated CL system, we can time advance, effectively taking a very large timestep on the order of the nonlinear oscillation period. 

[1] "Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms," A. Engel, G. Smith, S.E. Parker, Phys. Plasmas 28, 062305 (2021).   

PlasmaPy: current status, future directions, and ways to contribute

The mission of the PlasmaPy project [1] is to foster the creation of a fully open source software ecosystem for plasma research and education.  The PlasmaPy package is being developed to include the common core functionality needed by plasma physicists across disciplines.  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 new capabilities of PlasmaPy including for plasma diagnostics such as synthetic charged particle radiography.  We will present code development plans over the next year, in particular including expanded functionality for plasma diagnostics and simulations, as well as more integration with other community projects such as Gkeyll.  Finally, we will discuss how to contribute to open source projects such as PlasmaPy.

[1] https://www.plasmapy.org   

Quantum Signal Processing for simulating radiofrequency waves in plasmas

Quantum computing is gaining attention as a potential way to speed up simulations of physical systems. The most promising algorithm for general-purpose linear quantum simulations appears to be Quantum Signal Processing (QSP), which has been developed recently and scales optimally with the evolution time and the desired precision [1]. We show how to apply the QSP  to modeling cold linear radiofrequency waves in plasma. The electromagnetic wave field and plasma velocity are encoded into a ``state vector'' that satisfies a multi-dimensional Schrodinger equation with a Hermitian Hamiltonian. We show how to discretize this equation and how to construct a quantum circuit that implements the corresponding Hamiltonian evolution via QSP. The modeling is performed on an emulator of a noiseless quantum computer using a parallelized library QuEST [4]. We also discuss possible applications of the QSP framework to more complex plasma systems.

1. G. H. Low and I. L. Chuang, Quantum 3, 163 (2019).

2. A. Engel, G. Smith, and S. E. Parker, Phys. Rev. A 100, 062315 (2019).

3. I. Y. Dodin and E. A. Startsev, arXiv:2005.14369.

4. T. Jones et al., Sci. Rep. 9, 107736 (2019).   

Numerical instabilities in multistep symplectic methods triggered via krein collisions

Discrete variational integrators comprise an interesting class of symplectic integrators that can be applied to any Lagrangian system. In plasma physics, such integrators have been applied, for example, to the guiding center (GC) system [1]. However, these integrators may be multistep methods, and thus can suffer from parasitic instabilities [2]. It is known that instabilities in continuous Hamiltonian and symplectic systems are only triggered under specific conditions, namely via the Krein collision in which two eigenmodes with different signs of action resonate. We show that since symplectic integrators conserve the same symplectic form as the underlying continuous system, numerical spectral stability can only be lost by the same Krein collision mechanism. This formalism is used to explain the onset of parasitic instabilities observed in a particular variational integrator for GC dynamics [1]. We also explore the simultaneous application of Krein’s theorem and Dahlquist’s equivalence theorem to multistep symplectic methods and examine whether these can produce particularly robust numerical stability under certain spectral conditions.

[1] H. Qin and X. Guan, Phys. Rev. Letters 100, 035006 (2008).

[2] C. L. Ellison, Ph.D. thesis, 2006.   

Fermi Acceleration with Lorentz Scattering

The Fermi acceleration model was first used to describe how cosmic ray particles are accelerated to great speeds by interacting with moving magnetic fields. Since then, many variations of the model have been studied. We identify a new variation of the model where a multiple species plasma interacts with moving walls while undergoing interspecies pitch angle scattering. Due to the relationship between the mean free path for Coulomb collisions and the particle speed, the rate at which a particle is accelerated by the moving wall may be heavily dependent on its initial speed and the density of the background species. This would suggest that the system might be tuned with these parameters to produce favorable distributions of particles, such as a peaked energy distribution. A peaked energy distribution might optimize fusion reactivity or better characterize astrophysical phenomena.   

Computational Observation of Collisionless Damping of Langmuir Waves in Relativistic Plasmas*

Recent inertial confinement fusion experiments have generated underdense plasma conditions believed to be in the 10-20 keV regime. In this regime, Langmuir waves excited by laser light instabilities will have phase velocities for which a relativistic treatment is required. We conduct basic physics studies of such Langmuir waves using direct simulation of the relativistic Vlasov equations. Building on prior work, we address the significant computational cost associated with high-dimensional phase space approximation using high-order accurate numerical schemes as a means to reduce the cost required to deliver a given level of error in the computed solution. Fully conservative and minimally diffuse difference formulations of order four and six are used. Additionally, theoretical techniques indicate the existence of Langmuir waves with superluminal phase velocities in relativistic plasmas. The existence of these waves is investigated using simulations.

 

*This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344   

Measuring the relaxation times of momenta and temperatures in strongly coupled plasmas

The collision time of the Boltzmann operator can be determined by the relaxation times of the momenta and the temperatures of two species in a plasma. The most intuitive way to get these times is to perform molecular dynamics (MD) simulations. MD can provide the velocity distribution of a many-particle system, hence the time evolution of velocity moments. However, MD requires huge computational effort to calculate the Coulomb interactions between charged particles. In order to reduce simulation time, we constructed a code that utilizes the multipole expansion and GPU acceleration. We report on relaxation times of momenta and temperatures for a strongly coupled plasma with various parameters.   

On the kinetic theory origin of fluid helicity

Helicity,  a topological measure of the winding and linking of vortex lines,  is preserved by ideal fluid dynamics.   In the Hamiltonian description,  helicity is a Casimir invariant characterizing a foliation of the associated Poisson manifold.   Casimir invariants are special invariants that depend on the Poisson bracket, not on  the particular choice of the Hamiltonian.  The  total mass is another Casimir invariant, whose invariance guarantees the mass conservation. In a kinetic description (e.g. the Vlasov equation),  the helicity is no longer an invariant (although the total mass/particle number remains one in the Vlasov Poisson algebra).  Thus,  some "kinetic effect"  violates the constancy of the helicity. To see how the helicity constraint emerges or submerges, we examine the fluid reduction of the Vlasov system; the fluid system is a "sub-algebra" of the kinetic  Vlasov system. In the Vlasov system, the helicity can be conserved, if a special helicity symmetry condition holds -- breaking  helicity symmetry induces a change in the helicity. We delineate the geometrical meaning of  helicity symmetry, and show for a special class of flows how to explicitly write the symmetry.  Poster based on arXiv:2103.03990v1.   

A probabilistic approach for the computation of confinement and exit-time in local and non-local plasma transport problems

The exit time probability, which gives the likelihood that a particle leaves a prescribed region in the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems in general and in magnetically confined plasmas in particular. This talk presents a novel numerical method for computing this probability, and the confinement statistics, for local and nonlocal plasma transport problems described by time-dependent Fokker-Planck (FP) differential and integro-differential equations, and their equivalent stochastic differential equations (SDEs) [1,2]. The method is based on the direct numerical evaluation of the Feynman-Kac formula that establishes a link between the adjoint FP equation and the forward SDE. In the local transport case, the SDEs are driven by Brownian motion, and in the nonlocal case, by Poisson jump processes describing nonlocality with a finite horizon kernel in the corresponding integro-differential FP equation. The efficiency and accuracy of the proposed method rests on the reduction of the computational complexity of the problem to the evaluation of Gaussian quadratures. The method does not face the noise limitations of direct Monte-Carlo algorithms, and bypasses stability and efficiency issues of standard finite-difference methods for time-dependent FP equations.  In particular, the proposed method is unconditionally stable, exhibits second-order convergence in space, first-order convergence in time, and it is straightforward to parallelize. Several applications are presented, including the production of runaway electrons in tokamak disruptions, ExB transport, and non-local transport resulting from Landau-fluid type kinetic closures.

[1]  https://arxiv.org/abs/2104.14561 Accepted for  publication in Journal of Computational Physics (2021).

[2]  https://arxiv.org/abs/2001.05800 Springer Verlag Lecture Notes (2021).   

Efficiency of Current Drive via Rotating Magnetic Fields

The “rotamak” is a proposed thermonuclear fusion device which employs rotating magnetic fields (RMF) to generate an azimuthal current to produce a field-reversed configuration (FRC). The efficiency of the currents that produce the field reversal by RMFs was debated some forty years ago (1,2). The debate revolved around whether the currents would incur dissipation by the conventional Spitzer resistivity of plasma, perpendicular to a magnetic field, or whether some other relation between current and dissipation would be more appropriate. In a preliminary investigation that considers the problem afresh, more extensive computations capture rather curious plasma behavior that suggests a picture for current drive not easily related to the leading mechanisms for driving current.

1 N. J. Fisch and T. Watanabe, “Field reversal by rotating waves,” Nucl. Fusion 22, 423 (1982).

2 W. N. Hugrass, “Comments on the  paper by  N. J. Fisch, T. Watanabe, ‘Field reversal by rotating waves’,” Nucl. Fusion 22, 1237 (1982).   

Ionospheric plasma parameter measurement using the NRL SPADE plasma impedance probe

The Space PlasmA Diagnostic suitE (SPADE) instrument, developed by the U.S. Naval Research Laboratory (NRL), is a plasma impedance probe designed to monitor background space plasma conditions and provide early warning of the onset of hazardous levels of spacecraft charging.  SPADE has been operating on the International Space Station (ISS) since May 2019 as part of the Department of Defense Space Test Program’s STP-H6 mission.   The SPADE experiment consists of two dipole antennas, one active antenna that is used to excite the local plasma and another passive dipole antenna that observes the excitation.   The active probe is swept across a range of frequencies and DC voltage biases to determine the plasma impedance spectrum.  The impedance measurements yield properties of the plasma, such as density, plasma potential, and electron temperature, while also providing data indicating the charging level of the ISS relative to the local plasma. SPADE responds to slight changes in the plasma sheath that forms around a charged object, providing a unique method for the early detection of charging.  SPADE active dipole measurements of ionospheric plasma parameters, ISS charging, and comparisons to measurements made using other in situ and ground-based diagnostics will be presented.   

Surface Mounted Impedance Probe Antenna 3U-CubeSat Payload

Collaborations utilizing small spacecraft in near-earth orbit between the U. S. Coast Guard Academy (CGA), Navy Research Lab (NRL), the U. S. Naval Academy (USNA), Old Dominion University (ODU),  and the Air Force Institute of Technology (AFIT) have initiated scientific and engineering space-based experiments. We have constructed an impedance probe payload for launch in Fall 2021 derived from the existing ‘Space PlasmA Diagnostic suitE’ (SPADE) mission operating from NASA’s International Space Station. Currently, both space and laboratory plasmas are investigated with AC impedance measurements using a radio frequency antenna. Plasma electron density data collected from the 3U CubeSat will however use an innovative surface mounted dipole antenna to gather the required sheath-plasma and plasma resonance information. On that same launch, a compact multispectral ‘Pixel Sensor’ with a 450 nm - 1000 nm spectral range will add to the motion and position sensors baselined in previous launches. We have designed, built, and assembled custom components while and conducted laboratory experiments in both NRL and AFRL plasma chambers comparable to low earth orbit (LEO) densities. Impedance probe optimization, data collection obstacles, solutions, and procedures will be reported.   

Dissipation of Angular Momentum in Magnetic Reconnection

Magnetic reconnection is an important phenomenon that occurs throughout the universe in magnetized plasmas. It is a process whereby adjacent magnetic field lines embedded in a plasma gas break and reconnect to one another. One of the unresolved questions regarding magnetic reconnection is how it dissipates energy, an important aspect of reconnection’s energy budget and efficiency. It has been shown (Wendel et. al., 2021) that local electron vorticity is subject to an instability bifurcation that determines whether vorticity, and therefore electrons, remain fixed to a given filed line, exchanging angular momentum. The boundary conditions and E_⊥ impose vortex null points along each of the reconnecting magnetic field lines within the electron diffusion region (EDR). These predictions are supported by the PIC simulation analysis. Expanding on these results, we verify theoretical estimates of electron angular momentum dissipation against in situ space observations of magnetic reconnection. We engage in the calculation and analysis of the electron dissipation inferred from spacecraft observations of reconnection, using data from NASA's Magnetospheric Multi-Scale (MMS) mission. The use of quadratic spatial interpolation for four spacecraft was implemented to determine the existence of vorticity null points within the tetrahedron formed by the four spacecrafts in the MMS data, extracting useful statistical information in support of the theoretical arguments and simulations.   

Formulation of scale-dependent anisotropic energy transfer and conversion in compressible MHD turbulence and implications for space and astro plasmas

Turbulent fluctuations play an important role in processes such as the solar wind heating and transport of energetic particles. We present results from 3D compressible MHD simulations of turbulence. The turbulence is highly anisotropic with respect to the background magnetic field and is dominated by perpendicular structures, consistent with the turbulence observed in typical space plasmas. While local interactions dominate the cross-scale energy transfer in isotropic turbulence, the locality of energy transfer in anisotropic turbulence remains poorly understood. We present a spatial filtering technique to calculate various scale-dependent energy transfer and conversion terms including kinetic, magnetic and pressure dilatation processes. The analysis presented here allows us to compute the anisotropic cross-scale energy fluxes and demonstrate their locality (or nonlocality). The simulations also explore the parameter space such as the plasma beta, turbulent Mach number, and driving mechanism.   

DG FEM numerical simulation of a plasma jet in a stellar atmosphere

Motivated by studying an outflow of plasma caused by magnetic reconnection in Solar and stellar flares we use a novel, Discontinuous Galerkin Finite Element Method (DG FEM) MHD code to study the behavior of the jet and of subsequent turbulence. We show conditions, under which the turbulence develops and general behavior under various initial parameters: speed of the flow, plasma beta, background density, and magnetic configuration. Furthermore, we focus on the current sheet-like configuration of the magnetic field and super alfvénic flows.  Under these conditions, we present power-law fit of the energetic spectrum, energy conservation, and divergence-free nature of the simulation even without excessive artificial resistivity and viscosity.   

Magnetic Energy Conversion in Magnetically Dominated Systems and Implications for Particle Energization Processes

The mechanisms and pathways for magnetic energy dissipation are an important subject for many space and astrophysical systems, such as the solar corona and astrophysical jets. Here, we present a new perspective on describing the magnetic energy conversion through the relaxation of magnetic curves and the perpendicular expansion of magnetic lines. By analyzing the evolution of three nonlinear systems, 3D reconnection, kink unstable jets, and magnetized turbulence, we quantify the relative importance of the curvature relaxation vs. the expansion terms. Compressible MHD simulations of various physical systems show that the expansion term often has a more important, sometimes dominant, effect on the energization. In contrast, the curvature relaxation process, despite being crucial during the early evolution, may not be as important in converting magnetic energy overall. We discuss the physical interpretation of these processes and compare 3D MHD and 3D PIC results. Implications for particle energization processes are also explored. In particular, Parker Solar Probe (PSP) provides measurements of transonic velocity fluctuations that can drive significantly more compressible turbulence. We also discuss the dependence of density fluctuations on plasma beta, cross helicity, and polytropic index in the solar wind.   

Evolution and Particle Energization of the Electron Cyclotron Drift Instability

The electron cyclotron drift instability (ECDI) is often observed in the foot of heliospheric shocks and plays an important role in heating electrons and ions in collisionless shocks, as well as supplying anomalous resistivity. Although commonly observed in quasi-perpendicular interplanetary shocks and Earth's bowshock, the ECDI is a difficult instability to study in self-consistent particle-in-cell simulations of shocks, and isolated studies of the ECDI have generally been limited to simple geometries and initial conditions. Here, we present a study of the ECDI in a variety of conditions relevant to shocks by employing linear kinetic theory and the fully non-linear continuum Vlasov-Maxwell solver in the Gkeyll simulation framework. By drawing from perpendicular and quasi-perpendicular shock simulations, we employ realistic particle distributions as well as the full range of wavevectors available to the instability. In particular, we apply the field-particle correlation technique to examine the phase-space energization of electron and ions in the ECDI.   

Excitation of whistler waves in Earth magnetosphere with antennas

In this work, we revisit linear theory for excitation of electromagnetic waves in magnetized plasma. The theory is revisited to find whistler waves emitted by antennas. In-depth analysis indicates that previous studies did not properly account for wave damping due to collisions or Landau damping. The discrepancy is caused by improper dispersion relation used for waves in the presence of damping which resulted in unphysical radiation patterns. We correct this inconsistency and demonstrate a method for finding proper dispersion relations in anisotropic dispersive media with damping. The modified theory is applied to study excitation of waves in the VLF frequency range for space applications. The angular distribution of emitted power and the impedance of antenna if found numerically for various plasma parameters.   

Not Participating

First-principles propagation of low frequency (0.01-100 Hz) electromagnetic signals from the ionosphere to the Earth's surface requires algorithms that are accurate over orders of magnitude in electron and neutral density.

Starting from Maxwell's equations with a tensor conductivity, we present an algorithm for propagating EM signals from the ionosphere down to the surface of the Earth. This algorithm is shown to be stable at all altitudes for the parallel, Hall, and Pedersen conductivities. For unconditional stability, the parallel and Pedersen terms must be solved implicitly, and the Hall term must be solved via a Crank-Nicolson scheme. Despite its mixed-implicit nature, the novel algorithm is local in space, and hence is easy to implement efficiently on parallel architectures.

We demonstrate the advantage of the new mixed-implicit algorithm compared to the standard diffusion approximation for treating vacuum regions. Using the code Topanga, we model propagation of EM signals around the X-ray ionization patch formed in the aftermath of a high-altitude nuclear explosion. We show that the novel algorithm recovers the EMP blast signal from the Starfish nuclear test, whereas a standard diffusion model fails to match the data.   

Effect of Electron Precipitation on E-Region Instabilities: Theoretical Analysis

During periods of strong geomagnetic activity, intense currents flow from the magnetosphere into the high-latitude E-region ionosphere along the magnetic field. In this region, collisions between the plasma and neutral molecules allow the entire magnetosphere-ionosphere current system to close. These same currents cause strong DC electric fields in the E-region ionosphere where they drive plasma instabilities, including the Farley-Buneman instability (FBI). These instabilities give rise to small-scale plasma turbulence that modifies the large-scale ionospheric conductance that, in turn, affects the evolution of the entire near-Earth plasma environment. Also, during geomagnetic storms, precipitating electrons of high energies, $\gtrsim$~5 keV, frequently penetrate down to the same regions where intense currents and E fields develop. This research examines the effects of precipitating electrons on the generation of the FBI and shows that, under many common conditions, it can easily suppress the FBI in a predictable manner. We expect precipitation to exert a significant feedback on the magnetosphere by preventing the elevated conductivity caused by FBI driven turbulence. This suppression should be taken into account in global modeling of the magnetosphere-ionosphere coupling.   

Characteristics of plasmas formed from hypervelocity impact

Satellites are surrounded by orbital debris and meteoroids that cause mechanical or electrical damage. While mechanical damage is well studied, more than half of the electrical anomalies are undiagnosed which can be attributed to hypervelocity impact (HVI). HVI refers to a collision where the projectile speed exceeds the speed of sound in the target material and its impact energy ionizes the material near the surface, creates plasma and emits charged particles. Ground-based experiments have generated empirical power law relations which describe the impact charge produced as a function of impactor mass and speed.

The goal of this paper is to use past experiments to 1. Develop a new technique for calculating the impact charge produced and the power law for different species from the same impact conditions. 2. Use Time of Flight analysis to detect the charged particle compositions as well as their initial speeds. For the first time, the results suggest that the charge production power law is species specific and there are different formation mechanisms involved in a single HVI event, some of which are associated with positive to negative pairs that come from dissociation of a molecule. In addition, presence of species like SiO2 and SiO was detected which matches previous findings.    

Electron heating by remagnetization of demagnetized electron beams produced by magnetic reconnection – Theory, simulations, and observations

We show findings that the peak electron temperature downstream of a magnetic reconnection site is associated with electron beams getting remagnetized by the strong reconnected field in regions of compression of the displaced dense current sheet plasma population, known in magnetospheric physics as a dipolarization front. The remagnetized electrons form a ring distribution and we predict its major and minor radii in terms of conditions upstream of the reconnection site, then derive analytical expressions for the electron temperature and the electron temperature anisotropy in terms of the ring major and minor radii in the region of compressed reconnected field. We test the validity of the theory with 2.5-dimension particle-in-cell simulations with varying upstream plasma density and temperature, finding excellent agreement for predicted ring major and minor radii and good agreement for electron temperature and perpendicular electron temperature anisotropy. We show THEMIS satellite observation of the highest electron temperature in a dipolarization front, revealing an electron ring distribution, and we compare the theory to this observation. These results suggest that remagnetization of electron beams could be an important mechanism for heating electrons in reconnection exhausts.   

Whistler waves generated by nongyrotropic and gyrotropic electron beams in asymmetric guide field reconnection

 

We study electron beams and wave activity in the magnetospheric side in asymmetric guide field reconnection, using a 2D particle-in-cell (PIC) simulation. The guide field strength is 30% of the average asymptotic field. Strong whistler wave activity is observed along the separatrix in the magnetospheric side with a faster electron outflow speed, and waves are propagating almost anti-parallel to the magnetic field with propagation angles between 140 to 170 degrees. We investigate whistler wave generation using the fast Fourier transform and the linear dispersion analysis. Examining electron velocity distribution functions (VDFs), we separate fast electron beams and slow electron beams. The linear numerical dispersion analysis shows that there are two modes of the whistler waves in the separatrix. One is a temperature anisotropy mode due to the fast electron beam, and the other is a Landau resonance mode due to the slow electron beam. Outside the electron diffusion region (EDR), whistler waves are strong near the separatrix and become weaker in regions away from the separatrix. The reduction of the wave intensity away from the separatrix occurs due to the enhancement of the population with zero parallel velocity in VDFs. Inside the EDR, nongyrotropic electrons are found in the VDFs with crescent shapes in the perpendicular velocity plane. Wave intensities in the separatrix near the X line depend on the population density of crescent-shaped nongyrotropic electrons.   

A New Way to Include Inertia in the Rice Convection Model

The RCM-I model formulation published in 2019 represents a first attempt to generalize the long-standing assumptions of quasi-static slow-flow convection in the inner magnetosphere by including electrodynamic effects of the inertial drifts in the Rice Convection Model. Its most serious approximation is to assume that, when the inertial drift contribution is calculated, the mass is concentrated near the magnetospheric equatorial plane. In this paper, we present a reformulation of the model where plasma pressure and density are constant along each field line. That approximation still precludes getting the details of substorm timing right, but it is much more realistic than assuming that the all of the mass is in the equatorial plane. The constant pressure-density assumption is often used in simple plasma physics, e.g., interchange instability, which the physics that we are trying to represent closely resembles. Our new formulation of the RCM-I involves multiple coordinate systems, including a rectangular quasi-Cartesian system, a dipolar system, and a field-aligned system that is based on Euler potentials; the lattermost system it is not orthogonal, and it changes with time. We employ a Riemannian geometry to this end, for a flat space manifold. Tensor calculus is used to formulate a covariant set of self-consistent field equations with which we can easily transition between the coordinate systems with the use of metric tensors and Christoffel symbols. The covariant formulation facilitates the inclusion of inertia and allows representation of the auroral ionosphere at 1-10 km resolution and finer than 0.5 RE resolution in equatorial plane. The Riemann-tensor multi-grid approach to magnetospheric modeling might point a way to help other magnetospheric models bridge the scale gap between the ionosphere and magnetosphere.   

Reconnection Drive Cylinder for the Terrestrial Reconnection Experiment

The Terrestrial Reconnection EXperiment (TREX) at Wisconsin Plasma Physics Laboratory (WiPPL) [1] aims to explore the kinetic regime by driving an induced electric field through a cylindrical coil geometry. The enhanced drive will reduce the effective collisionality of the experiment, such that electron pressure anisotropy can develop unimpeded by Coulomb collisions providing a more accurate model of Earth’s magnetospheric plasma dynamics. The drive cylinder is composed of aluminum and Teflon, has a radius of 60cm, and is surrounded by 13 copper coils.  Compared to  TREX’s previous four drive coil configuration [2], we estimate that the drive cylinder reconnection current layer will be 70% longer, increase the absolute reconnection rate tenfold (up to E_rec ? 1kV/m), and reduce the collision frequency by a factor of four. These effects will allow us to reliably access the regime of kinetic reconnection where electron pressure anisotropy is known to strongly impact the reconnection dynamics.

[1] C. B. Forest et al., “The Wisconsin Plasma Astrophysics Laboratory,” Journal of Plasma Physics, vol. 81, Oct 2015.

[2] J. Olson et al., “Experimental demonstration of the collisionless plasmoid instability below the ion kinetic scale during magnetic reconnection,” Phys. Rev. Lett., vol. 116, Jun 2016.   

Simulation Study on Parametric Dependence of Whistler-mode Hiss Generation in the Plasmasphere

We conduct electromagnetic particle simulations to examine the applicability of nonlinear wave growth theory to the generation process of plasmaspheric hiss. We firstly vary the gradient of background magnetic field from a realistic model to a rather steep gradient model. Under such variation, the threshold amplitude in the nonlinear theory increases quickly and the overlap between threshold and optimum amplitude disappears correspondingly, and the nonlinear process is suppressed. In the simulations, as we enlarge the gradient variation of the background magnatic field, waves generated near the equator do not grow through propagation. By examining extracted typical wave packets from different gradient cases, we find the generation of wave packets is limited to equatorial region when background field is steep, showing a good agreement with what is indicated by critical distance in the theory. We then check the dependence of generation of hiss emissions on different hot electron densities. Since the overlap between threshold and optimum amplitude vanishes, the nonlinear process is weakened when hot electron density becomes smaller. In the simulation results, we find similar wave structures in all density cases, yet with different magnitudes. The existence of suitable values of the inhomogeneity factor S implies that nonlinear process occurs even at a low level of hot electron density. However, by examining J_E which is closely related to the wave growth, we find energy conveyed from particles to waves is much limited in small density cases. Therefore, the nonlinear process is suppressed when hot electron density is small, which is in agreement with the theoretical analysis.   

Bursty magnetic reconnection at the Earth's magnetopause triggered by high-speed jets

High speed jets, regions of enhanced dynamic pressure and flow velocity, are found in the Earth’s magnetosheath downstream of the quasi-parallel shock. Spacecraft observations have shown that the impact of jets on the magnetopause can lead to the triggering of magnetic reconnection. We perform a three-dimensional hybrid simulation to study the magnetosheath and magnetopause under turbulent conditions using a quasi-radial southward interplanetary magnetic field (IMF). In contrast to quasi-steady reconnection with a strong southward IMF, we show that after the impact of a jet on the magnetopause, the magnetopause moves inwards, the current sheet is compressed and intensified and signatures of local magnetic reconnection are observed, showing similarities to spacecraft measurements   

Exploring Kelvin Helmholtz Instability in the Magnetopause and Relativistic Regime

In space and astrophysical plasmas, shear flows upstream of reconnection current sheets may affect the onset of reconnection. For instance, it has been recorded that the evolution of Kelvin Helmholtz instability (KHI) in such shear flows can induce reconnection in the Earth's magnetopause. To better define the criteria for instability of the Kelvin Helmholtz mode in the relativistic regime, several modeling systems were used to explore KHI driven by velocity shear. An ideal MHD solver was developed to recreate the results of Miura (1982) showing the growth rate of the KHI for non-relativistic plasmas. Results from this solver, using plasma parameters collected by MMS in the magnetosphere, were compared to the results which identify KHI in the magnetopause during southward interplanetary magnetic field (IMF) periods. A relativistic kinetic simulation, performed using VPIC software to explore KHI in that regime, has produced results nominally consistent with previous non-relativistic VPIC simulations.   

The Scaling of Electron Heating in Low-beta Reconnection Exhausts with Kinetic Reconnection Simulations

Particle heating in reconnection exhausts is essential to understand the heating in the solar corona, solar flares and the magnetotail. It plays an important role distributing magnetic energy into different species and between thermal and nonthermal components. Previous observational and theoretical studies on electron heating in reconnection exhausts within the beta~1 regime suggest a simple linear scaling where the electron heating is proportional to the magnetic energy per particle. Using kinetic reconnection simulations in the low-beta regime (with beta down to 0.005), we demonstrate that electron heating is subject to a sub-linear scaling below beta~0.01, with or without guide fields. As a result, the maximum heating is limited to only ~5 times of upstream electron temperature. This electron heating scaling may be tested by MMS observations at the magnetotail. This new finding has strong implications for the efficiency of electron heating in reconnection at low-beta environments throughout heliosphysics.   

Exploring the Application of Field-Particle Correlations to Low Time Resolution Data

The Field-Particle Correlation Technique has been shown to successfully utilize single point measurements to uncover signatures of various particle energization mechanisms in turbulent space plasmas. Using this technique, the signature of Landau damping by electrons has been found in both simulations and in situ data from Earth's magnetosheath, but a challenge to discovering the full extent of this mechanism's presence in the solar wind is presented by inherent technological limits in spacecraft sampling rates. Theory predicts that field-particle correlations can recover phase-space energization signatures despite data that is under-sampled with respect to the characteristic frequencies at which electron Landau damping occurs. To test this hypothesis, we perform a high-resolution gyrokinetic simulation of space plasma turbulence, confirm the presence of signatures of electron Landau damping, and then systematically reduce the time resolution of the data to identify the point at which the signatures become impossible to recover. We find initial results in support of our theoretical prediction, and look for a rule of thumb that can be compared with the measurement capabilities of spacecraft missions to inform the process of applying field-particle correlations to low time resolution data.   

1D Solar Wind Simulations Using Cylindrical VPIC

The temperature of the solar wind plasma expanding from the hot solar corona does not decrease with the distance as fast as predicted by the adiabatic expansion law. The non-adiabatic solar wind cooling is a long-standing problem of space plasma physics. In this work we study how weak Coulomb collisions affect the temperature scaling of the isotropic part of the solar wind electrons using Cylindrical VPIC simulations. Cylindrical VPIC is a particle-in-cell code that imposes a B ~ 1/r scaling and has the scattering rates as a free parameter which can be changed independently, hence suitable to perform this study. The isotropic electrons are trapped in a parallel electrostatic potential that holds them back from escaping away from source to ensure quasi-neutrality with the ions. The level of the trapped population is a result of two competing processes- particle influx from the streaming population due to pitch-angle scattering and particle losses due to energy diffusion. The electron temperature was observed to scale with the ratio ν_ee/ν_ei,  as suggested by the collisional model.    

The Role of Coulomb Collisions and Large-Scale Electric Field in Shaping Electron Velocity Distributions in the Solar Wind

The solar wind undergoes an extreme change in collisionality from its base outward to one AU and beyond. In the process of this evolution, the electric field, which necessarily exists to lift the ions out of Sun’s gravitational well, goes from a small fraction of the Dreicer critical field to values that are larger than the twice the critical field. Nevertheless, the solar wind remains quasi-neutral and current free. Such a large electric field and the fact that the plasma profiles below the sonic point have Knudsen numbers not much below unity invalidates traditional transport theory and makes it challenging to obtain an accurate description of the overall energy balance in the solar wind. Furthermore, at the radial distances accessible to spacecraft measurements the velocity distribution function (VDF) of the electrons always shows clear deviations from a simple Maxwellian shape which often present as superthermal halo and a field-align Strahl population. In this contribution we describe our progress in describing the global kinetic structure of the solar wind using a model built around 1d drift-kinetic description that includes gravity, a self-consistent radial electric field to ensure quasi-neutrality, as well as a full Landau collision operator for robust description of the Coulomb collisions across the wide range of energies of interest.   

Second Harmonic emission by a 20keV Electron Beam in a Laboratory Plasma

Understanding the interactions between beams of electrons and magnetized plasmas is a fundamental and practical problem. For example, the Sun regularly ejects highly energetic particles due to unstable magnetic fields of the solar atmosphere. Electromagnetic radiation at the second harmonic of the plasma frequency is a signature of the type III radio bursts. These emissions are of great interest as they serve as probes to study the accelerated electrons and the plasma through which they travel. Presented here is an analysis of the plasma parameters for which second-harmonic waves are emitted by a 20keV electron beam in a magnetized plasma in the Large Plasma Device (LAPD) at UCLA. Emission of the second harmonic is observed by both in-situ probes and by an antenna outside of the plasma. Preliminary results indicated a close-to-simultaneous emission of the second harmonic once an amplitude threshold is met by the fundamental mode.   

Electron-only reconnection in 3D plasma turbulence in the low electron beta regime

A new regime of kinetic-scale plasma turbulence, consisting of inertial kinetic Alfven modes, has been shown to exist in plasma environments with low electron beta (Earth magnetosheath, regions close to the solar corona, etc) [1]. In this work we use spectral code SPS to run a 3D simulation of decaying turbulence in such a plasma environment. We look for indicators of electron-only reconnection, previously found by the MMS mission [2], and identify and characterize a few reconnection sites, expanding on our previous study of 2.5D kinetic-scale turbulence [3|.

Equilibrium of braided flux ropes with helical symmetry

Solar corona loops consist of interwoven braided magnetic strands as observed by the Hi-C Imager [2] and in a new Caltech lab experiment. Braiding and strand-strand reconnection [1] are likely fundamental to loop dynamics. No braided MHD equilibrium model has been reported to our knowledge but would be vital to describe loop evolution. A possible equilibrium is conjectured to be helically symmetric with all strands either having the same J_z polarity or having alternating J_z polarity. Since actual solar corona loops are expected to have net current flowing between footpoints, a plausible presumption is that strands should all have the same J_z polarity. Using the helical JOKF MHD equilibrium [3] we can construct alternating-polarity solutions (i.e., zero net current flowing between footpoints). By combining different JOKF modes, we can also construct net current solutions with the same-polarity flux ropes at the center and reverse current flux ropes at large radius. However, we cannot find same-polarity JOKF solutions. Because of this failure of the JOKF approach, a Biot-Savart-based, multiple wrapped helical wire model is being investigated.

[1] E. N. Parker, ApJ 174, 499 (1972)

[2] J. W. Cirtain et al, Nature  493, 501 (2013)

[3] J. L. Johnson et al., Phys. Fluids 1, 281 (1958)   

Evidence for extended active magnetic reconnection X-lines in three-dimensional plasma turbulence

The nature and role of magnetic reconnection in plasma turbulence has been a decades-long topic. Using a newly developed method based on magnetic flux transport (MFT), we can definitely identify active reconnection in turbulence, both in numerical simulations and in-situ observations of heliospheric plasmas [1,2]. This work demonstrates first evidence of such identification in a three-dimensional (3D) gyrokinetic turbulence simulation. Reconnection takes place in small-scale current sheets formed between turbulent flux ropes as they interact, in the form of flux rope merging, and in elongated current sheets inside flux ropes, which produces smaller-scale flux ropes. Contrary to ideas that reconnection in 3D turbulence would be patchy and unpredictable in nature, spatially extended and regular active reconnection X-lines, extending over the order of the system size, are present. These reconnection X-lines are plentiful throughout the volume. This work has implications on the nature of reconnection in heliospheric turbulent plasmas, including the solar corona and magnetospheres. MFT is applicable to in situ observations by spacecraft missions such as MMS and PSP, and laboratory experiments such as FLARE. 

[1] Tak Chu Li, Yi-Hsin Liu, and Yi Qi, "Identification of Active Magnetic Reconnection Using Magnetic Flux Transport in Plasma Turbulence," ApJL, 909, L28, 2021

[2] Yi Qi et. al. "Magnetic Flux Transport Signatures for Active Reconnection," in prep, 2021   

Analysis of ITER operational space with as-built stiffness of central solenoid modules

The as-built stiffness in the ITER central solenoid (CS) modules (CSM1 and CSM2 are currently manufactured) determines the range of vertical compression forces that can be tolerated by the CS during ITER operation. Analysis of the ITER operational space has been performed assuming that all six CS modules have a conservative stiffness (25GPa) lower than that of CS modules manufactured (~32GPa and ~34GPa for CSM1 and CSM2, respectively). The codes CORSICA and DINA have been used to explore the plasma equilibrium operational space (the plasma internal inductance versus the poloidal magnetic flux produced by the coils) at burn in 15 MA Q = 10 DT baseline scenario. In the studies, the codes used slightly different constraints on the plasma boundary shape. The as-built stiffness of the CS modules has been also used to update scenario of plasma start-up with fully charged CS. The value of poloidal magnetic flux at initial CS magnetization in the updated plasma start-up is 116.2 Wb, slightly reduced from the previously obtained value of 117.5 Wb. 15 MA Q = 10 DT baseline scenario has been re-developed using the DINA code with the updated plasma start-up. In this scenario, the as-built stiffness of the CS modules affects only the plasma initiation. The study of 12.5 MA Q > 5 hybrid and 10 MA Q ~ 5 steady-state scenarios performed with the CORSICA code have shown that these scenarios are well within the CS force limits derived from the as-built stiffness.   

Adaptive Allocation of ITER's External Heating and Fueling with Uncertain Actuator Dynamics for Nonlinear Burn Control

Burn control refers to the real-time regulation of a fusion-producing, or burning, plasma's temperature and density. Due to the plasma’s nonlinear dynamics, active nonlinear burn control will be necessary to sustain burning plasmas in ITER. Using Lyapunov techniques, a model-based, nonlinear, adaptive controller [1] was developed to determine the external heating and fueling required to drive the plasma to desirable regimes. In this work, an adaptive actuator allocation algorithm was designed to optimally map the controller’s heating and fueling requests to ITER's two neutral beam injectors (NBI), ion cyclotron system, electron cyclotron system, Deuterium pellet injector, Deuterium-Tritium pellet injector, and fueling gas injectors. The allocator considers the Deuterium fueling contribution from NBI and the state-dependent (i.e., depends on the temperature and density) fractions of NBI heating deposited in the ion and electron populations. It also considers state-dependent actuator dynamics, such the thermalization delay of NBI particles and the efficiency of the pellet penetration. Adaptive estimators handle uncertainties (e.g., the strength of the fuel recycling from plasma-wall interactions is not precisely known) in the actuator mapping and dynamics.

 

[1] V. Graber, E. Schuster, Proc. Am. Control Conf. (2020).   

Simulations of Effects of Plasma Parameters and Geometry on ITER Performance

The dependence of ITER fusion power production, temperature and density pedestals, and core profiles on varying magnetic-q, edge density fueling strength, neoclassical transport, magnetic field strength, alpha-heating, circular, elongated and general geometries are examined. It should be noted that the quasilinear model used in the simulations stays within the accuracy of 10^-2 of a fully nonlinear approach. Simulations are made with the same model and gridsize over the whole radial profile. It is found that a large edge q tends to provide hollow density while a small edge q gives normal density profile. The rise in the source of the edge particle increases the density of the edge and the reaction rate close to the edge increases temperature fluxes, resulting in weak pedestal barriers. When neoclassical transport is turned off or the strength of B-field is increased, pronounced edge barriers are identified.  The slope of the H-mode pedestal is found to be reduced due to the alpha-heating. In general geometry, there are weaker ETBs, comparable ITBs, but a higher edge particle barrier than in elongated geometry. Higher density near the edge, on the other hand, causes more wall erosion, so elongated geometry might be the best option.    

A Multi-Region Multi-Timescale Burning Plasma Dynamics Model for Tokamaks

Controlled thermonuclear fusion in tokamaks brings forth demands for burning plasma space-time dynamics computations. The deuterium-tritium fusion generates energetic alpha particles in the plasma core, which will collisionally transfer their energies first to core electrons and slightly later to core ions. The heated core electrons will produce electron cyclotron radiation, thereby transferring energy to the edge plasma and wall. The heated core electrons will also collisionally heat core ions on a slightly longer timescale, which can increase the core fusion reaction rate and possibly lead to a thermal runaway instability. Once energy is radiated or transported from the core to the edge, it will be radiated by seeded impurities in the edge plasma. The various timescales of radiation and transport in and among the different regions will determine the dynamics of the plasma. We are developing a multi-region multi-timescale transport model to simulate burning plasma dynamics in tokamaks. The core, edge, scrape-off layer (SOL), and divertor will be modeled as nodes, within and among which internodal transport and radiation will be calculated. The internodal transport times will be computed both theoretically and by comparison with DIII-D experiments. This model subsequently will be extrapolated to simulate ITER fusion plasmas and used to study the possibility of a fusion thermal runaway instability.   

Progress towards a Whole Device Model based on TRANSP

TRANSP [1] is a time-dependent 1.5D equilibrium and transport solver, used for modeling of tokamak plasma discharges and for experimental planning. TRANSP incorporates state of the art heating/current drive sources and transport models, implemented in a solver (PT-SOLVER) that is especially suited to treat stiff turbulence transport. With increasing number of users worldwide and with the upcoming ITER era, TRANSP is facing a new challenge: reducing the computational burden without compromising the physics fidelity. The code is undergoing substantial modernization for improved portability, as well as modularization towards compatibility with the ITER Modeling and Analysis Suite (IMAS) Interface Data Structure. Physics upgrades currently ongoing include MHD stability and Energetic Particle stability calculations and their effect on fast ion transport. A major upgrade of the code is the coupling with the Scrape-Off Layer.

    

Progress towards a modern software engineering approach for TRANSP

TRANSP [1] is a time-dependent 1.5D MHD equilibrium and plasma transport solver for modeling tokamak fusion devices. This software is used by hundreds of scientists at several research centers world-wide for interpreting experimental results, predictive analysis, experimental campaign planning, and rapid between shot analysis. The capabilities of the code has grown significantly over four decades of development, particularly with respect to the physics capabilities. Recently the TRANSP development team has undertaken a significant effort towards modernizing the software engineering approach and underlying software architecture to continue being an effective and reliable tool for the fusion community and to allow integration of more advanced physics models. This poster describes and highlights the efforts made towards this end, including dependency graph analysis, code deprecation, code spin-offs, continuous integration and deployment, containerization for portability, build system improvements, and documentation.   

Ushering the US integrated modeling community into the ITER IMAS era*

The Integrated Modeling and Analysis Suite (IMAS) ontology defines a standard for organizing ITER's experimental and simulation data. To interpret, understand, and exploit ITER's data the US will want to apply its most advanced modeling tools to it. We report on two ongoing software development efforts that work in tandem to address such needs. The first effort targets OMAS [https://gafusion.github.io/omas], an open source Python library designed to facilitate the manipulation of data consistent with the IMAS ontology. OMAS has been extended to enable efficient on-the-fly translation of experimental data to IMAS. The method is being widely applied to DIII-D and NSTX-U data. The second effort targets the physics workflows within the OMFIT [https://omfit.io] framework, which have been adapted to work with OMAS data. Not only are the resulting workflows now machine independent, but they are also compatible with how ITER will store its data. Such developments mark an important milestone towards a wider adoption of IMAS in the US, and the overall readiness of US modeling and analysis tools when ITER becomes operational.   

Near real-time streaming analysis of big fusion data

Fusion plasma diagnostics, such as electron-cyclotron emission imaging

(ECEI) diagnostics, routinely generate fast,

high-dimensional data-streams, typically of the order of Gigabytes per

second. Future devices, like ITER, are predicted to generate

multiple petabytes of measurement data per day. Such large datasets

can not be analyzed manually. Furthermore, interested

parties in the analysis results are scattered around the globe. To

address these issues, we are developing the Delta

(aDaptive nEar-raL Time Analysis framework) - a python framework that

allows to stream measurement data to a remote

compute center, perform data analysis using distributed compute

resources, and display visualizations of the analyzed

data on a web-based dashboard. In this contribution we demonstrate the use-case where we stream ECEi

measurements taken at the KSTAR tokamak in Korea

to the NERSC compute center in California. Using Delta, we achieve a

bandwidth of over 500 MB/seconds and perform

a turbulence analysis of the entire dataset in under 5 minutes. The

analyzed data can be presented in near real-time on a

web-based dashboard. Finally, we discuss how machine learning-based

classifiers can be used in Delta to automatically target data

analysis routines to relevant subsets of the data stream.   

Linear and nonlinear Analysis of Kinetic Ballooning Modes (KBM) with bootstrap current in High-beta Pedestal Plasma

We present the global 3D linear and nonlinear simulation of edge plasma instabilities based on the gyro-Landau-fluid (GLF) model with the BOUT++ framework. The geometry of the input equilibria are shift circular geometry considering the shafranov shift and bootstrap current without X-point. These initial realistic equilibria are generated by a global equilibrium solver CORSICA.

        The linear growth rate spectrum shows the stabilizing effect of the bootstrap current, both the growth rate and the unstable region of the instabilities decrease, and the spectra shift to the low toroidal mode number direction because of the kink drive of the edge current. And the Toroidal Resonance can drive the KBM unstable under the ideal peeling-ballooning threshold. Considering the global effect, we found that even though the system  becomes second stable at peak gradient position, it is still unstable at pedestal bottom and top.

      In the nonlinear simulation, we consider different  and different fraction of bootstrap current. The energy loss with bootstrap current is higher than the cases without bootstrap current. The turbulence with low  is mainly the ballooning dominant turbulence while the turbulence with high  is mainly the peeling dominant. And we have also proved the robustness of the EPED1.6 model well in nonlinear phase by fitting the relationship of pedestal width and height in the steady state.     

Sensitivity analysis of cross-field transport coeffcients with autoUEDGE

Using an autoUEDGE workflow, a large number of UEDGE simulations were performed to systematically examine the effects of various simulation parameters and assumptions on interpretive transport results.  Edge simulations codes such as UEDGE are regularly used to study SOL and divertor topics. However, important parameters, such as recycling and neutral density, in the tokamak edge are often not fully diagnosed, and are often assumed based on previous studies when they are not the focus of the current experiment. The automatic interpretive UEDGE workflow, autoUEDGE, has been upgraded by improving its accuracy in modeling the divertor, as well as adding cross-field drifts. This has enabled the workflow to robustly produce simulations approximating the accuracy of expert-made simulations automatically. This ability is used to perform systematic scans of past DIII-D experiments, to examine sensitivities and uncertainties. Some parameters considered includes neutral density, neutral density asymmetry, T_e,sep and T_i,sep, recycling rates, electron/ion power ratio. Neutral density and asymmetry are found to be under-constrained but important for divertor region.   

The First Tokamak Plasma Testing of Single-Channel Fiber Optic Bolometers at DIII-D

A novel bolometer utilizing fiber-optic based interferometry to measure radiated power was successfully tested on a tokamak for the first time at DIII-D. The fiber optic bolometer (FOB) avoids electromagnetic interference (EMI) using a Fabrey-Pérot resonator system to encode small temperature changes related to the incoming power. Off-line impulse-response calibration using a laser source is used to characterize the frequency response of the FOB and provides a means of solving for the radiated power by deconvolution. The FOB response during operations at DIII-D was compared with off-line results and DIII-D resistive bolometers. The FOB showed no increase in noise during operations (0.29mK) compared to the benchtop result (0.30mK) showing that FOBs do not suffer from EMI in a fusion environment. The absolute values of plasma brightness from the FOB matched the values calculated from the resistive bolometers in time through plasma discharges. The brightness was compared to the average brightness of two resistive bolometers with a similar path length and the back-calculated brightness from the tomographic reconstruction of resistive bolometers.   

Not Participating

Over the next several years, the operational space of two novel RF actuators designed for off-axis current drive will be extensively explored in the DIII-D tokamak. The goal of these programs is focused on evaluating the potential for efficient current drive in advanced tokamak scenarios. Previous experimental work on C-Mod and NSTX has determined that wave coupling with the scrape-off-layer (SOL) plasma can result in substantial core power loss. However, recent computational studies indicate that the SOL plasma can be optimized to minimize the undesired wave/SOL-plasma coupling. A diagnostic based on Doppler-free saturation spectroscopy (DFSS) was designed for direct measurement of the wave’s electric field vector (E_RF) in the edge plasma of DIII-D. The DFSS diagnostic was designed to provide a local measurement over a 2-D region with mm-scale spatial resolution and <10 V/cm electric field resolution. In this presentation, the DFSS diagnostics design and installation status will be presented.   

Non-parametric inference of impurity transport coefficients in the ASDEX Upgrade tokamak

 Controlling impurity ions is a critical requirement for a fusion reactor. Impurity accumulation in the core region dilutes fuel and radiates away power. However, a proper amount of impurity is likely to be required in the edge region in order to mitigate the heat load on the plasma facing components.

   The transport properties of impurity ions are often experimentally characterized by using a diffusion coefficient D and a convection velocity v. Since the realistic experimental setups usually necessitate the determination of D and v under ill-posed conditions, rigorous comparisons between simulations and experiments cannot be made without addressing the model selection and uncertainty estimation problems. To this end, the Bayesian formalism has been applied to the impurity transport studies in recent years.

   In this work, transport coefficients of light impurities (Ne, O, and C) in a Type-III ELMy H-mode plasma are inferred by using a non-parametric approach. Unlike spline functions, the non-parametric inference does not reduce the degrees of freedom for representing spatial profiles. Thus, all solutions that are consistent with the measurements and the prescribed smoothing conditions can be calculated. We report the D and v profile measurements from rho_pol=0.6-1.0.   

Not Participating

The mechanisms that drive toroidal rotation in torque-free tokamak plasmas have not been clearly identified, but the generation of intrinsic torque by turbulence via Reynolds Stress is a leading theoretical mechanism. Beam Emission Spectroscopy (BES) results from previous experiments on HL-2A L-mode plasmas exhibit a poloidal velocity reversal at $\rho \approx 0.7$. The poloidal velocity switches direction across the profile despite the only external momentum being input from a co-current neutral beam, suggesting that either the momentum is redistributed through transport, or a significant amount of intrinsic rotation is generated. To investigate this velocity reversal, experiments with varying temperature and q profiles will be performed and 2D density fluctuation data will be measured with BES. Spectral and correlation analysis are applied to derive spatiotemporal characteristics of turbulence. Velocimetry analysis is applied to obtain a 2D fluctuating velocity field and the derived Reynolds Stress. These BES results combined with other diagnostics will be used to predict the dominant instabilities, estimate the turbulent transport, and derive the intrinsic torque.   

Gyrokinetic modelling and experimental comparisons of radial correlation and time delay Doppler backscattering measurements in JET.

Radial Correlation Doppler Reflectometry (RCDR) [1] is routinely used to extract the radial correlation length of the underlying turbulence by cross-correlation of neighbouring Doppler backscattering signals (DBS). An evolution to RCDR using cross-correlation-time-delay estimations has recently been used to characterise the tilt-angle of turbulent eddies in the perpendicular direction to the background magnetic field [2]. We present a conceptual study of radial correlation and time delay measurements using nonlinear gyrokinetic simulations from GYRO [3] and GS2 [4] based on experimental NSTX H-mode and JET L-mode discharges. A linear response, local synthetic model for the DBS signal applied to gyrokinetic simulation output shows that DBS measurements are not sensitive to the real turbulence radial correlation length, but to the scale-dependent correlation length corresponding to the selected binormal wavenumber k_⊥. Nonlinear gyrokinetic simulations show that the turbulence naturally exhibits a power-law dependence of the radial correlation length with binormal wavenumber l_r ~ k_⊥^-α (α ~ 1), which may partly explain recent radial correlation length measurements [5]. The radial correlation length is only measurable when the radial beam dimension at the cutoff location W_n satisfies W_n << l_r, likely only satisfied for ion-scale measurements (k_⊥ρ_i ≤ 1). Initial measurements of the radial correlation length, eddy aspect ratio and eddy tilt angle are presented for the sweeping frequency Doppler backscattering system at JET, as well as comparisons to the model predictions. [1] Schirmer PPCF 2007, [2] Pinzón PPCF 2019, [3] Candy JCP 2003, [4] Kotschenreuther CPC 1995, [5] Fernández-Marina PPCF 2014.   

A tangential Upper View Bolometer for DIII-D

Measuring total radiated power in tokamak divertors is important for understanding divertor performance, in particular how changes in the divertor impact power balance. A new tangential Upper View Bolometer (UVB) installed on DIII-D provides views into both the ceiling and Small Angle Slot (SAS) divertors. Tangential lines of sight into these two upper closed divertors fill in gaps in radiated power measurements from existing radial bolometer arrays. The SAS requires sub-cm alignment of 3-m-long viewchords; we used a light source on a robotic arm to confirm chord alignment and perform spatial calibrations. UVB measurements in the ceiling show the chord-integrated radiated power increase by a factor of 2-4 at detachment onset. The first power measurements in the SAS show an increase of 3-4 in chord-integrated radiated power at detachment onset, with similar radiation in shots with main-chamber vs in-slot gas puff fueling. These initial measurements with the new UVB foil detectors show a faster response time, with ELMs resolved, and higher signal-to-noise ratio than the radial foil bolometers. Upgrades in 2021 will add chords and increase the temperature limit during vessel bakes.   

Impact of divertor closure on the path to complete detachment

Recent experiments on DIII-D have shown that divertor closure has a weak impact on the deeply detached state, where the divertor ion flux is reduced to a small level. Tests used a) a flat, open divertor geometry, b) a flat geometry with nearby baffling, and c) a tightly baffled geometry. The degree of closure impacts the onset of detachment, with changes of ~25-35% in the line-averaged density at which roll-over of the divertor ion saturation current (I_sat) is observed, consistent with previous results. When the divertor is pushed into deep detachment, the different divertor configurations are observed to behave similarly, with strong radiation localized near the X-point, highly reduced divertor ion flux profiles, and high divertor neutral pressure. All configurations also show a reduction in confinement (~20%) when deeply detached, although confinement is higher prior to detachment with more closed divertors. The more closed divertors show increased ratio of divertor to midplane to neutral pressure, indicating that closure can aid pumping even in highly detached conditions. The deeply detached state was not observed when the toroidal magnetic field was reversed, with back-transitions out of H-mode observed prior to strong I_sat reduction or clearly localized X-point radiation.   

A dissipative small-angle slot divertor for DIII-D high triangularity and low radius plasmas

A numerical assessment using SOLPS-ITER is presented of a new dissipative divertor for DIII-D high triangularity and low radius plasmas in the upper single-null configuration, with and without drifts. Sequential modifications to the DIII-D upper divertor are planned to explore a series of missions. Initially, the divertor will remain short to maximize the plasma volume for advanced tokamak scenarios. Later, it will be replaced by a dissipative divertor for power exhaust optimization. This contribution discusses a design for the second phase. To minimize divertor leakage of neutrals and impurities, the proposed design features tight wall baffling on both the private and common flux sides. Several slot shaping options are explored to minimize electron temperature, and thus erosion, across a large fraction of the SOL. These include a symmetric V-target (as in the SAS-V divertor now installed on DIII-D) and a progressive increase of the SOL target angle (as in the SAS divertor, formerly installed). To characterize the transition to divertor detachment, modeling is performed for a range of plasma densities and input powers, using in-slot pumping for particle control.   

Predictive modeling of a slot divertor in high triangularity double null magnetic topology using SOLPS-ITER

Simulations of double null divertor detachment reveal up/down power flow asymmetry due to the impact of divertor closure on the convected heat fraction in each divertor. Here, an assumed upper V-shaped divertor and a lower open divertor in DIII-D are investigated numerically using the SOLPS-ITER code [1] to predict closed divertor conditions and to study particle and heat balance. The simulations employ a symmetric double null magnetic topology with high triangularity ($/delta = 0.87$) to be used in DIII-D’s initiative for increased volume and plasma shaping. Boundary input power is 4 MW and upstream electron density is scanned around a nominal value of $10^{19}$ m$^{-3}$. Both conducted and convected heat fluxes flow toward the lower horizontal target. For the upper slot divertor, conducted heat flows into the slot as expected; however, convected heat flows out of the slot and is carried mainly by electrons. This heat flux reversal causes an asymmetry in the power entering the upper slot and lower divertors. A similar heat flux reversal is observed at the entrance to the slot divertor in single null simulations [2].

[1] X. Bonnin et al., Plasma Fusion Res. 11, 1403102 (2016).

[2] R. Maurizio et al., this conference.   

Interpretive Modeling of Pumping Experiments in DIII-D and Comparisons to Measurements using SOLPS-ITER

Using SOLPS-ITER to model H-mode experiments in the closed upper divertor of the DIII-D tokamak, downstream plasma conditions are found to be critically dependent on neutral pathways, including particle sources and sinks. Upstream plasma profiles are matched to Thomson scattering and charge exchange measurements by iteratively modifying the radial transport coefficients, while core particle and energy source rates are taken from the experiment. Resulting downstream plasma profiles generally do not match those measured using Langmuir probes without modification of core particle flux from experimental values. Cross-field drifts are not yet included in the calculations, but adding them would be expected to push the modeled results in the direction of the measurements in attached conditions. When downstream plasma conditions are matched to experiment, modeled divertor neutral pressures compare more favorably with pressure gauge measurements.   

Understanding the impact of divertor configuration on neutral leakage and main-chamber recycling in DIII-D

Neutral Leakage (NL) estimated using Window-Pane (WP) analysis in different divertor geometry shows that open divertor produces more neutral particles compared to others. Previously, particle flux density (I_wall) was calculated using a single embedded probe in an axisymmetric surface of main chamber wall, called the window frame (WF). I_wall was estimated using the fitted radial decay length of neutral particle flux density using the probe. Here, a modified version of the WP analysis is used to calculate I_wall using three diagnostics in the WF: high resolution radiometer – Filterscope, pressure gauge and Langmuir probes. NL is calculated as the ratio of I_wall to neutral particle flux received at divertor plate (I_div). This ratio compares unique divertor geometry and its impact on NL over a range of discharge conditions. It also takes into account the conservation of particles in the WF. Higher NL causes main chamber recycling which leads to surface erosion and production of impurities. Estimating NL improves the understanding of neutral dynamics, particle sourcing and particle control system efficiency for DIII-D and future tokamaks.   

Near SOL profiles in DIII-D H-mode plasmas

Near SOL plasma profiles (≤ 1cm outside the midplane separatrix) in DIII-D H-mode are found to be narrower than expectations from parallel transport and ideal MHD stability models. The narrow SOL profiles are accurately resolved with the DIII-D high resolution edge Thomson scattering diagnostic. The midplane T_e profile is ~30% narrower than would be expected from dominant electron conductive heat transport for both the divertor measured heat flux profile and the heat flux width empirical scaling. Comparisons with modeling from UEDGE and BOUT++ suggest this can be attributed to plasma poloidal drifts dominating the energy transport into the divertor. While the narrow profiles broaden at high density conditions, the radial pressure gradient near the separatrix can exceed the ideal MHD ballooning limit by as much as a factor of two. Sensitivity to assumptions of separatrix location and the ion pressure contribution is also examined. Explanations for the excessive pressure gradient are explored with BOUT++ modeling including plasma flow shear and finite resistivity.  Reconciliation of the measured SOL profiles with the most sophisticated models increases confidence in using these tools to project boundary solutions in future devices.   

Role of geometry and drifts on particle exhaust and detachment in DIII-D

Experiments demonstrate the impact of divertor geometry and cross-field drifts on particle exhaust and detachment with cryopumping: the exhaust rate in attached plasmas is higher with the ion B×∇B drift out of the divertor whereas the exhaust rate in detached plasmas is higher with the opposite drift direction. The upper divertor on DIII-D has the flexibility of flat, vertical and tight-private baffled configurations that provide trade-offs in neutral compression, detachment onset and pumping rate. In cases where the divertor is driven deep into detachment, neutral compression is maintained indicating divertor baffling can effectively trap neutrals, albeit with decreasing core confinement. Divertor conditions are modified by the B×∇B direction (change in compression, pumping rate, resulting pedestal density), but ultimately result in similar confinement, offering some flexibility. The drift direction can lead to a strong inner/outer exhaust imbalance in certain conditions: the inner cryopump can exhaust up to 10X more particles than the outer pump in single null configurations with the B drift direction into the divertor when both targets are in a high recycling regime.   

Role of radiative heating and neutrals in surface heat flux during detachment in the DIII-D small angle slot divertor

Data from surface eroding thermocouples (SETCs) in the DIII-D Small Angle Slot (SAS) divertor suggests that neutrals and radiative heating may contribute significantly to surface heat flux in the approach to detachment. Divertor detachment is one of the most promising ways to reduce heat flux at the divertor target through increased energy dissipation in the boundary region. It is widely observed in an open divertor that gas puffing is beneficial to power dissipation. However, the peak heat flux measured by the SETCs in the closed SAS divertor has been found to continuously increase at the beginning of a density ramp up induced by D₂ puffing while the T_e measured by Langmuir probes simultaneously decreases. The heat flux measured by SETCs near strike point in SAS divertor was higher than it inferred by Langmuir probes in the full detachment plasma while T_e was lower than 5 eV.  This evidence implies that radiated power and neutrals may be playing an important role in a closed divertor where the volume is relatively small and the neutral confinement is good compared to an open divertor, especially during detachment. A new set of recessed probes will be established to quantify these processes in a dedicated manner.   

A high resolution VUV spectrometer for study of radiated power in the tokamak divertor

A high resolution (HR) vacuum ultraviolet spectrometer with sub-1 Angstrom optical resolution has been designed, installed, and successfully operated on the DIII-D tokamak for study of the power radiated by emission lines and molecular bands at VUV and UV wavelengths in the divertor. The HR-VUV diagnostic was utilized in plasma discharges spanning the attached to fully-detached divertor regimes, revealing trends in the carbon ion and neutral deuterium emissions. Capable of monitoring the 110-600 nm range, the instrument is designed with a 445 mm focal length in a Czerny-Turner configuration with Al/MgF₂-coated mirrors and VUV-optimized gratings and a VUV-phosphor-coated detector. It is enclosed in a lightweight 316-stainless steel vacuum vessel for low magnetic permeability to operate near the machine magnetic field. The spectrometer includes three gratings to provide both survey (~50 nm bandwidth) capability as well as narrow, high resolution (<10 nm) capability for study of nearby emissions and molecular band structure. Data from the diagnostic and the impacts of radiation on the unshielded camera will be shown, as well as future improvements discussed.   

Electron temperature fluctuations in DIII-D divertor

For the first time electron temperature (T_e) fluctuations have been measured using a novel probe-based T_e fluctuation diagnostic with a bandwidth of 100 kHz in different regions of a tokamak divertor, revealing comparable levels and spectral characteristics to T_e fluctuations in the outboard scrape-off layer (SOL) under low density attached L-mode conditions. In most cases the relative T_e fluctuation levels in the divertor were between 0.2 – 0.6, comparable to those in the outboard midplane SOL. T_e fluctuation spectra had measurable energy up to the bandwidth of the diagnostics (100 kHz) and were rather similar in both regions at low density, while frequency roll-off was faster in the outboard midplane SOL at higher density. In the private flux near the divertor leg the maximum of T_e fluctuation energy is shifted towards lower energies compared to the adjacent SOL. The data suggests that turbulence originating upstream propagates to the divertor SOL under attached conditions. This new diagnostic provides a critical tool for validation of turbulence theory and codes in a diverted plasma configuration.   

Preparation of the Wisconsin In-Situ Penning (WISP) Gauge for the SAS divertor at DIII-D

The Wisconsin In-Situ Penning (WISP) gauge is a neutral pressure diagnostic developed at the UW-Madison to measure partial pressures in tokamak divertors. Augmented with spectroscopy, the WISP can determine the fractional neutral pressures of recycling impurities, including hydrogen, helium, neon and nitrogen. The in-situ design allows operation within the tokamak toroidal field behind the divertor baffle, substantially reducing neutral transport latency that determines the timescales of ex-vessel gauges. The WISP is designed to operate above 1 mTorr; higher total pressure than most other such gauges. It meets the criteria to survive the bake and the measurement requirements of the Small Angle Slot (SAS) divertor. It has recently been tested to diagnose pressures to 50 mTorr, with additional improvement under development. Qualifying work on an array of photomultiplier tubes (PMTs) and digitizer is also underway for the installation in DIII-D later this year. The WISP represents a significant advance to aid divertor neutral density measurements in high-pressure, impurity-containing regions behind the SAS divertor tiles and adds a capability to characterize local impurity concentrations in seeded detachment experiments.   

Spectroscopic observations of carbon transport in the near scrape-off layer following controlled axisymmetric injection of methane in DIII-D

Recent experiments in DIII-D have provided charge-resolved spectroscopic measurements of long-range transport pathways for impurities sourced in the outer divertor. Isotopically-enriched methane (13CD4) was injected from axisymmetric gas baffles into the outer divertor of attached L-mode plasmas, as a proxy for intrinsic impurities sputtered from the divertor target. Experiments were repeated at injected power levels ranging from 2.4-4.5 MW, which led to moderate changes in temperature in the near scrape-off layer (SOL). Results are presented from an array of spectroscopic diagnostics, tracking changes in C-II, C-III, C-IV, C-V, and C-VI emission in both the divertor and upstream SOL. A key finding was a strong increase in C-V emission in the upstream SOL during the puff, indicating long-range transport of the injected impurities. A collisional-radiative model is used to decouple changes in photon emission coefficients from changes in C densities, and the derived tracer carbon densities are compared to models that predict enhanced SOL impurity buildup in the presence of larger parallel temperature gradients. This experimental database will be utilized to benchmark models for SOL impurity transport and divertor leakage.   

Effectiveness of ELM mitigation techniques in reducing intra-ELM and inter-ELM tungsten erosion rates in DIII-D

We analyze ELM erosion that occurred to tungsten (W)-coated tiles installed in DIII-D during the Metal Rings Campaign (MRC) using WI filterscopes and Langmuir probes [1]. This study assesses the effectiveness of three ELM mitigation techniques used in attached plasma conditions: QH-mode plasmas, D₂ pellet injection, and resonant magnetic perturbations (RMPs). Most notably, QH-mode plasmas during the MRC avoided ELMs and reduced total W divertor erosion rate by 18% when compared to an ELMy H-mode plasma, and increased core stored energy by 20%. Fast pellet pacing at 60 Hz and no pellet injection resulted in a similar total W erosion rate, but injection at 60 Hz reduced the average erosion per ELM and fractional carbon impurities at the top of the pedestal by 47% and 36%, respectively. While RMPs had no conclusive effect on erosion, results show that higher injected powers correlated with more erosion. On average, simulations of intra-ELM erosion predicted by the ‘free-streaming plus recycling model’ (FSRM) [1] overestimate experimental measurements of intra-ELM W erosion during RMPs by a factor of 2 and underestimate W erosion during pellet injection by a factor of 0.5. The reasons for these discrepancies may have to do with a mixed-material C/W layer on the W tiles.   

Commissioning of a UV Spectrometer on DIII-D for Tungsten Erosion & Re-deposition Measurements

A new high-resolution and high-throughput spectrometer optimized for ultraviolet wavelengths is being installed on DIII-D  to resolve the most promising W line radiation arising from erosion during W sourcing experiments in the divertor. Spectral surveys between 200 and 400 nm have identified over 60 neutral and singly ionized W emission lines. These lines, combined with atomic predictions, allow for the determination of net erosion and re-deposition rates of W via the ionizations/photon (S/XB) method. Simultaneously monitoring multiple W emission lines is required to determine the W metastable level populations in order to accurately characterize erosion and re-deposition rates. The new UV spectrometer has a maximum resolving power of 0.16 Å at 250 nm with better than 1 kHz temporal resolution. Initial measurement calibrations will be presented with the spectrometer located inside of a shield box on the top of the tokamak and fiber-coupled to collection optics.   

Spectroscopically diagnosing gross tungsten erosion using time-dependent collisional radiative modeling

Improved diagnosis of tungsten gross erosion can be achieved with improved predictions of atomic rate coefficients and time-dependent collisional radiative (CR) modeling in combination with high-resolution ultraviolet spectroscopy. A CR model accounting for time-dependent effects due to the inclusion of a magnetic sheath at the plasma boundary is developed. CR coefficients for tungsten erosion measurements can be modified by up to a factor of ten by a sheath at ITER relevant conditions. Comparisons of electron temperature inferred from CR modeling and Langmuir probe measurements are in good agreement for Compact Toroidal Hybrid (CTH) plasmas suggesting the atomic data and CR modeling of neutral tungsten is accurate. Due to the importance of determining the effects of metastable levels on spectroscopy, CR modeling using ColRadPy is employed to analyze the impact of metastable states on tungsten emission and ionization. A technique for measuring non-steady state (time-dependent) metastable populations is presented using W I spectral lines around 260 nm. A high-resolution UV optimized spectrometer has been commissioned on the CTH experiment and the tungsten spectra are compared to modeled spectra using W I R-matrix excitation data.   

An update on atomic data for the low charge states of W for use in simulation codes and erosion/redeposition diagnostics

Spectroscopic techniques to measure gross and net erosion for tungsten plasma facing components require accurate atomic data. A brief review is given of the available atomic data for neutral W. Spectral comparisons of electron temperatures diagnosed from W I line ratios in the Auburn Compact Toroidal Hybrid (CTH) experiment agree favorably with Langmuir probe measurements. In support of tungsten redeposition experiments and model validation activities at DIII-D, a new R-matrix calculation for electron impact excitation of W⁺ has been completed and good agreement is also found with spectral observations from the Auburn CTH experiment. A significant number of W II lines are identified at ultra-violet wavelengths that could be useful for redeposition studies. The role of metastable levels in W⁺ is also discussed and plasma conditions are identified where their populations must be modelled time-dependently.   

The Role of Heating Power in Tungsten Transport to Collector Probes in the Scrape-off Layer of DIII-D

Modeling results are presented for scrape-off layer (SOL) transport of tungsten (W) sputtered from the DIII-D divertor for two discharges differing by twice the heating power, P_heat. Results show that W deposition on a collector probe at the outer midplane (OMP) increases with P_heat due to a combination of increased physical sputtering and enhanced SOL transport, in particular the radial and parallel transport near the divertor. Two H-mode discharges in the 2016 DIII-D Metal Rings Campaign had similar plasma conditions and magnetic geometry, but differed mainly by a doubling of P_heat and ELM frequency. An OMP collector probe measured significantly more W for the higher P_heat shot, with most of the additional W on the side facing toward the outer target along the magnetic field (the outer-target-facing (OTF) side). Spectroscopic sourcing data from a WI emission line showed significantly more sputtering for the higher P_heat shot. Each discharge was simulated using the OEDGE code package. The simulated transport of W ions showed that enhanced SOL transport between the divertor target and the OTF side of the collector probe is consistent with the observed deposition patterns.   

Modeling of Tungsten Transport in the SAS-VW Divertor with Mixed-Impurity Plasmas

A new workflow has been developed to model tungsten sourcing and transport in DIII-D that provides a more realistic treatment of multiple impurity species using the SOLPS-ITER and DIVIMP codes. New sputtering source routines are being developed for DIVIMP to directly read in all available impurity data from SOLPS-ITER when calculating the tungsten source. This presentation will demonstrate these new routines to model tungsten transport in the new V-shaped Small-Angle Slot divertor of DIII-D with tungsten-coated plasma-facing components (PFCs), SAS-VW, at various rates of nitrogen seeding. The SAS-VW geometry has been specifically designed to improve the control of neutral particles in the divertor, including to minimize impurity leakage, enabling experiments to address important questions about the sourcing and transport of tungsten in a closed divertor geometry.  These new results will expand upon recent work that predicts a tradeoff between tungsten accumulation and nitrogen seeding and suggests the existence of an optimal seeding rate to minimize overall impurity contamination in the core.   

Real-Time Wall Conditioning Experiments in the Wide Pedestal QH-Mode Regime

Wide Pedestal QH-Mode (WPQH-Mode) in DIII-D is an intrinsically non-ELMing enhanced confinement regime (H_98y2 up to 1.6) with a higher and wider pedestal regulated by broadband turbulence. Compatibility with future burning plasma conditions includes zero net NBI torque throughout and up to 77% electron-cyclotron heating without degradation. Previous studies show core impurity transport is favorable in WPQH-Mode. However, carbon content is higher than ELMy H-Modes, possibly due to increased carbon sputtering from high boundary temperatures or pedestal transport. Here, controlled injection of boron and lithium powders at measured rates during WPQH-Mode discharges successfully reduced carbon concentrations during injection without degrading confinement. Boron resulted in a cumulative wall conditioning effect. Nitrogen injection was particularly effective in reducing carbon content while radiating from the divertor. Densities of carbon, boron, lithium, and neon were measured by charge exchange recombination spectroscopy. Lithium in the upper divertor was observed by tangential TV camera. Divertor heat flux profiles comparing Standard and Wide Pedestal QH-Mode within the same discharge were measured by Langmuir probes and IR cameras using strike point sweeps.   

Comparison of DIII-D and AUG pedestal ballooning stability during 3D magnetic perturbations

Recent work has shown the importance of local 3D magnetic geometry on the stability of localized MHD ballooning instabilities in the presence of applied 3D magnetic perturbations in ASDEX Upgrade plasmas[1]. In this work, we extend this analysis to DIII-D discharges with ASDEX-like plasma shaping. While the 3D localized instabilities of [1] have been observed in the ECE signals for these DIII-D discharges, the instabilities appear to be less prevalent than expected when comparing to the similar AUG discharges. To better understand this discrepancy, we utilize VMEC to construct 3D MHD equilibria associated with comparable DIII-D and AUG discharges with applied 3D magnetic perturbations, and analyze the infinite-n ballooning stability of these equilibrium using the PYBALLOON code. We compare both the ballooning stability and local 3D magnetic geometry of the two experiments, considering the strength of the magnetic perturbations and plasma response, 2D plasma shaping, and error field effects. Additionally, benchmarking results between the PYBALLOON and COBRA codes are presented. [1] T.B. Cote et al., Nucl. Fusion. 59 (2019) 016015.    

Density propagation and triggering of ELMs following pellet injection in DIII-D Plasmas

New observations have been made on DIII-D of pellet ablation striations from high field side (HFS) and low field side (LFS) injected D2 and H2 pellets leading to density pulses with soliton like structure propagating along field lines in both directions from the ablation location.  Previously, density pulses observed to be propagating along field lines from HFS injected pellets were in plasmas with q95 = 6.  Now pulses have also been observed from HFS and LFS pellets at lower more ITER like q95 = 3.6.  Despite the ExB drift of pellet mass in the major radius direction and the triggering of ELMs, there are some cases of LFS injected pellets showing this field line  propagation effect.  The summary of density pulses and triggering of ELMs observed thus far are presented along with a comparison with the dynamics of density propagation predicted using the Pellet Relaxation Lagrangian code.  Implications for refining pellet deposition fueling models and the triggering of ELMs in large burning plasmas are discussed. 

 

 

Radiative Impurity Impact on 2D Inter-ELM Pedestal Fluctuation Measurements on DIII-D

Localized 2D measurements of low-to-intermediate wavenumber density fluctuations in the H-mode pedestal reveal a range of broadband modes that vary temporally and spatially during the inter-ELM cycle. Neon injected to radiate power significantly increases turbulence in the range of 50-300 kHz near ρ = 0.95, demonstrating a strong Z_eff and/or collisionality dependence.  These measurements are obtained with Beam Emission Spectroscopy and a new higher radial resolution (ΔR ~ 0.4cm) multichannel Charge eXchange Imaging (CXI) prototype diagnostic. Fluctuation characteristics will be presented as a function of collisionality and impurity density, which have been predicted to impact the growth rate of microtearing modes (MTM) and other pedestal-localized instabilities. A future optimized CXI diagnostic will measure carbon density fluctuations across the pedestal with higher sensitivity and complement the Beam Emission Spectroscopy (BES) system, which is limited to about 1 cm radial resolution. Simulated pySTRAHL and pyFIDASIM results confirm the enhanced spatial resolution of CXI and are being used to understand the origin and magnitude of electron impact and neutral charge exchange emission.   

Direct Measurements of Thermal Neutrals and their Impact on Particle Source Rates Using Spectrally Resolved Balmer-Alpha Measurements on DIII-D

Charge exchange between thermal ions and edge neutrals transfers energy and momentum between the populations giving rise to thermal neutrals with energies approximating the ions in the pedestal region. The increased mobility of these neutrals allows them to penetrate deeper into the confined plasma providing fueling inside the pedestal top. Spectrally resolved D-α measurements from a 16 ch edge main-ion CER system confirms the presence of these thermal neutrals. Spectral discrimination allows the measurement of thermal neutral densities inside the confined plasma while largely avoiding tomographic inversion challenges due to bright cold emission from the scrape off layer, which is not Doppler broadened. The FIDASIM code provides a forward model of the measured spectrum and allows the underlying neutral densities and localized ionization/source rates to be calculated. The spectra are accurately reproduced and the simulations show 40% of the radially integrated ion source located inside the pedestal top at the measurement location, largely due to the thermal neutrals. These results will be supplemented with more detailed neutral modeling using DEGAS2 and EIRENE and comparisons to 2D measurements based on a Ly-α emission using the recently installed LLAMA diagnostic.   

Pedestal confinement degradation in DIII-D ELMy H-mode plasmas with density ramp

In a DIII-D ELMy H-mode experiment with closed (small-angle-slot) divertor, as line-integrated electron density is increased by gas injection, electron pressure at the pedestal top and its gradient in the pedestal decrease, accompanied with increase of collision frequency υ_e. Experimental pedestal pressure p_exp agrees with EPED prediction p_eped at low υ_e but is below p_eped as υ_e increases. The ratio of p_exp and p_eped correlates with υ_e as p_exp/p_eped∝υ_e^-0.38. Two branches of low-k (k_θρ_s~0.1) magnetic and density fluctuations are detected by Faraday-effect polarimeter and Beam-Emission-Spectroscopy (BES) in the pedestal, respectively, one at low frequency (3-7 kHz) propagating in ion diamagnetic direction while the other at high frequency (200-500 kHz) propagating in electron diamagnetic direction. Fluctuation amplitudes for both branches increase as υ_e increases and pedestal degrades. The high-frequency branch has been identified as micro-tearing-modes [1] while the low-frequency branch is found consistent with kinetic-ballooning-modes [2], both of which can be destabilized by collisions. These observations indicate collision-destabilized turbulence may be critical to explain the pedestal degradation.

[1] Phys. Plasmas 28, 022506, 2021

[2] APS DPP 2020, TP15.015   

FIDASIM modeling of edge current density measurements to be performed using a new high-performance spectrometer at DIII-D

Motional Stark Effect spectroscopy is a well-established technique that allows for measurement of the magnetic field structure and plasma current distribution based on the Doppler-shifted and Zeeman-split n=3-2 emission of collisionally excited hydrogenic neutral beams. We show a design study for fast edge-current density measurements based on high-throughput, high-spectral-resolution spectrometers at DIII-D. The diagnostic setup uses an existing light collection system used for BES turbulence measurements near the edge-pedestal region that offers high spatial resolution and photon throughput. Our spectrometers utilize echelle gratings which provide excellent spectral resolution for resolving the sigma and pi lines of the beam emission, and a cooled EMCCD array with high quantum efficiency and a sampling rate of up to 10kHz. FIDASIM simulations predict a spatial resolution of less than 1cm and a sensitivity to changes of the poloidal magnetic field of 3mT. This will allow studies of the edge pedestal and ELM induced current redistribution.   

HBT-EP program: MHD dynamics and active control through 3D fields and currents

The HBT-EP active mode control research program aims to: (i) understand the physics of scrape-off layer currents (SOLC) and interactions between the helical plasma edge and conducting boundary structures, (ii) test new methods for measurement and mode control that integrate optical and magnetic detector arrays with both magnetic and SOLC feedback, and (iii) understand fundamental MHD issues associated with disruptions, resonant magnetic perturbations, and SOLC. A two-color multi-energy EUV/SXR tangential array has been used to study internal MHD mode structure and tearing mode dynamics. A biased electrode was used to induce a strong layer of sheared ExB flow to achieve H-mode plasmas with edge turbulence dominated by the ion temperature gradient mode extending previous findings of EAST and TCABR. Disruption dynamics and current paths in the SOL and the vacuum vessel have been studied, and a model developed for the MHD mode rotation frequency after the current quench phase. Stable non-disruptive operating space boundaries in HBT-EP have been mapped using a variational autoencoder neural network with a reduced dimensional representation. GPU active control system improvement is being pursued using tomographic reconstruction and improved basis function representation of the poloidal EUV emissivity for adaptive mode suppression.   

Enhancement of the gradient in the Reynolds stress due to applied shear flow on HBT-EP

A detailed understanding of the interaction between shear flow, which suppresses turbulence, and the generation of flow via the Reynolds stress is critical for elucidating the L-H transition dynamics on magnetic confinement devices. To this end, a systematic analysis of the edge turbulence on HBT-EP reveals that when shear flow is applied via a biasing electrode, the gradient in the Reynolds stress at the last closed flux surface (LCFS) is enhanced. The measurements indicate that under biasing, the Reynolds stress increases in a radially varying manner inside of the LCFS, while the Reynolds stress is reduced outside the LCFS. This reduction stems from the strong suppression of turbulence by the E×B shear flow in the scrape-off layer. The resulting Reynolds force is found to be comparable to the J×B force from the biasing electrode current. The connection between the Reynolds stress enhancement inside the LCFS and the anisotropization of the turbulent eddies due to shear flow will be discussed. The detailed edge turbulence measurements in this study are facilitated by the deployment of a novel rake probe array, which allows for the simultaneous acquisition of spatially and temporally resolved Reynolds stress information.    

Tearing mode structure study using tangential EUV/SXR diagnostic system on HBT-EP tokamak

Measuring and analyzing the intensity of the extreme ultraviolet (EUV) and soft x-ray (SXR) is an effective way to study the internal characteristics of MHD mode structures, including the temperature profiles. We present the progress on the two-color multi-energy EUV/SXR diagnostic system in the HBT-EP tokamak. This system includes a filter wheel with five different groups of dual-filter structure. By using a combination of 100 nm Aluminum and 200 nm Titanium filters with identical plasma views and two AXUV16ELG 16-channel diode arrays, this system can provide temperature profile information versus time by calculating the ratio of the amplitudes of the signals from different filters, calibrated with Thomson scattering system. To improve the frequency response of the amplifiers and advance the ability to study fast rotating modes, we built a new two-stage single-channel amplifier system. It has a bandwidth up to 200 kHz and gains varying from 1 MOhm to 50 MOhm corresponding to different channels of the diode array to optimize the signal amplitudes. The initial results on the dynamics of the m/n=2/1 tearing mode are studied using the system. The line-integrated signals are used to reconstruct the emissivity and temperature profiles of the tangential cross section of the plasma.   

Demonstrating the capabilities of EUV tomography as an estimator of controllable plasma parameters on the HBT-EP tokamak

This work addresses real-time optical signal processing as an alternative to magnetic pickup diagnostics for plasma feedback and control on the HBT-EP tokamak. The diagnostic used in this study collects photons in the Extreme Ultraviolet (EUV) range of 15 eV - 1 keV from four arrays of 16 channels each in a poloidal plane. Signals are processed with a 50 kHz bandwidth on a GPU, feedback is applied to the plasma via 40 internal magnetic coils. In the first phase of this work, we present results of real time feedback on plasma major radius as well as MHD 3/1 mode amplitude using a novel Maximum Likelihood algorithm. The most probable of a set of plasma emissivity profiles representing horizontal equilibria or DCON-generated mode shape is selected by minimizing the signal reconstruction residual. In the second phase, the above results are compared against offline analysis performed with a traditional tomography algorithm. Results are presented from a benchmarking of the inversion implementation is against known 2D emissivity surfaces from equilibrium reconstructions. A novel in situ calibration of the EUV sightlines is presented as well.   

Active mode control using current-injecting electrodes in a tokamak

Feedback control of instabilities is important for maintaining high performance tokamak plasmas near beta limits. A goal of this work is to expand the type of actuators, beyond 3D magnetic coils, that can be used to control instabilities. We demonstrate feedback control using an array of four biased electrodes that inject currents into the plasma along 3D paths. Electrode voltages are phased in response to magnetic sensors near the plasma surface. Resulting control current runs coherently along the magnetic field for some distance before conducting radially from electrodes to the wall, producing a geometry that naturally couples to modes. Injected currents suppress or amplify kink modes, depending on programmed phase between the detected fields and applied electrode voltages. Separate experiments with quiescent plasmas are used to map the driven current paths through the plasma by fitting magnetic sensors and wall currents. The VALEN code is then used to model the control system’s interaction with kink modes, including the fitted control filaments and passive wall segments. Biasing the electrodes 4cm into the plasma (r/a~0.85) leads to mode amplitude reduction of ~40%, while having the electrodes just inside the plasma edge (r/a~1) yields a suppression of ~30%.   

New post-disruption mode rotation scalings and halo current paths on HBT-EP

A new scaling law for the rotation seen during disruptions is presented, which has the rotation frequency scale with the inverse of the toroidal field and the square of the minor radius (1/B_ta²). This scaling law agrees well with observations seen on other devices, and helps to explain the fast rotation frequencies seen during disruptions on HBT-EP. The validity of this scaling law is supported by a multi-shot analysis of the HBT-EP database with varying scale-factors. Possible physical interpretations of this scaling law are also presented, as well as a projection to ITER-like parameters that sees a rotation frequency on the order of 30 Hz. Fluctuations in Halo currents have also been observed to correlate very well with this rotation. The path of these currents and their relationship to the plasma rotation has been investigated through a series of experiments which scan the resistance between adjacent vessel sections, and seeks to characterize the current paths based on their source location (either the plasma surface or the wall). Narrowing down the current source location helps to clear up ambiguities in interpreting current driving mechanisms that have been found to be an issue in the past [1].

[1] J.P. Levesque et al 2017 Nucl. Fusion 57 086035   

Operational space mapping on HBT-EP and DIII-D using Variational Autoencoder (VAE) neural networks

A Variational Autoencoder (VAE) is a type of unsupervised neural network which is able to learn meaningful data representations in a reduced dimension. We present an application in identifying the operational boundary of tokamak experiments. In contrast to disruption prediction by supervised learning algorithms, a VAE maps the input signals onto a low-dimensional latent space by their similarities with neighboring samples, creating a smooth operational space map in which individual shots form continuous trajectories. By projecting the operational parameters onto the same space, this provides an intuitive way for the operator to perform disruption avoidance using a relevant control actuator as a discharge approaches a stability boundary. We implemented a VAE using a dataset of over 3000 shots from HBT-EP and found it to be capable of forming a continuous operational space map and identifying the operational boundaries using a pre-specified warning time window. Pre-programmed control experiments were conducted to demonstrate the control technique using HBT-EP's saddle coils as a horizontal position actuator, showing the ability to avoid the oncoming disruptive event and extend the plasma's duration. The same analysis is presented using a selection of DIII-D signals and discharges.   

Characterizing MHD instabilities and scrape-off-layer currents in HBT-EP using the NIMROD code

The NIMROD [1] and PSI-Tet [2] codes are being used to validate multiphysics (xMHD+conducting wall) models for the prediction of Scrape-Off-Layer (SOL) currents in tokamaks using high-resolution current, magnetic, and optical diagnostics on the HBT-EP tokamak [3]. Early application of the NIMROD code using a perfectly conducting, circular wall and multiple equilibrium current and pressure profiles to characterize resistive MHD instabilities in the HBT-EP tokamak will be presented. Comparison of predicted signals for linear and nonlinear calculations of non-disruptive mode activity to experimental measurements, including a high-resolution poloidal EUV array, will be shown. Future plans for this project to investigate and validate numerical models for wall-connected currents within the SOL using the diverse, high-resolution diagnostics available on HBT-EP will also be presented. Results from this investigation will be used to validate and/or improve existing models for predicted current dynamics between the plasma and the first wall in ITER and next step devices.

[1] C. Sovinec et al., J. Comput. Phys. (2004)

[2] C. Hansen et al., Phys. Plasmas 22 (2015)

[3] J. Levesque et al., Nucl. Fusion 57 (2017)   

Plasma shape control options for edge physics studies on HBT-EP

The cross-sectional shape of tokamak discharges strongly influences plasma stability and confinement. Control of the plasma's outer shape is critical to divertor optimization and can improve diagnostic access to the scrape-off-layer (SOL). HBT-EP demonstrated the capability of creating fully diverted plasmas by energizing a ``zero-net-turn'' poloidal field coil-system located on the high-field side of HBT-EP.[1]  As compared to limited discharges, the inner x-point modified the kink mode's poloidal structure while keeping the plasma's response to resonant magnetic perturbations unchanged. Shaped plasmas are predicted to modify the multi-mode behavior of kink modes[2] and are necessary to control the helicity of driven SOL currents for feedback studies.[3] In this poster, we discussion options for new HBT-EP poloidal field coils and power supplies that will provide improved outer boundary control and give flexibility to explore novel edge physics and control techniques.

[1] P.J. Byrne, Dissertation (2017); https://doi.org/10.7916/D8R78SJ0.

[2] D.A. Maurer, et al., Plasma Phy Contr Fus, 53, 074016 (2011).

[3] J.P. Levesque, et al., Nuc Fusion, 57, 086035 (2017).   

Randomized-NLA methods for fast accurate real-time characterization of tokamak discharges from multiple data-streams

Modern magnetic fusion research involves high-resolution temporal and spatial diagnostics from multiple sensor arrays that generate large data streams well-suited to advanced scalable numerical linear algebra methods. This presentation introduces randomized numerical linear algebra (rNLA) and describes the application of these methods (i) to identify and optimize data reduction methods for real-time discharge control and (ii) to advance our understanding of fundamental behaviors of magnetically-confined plasma.  Randomized methods trade off accuracy for speed and are easily adaptable to distributed computing architectures and streaming data scenarios. We describe our development plans that will incorporate rigorous statistical guarantees, leverage high dimensional statistics, and provide measures of sub-optimality as quantified by tunable parameters. The Columbia University High Beta Tokamak-Extended Pulse (HBT-EP) facility will provide the initial data for algorithm development, and we seek to evaluate the broader use of our algorithms for critical data-intensive control needs in plasma science and related areas.