Session PP11: Poster Session VI: MFE:DIII-D and conventional tokamaks II;MHD and stability; Analytic techniques in MFE; ICF: Pinches and hohlraum physics SPACE: Astrophysical plasmas LTP:Low temperature plasma applications MC:Miniconference: Shocks 2:00 PM - 5:00 PM

Ion orbit losses and tokamak improved confinement in negative and positive triangularity

Ion orbit losses through the plasma edge are a pervasive, but often neglected, component of tokamak edge confinement. Orbit losses, especially from near a plasma boundary X-point, are known to be be able to drive a near-edge annulus of negative radial electric field E_r. Losses are enhanced at higher temperature T_i. Strong radial shear of the ExB velocity reduces turbulent transport and allows a strong edge pressure gradient to form. Negative and positive triangularity (NT and PT) have very different edge ion orbits. PT maximizes particle trapping (mirroring reversal of the parallel velocity), leading to more and wider banana orbits, while NT minimizes mirroring. In some NT shapes, the orbit effects of strong NT at a single D-corner can strongly suppress H-mode onset for quite small geometric changes, when added to the other NT properties. PT plasmas with lower ``sub-H-mode'' levels of improved confinement tend to have reduced ion trapping and banana width; their weaker E_r and E_r shear make it hard to reach full H-mode. In nonaxisymmetriy, ion orbits in some stellarator helical fields could enhance X-point losses and maybe related to the widely observed density pumpout seen in tokamaks with small nonaxisymmetric magnetic perturbations.   

Role of neutral particles on pedestal structure for H-mode experiments in DIII-D

We present a database study investigating the role of fueling versus plasma parameters in determining the separatrix and pedestal electron density for DIII-D H-mode plasmas. 

The database consists of multiple equilibrium (100-200ms stationary) lower single null ELMy H-mode discharges with engineering parameters ranging over toroidal magnetic field $B_{T}$ in [1.2, 2.2] (T), plasma current $I_{P}$ in [1.0, 1.8] (MA), Neutral Beam power $P_{NBI}$ in [1.0,13.0] (MW), safety factor $q_{95}$ in [3.0, 6.5]. Data in 50-98% of the ELM cycle are included. In our analysis, we will be able to infer neutral density profiles from the LLAMA diagnostic. The profiles of neutral density are fitted with an exponential function which allows us to link the neutral density at the separatrix and neutral penetration directly to the pressure in the divertor, gas fueling rate as well as plasma and operational parameters. The preliminary results indicate a correlation between the decrease of the neutral density in the separatrix (LFS) and the increase of the total power injected but this correlation is reversed, increasing of neutral separatrix density (LFS) with total power injected, if the toroidal magnetic field is reversed. It was also observed that the neutral density on the separatrix decays to a minimum value and less scattered for separatrix temperatures greater than 100 eV.   

Measurement of edge turbulence in negative triangularity plasmas with phase contrast imaging on DIII-D

Sweeps of the upper triangularity (δ_U in [-0.4,-0.2]) in negative-triangularity [1] discharges have been performed with fixed lower triangularity (δ_L=0.2) with a variety of plasma parameters , providing a platform for the study of the edge turbulence. The Phase Contrast Imaging diagnostic [2] provides measurements of line-integrated edge turbulence with good wavenumber resolution and wide frequency bandwidth and is especially sensitive to the turbulence in the sheared edge region of high-performance plasmas. The spectra of the ion-scale turbulence seen in negative triangularity discharges, even without auxiliary heating, is similar to that seen in plasmas with significant edge shear such as H-modes rather than L-mode plasmas. Two instability regimes were identified, corresponding to pure ohmic heating and moderate beam heating. With no auxiliary heating, the turbulence both above and below the midplane was sensitive to the upper triangularity. The edge turbulence in plasmas with moderate beam heating was independent of the upper triangularity. This demonstrates that the good performance edge observed in negative-triangularity plasmas is robust and persists over a variety of parameters and turbulence regimes.

[1] Marinoni et al 2021 Nucl. Fusion 61 116010

[2] Davis et al 2016 Rev. Sci. Instrum. 87 11E117   

Controlled low-Z melting experiment in DIII-D tokamak

Controlled melting of aluminum (Al) was performed in the lower divertor of DIII-D, and the molten surface deformation was modeled with the MEMENTO code [1]. The experiment was largely motivated by using Al as a proxy for beryllium in ITER. Three Al blocks sized 1×1 cm in the toroidal and poloidal directions, with the top surface angled at ~32 degrees towards the incident plasma heat fluxes, were exposed under steady L-mode discharge conditions using the Divertor Material Evaluation System (DiMES) manipulator. During the exposure, Al samples were imaged by visible and infra-red (IR) cameras, and the current through them was measured via a shunt with resistance of ~0.15 Ω. Heat fluxes incident on the angled surfaces were inferred from IR data aided by SMITER field line tracing. The block exposed to the incident heat flux of ~10 MW/m² for ~1 sec achieved the intended shallow melting. MEMENTO code was able to qualitatively reproduce the surface deformation profile and the melt onset timing, but detailed comparison was impeded by the unknown thermo-physical properties of the sample due to strong oxidation. Cross-sectional analysis of the molten surface for improved comparison is in progress.

[1] S. Ratynskaia, et al., Nucl. Mater. Energy 33 (2022) 101303   

Observations of energetic ion driven ion cyclotron emission and high frequency Alfvén eigenmodes in negative triangularity plasmas in DIII-D

Observations are presented for an investigation of energetic ion driven coherent ion cyclotron emission (ICE) and sub-cyclotron high frequency Alfvén eigenmodes (hfAE) in negative triangularity shaped plasmas in DIII-D obtained with a set of loops inside the vacuum wall with sensitivity to radio frequency emission at frequencies f < 200 MHz. This investigation contributes to a better understanding of the observed waves so that in the future, such observations can be used to diagnose the energetic ion population. In a 2023 negative triangularity campaign, many experiments were conducted which provided a rich data set for examining ICE and hfAE characteristics on plasma parameters in negative triangularity shaped plasmas. The ICE was observed to occur at low harmonics of the central ion cyclotron frequency and the dominant harmonic varied with plasma conditions but tended to be low (l ≈ 2). Frequency splitting was observed for some ICE harmonics, as well as hfAEs. Analysis showed that in some case the splitting was the result of the formation of propagating wave packets, suggestive of nonlinear dynamics. Work supported by US DOE under DE-FC02-04ER54698 and grant # DE-SC0020337.   

Radiation Dependence of Divertor Leg Length in Detachment on DIII-D

Experiments performed on DIII-D demonstrate that while increasing the outer leg length distributes radiation over a larger volume, the increased leg length does not prevent an eventual collapse of the X-point temperature at high density. Accommodating divertor radiation requires understanding the dissipation processes that takes place along a flux tube. Smaller core-volume plasmas in the open divertor were used to extend the poloidal leg length, L_pol, to 38 and 55 cm for two injected powers (8.3 MW and 5.4 MW). Gas puffing was used to increase the plasma density to the point of detachment to test the radiation volume required in the convective limit and extend beyond existing stable-detachment temperature gradient measurements (200eV/m for 15cm L_pol). The higher L_pol cases show a lower detachment onset density, but only by ~5%. The normalized confinement, H₉₈, drops from 1.2 before detachment and drops below one and continues to reduce as the divertor is driven deeper into detachment.  Radiated power is found to extend along the outer leg in detachment for all cases. Despite the extended radiating volume, the CIII radiation pattern is found to peak strongly at the separatrix near the X-point in the detached limit, indicating a 7-8 eV electron temperature at the X-point.    

Turbulence and Transport Dependence on rho* and Isotope Mass in H-Mode Plasmas on DIII-D

Normalized long-wavelength (k_⊥ρi<1) density fluctuation amplitudes are found to scale approximately linearly with the normalized local ion gyroradius, ñ⁄n~ρ* in ITER-like ELM’ing H-mode plasmas on DIII-D; ρ_I was systematically varied both via a ρ* scan in deuterium as well as by changing isotope mass in matched hydrogen and deuterium plasmas. Interestingly, confinement is found to increase at smaller ρ* as ρ* is varied within a single ion species (deuterium), consistent with gyro-Bohm predictions. However, when ρ* is reduced by changing isotope mass (D->H), confinement degrades, counter to simple gyro-Bohm predictions, potentially indicating that the dimensionless electron-to-ion mass ratio is important to confinement scaling. Comprehensive measurements of the spatiotemporal turbulence properties, obtained with 2D Beam Emission Spectroscopy, are compared as the local ion gyroradius is altered via magnetic field and/or isotope variation. The turbulence radial correlation length is found to scale with ρ_I in the deuterium ρ* scan, but not in the isotope scan. These turbulence measurements and analysis will be compared with linear and nonlinear gyrokinetic simulations to help resolve the conundrum of ρ* scaling of confinement and the isotope effect.   

Analysis on the Effect of Main Ion Density on High-Z Impurity Transport in the Scrape-off Layer of DIII-D Using Collector Probes

Experimental results from the 2022 tungsten (W)-coated Small Angle Slot (SAS-VW) divertor campaign at DIII-D indicate that while core plasma density is increased approaching detachment in the unfavorable (ion B×∇B out of the divertor) toroidal magnetic field (B_T) direction, W concentration at the midplane far-Scrape-off Layer (SOL) is reduced while core W concentration increases. To better understand high-Z impurity transport and contamination of the core, an experiment was performed including a series of upper-single-null L-mode discharges in each B_T direction. The discharges incrementally increased the plasma density,  (line-averaged density = 3.15-4.35e19 m^-3), which approaches and slightly exceeds the divertor detachment threshold. W deposition measurements using double-sided, graphite Collector Probes (CPs) inserted at the outer midplane far-SOL revealed a 75% decrease in W areal density over the  scan when operating in the unfavorable B_T direction. Observations of flattened W deposition profiles allude to increased radial transport with increasing Soft X-ray (SXR) imaging data from the same discharges shows core W content that increases by 77% over the same scan. Both W core content and CP deposition changed marginally with the onset of (partial) divertor detachment.   

Deuterium retention in Li-D co-deposits in the DIII-D tokamak

Deuterium (D) retention in lithium (Li) co-deposits was studied in DIII-D by injecting Li powder at 1.5-30 mg/s into H-mode plasmas with and without 3D fields applied. When Li is injected, a decrease in the Ly-α signal intensity is observed, indicating a decrease in the ionization source related with a reduction of the recycling coefficient due to D uptake by Li. Two sets of samples were exposed to the plasmas through DiMES, each consisting of seven samples, including: 1.6 μm of deposited W on graphite, polished stainless steel samples, several coated with 300 nm, and 600 nm Li layers, and a Si sample with micro-trenches. Observations with HRUV showed a substantial increase in Li emission during injection and confirmed that pre-lithiated samples were not significantly eroded. Ion fluxes of ΓD+= 4.3- 6.1x1020 D/m2 s were measured with Langmuir probes at DiMES. Considering the injected Li amount and assuming that 10% deposits outside of the OSP, the thickness of the lithium layer is estimated to be 4 nm. In post-mortem NRA spectra, Li and D peaks are observed in most samples, confirming co-deposition took place. TDS shows D retention in pre-lithiated and SS samples. Results from post-mortem analysis of the Li-D co-deposits with SIMS, XPS, NRA, and EBS will be presented and discussed.   

Simultaneous Regulation of the Electron Temperature and Safety Factor Profiles for DIII-D using Optimal Control Methods

A controller has been designed to simultaneously regulate the electron temperature (T_e) and safety factor (q) profiles on DIII-D.  Future scenario development efforts will require the capability to control both kinetic and magnetic profiles to achieve high performance plasmas while maintaining MHD stability. Optimal control solutions for the regulation of the Te and q profiles individually has been demonstrated for DIII-D [1, 2]; the controller presented here aims to extend these results by controlling both profiles at the same time. The controller is synthesized based on the linearized electron heat transport and magnetic diffusion equations.  Using this model, the Linear Quadratic Integral (LQI) controller is designed to minimize the integrated error between the actual and target profiles.  The controller has been tested in nonlinear simulations using the Control Oriented Transport Simulator (COTSIM).  Predictive simulation results demonstrate the effectiveness of this controller in regulating both the electron temperature and safety factor profiles simultaneously by using the available heating and current drive sources.

[1] S. Morosohk et al., APS Division of Plasma Physics, Spokane, WA, 2022.

[2] W. Wehner et al., Fusion Engineering and Design, vol. 123, pp. 513-517, 2017.   

Heat flux width scaling and detachment in high heat flux experiments on DIII-D

A multi-tokamak scaling predicts narrowing heat flux widths and increasing heat flux density in reactors well beyond the limits which existing armor materials can sustain. However, more recent experiments suggest that broadening effects observed at higher scrape-off-layer (SOL) pressure might change how the divertor heat flux profiles scale, easing this heat flux challenge. Experiments at the DIII-D tokamak use a range of plasma current (I_p =1.0-1.9 MA) and neutral beam heating power (P_inj=8-16 MW, for a power-into-SOL of P_SOL≈5-10 MW) H-mode discharges to investigate the physical processes that may limit the maximum parallel heat flux into the divertor. Analysis of infrared camera measurements in the divertor shows heat flux broadening between ELMs at the outer target in the P_SOL=10 MW case compared to the 5 MW case at I_p=1.9 MA. Density scans provide data both attached and detached conditions, with detachment onset in the high power case at about 59% the Greenwald limit. Detached cases at I_p=1.9 and P_SOL=10 MW give some of the highest normalized divertor parameters achieved on DIII-D, with neutral ionization length, heat flux width, and Lyman mean free path length within factors of ≈2.5-3.2 compared to that expected in a reactor.   

Identification of Multimode Interactions of Magnetic Fluctuations by Faraday-effect Polarimetry in DIII-D QH-mode Plasmas

Measuring nonlinear tearing mode (TM) coupling with high m/n near the magnetic axis can aid in understanding neoclassical TM seeding, growth, and decay mechanisms. For this tracking we use the Radial Interferometer-Polarimeter (RIP), which is sensitive to core-resonant magnetic fluctuations on DIII-D and has detected TMs well before they appear on the edge sensing coils [Pandya, DPP invited talk 2021]. Here we employ RIP to analyze the impact on pre-existing TMs of multiple, emerging MHD modes that are never detected by the coils. We focus on plasmas in QH-mode, where infrequent ELMs make TMs more clearly identifiable. In one example, RIP detects an n=3 mode coupled to both an n=2 mode and a lower-frequency intermittent mode. The n=3 mode loses up to 98 percent of its energy during the coupling, while the other two modes grow. When the intermittent mode disappears, the n=3 mode begins to grow robustly. All three modes are resonant near the magnetic axis, and their interaction is only visible using RIP. In another example, the edge coils show an n=2 mode apparently dissipating in the absence of other modes, but RIP shows instead that it loses energy through coupling to higher-order modes.   

2023 Status of the ECH System on DIII-D

The Electron Cyclotron Heating (ECH) system on DIII-D currently consists of five non-depressed collector 110-GHz Communications and Power Industries (CPI) gyrotrons which combine to inject a total of 3.2 MW of RF power into the plasma via eight transmission lines and four equatorial launchers. The available ECH power increased by 700 kW from last year after the refurbished gyrotron "Han" was successfully commissioned and added to operations earlier this year. Additionally, two more 110-GHz CPI gyrotrons will be joining operations by the start of the FY24 plasma campaign, potentially increasing the available ECH power to over 4.5 MW. The first gyrotron, "NASA", is a refurbished depressed collector gyrotron that is currently undergoing the testing and conditioning process at DIII-D. The second gyrotron, "Thor", is a new non-depressed collector gyrotron that is scheduled to arrive at DIII-D this summer after undergoing repairs by the manufacturer that interrupted its conditioning process at DIII-D earlier this year. Furthermore, DIII-D is also expected to receive its first two new depressed collector gyrotrons from Thales in 2024 and 2025, which are each designed to generate a maximum power of 1 MW at a frequency of 117.5 GHz.   

Upgrading DIII-D to Close the Gaps to Future Fusion Reactors

The DIII-D program is pursuing an ambitious plan to rapidly close critical design gaps to a Fusion Pilot Plant (FPP), including integrating performance and exhaust solutions, addressing plasma interacting material and technology issues through an expanded R&D effort, and resolving a high fusion gain path to ITER and a pulsed/steady-state FPP. Key to the DIII-D approach is major facility upgrades to access reactor-relevant physics regimes with increased flexibilities. A staged divertor program will allow for more plasma shaping, and higher current and density, to enable more reactor-relevant core-edge integration. The electron cyclotron heating (ECH) will be increased to 10 gyrotrons, with an extension to 20 gyrotrons by 2028, to furnish low-torque electron heating and profile control, while new reactor-relevant solutions for efficient off-axis current drive will be pioneered by high-field-side lower hybrid current drive, helicon waves and top launch ECH to enable FPP steady-state scenarios. Additional proposed facility upgrades include an expanded set of 3D coils, and disruption mitigation and materials testing capabilities. An exciting option for a negative triangularity path is being assessed. Together these elements will enable reactor solutions to be pioneered and projected with confidence.   

Flow, Mode Effects That Seed Neoclassical Tearing Modes

This poster discusses how perturbations seed a robustly unstable neoclassical tearing mode NTM) by exceeding a "gate." In the NTM instability equation the destabilizing bootstrap current drive d_NTM is approximately 3 (j_boot / j_parallel). It is balanced by an ion polarization current that produces a stabilizing flow dependent gate function F (f_m). The polarization current gate function in the plasma is proportional to the difference between the frequencies of the NTM instability mode and the radial electric field toroidal reference frame. In the DIII-D ITER Baseline Scenario (IBS) discharge 174446, the NTM drive d_NTM is about 0.5 and the ion polarization width w_pol of 2.7 cm is about twice the ion banana width. The NTM is unstable when the NTM drive exceeds the stabilizing gate in the island evolution equation: d_NTM > (w_pol^2 / w^2) F (f_m). Here, the island width w (cm) equals 3 B_rms(G)^1/2, where B_rms(G) is a transient external Mirnov signal (e.g. ELM). When the gate function is closed [F(f_m) equals 1], growing NTMs are seeded in 174446 if B_rms > 1.8 G (w > w_pol / d_NTM^1/2 simeq 4 cm). However, if the gate function F (f_m) is reduced because flow differences are reduced, NTM growth can be seeded by a slightly smaller B_rms, w.   

Manipulating density pedestal structure to improve core-edge integration towards low collisionality

By leveraging the benefits of low-density-gradient pedestal in the closed divertor, DIII-D has achieved a promising core-edge integrated scenario plasma which integrates a high-temperature, low-collisionality (n^*_ped<1) pedestal with a partially detached divertor. With a closed divertor and high heating power, strong gas puffing moves the pedestal peak density radially outward and reduces the density gradient in the pedestal region. These leads to a significant separation between density and temperature pedestals and result in high η_e - well above the stability threshold. Concomitantly, measured electron turbulence (kr_s>1) is enhanced at pedestal and strongly correlated with the high η_e. Nonlinear CGYRO simulations found a similar instability as seen in experiment driving significant heat transport that could broaden the pedestal to be wider than the EPED scaling. The wide temperature pedestal facilitates the achievement of high-temperature low-collisionality pedestal. Simultaneously, the outward shift of the density pedestal facilitates access to detached divertor conditions with low temperature and low heat flux towards target plate. Experiments also found that higher plasma current, strong shaping and higher heating power are beneficial for this promising core-edge scenario plasmas.   

Characterization of the radiated power operational space in negative triangularity plasmas at DIII-D

We report on the first experiments and related edge modeling performed to assess the integration of core performance with power exhaust in diverted negative triangularity plasmas. A database with a wide parameter range in terms of radiated fraction, Greenwald fraction, power, density, and current has been collected, indicating a core radiated power fraction up to 0.85 obtained through the injecting of mantle radiators such as Kr, Ar, Ne. Kr-seeded discharges exhibit an increase in β_N with increases in both radiation fraction and Greenwald fraction, while Ne seeding leads to a reduction of β_N for f_rad > 0.5. Scoping studies with SOLPS-ITER modeling guided the location choice of seeding during the experiments, and interpretive SOLPS-ITER modeling with multiple impurity species will be presented showing the effects of the experimental scanned parameters, edge impurity transport, and divertor characteristics.   

Measurements and SOLPS-ITER Modelling of Pumping Experiments in DIII-D

Carefully selecting cross-field transport coefficients, particle and energy sources, and particle removal rates to reflect experimental conditions is shown to improve agreement between boundary plasma and neutral modelling using the SOLPS-ITER code and experimental measurements from Langmuir probes and pressure gauges in H-mode plasmas in the DIII-D tokamak. However, modifying diffusive transport coefficients to match upstream plasma profiles alone is shown to result in a significant underprediction of target plasma fluxes in the cases explored. This result holds regardless of whether diffusive transport is expressed as poloidally symmetric or given a ballooning structure. Using ion temperature measurements from main ion charge exchange to determine ion thermal transport is also shown to enable agreement of upstream kinetic profiles between SOLPS and measurements, whereas the model finds measurements of impurity ion temperature to be inconsistent with other profile inputs. This work identifies boundary plasma model deficiencies and enables proper model validation exercises as models are improved.   

Limiting factors for achieving peeling-limited pedestals in present devices

An optimized pedestal regime called the Super-H Mode is leveraged to access peeling limited pedestals and study limitations on the integrated tokamak exhaust and performance gap. Analysis of DIII-D experiments demonstrates separatrix and mid-pedestal collisionality as key parameters in determining the state of both the pedestal and the divertor regions. Experiments were performed on DIII-D to determine the conditions where peeling and ballooning modes become strongly coupled. Primary actuators for these experiments included D<span style="font-size:10.8333px">2 puffing to match pedestal density in semi-open and closed divertors as well as varied strike point location to change the pumping efficiency in the divertor. Pedestal structure is modified by fueling and pumping such that the closed divertor requires higher gas puffing for a matched pedestal density due to the higher pumping efficiency. Due to ~2x increased pumping efficiency in the closed divertor configuration, approximately 5x higher fueling rates were required to achieve similar pedestal conditions as the open divertor. The difference in pumping efficiency and fueling for the same pedestal density indicates a change in pedestal particle transport, which leads to ~5x lower collisionalities at the separatrix and ~10x lower at mid-pedestal, allowing access to a peeling-limited pedestal.

Work supported by the U.S. Department of Energy under DE-FC02-04ER54698, DE-SC0014264, DE-AC02-09CH11466, and DE-AC05-00OR22725.   

Overview of High Field Side Lower Hybrid Current Drive Experiment at DIII-D

High field side lower hybrid current drive (HFS LHCD) is a potential tool for efficient, off axis current drive. From simulations, efficient off-axis current at r/a~0.6-0.8 with peak current density up to 0.4 MA/m² and 0.4 MA/MW coupled is achievable for target DIII-D discharges.  From the HFS, LH waves are expected to have improved accessibility and single pass absorption due to favorable wavenumber upshift.  A compact coupler utilizes a traveling wave, 4-way splitter and a multi-junction to distribute power poloidally and toroidally, respectively, and imbedded matching structures to maximize performance.  Laser Powder Bed Fusion (LPBF) GRCop-84, a high strength, thermal and electrical conductivity copper alloy, is used for the coupler and in-vessel waveguides allowing for embedded RF elements and waveguides with precise twists and bends.  Klystron commissioning has begun and the klystrons have been conditioned up to 20 kW into dummy load for short pulse.  The in-vessel waveguides and coupler have been assembled on the DIII-D vessel mock-up and are expected to be installed in 2023 vent. Initial HFS edge density measurements suggest the coupling is quiescent and within range the coupler was optimized.  The latest results and system status will be presented.   

Analysis of Final Loss Events due to Vertically Unstable Runaway Electron Beams in DIII-D

Runaway electrons (REs) in tokamak fusion plasmas pose a significant challenge. A non-collisional technique called the 'benign termination strategy' shows promise for RE beam termination with minimal first-wall heating. This work analyzes RE vertical displacement event (VDE) experimental data from DIII-D tokamak benign termination experiments and simulation with the TokSys code suite. This research aims to investigate correlations between experimental parameters related to equilibrium evolution and parameters associated with final loss events and MHD instabilities, which can provide valuable insights on accessing and optimizing the benign termination strategy . Equilibrium evolution analysis examines plasma stability in plasma current (IP)/ plasma minor radius (a-minor) and edge safety factor (qa)/internal inductance (li) spaces to gain insight on what influences the final loss events. Derivative metrics are applied to assess the speed of VDEs and its effect on access to the final loss event. Comparisons are made between experimental EFITs and simulated TOKSYS-derived EFITs. Analysis of bursts and final loss events includes the hard x-ray (HXR) loss duration, correlation with burst duration and time into current quench. This research enhances understanding of the crucial plasma compression phase and which details are most crucial for accessing the final MHD loss event, improving confidence in the benign termination strategy for RE beams.   

Emulation of ITER Axisymmetric Control Characteristics on DIII-D

D3D is well suited to provide a testing ground for remaining unknowns in ITER control and exception handling. Control software have been developed to emulate ITER-like control characteristics aimed at enabling D3D to act as a scaled model for ITER development. Currently, we focus on the emulation of the magnetic control characteristics, which is implemented in two ways dependent on experimenter’s choice. A static method uses a model linearized around a scaled ITER plasma. First, a linearized model is used to calculate the ITER coil current dynamics from the power supply voltage. Then the ITER coil currents are mapped to D3D coils. Finally, a D3D current feedback controller achieves the currents calculated. The alternate method instead calculates the expected ITER field, and then calculates in real-time, the D3D coil currents that best achieves the D3D scaled equivalent. Simultaneously, vertical control characteristics are emulated by using active control to slow down the vertical instability growth rate to the ITER timescale. The emulation has been tested in D3D vacuum shots, and in control simulations. The development of a stand-in ITER controller is ongoing to enable the first experiment of emulated ITER control on D3D.   

Dependence of EC toroidal injection angle on effective EC assisted startup

The effect of electron cyclotron (EC) wave toroidal injected angle on the quality of pre-plasma for the EC assisted startup is studied experimentally at DIII-D in support of ITER. The Deuterium alpha filterscope signal shows for the first time that the post-reflection, second pass absorption efficiency depends heavily on the toroidal injection angle and results in the change in pre-plasma density and temperature that is necessary for a successful startup. A 110 GHz, extraordinary-mode polarized EC wave is injected into the DIII-D vacuum vessel aimed for the second harmonic resonant absorption at a poloidally oblique angle from the upper outboard launcher. The toroidal injection angle is systematically scanned from radial to 20 degrees off-radial angle. It has been reported previously that the EC beam is absorbed at least twice at the resonance radius due to the reflection near the inboard midplane. The DYON and RT-4 simulations indicate that the power absorption efficiency changes with the toroidal injection angle and explains the experimental observation qualitatively. This result provides valuable data to validate models and optimize ITER's startup strategy, where the EC assist is necessary and EC is designed to be injected at a toroidally oblique angle.   

Modeling dissipative divertor designs for DIII-D with variations in wall baffling and pump location

In the upcoming DIII-D 5-year plan, a deep-baffled dissipative divertor with a long outer poloidal leg length of ~50 cm is planned, with the aim to provide data to constrain models for predicting radiation and detachment processes in a fusion pilot plant. The plasma boundary codes SOLPS-ITER and UEDGE are used to evaluate designs of this dissipative divertor for plasmas with up to 25 MW of heating power, focusing on the effects of baffle geometry (including particle drifts) and pump location on the divertor solution. Cross-field transport coefficients are tuned to match the heat flux width from the ITPA scaling and the pedestal shape of a recent 16 MW DIII-D plasma. Increasing divertor baffling in the scrape-off-layer (SOL) better confines neutrals in the divertor, but the overall effect is small for detached solutions, with just 5 to 10% electron density increase in the divertor far-SOL when the baffling is approximately conformal to SOL flux surfaces. Increased baffling in the private flux region (PRF) restricts neutrals sourced at the inner divertor from reaching the outer divertor leg through the PFR, and compresses neutrals at the X-point. Moving the pump location upstream from the divertor target reduces pump throughput for a given upstream separatrix density, but increases the local density near the target and thus dissipation, highlighting a robust trade-off between the ability to exhaust particles and dissipate power.   

Investigating the dependence of a Long-Leg, Dissipative Low-Field Side Divertor on High-Field Side Divertor Leg Length in DIII-D Using UEDGE Simulations Including Drift Flows

UEDGE simulations of upper-single null plasmas with a 50 cm baffled low-field side (LFS) divertor leg, including drift flows in the favorable direction, predict a 25% decrease in LFS target separatrix electron temperature (T_e,LFS-t,sep) and a 5% increase in LFS midplane separatrix electron density when the high-field side (HFS) divertor leg length is reduced from 20 cm to 15 cm. The simulations indicate E_θ×B radial drift flows through the private flux region are responsible for the observed T_e,LFS-t,sep-dependence on HFS divertor leg length. Simulations in the unfavorable drift direction predict a negligible impact on LFS divertor conditions as the HFS divertor leg length is reduced from 20 cm to 15 cm. In the unfavorable drift direction, the drift flows are directed towards the pump, increasing the particle removal rate. Consequently, T_e,LFS-t,sep increases by 15% and 50% compared to the favorable drift direction for 20 cm and 15 cm HFS divertor leg lengths, respectively, for the same boundary conditions. The long legged, baffled divertor of the DIII-D Staged Modular Divertor program will explore the feasibility of a large-volume dissipative divertor, by increasing the LFS divertor volume without internal magnetic field coils, without degradation of core plasma performance.   

Density turbulence measurements by using fast sweep reflectometry in DIII-D

The fast RF frequency sweep reflectometry, with the state-of-art capability of electron density radial profile measurement, is able to determine the density turbulence radial profile by the analysis of reflectometer phase fluctuations¹. In DIII-D, the ordinary mode launch/receive phase fluctuations have been used to derive the radial profile of n_e fluctuations analytically. The calculated radial wavenumber range of the turbulence is from ~1 cm^-1 to ~10 cm^-1, which is limited by the Bragg scattering condition. Initial turbulence measurement results by this technique in various DIII-D plasma conditions, such as L-H mode transition and the wide pedestal QH mode to standard QH-mode transition, are obtained. In a typical L-mode plasma the relative fluctuation level (δn/n) varies from ~1% in the core (rho < 0.6) to more than 10% in the edge. A significant reduction in δn/n is observed when H-mode occurs. The comparison with other turbulence diagnostics, e.g., DBS and BES, has shown reasonable qualitative agreement (e.g., with BES showing ~4% and reflectometry showing ~5% at rho=0.9 for a QH mode plasma). The analysis of turbulence fluctuations via extraordinary mode reflectometer phase fluctuations is comparatively more challenging and will also be presented. 

[1] Clairet F., et al, Nucl. Fusion 56 (2016) 12619   

Pellet Fueling Research on DIII-D

Core fueling by pellet injection will be an essential technique for sustaining burning plasma scenarios in ITER and in a fusion pilot plant. The physics of core pellet fueling is an area of active study on DIII-D, with current emphasis on understanding the interaction of the core fueling process with edge and boundary phenomena that are also essential for a high-performance plasma scenario. Interactions of concern include the possible return or onset of edge-localized modes due to perturbation of the edge pedestal, and the effects on stability of the divertor plasma detachment. Modeling of the magnetohydrodynamic stability of the pedestal under the pellet particle source, and a series of upgrades to the DIII-D pellet injection system to enable experimental study of such interactions, are underway. The ability to vary pellet mass and delivery location, with absolutely calibrated mass measurements, allows for flexible variation and quantitative analysis of the pellet particle source. These capabilities and future upgrades to increase pellet injection rates to levels relevant for divertor detachment studies, along with planned approaches for modeling the detachment response to the dynamics of the pellet particle source, are described.   

Connecting DIII-D and NERSC to support DIII-D Operations through Kinetic Equilibrium Analysis

The CAKE (Consistent Automatic Kinetic Equilibrium) OMFIT workflow to reconstruct magnetic equilibria in the DIII-D tokamak with kinetic constraints has been automated to run in the NERSC realtime queue, connected to DIII-D via the ESnet network.  These reconstructions had been carried out on the DIII-D local cluster, Iris, but took too long to make an impact on control room decisions.  Optimizing the time to solution on NERSC’s Cori system (launched via the NERSC Superfacility API), with its greater parallelization possibilities, resulted in a run time for less well-converged cases of 22 minutes.  Further improvements in runtime are anticipated in moving the workflow to Perlmutter at NERSC and improving the method for finding the optimal EFIT internal spline knot locations, including more parallelization.  The solutions are written back into DIII-D’s MDSplus data management system and are then available to the entire DIII-D team, including visualization through the omas library.   

Error Field Identification through Torque Balance on a Saturated Island

Measurement of the electromagnetic torque on a magnetic island could be an attractive method for error field identification in the early (PFPO-1) phase of ITER operation. Previous DIII-D experiments [1,2] have demonstrated the principle of this approach using a stationary island, while recent developments in magnetic data analysis [3] allow the field of a rotating island to be distinguished from that of the wall currents induced by its rotation. In a recent experiment, a slowly rotating n=1 magnetic perturbation forced a saturated magnetic island to rotate, thus sampling all toroidal phases periodically in a single discharge. The phase and amplitude of the error field are inferred from analysis of the torque balance on the island, including torques from the error field, the applied magnetic perturbation, and the wall currents induced by rotation of the applied perturbation and the island. Results will be compared with those from more conventional methods. --- Refs.: [1] E.J. Strait, NF 2014; [2] D. Shiraki, NF 2014; [3] R.M. Sweeney, PoP 2019   

Overview of Results from the DIII-D Negative Triangularity Campaign

In early 2023, a dedicated multiple-week experimental campaign was conducted to qualify the negative triangularity (NT) scenario for future reactors on the DIII-D tokamak after previous initial promising experiments on TCV and DIII-D. During this campaign, high confinement (H_98y,2≥1), high current (q₉₅<3), and high normalized pressure plasmas (β_N>2.5) were achieved at high-injected-power in strongly NT-shaped discharges with δ_avg= - 0.5. The experiments with a lower outer divertor X-point shape covered a wide range of DIII-D operational space (plasma current, toroidal field, electron density and pressure) in contrast to other high-performance ELM-suppression scenarios that have narrower operating windows. Also demonstrated was high normalized density (n_e/n_GW≤2), particle confinement comparable to energy confinement, a detached divertor without impurity seeding, and high core radiation fraction.  Plasmas with strong NT maintained a non-ELMing NT-edge with an electron temperature pedestal, exceeding that of typical L-mode plasmas, whereas plasmas with reduced δ_avg~ - 0.18 transition into H-mode. These results are promising for a NT fusion pilot plant and further results on performance, stability, transport, scenario development, and core-edge integration will be presented.   

Withdrawn

Initial divertor neutral density (n_D) measurements in an experiment exploring the role of neutrals on detachment in DIII-D indicate that n_D during L-mode, attached condition is ~25 - 35% of the local electron density. Neutral density measurements in tokamaks are critical to characterize particle sources and energy loss mechanisms in the plasma edge. Neutral densities are derived from calibrated line-integrated Deuterium Balmer alpha (D_α) brightness, using local n_e and T_e measurements to determine the photon emissivity coefficients and a characteristic emissivity decay length along the line of sight from UEDGE simulations. The n_D obtained is an upper estimate of the atomic density due to contributions from molecular dissociative excitation and recombination processes. To unravel the relative contributions, the derived D_α emissivity and n_D are compared to DEGAS 2, which calculates neutral (atomic and molecular) densities and emissivities from measured profiles. Atomic densities obtained with this technique and interpreted by DEGAS 2 are validated using Lyman-alpha measurements, which have negligible contributions from molecular processes. By sweeping the outer strike point past the diagnostic line-of-sights, this measurement technique can be extended into 2D.   

Temperature fluctuation measurements in negative triangularity plasmas in ASDEX Upgrade

Negative triangularity (NT) experiments in TCV [1] and DIII-D [2] have shown H-mode level confinement without Edge Localised Modes (ELMs), setting a path for NT as an operating scenario for burning plasmas. At ASDEX Upgrade, NT plasmas with |δ_av| < 0.2 can be achieved, and these plasmas can undergo the L to H-mode transition depending on ∇B drift configuration and heating power [3]. In this work, we present Correlation ECE measurements in NT plasmas of T_e fluctuation spectra, fluctuation amplitude, and correlation lengths in the outer core and the edge.  We compare power-matched discharges with low (|δ_av| ≈ 0) and moderate (|δ_av| ≈ 0.2) average triangularity.  At moderate |δ_av|, the plasma enters H-mode with ELMs. The low |δ_av| discharge stays in L-mode for the same heating power, contrary to the current understanding that higher negative |δ_av| means H-mode avoidance.  H-mode phases of ECRH-heated and NBI-heated NT plasmas are also compared.  An increase in T_e fluctuation amplitude with radius is observed in both plasmas, but the details of spectral features differ. Initial gyrokinetic simulations are performed for the ECRH and NBI discharges in the outer core and pedestal top.

[1] Camenen et al 2007 Nucl. Fusion 47 510

[2] Austin et al, 2019 Phys. Rev. Lett. 122, 115001 

[3] Happel et al 2023 Nucl. Fusion 63 016002   

ECE-Imaging characterization of edge magnetic islands affecting pedestal transport and stability in a net-zero torque plasma

Characterization of a m=5, n=1, and f~0.5-3 kHz rotating island at the pedestal top (psiN~0.89) of a net-zero torque low-collisionality, wide pedestal QH-mode is presented. The characterization is made with ECE-Imaging and other diagnostic systems at the DIII-D tokamak. The magnetic island is observed to exert a profound effect on the pedestal structure and the axisymmetric peeling-ballooning mode stability. Though the discharges have no Resonant Magnetic Perturbation (RMP) applied, the observations of edge island and peeling mode serve to improve the understanding of Edge-Localized-Mode (ELM) suppression with 3D fields. As the edge island grows, the pedestal pressure ceases increasing and holds relatively unchanged until a large ELM is triggered after ~ 100 ms. The island rotation also displays a clear modulation on the amplitude of the peeling mode, which eventually grows to a large amplitude and triggers the ELM. These observations suggest that an edge magnetic island plays a complicated role in RMP-ELM suppression. Though it enhances the pedestal transport that benefits ELM suppression, the rotation of the island also periodically excites a high frequency (~50 kHz) ELM-trigger peeling mode, which can be a result of the 3D field effect on the peeling mode stability boundary.   

Wall current compensation for rotating magnetic perturbations through the magnetic diagnostic response function

The method of magnetic diagnostic response function (MDRF) [1] is well suited to estimating the magnetic fields of wall currents induced by rotating resonant magnetic perturbations (RMP). The MDRF provides a set of time dependent Green’s functions for the magnetic diagnostics, obtained by fitting magnetic measurements with individual coils energized at varying frequencies. The wall current field from RMP is then predicted by the response functions when using the RMP coil currents with arbitrary waveforms. These predictions will be validated by vacuum shots with rotating RMP fields in DIII-D. The wall current field from the rotating RMP is separated in magnetic signals to evaluate the effect of the wall currents on electromagnetic torque analysis of magnetic islands. The present work can provide the wall currents compensation in error field identification experiments, which use a rotating RMP field to drive rotation of an n=1 magnetic island. Additionally, this work will benefit the analysis of other experiments with time-varying applied fields by accounting for the effects of induced currents in the wall and other conducting structures.

[1] Y. Jiang, RSI 2017   

Bayesian inference of axisymmetric plasma equilibria

We present a Bayesian approach for inferring axisymmetric plasma equilibria from measurements of the magnetic field and plasma pressure. This method delivers a set of posterior solutions for plasma current and pressure distribution that align with the given measurements and satisfy magnetohydrodynamic (MHD) force balance. In this method, the toroidal plasma current and magnetic field coils are modelled as a collection of axisymmetric current-carrying beams. The remaining parameters, such as plasma pressure and poloidal current flux, are represented as a function of poloidal magnetic flux, determined by a two-dimensional distribution of axisymmetric current. The profiles of plasma pressure and poloidal current flux are modelled as Gaussian processes, and their smoothness is determined according to Bayesian model selection based on the principle of Occam's razor. The force balance constraint derived from MHD is taken into account at every plasma current beam. Experimental observations collected by diagnostics are compared with predictions from the predictive (forward) models. The complex, high-dimensional posterior probability distribution is explored by using a novel algorithm leveraging the Gibbs sampling scheme. The method is developed within the Minerva framework and applied to the JET tokamak experiment.   

Enhancing Machine Learning of the Grad-Shafranov Equation with EFIT's Green's Function Tables

This work presents a method for predicting plasma equilibria in tokamak fusion experiments and reactors. The approach involves representing the plasma current as a linear combination of basis functions using Principal Component Analysis of plasma toroidal current densities (J_t) from the EFIT-AI equilibrium database. Then utilizing EFIT's Green's function tables, basis functions are created for poloidal flux (ψ) and diagnostics generated from the toroidal current. First, the predictive capability of a least squares technique to minimize the error on the synthetic diagnostics is employed. Results show that the method achieves high accuracy in predicting ψ and moderate accuracy in predicting J_t with median R² = 0.9995 and R² = 0.973, respectively. A simple neural network (NN) is also employed to predict the coefficients of the basis functions. The NN demonstrates better performance compared to the least squares method with median R² = 0.9997 and 0.988 for J_t  and ψ respectively. The robustness of the method is evaluated by handling missing or incorrect data through the least squares filling of missing data, which shows that the NN prediction remains strong even with a reduced number of diagnostics. Additionally, the method is tested on plasmas outside of the training range showing reasonable results.   

Towards a high fidelity tokamak pulse simulator

A range of efficient and robust IPS-FASTRAN integrated modeling workflows has been developed to predict time evolution of tokamak plasma discharges from plasma current ramp-up to termination. The TGLF quasi-linear transport model is employed in the core region with the new 3-D saturation model SAT2 for the Ohmic L-mode current ramp-up, where the boundary conditions are given at the separatrix. The coupled EPED/SOLPS-ITER modeling predicts self-consistent profiles in the pedestal and SOL/divertor regions during the H-mode phase of discharge flattop. Testing with TGLF-SAT2 against the ITER demonstration discharges on DIII-D reproduces the magnetic flux consumption and time evolution of the internal inductance during the plasma current ramp-up reasonably well, which strongly depends on accurate estimation of the electron temperature profile and electrical conductivity in the outer radius region. Recent progress on the Predict-First approach will be discussed to design an optimum access to high β_N Advanced Tokamak scenarios on DIII-D.   

Multi-fidelity neural network representation of gyrokinetic turbulence

This presentation will introduce a multi-fidelity neural network model of gyrokinetic turbulence GKNN-0, which has been trained and validated against a database of 5 million TGLF simulations and 5000 linear CGYRO simulations with experimental input parameters from the DIII-D tokamak. The first half of the presentation will review the TGLF saturation rules - SAT0, SAT1, SAT2 - and present a big data approach to validating both the linear model of TGLF and the saturation rules using experimental data from the DIII-D and MAST-U tokamaks. As a highlight, the TGLF model is shown to accurately reproduce both experimental and quasi-linear CGYRO fluxes for electrostatic turbulence, and the SAT2 model shows improved accuracy compared to SAT1 at capturing physics of trapped electron modes and the instability threshold of kinetic ballooning modes. The second half of the presentation will focus on database generation and benchmarking of a single-fidelity, retrained TGLF-NN and a multi-fidelity GKNN-0. The training database uses synthetically extended data from DIII-D as input, and both single- and multi-fidelity models show good convergence within a flux-driven transport solver. The big data validation approach allows efficient extensions of the training database, positioning GKNN-0 as a fast and accurate surrogate model of gyrokinetic turbulence.   

Prediction of kinetic profiles of D-T plasma using the TGYRO transport code in the JET DTE2 discharges

        JET DTE2 experiments have demonstrated the highest-ever fusion energy production. Prediction of transport in these discharges has been made using the TGLF and NEO models in TGYRO transport code. A new model TGLF-SAT2 [1] of the saturated 3-D fluctuation spectrum fit to a large set of non-linear CGYRO turbulence simulations was developed to address discrepancies uncovered by validation with JET deuterium discharges. The predicted kinetic profiles of D-T plasma using TGYRO have been validated by the JET DTE2 experiment and were found to be an accurate predictor when using the measured boundary values at r/a=0.85. TGYRO predicts the temperature profiles well for a wide radial window, except for a minor discrepancy in T_i in the plasma core. The electron density profiles n_e are underpredicted by 20% at mid-radii for both baseline scenarios and hybrid scenarios.

        An integrated modeling workflow TGYRO-STEP that iterates between the core transport with TGYRO, the pedestal pressure predicted with EPED and the MHD equilibrium computed with EFIT to find a self-consistent steady state solution is also reported. Comparing the STEP result with the fixed boundary runs shows how well the integrated modeling can predict the discharge without taking boundary conditions from the data. 

        This work was supported by the U.S. Department of Energy under DE-SC0019736 and DE-FG02-95ER54309.

[1] G.M. Staebler, et al., Nucl. Fusion 61 (2021) 116007

Disclaimer: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.   

Developing novel group theoretical algorithms for evaluating MHD stability in complex geometry

We present recent progress on the development of a new code for evaluating linear (global) ideal MHD stability in stellarator geometry, using Julia’s high performance mathematical libraries. Here, we focus on the exploration of novel algorithms, based on representation theory of finite groups, that serve the dual purpose of (i) reducing the complex, global problem to simpler eigenvalue problems over the invariant subspaces of symmetry groups in stellarators and; (ii) minimize the impact of spectral pollution, allowing accurate location of continuous spectra and discrete eigenvalues for scalable, high-performance calculations. 

Efficient and accurate evaluation of linear ideal MHD stability is a crucial step in the design and analysis of next-generation stellarators for fusion energy. In ideal MHD, spectral pollution is an error that occurs in numerical eigenvalue calculations, which grows with increasing wavenumber and is compounded by the presence of the Alfvén continuum. This makes the development of mathematically rigorous algorithms key in developing modern tools for high performance evaluation of MHD stability in complex 3D geometry.   

FIRST tokamak in progress

A conceptual design of FIRST (Formosa Integrated Research Spherical Tokamak)  is in progress. The scientific goals of the device are to perform research on (1) high β plasmas, (2) high bootstrap current density fraction (preferably 100%) operation, (3) the possibility of improved neoclassical ion confinement and the possibility of suppressed turbulent fluctuations, and (4) the maneuverability of particle transport. Here, β is the ratio of the plasma  pressure to the magnetic field pressure. These goals are consistent with the desirable features of tokamak fusion energy reactors, i.e., configurations with good plasma confinement but with ash  removability without sacrificing plasma β and without the need of the non-inductive external current drive for steady state operations. Thus, a tokamak can be an intrinsically steady state plasma confinement concept when its collisioonality parameter ν_* < 1. Here, ν_*  is the ratio of the effective collision frequency to the bounce frequency of the trapped particles. To achieve high β plasmas but with acceptable economic consequences, the device will be a low aspect ratio tokamak. The targeted aspect ratio is in the vicinity of 1.5. The magnetic field will be in the range of 0.1T to 0.5T (or higher when it is upgraded). Plasma minor radius is 30cm and elongation is 2.5 with a positive triangularity parameter. The  stability property, and the β limit of the equilibrium with a high bootstrap current density fraction of the design together with the relevant physics, and the future plan will be reported.   

FLIPEC, an Ideal MHD free-boundary equilibrium solver for plasma with flows in axisymmetric geometries.

The ability of calculating ideal MHD equilibria is needed not only during the design of a magnetic fusion device, but also in its normal operation. In the case of tokamak axisymmetric configurations with significant plasma flow, the plasma edge is maintained fixed as the code searches for the equilibrium in the majority of codes. However, plasma flows may induce changes such as displacements of the position of the X-point, the magnetic axis or the shape of the plasma boundary, to name a few, that cannot be quantified properly in a fixed-boundary setup. In this contribution we present a new equilibrium code and its most significant and recent upgrades. In this context, FLIPECode was written to obtain free-boundary axisymmetric ideal MHD equilibria for arbitrary plasma flows. Particularly, the free-plasma-boundary scheme has been previously applied to 3D, non-axisymmetric configurations in the absence of flow within the SIESTA equilibrium code.

The upgrades open the code to many other possibilities. FLIPEC was originally written in toroidal coordinates, (r,θ,ξ), providing the code with a circular domain section, what made the code incompatible with many tokamaks, since the coils and solenoid leads to a singularity in the magnetic field when included in the domain. Currently, general coordinates have been implemented and the computational mesh can be adapted to any plasma shape. Additionally, the onset of a vertical instability has been successfully addressed by the use of a control stability scheme which utilizes two stabilization coils.

Examples of application of the code to ITER and NSTX configurations will be used to showcase the capabilities of the code. Additional developments currently in progress, such as the possibility of keeping fixed some geometrical locations (magnetic axis, x-point) and the targeting to significant parameters (integrated current) will be discussed as well.   

Multi-Modal analysis of linear MHD response to resonant magnetic perturbations in DIII-D plasmas

The impact of plasma triangularity on the plasma response to 3D magnetic perturbations for DIII- D plasmas is investigated to understand its role in suppression of edge localized modes. Evidence suggests the dynamics of ELM suppression can be significantly altered by the 2D plasma shaping, namely triangularity, to the point where suppression may not be achieved [1]. By varying triangularity, pedestal density, and plasma beta using the SEGWAY framework, and calculating the 3D plasma response with GPEC, we examine the combined effect of 2D plasma shaping and 3D perturbations on ELM suppression. Preliminary results show qualitative agreement between the triangularity dependence of the kink response from GPEC and that of a related study using MARS-F[2]. Using singular value decomposition techniques, we analyze changes in dominant mode harmonics to assess the dependence of plasma response on plasma shaping. This comprehensive study identifies key factors influencing the response, providing valuable insights for optimizing plasma configurations and control strategies. [1] Paz-Soldan C. et al, Nucl. Fusion 59, 056012 (2019). [2] S. Gu et al, Nucl. Fusion 62 076031 (2022).   

Gyrokinetic modeling of neoclassical tearing modes using the electromagnetic X-point Gyrokinetic Code (XGC)

Neoclassical tearing modes in tokamak plasmas are an active area of research due to their impact on global plasma stability. They have been mainly studied with magnetohydrodynamic (MHD) codes due to the relatively smaller computational cost compared with kinetic models. The downside of fluid methods is the approximate treatment of kinetic effects such as collisional parallel or turbulent cross-field transport through simple fluid closures and turbulence models. In contrast, this work uses the electromagnetic total-f gyrokinetic particle-in-cell code XGC to model low toroidal mode number ("low-n") tearing modes using a recently installed hybrid spectral/finite-element field solver that provides higher accuracy and greater numerical stability for low-n modes than XGC's standard field solver. We present verification studies of low-n tearing mode physics using XGC's delta-f option against linear eigenvalue solvers and MHD codes. Using XGC's total-f algorithm, we study neoclassical tearing modes in a single first-principles kinetic model without relying on fluid closures or coupling to other codes.   

Non-linear saturation of non-resonant ideal long wavelength instabilities and application to sustained hybrid operational regimes

A new theory is presented unifying the non-linear saturation of non-resonant n=m=1 internal kink modes with reverse shear [1], and non-linearly saturated n=m=1 quasi interchange modes with an extended region of very low shear [2].  The generalised set of new equations also describes n=m>1 modes [3] with arbitrary non-resonant q-profiles. By explicitly evaluating the non-linear effect of these modes to, and on, the magnetic flux, it is possible to analytically quantify the effect of the 3D magnetic structures on the q-profile.  Over the initial phase of the resistively diffusing plasma scenario, the associated growing 3D magnetic perturbations are assumed to cause strong cross-field transport.  Under these conditions the plasma will cease to resistively diffuse, and the modes cease to grow, so that the hybrid regime can in principle be sustained, possibly in line with previous ideas concerning a magnetic flux pump [4].  The picture remains robust to potential kinetic corrections of core instabilities in the weakly collisional regimes of future tokamak reactors.

[1] K. Avinash Phys. Fluids B 2 2373 (1990)

[2] F. L. Waelbroeck, Phys. Fluids B 1 499 (1989)

[3] J. P. Graves, M. Coste-Sarguet and C. Wahlberg, Plasma Phys. Control. Fusion 64 014001 (2022)

[4] I Krebs, S.C. Jardin, S. Günter, et al., Physics of Plasmas 24, 102511 (2017)   

Fluctuation-induced electromotive forces in current-driven tokamak sawtooth relaxation

We show via nonlinear MHD modeling a causal relationship between the fluctuation-induced 'dynamo' EMF and the cyclic equilibrium profile relaxation in current-driven tokamak sawtooth activity. Sawteeth have been of keen interest in tokamak research (see Jardin et al. 2020, Heidbrink & Victor 2020, e.g.), and we highlight the role of dynamo EMF in impulsive sawtooth magnetic relaxation. Using the NIMROD code, we perform nonlinear zero-beta 3D visco-resistive MHD simulations initialized with q profiles reaching just below 1 on axis. This leads to current-driven sawtooth cycles, originally described by Kadomtsev. A dynamo EMF, the spatial average of the nonlinear product of velocity and magnetic fluctuations in Ohm's law, arises naturally in the relaxation process. In 3D simulations, with fluctuations of multiple toroidal mode numbers included, the dynamo EMF is localized to the core near the q=1 surface and is correlated in time with quasiperiodic bursts in fluctuation amplitudes, driving the core q profile above 1, a change of several percent, during the corresponding crash events. Comparing these cases to the quiescent equilibria in 2D simulations highlights the causal character of the dynamo EMF in the sawtooth dynamics. Details of the fluctuation dynamics are observed to vary with the location of the q=1 surface. For example, for larger q=1 radius, a subsequent oscillation in n=1 energy occurs after the main n=1 crash, possibly reflecting partial rather than complete reconnection in the main crash.   

Error field predictability and consequences for ITER

We conduct a linear study of n=1 error fields due to tilted and shifted misplacements of central solenoid and poloidal field coils within tolerance. Error fields in magnetic confinement fusion can cause large, sometimes sudden, losses in confinement, which has severe consequences for fusion performance. Their origin and optimal correction therefore remains a topic of pertinent interest for study in planning future magnetic confinement devices. We thus begin with an analysis of the necessity of error field correction for daily operation in ITER using updated scaling laws for the error field penetration threshold. We then investigate the optimal correction of each error field using the error field correction coils as well as the RMP ELM coils. We also consider the predictability of error field overlap across early planned ITER scenarios and, as measuring error fields in high power scenarios poses risks to the device, the potential for extrapolation to the ITER Baseline Scenario (IBS). We find that some error field sources extrapolate well to IBS, while others do not and could benefit from careful metrology.   

Improving SIESTA numerical convergence

SIESTA is a well known ideal MHD non linear equilibrium solver [1] capable of finding solutions that may exhibit rather complicated topologies including both magnetic islands and stochastic regions. Recently, it was extended to be capable of providing free-plasma boundary solutions as well [2]. In this work, various advances targetting the improvement of the numerical convergence of SIESTA  towards the equilibrium are presented. These advances will be of use, not only for increasing the computational efficiency for cases that SIESTA already solves with ease, but to significantly improve the performance of SIESTA in configurations where convergence is slow, is plagued by plateaus of apparently no convergence or simply fail to converge. To achieve this, it has been developed a new second order advance for both p and B perturbations (currently, it is only first order) that allows to improve the equivalence between the MHD energy variation and the work associated with the force for any given displacement. By carefully discretizing the resulting advance equations, this equivalence can be made exact for the pressure term (up to machine accuracy) and second order accurate in the displacement for the magnetic field term.This equivalence has the additional associated benefit of ensuring a fully symmetric Jacobean down to machine precision. Analytical results and first numerical tests will be presented.

[1] S. P. Hirshman, R. Sanchez, and C. R. Cook, Phys. Plasmas 18, 062504 (2011)

[2] H. Peraza-Rodriguez, J. M. Reynolds-Barredo, R. Sanchez, J. Geiger, V. Tribaldos, S. P. Hirshman, M. Cianciosa, Phys. of Plasmas 24, 082516 (2017)   

Investigation of changes induced in the MHD spectrum by the presence of magnetic islands/stochastic regions with the SIESTA 3D MHD equilibrium code

SIESTA [1] is a well known 3D MHD equilibrium solver that is capable of finding ideal MHD equilibrium solutions without assuming the existence of nested toroidal magnetic surfaces everywhere in the plasma volume. As a result, SIESTA solutions that exhibit both magnetic islands and stochastic regions are possible. In addition, SIESTA uses Eulerian coordinates in which the pressure and magnetic field response to arbitrary plasma displacement can be easily calculated. SIESTA also estimates the local Hessian of the problem (i..e, the derivative of the force with respect to the local displacement) at each step of its nonlinear iteration towards equilibrium since it is often used as preconditioner for the linear problem that must be solve at each step. Once the equiilibrium is reached, the Hessian is available and the study of its eigenvalues/eigenvectors allows to explore and quantify the ideal MHD stability properties of the reached solution. In this work we will use this capability to characterise the changes that are induced in the MHD ideal spectrum, with respect to that of neighbouring solutions that assume nested tori everywhere, by the presence of islands/stochastic regions, their size and location, for both tokamak and stellarator configurations. [1] Hishman SP, Sanchez R and Cook, CR. Physics of Plasmas 18, 062504 (2011).   

Analysis of Kelvin-Helmholtz-like instabilities in strongly rotating tokamak plasmas

Toroidal rotation in tokamak plasmas has been shown to stabilize several performance-limiting instabilities. However, for toroidal flows of the order of the ion sound speed a new rotation and rotation shear-driven Kelvin-Helmholtz-like instability can grow [1]. Experimental evidence for this mode may have been observed in previous NSTX data.  The experiments indicate that gradients in density co-existing with sonic-ordered flows could play an important role in its drive [2].  In [1], only strong gradients in plasma rotation were considered.

A large aspect ratio magnetohydrodynamic model with sonic ordered flows was therefore used to analyse the driving and damping effects of strong density, temperature, pressure and rotation gradients on the Kelvin-Helmholtz-like instability. Performing an asymptotic expansion for large, sonic toroidal rotation allowed for the parametric dependences of the mode growth to be investigated. These analytic results were additionally compared against a full magnetohydrodynamic code, VENUS-MHD, which was further used to model relevant low magnetic shear NSTX discharges.

[1] C Wahlberg et al 2013 Plasma Phys. Control. Fusion 55 105004

[2] Hao, G.Z., Heidbrink, W.W., Liu, Y.Q., Yang, S.X., Fredrickson, E.D., Podestà, M., & Crocker, N.A. (Oct 2018). Centrifugal Force Driven Low Frequency Modes in Spherical Tokamak (IAEA-CN--258). International Atomic Energy Agency (IAEA)   

Status and overview of the Wisconsin HTS Axisymmetric Mirror experiment

The Wisconsin HTS Axisymmetric Mirror (WHAM) is a magnetic plasma confinement experiment developed by UW-Madison. The setup, with its 17-Tesla superconducting magnets and class-record volumetric density of heating power (3MW/40l) will explore the performance limits of simple axisymmetric mirrors by capitalizing on better understanding of MHD-stable operation of such systems and on the significant technological advances of recent years. The goals of the experiment include achieving the so-called classical mirror ion confinement regime that could be upscaled to Q ~ 1 fusion power gain factor in the upcoming next-generation device. A major part of the experimental program is devoted to plasma micro-stability, that was previously seen as a major obstacle to unlocking the full potential of simple mirrors. As a critical piece a larger fusion program, the experiment will also provide valuable data for advanced mirror concepts such as the axisymmetric tandem mirror reactor.

The report focuses on the design features and predicted performance of WHAM, including its magnet system, 1MW/25keV neutral beam and 0.9MW/110Ghz electron-cyclotron heating systems, as well as its sophisticated electrode structure that controls the shearing rate of plasma to minimize the MHD-related losses. The first plasma will be achieved in short pulses (10 – 20 ms), but the critical systems are essentially designed for long-pulse operation that can be attained after a few upgrades to the facility are made.   

Bifurcation of radial electric field in tokamak edge pedestal in response to resonant magnetic perturbations

The radial electric field E_r can significantly influence the transport and stability of plasma in tokamak edge pedestal, as well as the plasma response to resonant magnetic perturbations (RMPs). Through the radial force balance, the radial electric field E_r can be determined from toroidal and poloidal flows, along with the pressure profiles. In presence of RMPs, the non-resonant neoclassical toroidal viscosity torque is able to drive toroidal rotation in the edge pedestal due to large diamagnetic drifts, in addition to the resonant electromagnetic torque on a rational surface. Both torques depend on the radial electric field E_r, which may eventually settle into a steady state through the torque balance. In this work, we solve for the steady state E_r in presence of RMPs through numerical iterations, based on the plasma response computed from the modified Rutherford equation or the MHD simulations using the NIMROD code. Mostly due to the existence of multiple neoclassical offset rotation roots in certain parameter regimes, the steady state E_r in the edge pedestal region tends to be multiple-valued as well, demonstrating bifurcation behaviors and suggesting potential mechanisms underlying the edge pedestal processes that rely on the plasma response in E_r to RMPs.   

Adjoint methods for Transport Equations

Gyrokinetic simulations of plasma transport have been the workhorse of numerical understanding of magnetically confined plasmas for nearly two decades. With increasing focus on designing the core of a fusion pilot plant, the focus of simulations has moved from highly accurate verification and validation simulations to the task of trying to design

and optimize whole devices.

The framework into which advanced gyrokinetic simulations fit, that of multiscale plasma transport, is well-known [Abel et. al. 2013 Rep. Prog. Phys.]. Advanced numerical methods for solving the transport equations are being deployed (see poster by M Kelly, this conference). However, to integrate such transport calculations within an optimisation framework some knowledge of the sensitivity of the solutions to these equations is needed. Typically, we wish to examine a small number of global figures-of-merit from a transport simulation, such as stored energy or fusion yield, and calculate their derivatives with respect to many design parameters. For such problems, where the number of quanties is small and the number of variables is large, adjoint methods are known to be advantageous [see, e.g. Plessix et. al. Geophys. J. Intl. 2006]. Adjoint methods for sensitivity calculations are now well-established in

plasma physics [Paul et. al., Nucl. Fusion 2018; Paul et. al. J. Plasma Phys. 2019], and in this work we apply them to the transport equations of multiscale gyrokinetics.

To use the notion of an adjoint, we first introduce an inner-product structure on the space of perturbations about solutions of the transport equations. From this, we derive fully-general adjoint equations that can be used to analyze generic derivatives in the full transport framework. As a proof-of-concept example, we take classical transport in a cylindrical screw pinch and calculate derivatives of several important global functionals. In particular we show derivatives of the integrated fusion yield with respect to the location of an applied heat source. We also discuss the possible applications of these derivatives in a control system and how efficiencient the various underlying numerical calcualtions would have to be to apply this.   

Basis Dispersionlet Bispectral Analysis

Ritz-type bispectral analysis¹ is a class of techniques that use statistical correlations in turbulence fluctuation data to infer the underlying model equations.  This offers a novel approach to theory-experiment comparison, and more recent algorithms can additionally infer profile functions or topological boundaries from fluctuation data.  Out of this class, basis dispersionlet analysis is a technique in which model equations are represented using wavelet-like operators, or dispersionlets.  This offers a compromise between accurate modeling of dispersion relations, as with the basis function method, and accurate modeling of profile functions, as with the basis operator method. 

The present work will demonstrate this technique on SOLT simulation data.  It will also compare different dispersionlet sets by a variety of metrics, such as residual error, accuracy of dispersion curve, and ability to resolve spatial features in the model. 

 

References:

1.  Ch. P. Ritz and E. J. Powers, Physica D 20, 320 (1986).   

GPU-capable RF Ray tracing using a domain-specific compiler

Designing an optimized fusion pilot plant requires rapid prediction of whole-facility performance. High-fidelity models such as full wave radio-frequency (RF) for determining power deposition profiles require too much time and resources to explore a vast array of design parameters. Geometric optics, commonly called ray tracing offer a faster approach to determine such models. However, legacy codes have not been built to exploit the hardware architectures of modern computers and their graphical processing units (GPUs). To compound the problem, GPU coding is not compatible between different manufacturers. Without proper abstraction, codes written for the CUDA architecture of Summit need to be rewritten to support the AMD architecture of Frontier. We present a new ray tracing code built using a graph computational framework. Physics equations are compiled into a graph of mathematical operations. Transformations of that graph apply auto differentiation to build ray update expressions. Reductions of the graph to reduce the problem to its simplest form. This graph of operations can be just in time (JIT) compiled to an optimized GPU or CPU kernels for a specific architecture. Using this framework, we demonstrate correct fully 3D ray behavior for realistic tokamak geometries for different plasma dispersion functions.   

Numerical near-axis expansion of weakly quasisymmetric MHS equilibria to all orders

Quasisymmetric stellarators can achieve tokamak-like neoclassical confinement without driven current. However, QS equilibria are notoriously hard to construct. It is widely believed that isotropic pressure MHS equilibria with global QS may not exist. When expanded in effective minor radius, the governing equations become over-determined at the 3rd order.[1] This does not forbid the existence of special solutions, as recent optimization works have indeed produced equilibria with precise QS.[2] It also does not apply to anisotropic equilibria. Rodriguez and Bhattacharjee has shown that adding a pressure anisotropy allows the expansion of global weak QS equilibria to any order.[3] This expansion is likely divergent,[4] but its optimal truncation and higher order behavior remain unclear. 

We present pyAQSC, the first numerical near-axis expansion code for anisotropic QS equilibria to any order. We also present numerical correlations of the optimal truncation and divergence rate to common QS metrics. In all examined cases, the expansion diverges after the 4th order, consistent with the accuracy of scalar pressure NAE.[5] Our code explores new regions in QS configuration space by relaxing pressure isotropy. It allows the study of higher order quantities, like magnetic shear, without special parameter choices. PyAQSC supports GPU acceleration and auto differentiation. Along with a new anisotropic equilibrium solver developed for DESC, it provides an efficient tool for designing QS stellarators.   

Implementation of the logical sheath boundary condition in the COGENT code

Accurate modeling of the boundary sheath layer in plasma simulation necessitates addressing the fine-scale features of the sheath region. These scales are typically much smaller than the characteristic length scales of the plasma bulk, therefore including a sheath region in a numerical model would significantly increase the cost of simulations. To overcome these difficulties, the logical sheath boundary condition (BC) is used where the sheath is replaced by a boundary potential that reflects fast electrons and enforces the total electron and ion current through the boundary to be equal. Implementation of the logical sheath BC in the finite volume COGENT code requires assigning proper values of the probability distribution function (PDF) in the ghost cells, since the fluxes on the boundary cell faces are computed based on the values of the PDF in nearby cells. This procedure depends on the advection scheme used in the code and has been implemented and tested it for first and third order upwind schemes. When electrons are reflected by the sheath potential, it inevitably yields to formation of a sharp interface of the PDF in the velocity space. That in turn leads to Gibbs oscillations when high order advection schemes are used. Different approaches for smearing the interface and mitigating the oscillations are discussed.   

ThinCurr, TokaMaker and friends: Open-source fusion modeling tools for engineering, analysis, and education

The PSI-Tet [1] and PSI-Tri [2] code bases have been merged into a common framework of reusable infrastructure for fusion-relevant simulation tools based on finite element methods on unstructured grids. In addition to the existing 3D force-free ideal MHD equilibrium [3] and 3D time-dependent extended MHD [4] tools, two additional capabilities have been added: 1) A 3D thin-wall current modeling tool named “ThinCurr” [5] that is being used to study non-axisymmetric currents in 3D device structures (eg. ports and REMCs) and as an alternative to fourier-based current potential formulations in stellarator coil optimization. 2) A 2D static and time-dependent Grad-Shafranov equilibrium tool named “TokaMaker”, that is designed to be a user-friendly and open tool for device design, control development and education. The core framework provides common capabilities to all tools, including: meshing directly from CAD models, access to scalable linear and nonlinear solvers, extensible finite element representations, parallelization via OpenMP+MPI, and 3D visualization through VisIt and similar tools. Information and development plans for ThinCurr, TokaMaker, and the full toolkit will be presented.

[1] C. Hansen, PhD Thesis (2014)

[2] C. Hansen, Phys. Plasmas 24 042513 (2017)

[3] T. Benedett, Nucl. Fusion 61 036022 (2021)

[4] C. Hansen, Phys. Plasmas 22 042505 (2015)

[5] A. Battey, APS-DPP poster (2022)   

An anisotropic hybrid structured-unstructured mesh approach enabling PIC simulations of the Scrape-Off-Layer

In this research, we introduce an anisotropic hybrid structured-unstructured mesh approach for Particle-In-Cell (PIC) scheme based kinetic simulations of the Scrape-Off-Layer (SOL) for cases with non-trivial wall shapes. The steep gradient of the electrostatic potential results in an anisotropic solution variation, e.g., in the plasma-sheath region, for which using a uniform mesh, or even a nonuniform/graded isotropic mesh, leads to an excessively large mesh. To address this challenge, we propose an anisotropic hybrid mesh approach. This approach employs a structured or layered anisotropically refined mesh, including near the non-trivial wall shapes, and smoothly transitions into a relatively coarse unstructured triangular mesh with rapid gradation for regions with a marginal solution variation. The anisotropic layered mesh uses a much smaller mesh size in the direction of the solution variation, e.g., mesh size of the Debye length in the wall-normal direction in the sheath region, while using a larger mesh size in the other directions. The effectiveness of the proposed approach is demonstrated through kinetic simulations of large-scale SOL using the hPIC2 code on multi-GPU computers.   

GITRm: A 3D Unstructured Mesh-based Particle Tracking Code for Global Impurity Transport in Fusion Devices

GITRm is a 3D unstructured mesh-based Monte Carlo particle (neutral atom and ion) tracking code for global impurity transport in fusion-relevant devices. It is designed to target complex wall geometries, including non-axisymmetric local features such as bumpers, probes, etc., and account for their interactions with the plasma. It is capable of resolving the gyro-motion of impurity particles in 3D. It is built on the PUMIPic infrastructure that is designed to be performant on multi-GPU computers. It uses strongly graded and anisotropic elements to efficiently and accurately represent the plasma fields from multiple sources, especially in a 3D/volumetric fashion. The sheath electric field can be calculated analytically or obtained from a sheath simulator. For example, procedures have been developed in GITRm to integrate a sheath mesh on which an electric field has been calculated from the particle-in-cell based kinetic code hPIC2. Furthermore, the capabilities of GITRm have been extended to simulate multiple impurity species simultaneously and their interactions with different material surfaces including mixed surfaces. Results of the impurity transport simulations will be shown for multiple cases such as the ITER and DIII-D geometries including local features.   

Contour Method for Resistive Evolution of Grad-Shafranov Plasma Equilibrium and Its Application to MTF Studies at General Fusion

We present a numerical code based on a contour method, which is developed at General Fusion (GF) for simulating magnetized plasma dynamics. The goal of this code is to model the existing GF plasma experiments and to guide the design of future GF magnetized target fusion (MTF) systems, in which metal liner compresses compact toroid plasma. The method assumes that the tokamak-like plasma goes through a sequence of axisymmetric Grad-Shafranov equilibria, which are linked together through the transport processes. The plasma is represented as a set of nested contours (flux surfaces), each of them encloses a fixed amount of plasma particles and corresponds to some values of poloidal flux Ψ_c, toroidal flux Φ_c and entropy S_c. The contours are reconstructed as levels of poloidal flux function Ψ(r,z) on 2D Eulerian quadrilateral mesh. At every time step, the code alternates between 1D transport sub-step, where updated values of Ψ_c, Φ_c and S_c are calculated using contour averaged transport equations, and 2D Grad-Shafranov sub-step, where new equilibrium mesh function Ψ(r,z) is found by iterations. The main advantage of this code is its speed: the time step is limited by a large resistive diffusion timescale and not by a small Alfven timescale as in usual MHD codes. The code can be generalized to include moving boundaries of plasma domain, which is especially useful in modeling MTF systems. Verification of our code against open source code MHD OpenFOAM and comparison of results with ongoing GF experiments will be demonstrated.   

Testing multispecies MHD algorithms within the accelerator-enabled NIMROD code

Multispecies MHD simulation is critical to fusion-energy applications such as core-edge integration with a radiating detached divertor; disruption mitigation through impurity injection; and burning-plasma physics with multiple fuel species and fusion by-products. Hierarchical models for multicomponent MHD that include closures for a diffusion velocity or evolving a momentum equation for each species are described. The NIMROD code uses a mixed implicit, semi-implicit leapfrog algorithm for single- and two-fluid (electrons and a single ion species) simulations. A semi-implicit operator in the momentum equation is essential for numerical stability for the single and two-fluid models. Approaches to generalize the semi-implicit operator for multiple momentum equations are tested. These capabilities are implemented within a version of the NIMROD MHD code that incorporates device accelerated computing through OpenACC and abstract types as enabled by modern Fortran.   

Modeling neoclassical impurity transport with the full-f gyrokinetic code COGENT

In recent years, various collision operator models have been implemented in numerous gyrokinetic codes to simulate Coulomb collisions in tokamak plasmas [1–7]. Because of high computation cost, only some gyrokinetic codes [9,10] include the correct collision operator, typically referred to as the Fokker-Planck operator. Instead, recent reports [2–7] focus on implementing increasingly complex reduced collision operators and extending these operators for the case of unlike species. Proposed models differ in physical properties, and have different scopes of use. In particular, some recent implementations of unlike collisions (e.g., [9,10]) produce no thermal force, which is important for impurity transport in the tokamak edge [11,12].

The poster reviews multi-species linearized collision operator [13], based on the approach proposed by Kolesnikov [14], in the continuum full-f gyrokinetic code COGENT. The operator is based on the Landau operator and preserves the dependence of the Coulomb mean free path on a relative velocity of colliding species. This enables to recover Braginskii thermal force in the COGENT simulations of highly collisional plasmas.

We analyze simulation results with the Braginskii fluid model, show that COGENT recovers friction and thermal forces, and present study of the neoclassical impurities transport using the new collision operator.

This work was supported by the U.S. DoE under Award No. DE-SC0016548 at UCSD, and under Contract No. DE- AC52–07NA27344 at LLNL.

[1] H. Sugama et al., Phys. Plasmas 16 (2009) 112503.

[2] H. Sugama et al., Phys. Plasmas 26 (2019) 102108.

[3] P. Donnel et al., Comput. Phys. Commun. 234 (2019)

[4] P. Crandall et al., Comput. Phys. Commun. 255 (2020) 107360.

[5] M. Francisquez, et al., J. Plasma Phys. 88 (2022) 905880303.

[6] P. Ulbl et al., Contrib. Plasma Phys. 62 (2022) e202100180.

[7] B. Frei et al., Phys. Plasmas 29 (2022) 093902.

[8] L. Landau, Phys. Z. Sowjetunion 10 (1936) 154–164.

[9] R. Hager et al., J. Comput. Phys. 315 (2016) 644.

[10] M. Dorf et al., Contrib. Plasma Phys. 54 (2014) 517.

[11] P.C. Stangeby, CFFTP-G–9042, 1990.

[12] S. Yamoto et al., Comput. Phys. Commun. 248 (2020) 106979.

[13] A. R. Knyazev et al., Comput. Phys. Commun.  (2023): 108829.

[14] R. Kolesnikov, et al. J. Comput. Phys. 229 (2010) 5564.

[15] S. Braginskii, Consultants Bureau, New York, 1965.   

Implementing general moment equations for parallel closures in NIMROD

Implementing an advanced closure module significantly extends the capability of MHD fluid codes such as NIMROD [1]. Non-Maxwellian parallel moment equations are implemented in NIMROD to obtain parallel closures. To derive the moment equations, we take moments of the first-order drift kinetic equation using orthogonal velocity polynomials. The system of parallel moment equations is then solved using 2D finite elements in the poloidal plane, considering an axisymmetric magnetic field. To overcome the memory limit associated with large problem sizes, the GMRES algorithm is used without the need for explicit matrix construction. The solution is shown to converge as the system size increases. The steady-state results are compared to analytic results using the moment-Fourier approach, which involves expanding moments and quantities related to the magnetic field in terms of Fourier series [2].

[1] C. R. Sovinec, A. H. Glasser, T. A. Gianakon, D. C. Barnes, R. A. Nebel, S. E. Kruger, D. D. Schnack, S. J. Plimpton, A. Tarditi, M. S. Chu, and NIMROD Team, “Nonlinear magnetohydrodynamics simulation using high-order finite elements”, Journal of Computational Physics, vol. 195, 355 (2004). 

[2] J.-Y. Ji, E. D. Held, J. A. Spencer and Y.-S. Na, “Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma ”, Plasma Physics and Controlled Fusion, vol. 65, 035018 (2023).   

High-order finite element arbitrary Lagrangian-Eulerian resistive magnetohydrodynamics coupled to a multi-physics code

We present a high-order finite element, arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured 2D and 3D high-order meshes. For the case of 2D, we consider two polarizations of the magnetic field: in-plane and out-of-plane. In each case, the resistive magnetic induction equation is discretized using compatible mixed finite element methods which preserve the divergence-free nature of the magnetic field. We augment the magnetic diffusion equations with an additional scalar potential solve driven by voltage source boundary conditions to facilitate the coupling of the MHD model with an external circuit solver. Electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. The coupled magnetic diffusion and Lagrangian hydrodynamics equations are solved in time using a novel multirate implicit/explicit (IMEX) approach where the magnetic diffusion solve is performed implicitly over a large timestep while the Lagrangian hydrodynamics is solved with an explicit, energy conserving two-stage RK method. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with an optimization of the mesh, followed by an ALE remap step of the MHD state variables. To remap magnetic flux, we use a high-order constrained transport (CT) method to maintain the divergence-free nature of the magnetic field. Finally, we verify each stage of the discretization via a set of numerical experiments. Such an algorithm has applications to magnetically confined fusion and high-energy density physics.   

A Grad-Shafranov-like equation for quasisymmetric stellarators

The near-axis expansion has been a successful analytical model for stellarators; however, it cannot account for shear in quasisymmetric devices easily. To get around this issue, we previously considered a large aspect ratio expansion of the 3D equilibrium equations, which, when combined with quasisymmetry, gives a Grad-Shafranov-like equation*. However, the large aspect ratio expansion only allows quasisymmetric stellarators that can be obtained from a tokamak by applying a toroidally-varying vertical shift to each poloidal plane, thus excluding rotating-ellipse-like shaping. A more general Grad-Shafranov-like equation can be obtained by expanding the magnetic field around a curl-free vacuum field. In order to make the problem tractable, we apply a subsidiary expansion of the vacuum field around a purely toroidal vacuum field. In this subsidiary expansion, the zeroth order corresponds to the large aspect ratio model previously considered, and corrections allow us to overcome some of the limitations. We then compare the analytical solutions to numerical results from VMEC. We also consider the construction of a stellarator s-alpha model from the present equilibrium model.

*W. Sengupta, N. Nikulsin, R. Gaur, A. Bhattacharjee. Quasisymmetric reduced MHD 3D equilibria near axisymmetry. In preparation for submission.   

Plasma control system design and disruption forces modelling with the open-source platform ERMES

Plasma control is essential for the correct operation of a magnetic confinement nuclear fusion reactor. The plasma must be properly shaped and positioned to make possible the generation of fusion energy. Control systems are composed of a set of coils interacting with this plasma through magnetic fields. These fields can be distorted by the different components of the reactor. These perturbative effects must be considered during the design phase and be adequately compensated to guarantee the successful performance of the machine. Also, in the event of losing control of the plasma, we need to calculate the induced forces to design the supporting structures accordingly and avoid damage.

For the modelling of those problems, we have developed the C++ open-source finite element code ERMES. Thanks to its stabilized formulations in the frequency domain, it can solve realistic geometries with low memory requirements. Also, it saves computational time by treating each frequency independently and in parallel. Once the frequencies of interest are calculated, we generate a transfer function characterizing the fusion machine. This transfer function can be used in a real time controller. Alternatively, we can generate the time evolution of the fields and forces via Laplace or Fourier transforms. We can even reproduce the movement of the plasma and the halo currents. Complex frequencies and plasma modes have been implemented in a new version of ERMES to increase its modelling capabilities. The inclusion of non-linear materials using frequency domain techniques is the next stage of development.   

Time-resolved biphase signatures of quadratic nonlinearity observed in coupled eigenmodes on the DIII-D tokamak

We report the detection of quadratic coupling between toroidicity-induced Alfven eigenmodes (TAEs) on sub-millisecond time scales (~750 μs). Identification of phase-coherency between multiple TAEs and nonlinearly-generated modes is facilitated by wavelet-based bicoherence analysis of time-series from inductive coils, taken from 4 DIII-D shots heated by neutral beam injection (NBI). A three-point scan of beam power (3, 4, and 5MW) compares coupling in different regimes of fast-ion drive.

Characterization of nonlinear three-wave interaction is inferred by stationary bispectrum phase (biphase), and confirmed via band-pass filtering. Biphase dynamics associated with prominent bispectral features are well-resolved in time and consistent with intermittent quadratic coupling. Onset and duration of nonlinearity are correlated with enhanced amplitude of one or both contributing TAEs; coincident changes in amplitude are observed for modes at the sum and difference frequency.   

Finding Magnetic Surfaces via a Single Trajectory

Many important qualities of nuclear plasma confinement devices can be determined via the Poincare plot of the magnetic field return map. These qualities include the locations of the invariant circles (magnetic flux surfaces), chaotic regions, and magnetic islands. The convergence rate of ergodic averages has been shown to successfully categorize these orbits, but many iterations of the return map are needed to implement this directly. Recently, it has been shown that a weighted average can be used to accelerate the convergence, resulting in a useful method for categorizing trajectories. 

In this poster, we will show how a technique from sequence extrapolation, the reduced rank extrapolation method (RRE), can also be used to classify trajectories with a single linear least-squares solve.  For the islands and invariant circles, a subsequent eigenvalue problem gives the number of islands, the rotation number, and the Fourier coefficients of the trajectory. We will show examples of this method on the standard map and a candidate stellarator configuration.   

On Magnetic Compression in Gyrokinetic Field Theory

The issue of finite magnetic compressibility in low-beta magnetised plasmas is considered within the gyrokinetic description. The gauge transformation method of Littlejohn is used to obtain a Lagrangian which contains this effect additionally. The field theory version obtains a system model which guarantees exact energetic consistency. Gyrocenter drifts under this model are considered within a Chew-Goldberger-Low MHD equilibrium allowing for pressure anisotropy. The contributions to the current divergence balance, hence the dynamics, due to the difference between the curvature and grad-B drifts and to the compressibility are shown to cancel up to corrections of order beta. This recovers an earlier result with the same conclusion within linear theory of kinetic ballooning modes.   

Unstructured Mesh tools for Fusion Energy System Simulation Codes

Historically fusion plasma simulation codes have employed structured grid methods that are effective for dealing with simplified geometric regions. However, structured mesh methods are not well suited for the design of the geometrically complex components of the upcoming commercial fusion energy systems such as divertors, baffles, RF antennas, etc. Therefore, a substantial number of the developers of fusion energy system simulation codes are employing unstructured mesh methods. This poster will present a set of tools developed to support unstructured mesh fusion energy system simulation codes. The poster will present:

A set of tools that combination multiple methods to meet the specific mesh generation requirements of selected fusions simulation codes.

An infrastructure to support parallel adaptive unstructured mesh simulations that has been applied to core plasma and tokamak RF simulations.

An unstructured mesh infrastructure to support massively parallel particle in cell simulations that has been used for impurity transport and edge plasma simulations.

An infrastructure for the in-memory coupling of massively parallel fusion energy systems simulation codes that employ unstructured and structured mesh methods.     

Kinetic effects on plasma flow in the magnetic mirror

This work describes the results of quasi-two-dimensional kinetic modeling of plasmas in the magnetic mirror using Particle-in-Cell methods. The drift-kinetic equations of motion for electrons and ions were implemented into the EDIPIC code [1]. The effects of the inhomogeneous magnetic field are included by varying the cell's volume and using the modified Poisson equation corresponding to the flux tube approximation. The electron collisions are included using the Langevin approach. Results of full kinetic simulations are compared with fluid analytical theory and quasineutral simulations. The role of the boundary sheath on the total potential drop is investigated at different expansion ratios in full mirror and expander only configurations. The simulations were performed in full self-consistent (full electron and ion dynamics) and reduced models with fixed potential and/or fixed ion density. The effects of electron collisions on the electron flux into the loss cone were studied and compared with earlier analytical and computational results [2-4]. The role of electrons trapped in the expander region and the effects of inherent PIC numerical noise are investigated in different regimes.

    

References

[1] D. Sydorenko, Ph.D. Thesis, University of Saskatchewan (2006); D. Sydorenko, A. Smolyakov, I. Kaganovich, and Y. Raitses,  Physics of Plasmas 13, 014501 (2006); https://github.com/PrincetonUniversity/EDIPIC.

[2] V.P. Pastukhov,  Nuclear Fusion 14 , 3-6 (1974).

[3] V. N. Khudik,   Nuclear Fusion 37, 189-198 (1997).

[4] R. H. Cohen, M. E. Rensink, T. A. Cutler, and A. A. Mirin, Nuclear Fusion 18, 1229-1243   (1978).   

Scenario Planning in Tokamaks by Integrating Free-boundary Equilibrium and Fast Transport Solvers into a Model-based Optimization Scheme

Model-based optimization in tokamaks has the potential of successfully generating feedforward-control policies capable of achieving an advanced scenario characterized by weak magnetic shear, electron internal transport barriers (e-ITBs), and an unfavorable plasma configuration. The optimization scheme integrates free-boundary equilibrium (FBE) and fast transport (FT) solvers, enabling efficient trajectory planning for the powers of available heating and current drive systems (H&CDs) and the currents of the poloidal-field (PF) coils. In the FBE solver, the toroidal current density is parameterized by using polynomials based on the normalized poloidal flux function. This parameterization is constrained by the plasma current prescribed by the designer and the poloidal beta computed by the FT solver. The FT solver, utilizing different transport and source models while leveraging the equilibrium configuration computed by the FBE solver, provides solutions for the electron heat transport equation (EHTE) and the magnetic diffusion equation (MDE). The optimization scheme takes into account limitations imposed on actuators and the plasma state, including the requirement to maintain q_min above specific thresholds to avoid associated MHD instabilities. Optimized evolutions are determined for the PF-coil currents and the H&CD powers of the EAST tokamak to illustrate the effectiveness of the proposed method.

    

Electromagnetic gyrokinetic mode simulations in XGC with an improved finite-grid stable implicit particle-in-cell algorithm

An implicit particle-in-cell method for electromagnetic gyrokinetics using parallel velocity as a coordinate has been developed in the XGC code as a means of avoiding the Ampère cancellation problem for long-wavelength MHD-type modes [1]. Here, we present an improved formulation for the implicit method, based on the work in [2], which demonstrates robust stability properties with respect to both finite-grid and temporal instabilities. We demonstrate the ability of the scheme to simulate various electromagnetic modes such as the shear Alfvén wave, kinetic ballooning modes [3], and low-n cylindrical tearing modes [4]. Finally, we study the performance of the scheme by evaluating the cost of solving the system of equations arising from the implicit discretization.

[1] B. Sturdevant, S. Ku, L. Chacón, et al., Phys. Plasmas, 28, 072505 (2021).

[2] B. Sturdevant and L. Chacón, J. Comput. Phys., 464, 111330 (2022).

[3] T Görler, et al., Phys. Plasmas, 23, 072503 (2016)

[4] Y. Chen, et al., Phys. Plasmas, 22, 042111 (2015)   

Magnetic field distribution estimations with Zeeman splitting spectroscopy at the radial phase of the PF-400J device

Discharge current measurements in Plasma Focus discharges are usually made with inductive probes such as Rogowskii coils, which present the disadvantage that it cannot determine the current circulating through the plasma column. This indetermination makes it more difficult to estimate plasma characteristics such as the temperature inside the column through the Bennett relation.  

Zeeman splitting, based on the spectral separation of optical emission lines, enables the estimation of the magnetic field in the plasma column when a high current is present. The emitted photons have a distinct polarization identified as σ⁺ and σ^-, possible to be separated by a λ/4 polarizing plate.

This work presents preliminary measurements of the magnetic field present at the plasma column of the PF-400J discharge in a high current density configuration (Φ_anode = 4.5 - 6.0 mm and Z_eff = 10 - 20 mm), by using the Zeeman splitting spectroscopic technique of the Ar III emission at 330.18 nm. The measurements are spatially resolved in the radial direction, with the use of the combination of a polarizing crystal and λ/4 polarizing plate, and a bifurcated fiber optic bundle focused on the entrance of a 0.5m spectrometer with a 2400 l/mm grating.

With this experimental configuration a magnetic field of around 2T is estimated at the pinch volume, when the maximum current (~100kA) is achieved.   

X-ray Spectroscopic Studies of Multi-material Twisted Wire Hybrid X-pinches

The Hybrid X-Pinch (HXP) has been shown to be an excellent point source of X-ray emission on the XP pulsed-power machine for radiography, producing X-ray radiation with photon energies up to 4keV ¹. Spectroscopic analysis of x-pinch dynamics has shown L-shell line emission during the compression phase, followed by a ~10ps continuum burst, with many emission lines in the expansion phase². Current studies are exploring the use of multi-material twisted wire HXPs to produce two temporally spaced X-ray bursts, while also investigating the possibility of using this load configuration to produce line radiation in different soft X-ray energy bands at the time of micro-pinch formation. This study is utilizing the 450 kA peak current XP pulsed power generator with a rise time of 60 ns (10 to 90%). Its goal is to determine if the multi-material twisted wire HXP load configuration can predictably produce temporally spaced x-ray sources within the desired soft X-ray energy bands through material selection.   

Upgrades To LLNL's MJOLNIR Dense Plasma Focus (DPF) Power Flow Region and Mounting Structure

There is an updated design for the Lawrence Livermore National Laboratory’s Megajoule Neutron Imaging Radiography (MJOLNIR) Dense Plasma Focus (DPF) machine.

The first feature is clamp convolutes within the power flow region that provide both high compression and high voltage stand-off (~100kV) required to prevent plate separation due to the J × B force (3.7 MA with 5 microsecond rise time) present during high current operations. The clamping mechanism being planted in the cathode transmission plate and penetrating the anode transmission plate requiring a complex series of nested high strength steel bars and insulation that can withstand the pinch voltage (300 kV for 100 ns).

 

There is a programmatic need to quickly change DPF hardware to decrease down-time and increase the ease of these hardware swaps by firstly incorporating a removable slide rail system which allowed for faster mounting and unmounting of the docked load and secondly by fielding an assembly stand that allowed the load to securely rotate during the assembly and disassembly process.  

 

The previous design showed signs of current joint failure in several locations. Literature search results guided an improved joint design where minimum contact forces could be calculated for given metal parameters and current action. Therefore, all current joints have been redesigned by switching to a method allowing higher than typical metal-metal contact methods can support. 

 

For measuring gun current, a novel vacuum embedded, triple shielded Rogowski probe was constructed and operated.   

Yield scaling and operating conditions for highest observed neutron yield shots above 3.5 MA on MJOLNIR DPF

MJOLNIR DPF requires high yield neutron pulses to perform flash neutron radiography with more neutrons contributing to a better image.  Commissioning MJOLNIR above 3.5 MA requires operational modifications to take advantage of the higher current to produce higher yields. 

Interleaving: Shots above 3.5 MA change the machine in a way that precludes back-to-back shots, requiring a low current (2.7 MA) “recondition shot” to reset the machine.  The yield on the 3.5 MA shots was independent of the recondition shot yield and the number of reconditioning shots performed.  Although interleaved, the 3.5 MA high yield shots still exhibit suitable consistency in pinch time, yield, and neutron shape for time-gated flash neutron imaging.

Regimes with lower than simulated yields: Above a critical pressure, the yield performs lower than simulations, coincident with the onset of asymmetries observed in the sheath.  At low pressure, the measured pinch voltage spike reaches a ceiling of 200 kV, which is suppressed below model predictions and coincident with lower than expected yields and scalings.  Measurements of rundown velocity and breakdown time for different fill pressures will be compared to determine when the shots diverge from simulations.

The highest yield shots at intermediate pressures exhibited favorable scaling ~I^4 from 2.7 up to 3.8 MA peak current and 1.2x10^12 neutrons.   

Neutron Anisotropy Measurements on MJOLNIR Dense Plasma Focus

Dense plasma focus (DPF) Z-pinches are compact pulse power driven devices consisting of two coaxial electrodes, separated by an insulator, and filled with a low-density gas.  MJOLNIR is a dense plasma focus (DPF) located at LLNL being developed to produce a neutron source for flash neutron radiography which has produced neutron pulse when driven with > 3.8 MA. DPFs produce neutrons through a combination of thermal and beam-target processes.  Results will be on inferred neutron fluence angular distribution and energy spectrum from time of flight and activation detectors. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory (LLNL) under Contract DE-AC52-07NA27344.   LLNL-ABS- 851333   

Anode Implosion Radius Effects on Dense Plasma Focus Performance

Dense plasma focus (DPF) Z-pinches are compact pulsed power driven devices consisting of two coaxial electrodes, separated by an insulator, and filled with a low-density gas. MJOLNIR is a dense plasma focus (DPF) located at LLNL being developed to produce a neutron source for flash neutron radiography and has produced greater than 10^12 neutrons when driven with up to 3.8 MA. Producing a neutron source for radiography requires both a bright neutron pulse as well as the neutrons emanating from a small volume. Simulation and experimental results will be presented on neutron yield, and stagnation characteristics for anodes with a variety of implosion radii, the radius at which the implosion starts for both the 100 kA and 3 MA DPFs at LLNL.   

Meeting Flash Neutron Radiography Requirements with the MegaJoule Neutron Imaging Radiography (MJOLNIR) DPF

A dense plasma focus (DPF) is a compact coaxial plasma gun which completes its discharge as a Z-pinch, producing short (<100 ns) pulses of ions, X-rays, and/or neutrons. In 2018, LLNL constructed and brought into operation the MJOLNIR (MegaJOuLe Neutron Imaging Radiography) DPF, which is designed for flash neutron radiography. This device has achieved neutron yields of up to 1.2e12 neutrons/pulse at 3.7 MA peak current and 1.2 MJ stored energy, with a measured neutron spot size as small as 3.8 mm FWHM. Higher stored energy (up to 2 MJ) commissioning is underway. The MJOLNIR team recently performed an assessment of the DPF's ability to meet neutron radiography requirements for dynamic experiments, including 1.0e13 yield, and 1 mm spot size FWHM. Further spot size improvements may be achieved through the use of noble gas dopants, a re-entrant cathode, and control of the anode's implosion radius. Further yield improvements may be obtained with anode shaping and an on-axis gas jet that creates a differential gas load. We present progress so far on these metrics, and potential paths forward for meeting these requirements.   

Optimization of the Neutron Source Size for Dense Plasma Focus using Particle-In-Cell Simulations

The dense plasma focus (DPF) devices can serve as portable neutron sources for radiography when deuterium is utilized as the filling gas. Improving the resolution of the radiography system relies on reducing the size of the neutron source generated by DPF. In this study, we employ the particle-in-cell (PIC) code Chicago¹ to simulate different anode shapes at varying pressures. Our findings reveal that both the implosion radius and the slope angle of the anode significantly influence the size of the pinch column during stagnation. This aspect has a considerable impact on the neutron source size, particularly in the early stages of the neutron production process. Additionally, the pressure of the filling gas determines the collisionality of the pinch plasma, which further affects compression. We will present a detailed comparison of these factors.

[1]. C. Thoma, D. R. Welch, R. E. Clark, D. V. Rose, and I. E. Golovkin. Physics of Plasmas, 24, 6 2017.   

FLASH Simulations of a Gas-Puff Xe Liner Staged Z-Pinch

The staged Z-pinch (SZP) is a pulsed-power–driven magneto inertial fusion concept under development at Magneto-Inertial Fusion Technology, Inc. (MIFTI) [1,2]. There are now several SZP variations in the literature, but they all use a high atomic number liner. In this work, we focus on FLASH simulations of a low-density gas-puff Xe liner, driven by the pulsed-power Z machine at Sandia National Laboratories, imploding on DT fuel. This configuration differs from previous ones in a crucial way: the thermal losses in the fuel are dominated by thermal conduction rather than radiation. Therefore, if the fuel can be sufficiently magnetized, thermal conductivity and losses can be reduced. We include comparisons with results from the MACH2 code and show that there is a significant difference in fuel magnetization resulting in discrepancies in convergence ratios (CR) and stagnation. Despite this, both codes’ results are encouraging as fuel ion temperatures > 15 keV are achieved. The 1D FLASH results reach CR > 300, which is likely to be experimentally unattainable, and we see Rayleigh Taylor instability (RTI) growth in 2D simulations. We hypothesize that an applied axial magnetic field would help the fuel retain heat and improve stability, resulting in a CR that could be achieved experimentally.

[1] H. U. Rahman et al., Phys. Plasmas 26, 052706 (2019)

[2] E. Ruskov et al., Phys. Plasmas 28, 112701 (2021)   

Simulation of X-Ray Spectra in Multi-Material Micro-Pinches

The dynamics of micro-pinch formation is often investigated through time-resolved measurements of x-ray emission, including L- and K-shell lines. Previous studies of single-material micro-pinches have measured L-shell emission during compression and a continuum burst at stagnation, followed by L- and K-shell emission during expansion [1]. A micro-pinch containing multiple materials offers the opportunity to tailor the x-ray spectra so line emission occurs at key times during the compression phase. Simulations of multi-material micro-pinches are presented for several candidate materials to determine the best combinations for future experiments. The dynamics of the micropinch is handled with the XMHD code PERSEUS and the output is coupled to SPECT3D, a radiation transport code. The combination of codes predicts the observable x-ray spectra during the compression stage of the micro-pinch. These results will inform ongoing experimental efforts on the XP pulsed power driver at Cornell University’s Laboratory of Plasma Studies.

 

[1] Elshafiey, A. T. “Investigation of X-Pinch Plasma Dynamics Using a Ps Time-Resolved X-Ray Streak Camera” Doctoral thesis (Cornell University 2023).   

Comparison of hydrodynamic and kinetic simulations of an ICF hohlraum surrogate

Recently, Le Pape et. al studied the plasma interpenetration in a surrogate hohlraum environment [1]. Using 3$omega$ (351nm) laser light, they drove counterpropagating carbon and gold plasmas both in vacuum and with a low-density He4 gas fill, and found the presence of the gas fill significantly inhibited interpenetration of the gold and carbon. In this work, we present computational studies of this experimental setup using both 2D (axisymmetric) hydro simulations with xRage [2,3] and 1D kinetic simulations with the Vlasov-Fokker-Planck code iFP [4,5]. We compare both to the experimental measurements of inferred plasma temperature and relative number fraction, as well as directly to the reported experimental Thomson Scattering spectra. Contrary to naïve expectation, we find that iFP reproduces the gas-fill results (which ought to be more “hydro like”) better than xRage, and vice versa for the vacuum results. We hypothesize this is due to significant 3D hydrodynamic effects in the vacuum case (e.g., plasma “fingering”), which are less present in the gas-fill case. Further, the gas-fill case presents kinetic interpenetration and mix of the He4 into the carbon and gold, which is not well represented in a hydro code.

References:

[1] S. Le Pape, et. al, Phys. Rev. Lett. 124, 025003 (2020).

[2] B. M. Haines, et. al, Comput. Fluids 201, 104478 (2020)

[3] B. M. Haines, et. al, Phys. Plasmas 24, 052701 (2017)

[4] S. E. Anderson, et. al, J. Comp. Phys. 419, 109686 (2020).

[5] W. T. Taitano, et. al, Comp. Phys. Comm. 263, 107861 (2021).   

Nonlocal non-Maxwellian electron distributions in radiating laser-plasmas

At laser irradiances relevant to ICF, steep temperature gradients lead to nonlocal electron thermal transport. The electron heat flux from the nonlocal anisotropy f₁ of the electron distribution function (EDF) alters the self-emission from the laser-heated plasma. This deviation of f₁ from classical to nonlocal is caused by the deviation of the isotropic component of the EDF, f₀, from Maxwellian. Consequently, this work considers both the nonlocal heat flux from f₁ and the non-Maxwellian distortion from f₀ on the plasma’s self-emission.

 

HYDRA radiation-hydrodynamics simulations are performed utilizing the Schurtz-Nicolai-Busquet (SNB) nonlocal transport model. Kinetic EDFs from HYDRA plasma conditions are calculated with the Vlasov-Fokker-Planck code K2. Nonlocal, non-Maxwellian emissivities and radiative fluxes are then calculated with CRETIN. These studies find that the non-Maxwellian f₀ affects the emissivity of plasma states in the laser-ablation front. In addition, the effect of other sources of non-Maxwellian distributions in laser-plasmas are assessed.   

Delayed shock breakout from aluminum samples in a halfraum due to hot electron beaming from the LEH window

We have shot gas filled Au halfraums at the National Ignition Facility with a sample on the back wall. With Au samples we measure radiation burn-through to assess opacity and equation of state at 300 eV. The Dante instrument measures halfraum drive via x-ray emission through the laser entrance hole (LEH). To more accurately assess the drive at the sample position, we measured shock breakout from Al samples.  The shock broke out 1 nsec later than expectations based on a drive that matched the Dante. We attribute that discrepancy to hot electrons beaming from the LEH window, and preheating the back surface of the Al samples. This causes motion of that back surface, which delays the shock breakout. We quantify this effect by measuring the time resolved hard x-rays produced by those hot electrons, and analytically calculate a 6 eV preheat. Simulations show that precisely such an amount leads to the observed 1 nsec delay in shock breakout. Future experiments will eliminate this preheat by using a small pre-pulse to blow down the LEH window before it is illuminated by the high power pulse.   

Evidence of suppressed beam-plasma instabilities in a laboratory analogue of blazar-induced pair jets

We report on an experimental platform at the HiRadMat facility, within CERN’s accelerator complex aimed at recreating a laboratory analogue of ultra-relativistic blazar-induced pair jets propagating into the intergalactic tenuous plasma. More than 10¹³ electron-positron pairs are produced by irradiating a target with 440 GeV protons from the Super Proton Synchrotron. The pair yield and plasma extent are orders of magnitude larger than currently achievable at laser facilities, producing for the first time pair plasma conditions necessary for the study of relativistic kinetic plasma instabilities. In our experiment, the pair beams are remarkably stable as they propagate through 1-m of plasma. We compare the results with theory and particle-in-cell simulations, which predict that the growth of kinetic instabilities is strongly suppressed when non-idealized beam conditions are assumed, such as the inclusion of a small transverse temperature. An experimentally inferred growth rate, when scaled to blazar's jets, is comparable to the inverse-Compton cooling time of the pairs on the cosmic microwave background. Given that a cascade of GeV inverse-Compton scattered photons is not observed from blazar's jets, our results imply that such an absence must be the related to the presence of intervening magnetic fields in the intergalactic plasma of primordial origin.   

Extended Magnetohydrodynamic Effects on Dynamics and Stability of Magnetically Driven High Energy Density Plasma Jets

A novel experiment resembling a planar plasma gun has been developed to produce magnetically driven high-energy-density (HED) plasma jets on the 1 MA, 220 ns rise time COBRA generator at Cornell University. The experimental setup consists of a central pin electrode that injects a single gas puff on axis, surrounded by a second annular electrode with a continuous gas injection slit. A permanent ring magnet is housed within the central electrode to provide an initial poloidal magnetic field which links the two electrodes. In this way, the experiment mimics a magnetized central object such as a star or blackhole surrounded by a rotating accretion disk. The resulting free-boundary, high aspect ratio plasma jets strongly resemble naturally occurring astrophysical jets. Here, we investigate extended magnetohydrodynamic (XMHD) effects on jet dynamics and stability via the ability to have the cathode as the central pin electrode and anode as the annular electrode or vice versa with the added flexibility to reverse the polarity of the background poloidal magnetic field independently of the cathode and anode. Measurements of densities, temperatures, velocities, and magnetic fields are collected using Thomason scattering, B-dot probes, Faraday rotation, laser interferometry, and optical spectroscopy. The experimental results are supported by 3D modelling using PERSEUS an XMHD code; simulation results are used to study the evolution of canonical fields, flux tubes, and helicity in the plasma jets.   

The electron cyclotron maser instability in laser ionized plasmas

We propose the use of laser-ionized plasmas as a way to probe the electron cyclotron maser instability in the laboratory. Due to the conservation of canonical momentum, the laser imprints its polarization in the momentum distribution function of the electrons [1]: the distribution after the laser passes the region is closely connected to the laser vector potential at the ionization instant. Therefore, circularly polarized lasers can generate ring-shaped distribution functions [2]. Recent results have shown that these distributions may be much more common in astrophysical plasmas than previously thought [3].

Under the presence of external magnetic fields, these ring distributions can live over larger timescales. They present inverted Landau populations, so in a magnetized plasma, they are prone to kinetic instabilities such as the electron cyclotron maser [4]. Using theory and particle-in-cell simulations with the code OSIRIS [5], we investigate conditions for the unset of the maser and other competing instabilities using state-of-the-art laser systems. We show parameter regimes where the maser dominates and compare results for the radiation signature observed in simulation with results from kinetic theory.

[1]  X. Xu et al., PRAB 25, 011302 (2022)

[2] C. Zhang et al., Sci. Adv. 5, eaax4545 (2019) 

[3] P. J. Bilbao and L. O. Silva., PRL 130, 165101 (2023)

[4] K. R. Chu, Rev. Mod. Phys. 76, 489 (2004)

[5] R. A. Fonseca et al., in Computational Science — ICCS 2002, edited by P. M. A. Sloot, A. G. Hoekstra, C. J. K. Tan, and J. J. Dongarra (Springer Berlin Heidelberg, 2002) p. 342   

Characterization of the nonaxisymmetric MHD mode in the Princeton magnetorotational instability experiment using simultaneous velocity and magnetic field measurements

We report comprehensive experimental and numerical characterization of the recently identified magnetohydrodynamic (MHD) instability in a modified Taylor-Couette experiment using Galinstan as the working fluid [Wang et al., Nat. Commun. 13, 4679 (2022)]. In the experiment, the inner cylinder, outer cylinder and upper (lower) endcaps corotate independently at an fixed angular velocity ratio Ω₁:Ω₂:Ω₃=1:0.1325:0.55, creating a hydrodynamically stable (quasi-Keplerian) flow in the bulk of the container. Coils surrounding the outer cylinder provide a uniform magnetic field Bi along the rotation axis. We used Hall probes and ultrasound velocimetry to simultaneously measure the radial magnetic field B_r and azimuthal velocity u_φ at different azimuths in a single run. The B_r measurements were made on the inner cylinders surface at different heights, and u_φ measurements were made from the outer cylinder at the midplane. The nonaxisymmetric instability is observed in B_r and u_φ. It has an exponential growth at its onset and a dominant azimuthal wavenumber m=1. The instability is global with a radially uniform rotation frequency (angular phase velocity), and an axial phase velocity as well. Our numeral simulations reproduce the experimental findings, and further reveal that the nonaxisymmetric instability contributes to outward radial angular momentum transport, as with the magnetorotational instability. Possible mechanisms for the instability are also discussed.   

Advancing Multi-Scale Physics Modeling in Strongly Magnetized Relativistic Plasmas: A Sub-Cycling Approach of Analytic Particle Pusher

Modeling multi-scale physics in astrophysical and laboratory plasmas with strong magnetic fields for particle acceleration poses challenges for conventional explicit relativistic Particle-in-Cell (PIC) simulations that employ the leapfrog scheme. The leapfrog scheme utilizes a fixed time step for both fields and particles, which works well when the time step determined by the field solver (CFL condition) is the smallest time-scale of the simulation. However, in the presence of a strong magnetic field, a gyro-motion timescale may be even smaller than the CFL-determined time step. To address this issue, we propose a particle sub-cycling approach [1] by employing a known analytical solution of particle motion in arbitrary constant electromagnetic fields [2] to construct approximate solutions with non-uniform fields. By incorporating the analytic particle pusher with sub-cycling, our method enables significant improvements in achievable scales within the kinetic model for systems with strong magnetic fields, surpassing the limitations of standard approaches. We demonstrate the effectiveness of the proposed particle pusher in test particle problems and the PIC algorithm through standard benchmark tests such as Landau damping and 2-stream instabilities. Additionally, we compare the performance of the new algorithm with standard PIC simulations on problems spanning a range of magnetization strengths from relatively weak to strong regimes. Overall, our study presents a novel approach to address the challenges of multi-scale physics modeling in plasmas with strong magnetic fields, offering improved capability and accuracy.

[1] COHEN, BRUCE I. "Orbit averaging and subcycling in particle simulation of plasmas." Multiple Time Scales. Academic Press, 1985. 311-333.

 

[2] Landau, L. D., and E. M. Lifshitz. The Classical Theory of Fields: Volume 2. Butterworth-Heinemann, 1994.   

Discontinuous-Galerkin Representation of the Maxwell-Juttner Distribution

Accurately projecting the Maxwell-Juttner (MJ) distribution onto a discrete simulation grid can be a challenge for relativistic kinetic continuum simulations. This arises from the finite velocity bounds of the domain which may not capture the entire distribution function, as well as errors introduced by projecting the function onto a discrete grid. Here we outline a procedure for projecting the MJ in a Discontinuous Galerkin scheme, which itself adds complication in calculating nonlinear quantities on the grid. By computing the moments of the projected distribution function, using Gauss-Legendre quadrature for nonlinear quantities, and iterative correcting moments calculated by this procedure they converge, we can correct for these inaccuracies in the discrete projection. The result is a method that accurately captures the distribution function and ensures the moments match the desired values to machine precision.   

The Large Scale Impact of Localized Cosmic Ray Injection

Supernova explosions are a major driver of galaxy evolution, and cosmic rays are a major component of that driving. This 'cosmic ray feedback' presents a challenging multiscale problem in galaxy simulations. The supernova explosions on small scales (<< 1pc) which accelerate cosmic rays eventually produce the background of cosmic rays streaming throughout a galactic disk. They also affect the vertical structure of a galactic disk on large scales (> 1kpc). We examine the connection of cosmic ray production by supernovae to the vertical structure of a galactic disk using galactic patch simulations in the Athena++ code. We randomly place point-like injections of cosmic rays in the mid-plane of a 1kpc² patch of a galactic disk. These injections disrupt the vertical hydrostatic equilibrium on large scales. We observe significantly different results when using random, point-like injections instead of a constant cosmic ray flux.   

Withdrawn

As stars evolve beyond their core-hydrogen-burning phase, angular momentum conservation forces their contracting cores to spin up and their expanding envelopes to spin down. However, observations show a much smaller core-envelope rotation difference than expected, indicating anomalous transport of angular momentum between the core and envelope. One proposed source of this transport is MHD turbulence driven by the Tayler-Spruit dynamo, which might provide significant transport despite the rotating and strongly stratified nature of these plasmas. However, conflicting reduced models have been put forth to predict the efficiency of this transport and how it varies with properties of the star. These conflicting predictions stem from different assumptions regarding the saturation mechanism of the Tayler instability, a key element of the Tayler-Spruit dynamo. 

Here, we present a suite of 3D MHD simulations of the Tayler instability in a rotating, stratified cylinder to model the local dynamics near the rotation axis of a star. To test the assumptions of different reduced models, we investigate how this instability saturates, and how the saturated state varies across different parameter regimes relevant to stellar interiors.   

Entity: Architecture-agnostic General Coordinate (QED)(GR)PIC Code for Simulating Astrophysical Plasmas

Over the past decade, particle-in-cell (PIC) has become the preferred method for simulating plasma physics in the vicinity of compact astrophysical objects. However, there is currently no publicly available code that encompasses all the necessary radiation-plasma coupling processes and can effectively model large-scale systems. In this presentation, I will introduce Entity, a state-of-the-art open-source PIC code specifically designed for extreme astrophysical plasmas. Built upon the Kokkos framework, Entity boasts efficient implicit multi-architecture portability, including GPU utilization. Notably, the code incorporates advanced algorithms to handle diverse radiation-plasma coupling phenomena, such as Compton scattering, electron-positron pair production, and annihilation. Entity is constructed within a general coordinate system defined by metric functions, enabling it to successfully tackle global models of compact object magnetospheres. These models necessitate algorithms operating on non-cartesian grids (e.g., spherical, cubed-sphere) with varying densities, and even encompassing full general relativity. To enhance usability, Entity is packaged with a runtime GUI based on OpenGL for real-time data visualization and a Python-based post-processing framework.   

Neutral-charged-particle Collisions as the Mechanism for Accretion Disk Angular Momentum Transport

The matter in an accretion disk must lose angular momentum when moving radially inwards but how this works has long been a mystery. By calculating the trajectories of individual colliding neutrals, ions, and electrons in a weakly ionized 2D plasma containing gravitational and magnetic fields, we numerically simulate accretion disk dynamics at the particle level [1]. As predicted by Lagrangian mechanics, the fundamental conserved global quantity is the total canonical angular momentum, not the ordinary angular momentum. When the Kepler angular velocity and the magnetic field have opposite polarity, collisions between neutrals and charged particles cause: (i) ions to move radially inwards, (ii) electrons to move radially outwards, (iii) neutrals to lose ordinary angular momentum, and (iv) charged particles to gain canonical angular momentum. Neutrals thus spiral inward due to their decrease of ordinary angular momentum while the accumulation of ions at small radius and accumulation of electrons at large radius produces a radially outward electric field. In 3D, this radial electric field would drive an out-of-plane poloidal current that produces the magnetic forces that drive bidirectional astrophysical jets. Because this neutral angular momentum loss depends only on neutrals colliding with charged particles, it should be ubiquitous. Quantitative scaling of the model using plausible disk density, temperature, and magnetic field strength gives an accretion rate of 3 × 10⁻⁸ solar mass per year, which is in good agreement with observed accretion rates.

[1] Y. Zhang and P. M. Bellan ApJ 930 167 (2022)   

The Structure of the Beginning of the Universe - Point Circle Structure

The radiation radius of any object is equal to the speed of light divided by the angular velocity of the object's rotation. R=c/ ω, R is the radiation radius, c is the speed of light ω It's angular velocity. When the rotational speed of an object is equal to the speed of light, the radiation radius is equal to the radius of the object. The high-speed rotation of air can create a vacuum inside, without air. Dense solids that rotate at the speed of light can also form a vacuum inside them, free of matter. Due to the constant speed of radiation and the speed of light, the radiation radius must exist inside objects that rotate faster than the speed of light. When a dense object far exceeds the speed of light, the radiation radius R tends to be infinitely small, similar to a point. Due to the object's rotation speed far exceeding the speed of light, the internal vacuum of the dense object, the outer circle, is bound to be extremely large, and there is a radiation circle with a very small radius inside - a point, forming a point circle structure. At this point, the entire matter of the universe is concentrated on this dot and circle structure, and the universe is about to perish and start a new universe.   

The Effect of Heat Transport on Compressible Fluctuation Dynamo in Multi-temperature Plasmas

The existence of magnetic fields of dynamical significance, as measured through astronomical observations, poses several questions regarding the mechanisms behind their origin, the processes that result in their amplification, and how they maintain their magnitudes. Fluctuation dynamo, wherein turbulent motions drive the amplification of small seed magnetic fields to magnetic energies that are a non-trivial fraction of the turbulent kinetic energy, is one of the leading theories to account for the observed magnetic fields. First numerically demonstrated in the foundational work of Meneguzzi et al.,[1] several numerical studies have explored fluctuation dynamo in magnetized turbulence in different regimes, but few have ventured beyond the constant diffusivity magneto-hydrodynamics (MHD) ansatz. The recent experimental demonstration of fluctuation dynamo [2, 3] at the Omega Laser Facility has brought about the urgent need for such excursions, which will lay the theoretical foundations to understand the mechanism when plasma effects are prevalent. To start exploring plasma conditions that are relevant to laser-driven, high energy-density (HED) plasma turbulence, the one-temperature, isothermal, resistive-MHD ansatz broadly used in current theoretical and numerical models must be relaxed (for a recent review, see Rincon [4]). Leveraging FLASH’s new extended MHD and HED physics capabilities, we present the first set in a series of simulations that explore how three-temperature physics affect the workings of fluctuation dynamo in HED-relevant plasma conditions.   

Whistler Lion Roars within Mirror Modes in Galaxy Clusters

Lion roars are bursts of whistler waves associated with low magnetic field regions of mirror modes. They are observed in plasmas near Earth, Saturn and the solar wind. In the intracluster medium (ICM) of galaxy clusters, mirror instability is also expected to be excited, but it is not yet clear whether whistler lion roars can also be present in this high-β environment. In this work, we perform fully kinetic particle-in-cell simulations of a plasma subject to a continuous amplification of the mean magnetic field to study the nonlinear stages of the mirror instability and the ensuing excitation of whistler lion roars under ICM conditions. Once mirror modes reach nonlinear amplitudes, a simultaneous excitation of whistler lion roars and ion-cyclotron waves (IC) is observed, with sub-dominant amplitudes and quasi-parallel propagation. We show that the underlying mechanism of excitation is the pressure anisotropy of electrons and ions trapped in mirror modes with loss-cone type distributions. We observe that IC waves play an essential role in regulating the global ion pressure anisotropy at nonlinear stages. We argue that lion roars are a concomitant feature of mirror instability even at high β, therefore expected to be present in the ICM. We discuss the implications of this work on the ICM turbulent heating via magnetic pumping.   

Wave Interactions and Turbulence in High-β Collisionless Plasmas

Employing numerical simulations and analytic theory, we investigate the nature of hydromagnetic wave interactions and their effects on magnetized turbulence within high-β, collisionless plasmas. In particular, the interactions of parallel-propagating Alfvén waves with acoustic and other Alfvén waves are studied using a CGL-MHD framework with Landau-fluid heat fluxes. We find that strong modifications can occur to Alfvén-wave packets on timescales comparable with their linear propagation in response to the spatially varying pressure anisotropy generated by other modes. These interactions have consequences for our understanding of magnetized turbulence in environments such as the intracluster medium of galaxy clusters and black-hole accretion flows. With this physics borne in mind, we reexamine the interaction between compressive and Alfvénic fluctuations in a turbulent cascade, as well as the ability of Alfvén waves to establish a weak cascade parallel to the guide magnetic field (otherwise forbidden within standard MHD). Our conclusions are further tested using hybrid-kinetic particle-in-cell simulations, which self-consistently capture feedback from kinetic microinstabilities such as firehose and mirror.   

MHD turbulence and the dynamo problem

Finding the origin of global magnetic fields around stars and planets is called ‘the dynamo problem.’ These global magnetic fields arise from layers of turbulent plasma that can be modeled as a spherical shell of magnetofluid in which magnetohydrodynamic (MHD) turbulence occurs due to convection. Ignoring compressibility, the  problem reduces to examining incompressible MHD turbulence in a spherical shell. Velocity and magnetic fields and represented by orthogonal function expansions whose coefficients form a dynamical system. Assuming that the magnetofluid is ideal (no dissipation), we can apply equilibrium statistical mechanics based on the ideal invariants of incompressible MHD. For a rotating system, the ideal invariants are energy and magnetic helicity; if there is no rotation, cross helicity is also an invariant. Expectation values such as means and variances of the dynamical variables are then calculated and tested numerically using Fourier codes, since the statistical mechanics for a spherical shell and a periodic box are equivalent. Expectation values mostly agree with numerical time averages, but there is a surprise: Although all mean values are predicted to be zero, the largest-scale modes have dynamical mean values that are large and quasi-stationary. This ‘broken ergodicity’ is due to a dynamically broken symmetry. Here, we review the theory and computation that lead to this solution of the dynamo problem, as well as discuss its applicability to real MHD turbulence.   

Turbulent nonlinear dynamics of magnetic flux ropes in reduced magnetohydrodynamics

Magnetic flux ropes are integral to the dynamics of many plasma physics phenomena, including coronal heating, astrophysical jets, and 3D magnetic reconnection. While interactions between multiple flux ropes play an important role in some of these systems, the evolution of a single flux rope under its own dynamics is also relevant. We present results from numerical simulations of magnetic flux ropes in reduced magnetohydrodynamics, in which resistive instabilities of the flux rope result in a turbulent nonlinear state where the intense current sheets associated with unstable modes produce a magnetic energy spectrum E_M ~ k_⊥^-2. We show that the number of linearly unstable rational surfaces is an important parameter for determining the fraction of magnetic energy available to the turbulence and discuss the mechanisms by which the system can be maintained in a quasi-steady nonlinear state accompanied by dissipation of a large fraction of the initial magnetic energy. This work may have implications for the study of particle acceleration in astrophysical systems, as well as plasmoids in 3D magnetic reconnection.   

Simulations of the Radiative Collapse of Plasmoids in Extreme Astrophysical Environments

In extreme HED astrophysical environments such as black hole coronae, jets and pulsar magnetospheres, radiation is an important signature of reconnection that modifies the energy partition, leading to cooling instabilities such as radiative collapse. Initial theoretical work done by Uzdensky and McKinney [Uzdensky & McKinney, 2011] describes radiative reconnection using a modified, compressible Sweet-Parker model, but this model does not include the effects of the plasmoid instability, which serves as a trigger for fast reconnection and forms magnetic islands or “plasmoids” [Loureiro et. al., 2007]. Simulations of the reconnection layer generated by a dual exploding aluminium wire array, using the Eulerian 3D resistive MHD code GORGON [Ciardi et. al., 2007], showed the formation and collapse of plasmoids in the presence of radiative cooling. Additionally, it was found that larger plasmoids collapse before smaller plasmoids. The presented work aims to elucidate the underlying mechanism of plasmoid collapse using AthenaPK, an astrophysical MHD code, whilst considering all terms involved in the balance of power density, including radiative loss, thermal conduction and ohmic heating, in a more fundamental geometry.   

Simulation study of energy partition in non-relativistic collisionless shocks

Collisionless shocks are common in astrophysical plasmas and are known to be important for the magnetic field amplification and acceleration of both high energy electrons and protons. While diffusive shock acceleration is well established, particle injection into the nonthermal tail remains an important puzzle. In this work we present the results of large-scale one-dimensional particle-in-cell simulations of magnetized, non relativistic, collisionless shocks to discuss how the properties of the injected particles depend on the plasma parameters, namely the Alfvénic Mach numbers and the orientation of the ambient magnetic field with respect to the shock normal. Quasi-parallel and quasi-perpendicular shocks are analyzed. We analyze electron heating and the development of a nonthermal power- law-like tail in the energy spectra, finding that quasiparallel shocks with high Mach number are the most efficient in terms of injection to the highest energies. Reflected particles exchange energy through wave-particle interactions, exciting modes in the upstream and promoting electrons heating. We analyze the nature of these modes and compute the ratio Te/Ti. We analyze individual trajectories of the most energetic particles to discuss how they achieve non-thermal energies.   

Spectral studies of the Weibel turbulence via PIC simulations

Unmagnetized plasmas with (interpenetrating) plasma beams are highly unstable to electromagnetic instabilities such as the Weibel filamentation instability. High-energy-density plasmas in astrophysical systems are ubiquitous, and are present in collisionless shocks of gamma-ray bursts and supernova explosions, for instance. These are the locations where the beam-plasma Weibel instability naturally occurs. It affects plasma dynamics and observable electromagnetic radiation. Here we investigate collisionless, unmagnetized, counter-propagating plasmas with PIC simulations using TRISTAN-MP code. We developed a spectral analysis software suite which we now use at the post-processing stage. Here we present the time-dependent spectral analysis in the omega-k space and the angle-dependence of the plasma modes present in the system as it evolves in time. Various properties the excited plasma modes are discussed.   

Spectral characterization of the Hall Effect thruster operation on argon propellant

We continue non-invasive characterization of the BHT-200 Hall Effect Thruster performance. First, vacuum EUV spectra of the HET's operation on Ar propellant are collected and the emission lines of plasma species including natural impurities are identified. Next, FUV-MUV spectrum is examined for notorious boron nitride lining erosion products as a function of the discharge parameters. Finally, the upgraded high-resolution NUV-NIR system [1] is used to measure the axial velocity of Ar ions along the plasma plume. New results are compared to the old data [2,3] of the thruster operating on Xe and Kr propellants.   

Evaluation of Plasma Flow and Acceleration Effect Using Rotating Magnetic Field Current Driving Method in Magnetic Nozzle

Rotating Magnetic Field (RMF) current driving is utilized to form Field Reversed Configuration (FRC) in the field of nuclear fusion research [1] and accelerate plasma in electrodeless Radio Frequency (RF) plasma propulsion [2]. The RMF plasma acceleration is proposed for performance improvement of the RF plasma thruster by increasing an electromagnetic force under a magnetic nozzle [3]. The RMF method drives an azimuthal electron current owing to the non-linear Hall-term effect, and the additional force is generated in the presence of the external divergent magnetic field.

To optimize the plasma acceleration effect in our proposed RMF thruster concept, we measured and investigated the spatial profiles of plasma parameters, including Ion Velocity Distribution Function (IVDF) using laser-induced fluorescence velocimetry [4]. An increase in the axial component of the IVDF was found showing the additional plasma acceleration effect via electron current driving under the magnetic nozzle. We also compared two-dimensional spatial profiles of the ion flow vectors varying the RMF rotational frequency, which affects the RMF penetration into plasma, to clarify the dependence of the ion flow on the frequency. It was suggested that multiple plasma acceleration is yielded by the RMF method, not only for the full penetration of the RMF but also even when the RMF penetration is not fully accomplished [5].   

Preliminary concept for an electrodeless Magnetic Reconnection Thruster (e-MRT)

Advanced thrusters are needed for deep space missions to Mars and beyond. Critical issues for such thrusters include (1) how to generate large thrust-to-power at (2) sufficiently high specific impulse with (3) long lifetime and (4) flexibility in propellant. To address these challenges, we are exploring a new electrodeless Magnetic Reconnection Thruster (e-MRT), which will use asymmetric, inductively-driven magnetic reconnection outflows to provide spacecraft thrust. Not requiring electrodes would mitigate electrode erosion, which is a key constraint on the lifetime of magnetoplasmadynamic (MPD) and Z-pinch thrusters–other candidates for these missions.   

Nanosecond dielectric barrier discharge aircraft ice protection system

The Earth's atmosphere contains lots of water vapor at every level. Liquid water droplets in clouds can be below the freezing point, a matter phase state with the thermodynamic name of "supercooled". It so happens that all aircraft flying at subsonic speeds into clouds in these conditions collect ice on every forward exposed structure. The big engineering challenge is to design and develop ice protection systems that use the least amount of engine power, which at this point is why, numerically, the number of ice-protected aircraft is the minority compared to overall global number of aircraft. This paper presents results of numerical modeling of nanosecond surface dielectric barrier discharge (ns-SDBD) for aircraft ice protection system using a heat release in highly nonequilibrium pulsed plasma. The major attention is paid to the effects based on ultrafast (on nanosecond time scale at atmospheric pressure) local heating of the gas, since at present the main successes in ice protection using gas discharges are associated with namely this thermal effect. The mechanisms of ultrafast heating of air at high electric fields realized in these discharges, as well as during the decay of discharge plasma, are analyzed.   

Development and Analysis of a Multiscale Numerical Model for Ionic Electrospray Emission

Electrospray thrusters, a rapidly evolving class of electric propulsion devices, hold significant potential for enhancing the efficiency of miniaturized spacecraft. These thrusters operate by applying an electrostatic field to a liquid ion source, from which ions are extracted and accelerated, thereby generating thrust. Despite their high propulsive efficiency, particularly those operating in a purely-ionic emission regime using room-temperature molten salts (ionic liquids), their broader adoption has been limited. This is primarily due to various uncharacterized failure modes that impede their reliability in mission-critical applications.This study aims to address this gap by developing a comprehensive, multiscale numerical model of a purely ionic emitting electrospray thruster. The model is designed to guide future thruster design optimization and enhance their reliability. The methodology involves an electrohydrodynamic meniscus model that links upstream geometric and fluid properties to the current emitted at the interface. A dual direct simulation Monte Carlo and particle-in-cell approach, a method that simulates the movement of ions within the plume, is then implemented. Preliminary results indicate that this model can successfully predict the behavior of these thrusters under various conditions. This understanding can help identify key design parameters that influence thruster performance and reliability. By illuminating the dependencies of emission characteristics, this research provides valuable insights into potential strategies for mitigating electrospray failure mechanisms.   

Investigation of Plasma-Induced Magnetic Flux Compression on Induced Current in a Stator Coil Within Different Magnetic Field Configurations

In this experiment we investigated the effect of magnetic flux compression using different magnetic field geometries on induced current in a solenoid-shaped stator coil. A laser-produced plasma (LPP) was created to induce magnetic flux compression. In this experiment, a pulsed Nd: YAG laser with a wavelength of 532 nm was focused through a plano-convex lens and fired at a graphite target within a solenoidal stator coil in a vacuum chamber. The stator coil was placed in between two permanent block magnets and contains 22 turns of wire. The block magnets are arranged in different positions to analyze how different magnetic field configurations affect current produced during magnetic flux compression. These configurations include axial, transverse, and magnetic cusp geometries. The experiment was carried out in a pressure range of 10^-4 Torr to 250 mTorr and used a laser energy of 200 mJ. A Pearson coil was connected to an oscilloscope and was used to detect current induced in the stator coil during the LPP-induced magnetic flux compression.

 

 

    

Laser produced plasma expansion into high magnetic field gradients.

Laser produced plasmas expanding into background magnetic fields is a good analogue for many plasma phenomena. We have extended our previous work by initiating a laser produced plasma expansion into a nonuniform, high gradient background magnetic field. The highly uniform magnetic fields produced by the Magnetized Dusty Plasma Experiment (MDPX) were combined with the field of 2” x 2” cylindrical permanent magnet to create our desired fields within a vacuum chamber pumped to pressures of ~ 4 mTorr. We captured the emission from the laser ablating a solid carbon fiber sheet with an ICCD camera, and the input laser energy, applied MDPX field, and camera gate delay time relative to the laser pulse were all varied. Increasing laser energy led to a broadening of the plasma emission transverse to the magnetic field and increasing the applied MDPX field led to a focusing of the plasma emission. Varying the camera gate delay allowed us to observe the dynamics of the expansion, and the resultant gradient field also lead to a much longer confinement time than that of laser produced plasmas expanding directly transverse to the applied magnetic field with the emission lifetime lasting upwards of 10 μs. Additionally, the plasma emission seemed to have two distinct components with one fast lived component reaching maximum expansion within 1 μs and another slower component reaching maximum expansion at > 10 μs.   

Gas-Bubble Mixing Improves Liquid Treatment with Cold Atmospheric Plasma

This research addresses the treatment uniformity of liquid (TUL) treated with cold atmospheric plasma (CAP), a key challenge in plasma-liquid interactions. In CAP treatment of liquids, it is crucial to render the effects of CAP on all parts of a liquid sample such as protein solutions. Existing methods have limited effectiveness due to the restricted liquid diffusion of short-lived reactive species into liquid, complexities of liquid samples and their interface with plasma, and variations in plasma parameters. Consequently, either the liquid surface is overtreated, or its bottom part is rarely modified, resulting in undesirable outcomes. In this work, we used the controlled hydrodynamics of gas bubbles rising in the liquid as a method to improve liquid mixing for enhanced TUL treated with CAP generated on the liquid surface. Proof-of-concept experiments were performed using various liquids containing organic molecules, including bromophenol blue, terephthalic acid, coumarin, and myoglobin. We employed our CAP technology called Plasma-Induced Modification of Biomolecules (PLIMB) [1,2] and integrated it with a gas-bubble mixing system to treat these benchmark liquids. Our preliminary results demonstrated that TUL was significantly improved with this mixing process. Furthermore, the mixing facilitated faster modification of these molecules with PLIMB, substantially reducing treatment time. Overall, we anticipate that the coupling of any CAP device and gas-bubble mixing presents an innovative approach [3] to enhance CAP-based liquid treatment, with potential applications to both engineering and basic research on plasma-liquid interactions, shedding light on transport phenomena of multiple  phases.   

Enhanced Neutron-Induced Damage Testing through Plasma Window Technology

One of the greatest needs in the development of today’s fusion technology is the ability to test neutron-induced damage to components relevant to proposed fusion sources. There are no available sources that can generate both the neutron flux and relevant energy spectrum necessary. This has forced researchers to utilize simulation and lower energy sources to approximate component response. 

From 2019, SHINE Technologies, LLC, has built and operated accelerator-based deuterium-tritium systems yielding a continuous output of 46 trillion neutrons per second. The flux of said system is limited by the distance over which the generated neutrons can be stopped which is a function of the pressure differential between the low-pressure acceleration region and high-pressure gas target region. SHINE has investigated the use of a plasma window composed of a wall-stabilized vacuum arc generated within a specially designed aperture. The high-pressure gas target region, utilizing SHINE’s current aperture size and accelerator-side pressure, saw an increase of nearly 600%. Alternatively, with accelerator and target pressures held constant at SHINE-relevant levels saw over a 550% increase to aperture diameter.

Simulations have shown that utilizing these advancements and multiple neutron-producing SHINE systems would result in a displacement per atom per power year of 0.1-0.3. This represents a vast improvement over existing current SHINE capabilities and offers a complementary route to fusion components testing.    

Optimizing UV/VUV Transmission Through Capillary-array Windows From Utilizing Statistical Experimental Designs

Capillary-array windows have gained interest in semiconductor industries for plasma-assisted materials processing applications. They enable the transmission of desired optical radiation such as UV/VUV photons to the processing chamber while protecting the target sample from producing damage by bulky debris, thus leading to enhanced quality of plasma processing. Here, we report a new approach in which a capillary-array window can show its efficacy over conventional solid thin films in the transmission of UV and VUV photons in an ECR plasma reactor. By benchmarking windows of varying capillary size and thickness as a key factor of three levels (nanometer-sized pore, micrometer-sized pore, and millimeter-sized pore), we demonstrated that the transmission could achieve as high as 58.93%. This optimized transmission can be attained by carrying out a factional-factorial design to examine the interaction of various factors, namely, pore diameter, window thickness, window area, and incident angle of radiation properties. In addition, the windows can hold pressure differentials from 10^-6 torr to 20 mtorr and 20 mtorr to 760 torr without mechanical failure. The capillary-array windows also survived the tests of differential pressure of several hundred psi. Overall, our approach to use capillary windows for plasma UV/VUV transmission in a processing chamber with differential vacuum levels is very promising.   

Understanding the effect of magnetic field configuration on preferential transport of impurities in PISCES-RF

Helicon plasma sources driven by the radio frequency of 13.56 MHz have proven to be an efficient way of producing high density plasma (n_e ≥ 10¹⁹ m^-3) in linear plasma devices^1–3. Such devices are being built to study the plasma-material interaction under fusion reactor relevant conditions. A helicon source when operated under high RF-power¹ was found to generate impurities originating from its vacuum-window (e.g. Al₂O₃, AlN, Si₃N₄) as a result of the strong rectified sheath voltage on the ceramic. Previous studies revealed that the helicon window is eroded by deuterium and oxygen¹. However, self-sputtering of Al or Si could contribute significantly. The present study reports on the transport of the released impurities towards the plasma upstream side in PISCES-RF device². Deposition of the Al-impurities were traced at various locations of the vacuum vessel. A strong deposition of Al was observed on the upstream side walls when the magnetic field is terminated at the sides wall in a “cusp” configuration. The physics of the impurity generation and its transport in PISCES-RF will be presented and corroborated with modeling of the RF sheath, plasma-, neutral and impurity transport for various magnetic field configurations.

References:

¹Beers, C. J. et al. Phys Plasmas 28, (2021).

²Thakur, S. C. et al. Plasma Sources Sci Technol 30, (2021).

³Caneses, J. F., Blackwell, B. D. & Piotrowicz, Phys Plasmas 24, (2017).   

Ion Velocity Distribution Function Effects on Atomic Layer Etching in a RF Discharge

RF Discharges are used in a range of systems with notable applications in semiconductor processing [1], surface treatment [2], medicine [3], and water purification [4]. In this work, we model RF discharges through 1D PIC simulations and measure ion velocity distribution functions (IVDF) at the surface of a substrate immersed within the plasma. We implement the resulting IVDFs into molecular dynamics (MD) simulations to more accurately study substrate etching [5]. We discuss differences between our MD results and prior MD simulations which assumed a delta function IVDF of incident ions. Our analysis considers various plasma compositions (eg. argon) and substrate materials (eg. silicon).

[1]        W. R. Harshbarger, R. A. Porter, T. A. Miller, and P. Norton, Appl Spectrosc 31, 201 (1977).

[2]        P. D. Davidse, Vacuum 17, 139 (1967).

[3]        D. B. Graves, J. Phys. D: Appl. Phys. 45, 263001 (2012).

[4]        P. J. Bruggeman, et al., Plasma Sources Sci. Technol. 25, 053002 (2016).

[5]       J. R. Vella, D. Humbird, and D. B. Graves, Journal of Vacuum Science & Technology B 40, 023205 (2022).   

Measuring Tungsten Fuzz Growth with Transient Grating Spectroscopy

Tungsten is a candidate material for plasma facing components (PFCs) in magnetic confinement fusion (MCF) power plants and will be used for the first wall and divertor of ITER and Commonwealth Fusion System’s SPARC tokamak. When exposed to high temperatures and helium (He) plasmas, a nanostructured layer called fuzz forms on the originally smooth tungsten surface, which changes the local material properties and could potentially contaminate MCF plasmas. Transient grating spectroscopy (TGS) is a nondestructive, picosecond time scale characterization technique that reveals the material’s elastic properties, thermal diffusivity, and energy dissipation by measuring the decay of acoustic waves and temperature gratings on the surface of the material created from a laser-induced transient diffraction grating. Polished tungsten samples heated to 800°C will be exposed to a 13.56 MHz He plasma in the Dynamics of ION Implantation and Sputtering Of Surfaces (DIONISOS) experiment to show that the thermal diffusivity decreases with increasing fuzz production from two different TGS measurements. Scanning electron microscopy will confirm the fuzz microstructure evolution as a function of the plasma fluence. The first measurement will be taken on a benchtop TGS after He plasma irradiation, and the second will be in real-time on the Plasma In-situ Ion Irradiation TGS (PI³-TGS), which is installed on the DIONISOS beamline. Agreement between the benchtop and in-situ TGS measurements would point to the necessity for a diagnostic to detect the onset and severity of fuzz growth in future MCF devices using tungsten PFCs.   

Computational Investigation of Ion Energy Angle Distribution within Trench Structures using the hPIC2 Particle-in-Cell Code

Plasma-materials interactions are sensitive to a plasma's ion energy-angle distribution (IEAD). Accurately characterizing the IEAD of a processing plasma can aid the use and development of pattern transfer methods used in high aspect ratio etching for MEMS and integrated circuits. In particular, the variation in ion flux in different areas of a microstructure can cause variation in etch rates. hPIC2, a GPU-accelerated electrostatic particle-in-cell code, is able to simulate plasmas in unstructured finite element meshes using the finite element C++ library, MFEM. This is used to model the geometry of various trench structures often found in etching process flows, enabling a spatially varying IEAD output. We investigate the effect of varying plasma parameters and aspect ratios on the IEAD incident on trench surfaces.   

Sheath models for thermionically cooled surfaces in two-temperature plasmas

Electron transpiration cooling (ETC) is a proposed thermal management technique for the leading edges of hypersonic vehicles. This technique leverages the well-understood property of thermionically emitted electrons by carrying away heat energy at the surface as potential and kinetic energy. Computational fluid dynamics (CFD) modeling approaches for this phenomenon have developed emissive boundary conditions for ETC. These account for space-charge-limited emission to accurately determine the level of electron emission from the surface. However, CFD modeling approaches for ETC have only considered the thermionic emission from a negatively biased surface. In reality, emitted electrons are expected to travel downstream of the emission point and reattach to the vehicle surface and re-deposit their energy. In this work, we propose an approach to model electron absorption downstream of the thermionic emitter at a positively biased surface. Physics of an electron sheath near a positively biased anode in a 2-T quasineutral plasma are investigated and electron absorption treatment is discussed. Comparison of CFD prediction of the reabsorption model to an ETC experimental investigation is underway.   

Direct measurements and spectroscopic analysis of secondary electron emission from carbon foams

Secondary electron emission (SEE) from plasma-facing components can significantly impact the performance of many devices such as electric propulsion thrusters, plasma gun components, fusion device first walls, divertors, and bias electrodes. To this end, materials with geometrically complex morphologies have been found to be effective at suppressing SEE yield compared with flat surfaces. SEE measurements of carbon foams and flat graphite are presented and agree with recent experimental and analytical findings. An optimal geometric configuration for reticulated carbon foams showing up to to 45% reduction of SEE yield compared with flat graphite was also determined. SEE angular measurements also revealed a loss of angular dependence for carbon foams with < 100 geometric features, as has been shown in previous studies of tungsten nano-fuzzes. A double-pass cylindrical mirror analyzer (CMA) typically used for Auger electron spectroscopy was also used to study the SEE spectra from foams compared to flat graphite surfaces. This analysis revealed that generation of true (0 – 50 eV) SEs may be enhanced by up to 5% from foam surfaces compared to flat graphite surfaces, and that foams may suppress backscattered secondary electrons by > 80%. These results can inform the basic SEE physics and design space of plasma-facing components, particle accelerator walls, electron microscopy, and RF components for multipactor effect mitigation.   

Optimization of Additively Manufactured Plasma-facing Surfaces with Consideration of Plasma Infusion Effects

While volumetrically complex materials (VCMs) have shown to be robust when exposed to plasma-facing environments, this study seeks to examine the performance of additively manufactured VCMs and investigate their capability to volumetrically conduct current. This research builds upon advanced ion-solid interaction simulation codes and optimization algorithms to determine optimal VCM designs that seek to minimize sputtering erosion. Optimized VCM geometries have demonstrated a reduction in sputter yield by approximately 80%; these complex designs have been realized only through the advanced capabilities of the additive manufacturing process. This research also seeks to understand the transport mechanisms of electrical current through VCMs, a critical factor for determining the current-bearing capacity of high-power cathodes. This investigation underlines the potential of VCMs to bolster durability in applications such as nuclear fusion, plasma electrodes, and space propulsion, thereby pushing the boundaries of current technological capabilities.   

Effects of Oxides on Hydrogen Uptake and Release in Dispersion-Strengthened Tungsten

To further our understanding of hydrogen (H) retention in PFCs, it is important to consider tungsten-oxide systems. Oxides form naturally on the surface of tungsten (W) due to the strong chemical affinity. This effect becomes more prominent in extreme environments e.g., in fusion reactors. As materials are exposed to the plasma, they will experience erosion and re-deposition, which could significantly modify fuel retention. Therefore, the topic of oxidative mechanisms for hydrogen retention warrants further discussion. In collaboration with Sandia National Lab, we will elucidate how both the partial coverage of oxygen (O), as well as the presence of oxide thin films, affects H chemisorption and uptake in dispersion-strengthened tungsten (DS-W) samples. We will be using W-1%ZrC, W-5%TiC, and W-10%TiC to compare the effects of different dispersoids on O and H interactions in W. We will apply low energy ion scattering (LEIS) and direct recoil spectroscopy (DRS) to investigate how the partial coverage of O affects H chemisorption on the surface, as well as x-ray photoelectron spectroscopy (XPS) and Auger spectroscopy to characterize both the material’s chemical and elemental composition before and after dosing. We will then grow oxide films on the materials to further investigate the effects of oxides on these surfaces. Subsequently, we will perform ellipsometry in-situ with deuterium (D) plasma exposure to obtain optical properties in real time. Finally, we will use LEIS and DRS again to quantify the chemisorbed H and D under the presence of these thicker oxide layers.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

 

Development of the Particle-Mesh, Material-Interaction Particle-In-Cell Code Package (PEMMICAN) for the Simulation of Plasma Facing Component Wall Effects

The vapor shielding effect occurs when a plasma impinges on a surface, depositing energy and inducing vaporization, leading to interaction with the impinging plasma. This plasma-vapor interaction results in an overall reduction of the energy deposited at the material surface. The Particle-Mesh, Material Interaction Particle in Cell code package (PEMMICAN) was developed to simulate vapor generation as a result of plasma energy deposition on tungsten, iron, carbon, and lithium targets. PEMMICAN is also capable of simulating plasma-vapor interaction between a tungsten vapor and a deuterium-tritium plasma via electron impact ionization and radiative recombination. The development and verification of PEMMICAN is presented in this paper. The underlying model implemented in PEMMICAN is described and relevant theory is discussed. Verification tests are presented, including measurement of simulated electron and ion gyrofrequencies and Larmor radii, electrostatic repulsion, E⨯B drift, grad-B drift, spatial and temporal stability analysis, vaporization mechanics, and electron impact ionization and recombination mechanics. Good agreement between the underlying model and simulation results were found. Notably, near exact agreement was found between simulated electron and ion Larmor radii in a strong magnetic field and the corresponding analytical value. Concluding thoughts, current efforts, and future work are discussed.   

A new hybrid: kinetic ions with parallel-kinetic-perpendicular-moment (pkpm) electrons

The hybrid kinetic formalism, wherein one retains the complete Vlasov dynamics for some number of ion species while reducing the electron dynamics to a fluid model, is a workhorse simulation model for the plasma community, especially in applications to collisionless shocks. However, a known deficiency of this approach for collisionless shock applications is one must prescribe the ultimate temperature partition of the shock downstream between electrons and ions. Such a partition is fraught with difficulties due to the complex non-equilibrium dynamics of the shock, with the electrons typically undergoing significant non-adiabatic heating through their kinetic response to, for example, parallel electric fields which develop in the shock-wave. 

In this presentation, we discuss a recently developed formalism which extends the capabilities of the hybrid-kinetic approach by decomposing the electron dynamics into a kinetic response parallel to the magnetic field and a hierarchy of fluid equations which govern their perpendicular motion. This approach, known as a parallel-kinetic-perpendicular-moment (pkpm) model, has natural connections to high magnetization asymptotic models such as drift-kinetics, but with the added flexibility that the model can be derived independently for each plasma species, thus avoiding the challenges of trying to reduce the electron dynamics while leaving the ion dynamics unordered. We demonstrate the utility of this novel hybrid approach for a collisionless shock in which significant non-adiabatic heating of the electrons occurs.   

Investigation of the Ion Reflection Rate at Quasi-Perpendicular Shocks

Particle reflection at collisionless shocks plays an important role in the dynamics of the shock layer. In this study we investigate the rate of ion reflection from quasi-perpendicular shocks under different upstream conditions. We use in-situ observations from NASA’s Magnetospheric Multiscale (MMS) Mission during 225 shock crossings as these shocks provide a wide range of parameters. For each event, different ion populations, including the solar wind and reflected ions are identified in the data, and associated plasma moments for each population are determined. We then looked at correlations between shock and plasma parameters, and ion reflection rate. These parameters include: ΙBΙ amplification rate, Alfvénic Mach Number (M_A), the shock angle (Θ_BN), upstream plasma density (n_Up), temperature, and velocity. We find that the reflection rate is not constant, and increases with the Alfvénic mach number and the magnetic amplification rate across the shock. This information will help further the understanding of the solar wind and how it interacts with our magnetosphere.   

Electron acceleration mechanisms in magnetic reconnection and flux ropes in the Earth's quasi-parallel bow shock

Recent shock observations by NASA’s Magnetospheric Multiscale (MMS) have revealed numerous reconnecting current sheets in the Earth’s bow shock. Magnetic reconnection can produce energetic particles, but the role of reconnection in shock heating and acceleration remains to be investigated. 

 

To understand electron acceleration and heating in reconnection in shocks, we perform 2D particle-in-cell (PIC) simulations of quasi-parallel shocks. In a shock with its Alfven Mach number around 10, reconnecting current sheets show both ion-coupled reconnection and electron-only reconnection. The electron temperature increases significantly in ion-scale flux ropes. The energy spectrum in the shock transition region shows a non-thermal power-law component.

 

Tracing electron trajectories in the PIC simulation, we identified five energization mechanisms. Fermi acceleration in contracting islands, acceleration in a moving flux rope, a new type of betatron acceleration (“island betatron acceleration”), and two conventional shock acceleration mechanisms (parallel electric field, and shock drift acceleration). 

 

Energization in a moving flux rope and island betatron acceleration account for the higher energy part in the electron spectrum. Fermi acceleration and the conventional shock acceleration mechanisms produce the lower to medium energy part of the spectrum. We conclude that reconnection plays a major role to energize electrons in the shock transition region.   

Reconnection diffusion region in a shock ramp

We present a new possibility based on observations of a reconnecting current sheet that occurs within the ramp of a bow shock at Earth. Observed reconnection signatures include electron jet reversals, intense electron heating, inward and outward convecting magnetic fluxes, and features of electron distribution functions consistent with those in a fully developed electron diffusion region at the terrestrial magnetopause. The observations suggest that reconnection can contribute substantially to electron heating at collisionless shocks in planetary and astrophysical systems, and potentially has large-scale impact on the shock structure and function.   

Conditions of structural transition from collisionless electrostatic shock to double-layer structure

In unmagnetized plasmas, collisionless shocks can be sustained by electrostatic potential alone when electron temperature is significantly larger than ion temperature. These shocks, known as collisionless electrostatic shocks (CES), can be generated in laboratory settings through the interaction between intense lasers and near-critical density targets. Another structure having a similar presence of localized electrostatic potential is double-layer structure (DL) which has been frequently observed in space plasmas. Using particle-in-cell (PIC) simulations, we investigate the formation of CES at the interface between two plasma slabs with varying pressures and reveal a natural transition from CES to DL. From the numerical results, we identify that the transition to DL occurs when the initial density ratio between the two plasma slabs exceeds 40, independent of the temperature ratio. Motivated by this result, we propose a new model based on previous CES studies to also describe DL dynamics. In addition, our model successfully explains the transition observed in PIC simulations, providing new insights into the physics of CES and DL in space and laboratory plasmas.   

Hydrodynamic Shock Modifications by the Heat Flux of Non-Thermal Particles

Collisionless plasma shocks are a common feature of many space and astrophysical systems and are sources of high-energy particles and non-thermal emission, channeling as much as 20% of the shock's energy into non-thermal particles. The generation and acceleration of these non-thermal particles have been extensively studied, however, how these particles feedback on the shock hydrodynamics has yet to be fully treated. This work presents the results of self-consistent, hybrid particle-in-cell simulations that show the effect of self-generated non-thermal particle populations on the nature of collisionless, quasi-parallel shocks, which contribute to a significant heat flux upstream of the shock. Non-thermal particles downstream of the shock leak into the upstream region, taking energy away from the shock. This increases the compression ratio, slows the shock, and flattens the non-thermal population's spectral index for lower Mach number shocks. We incorporate this into a revised theory for the jump conditions that include this effect and show excellent agreement with simulations. The results have the potential to explain discrepancies between predictions and observations in a wide range of systems, such as inaccuracies of the predicted arrival times of coronal mass ejections and the conflicting radio and x-ray observations of intracluster shocks. These effects will likely need to be included in fluid modeling to predict shock evolution accurately.   

Understanding the Breakdown of the Bell Instability in the Limit of High Cosmic Ray Current Density

A critical component to explaining the observation of cosmic ray acceleration at supernova remnants is the non-resonant Bell's instability, where the relative drift between the thermal ions and the cosmic rays lead to the amplification of magnetic fields necessary to accelerate particles with diffusive shock acceleration. In order to extend our understanding of particle acceleration in other astrophysical systems, and to inform limitations on the amount of heating possible from the Bell instability in supernova remnants, in this work we investigate the instabilities present in the high cosmic ray current density limit, where the assumptions underlying the Bell instability break down. Despite the increase in the free energy in the particles, in this limit significantly less magnetic field amplification is observed. We discuss the saturation of the instabilities in this regime, how they scale with respect to the sources of free energy in the system, and, critically, their relevance for the injection of electrons into the process of diffusive shock acceleration.   

Experimental Observations of Electrode Plasma-Surface Chemistry in Air-Breathing Gridded Ion Thrusters

Electrode surfaces inside air-breathing electric propulsion (ABEP) plasma discharges are exposed to reactive oxygen and nitrogen species which can form insulating layers and quickly degrade thruster performance. Previous literature has shown titanium and stainless steel both have potential for mitigating electrode surface degradation, but limited analysis of electrode surfaces was performed (Lotz 2013, Tejeda and Knoll 2023). In this work, stainless steel and titanium electrodes are tested in a radiofrequency (RF) gridded ion thruster running on nitrogen and oxygen. Surface layer growth and composition are analyzed via SEM and EDS imaging. Material recommendations which limit electrode performance degradation in ABEP thruster electrodes are made.   

Imaging Refractometry Technique Development

The imaging refractometry technique is a valuable diagnostic tool for studying high energy density plasmas. Density fluctuations in these plasmas are challenging to measure, particularly in gas-puff Z-pinch implosions where turbulence is thought to be present [1,2,3]. After its introduction [4], the technique has been further developed at Cornell’s Laboratory of Plasma Studies for diagnosing imploding gas-puff Z-pinch plasmas using a 40 mJ, 150 ps, frequency doubled Nd:YAG laser pulse at 1064/532 nm. To obtain time-resolved wavenumber spectra a visible light streak camera is being used along with a ~150 mJ, ~12 ns, frequency doubled Nd-YLF laser pulse at 532 nm.

The imaging refractometry technique measures the angular deflection of a collimated laser beam as it passes through a plasma to generate, on a detector screen, an image where the y-axis is the deflection angle and the x-axis is the spatial direction axis. The spectrum of angular deflections can be linked to the wavenumber spectrum by measuring a stationary target with an analytically known Fourier transform [5].

The Beam Propagation Method (BPM) simulation [6] was developed to provide predictive ability for the Imaging Refractometer in specific plasmas and synthetic spectra for analysis of observed spectra. The PERSEUS 3D Extended MHD code [7] is being employed to obtain a 3D density pattern of a plasma column at a given time to provide the specific plasma for the BPM code. PERSEUS and the BPM simulation are run in combination using the Bridges-2 system [8] to obtain high spatial resolution.

Recent results, challenges, and future plans will be reported.   

Characterization of Circular Arc Electron Source for Air Ionization in a Self-Neutralizing Air-Breathing Plasma Thruster

Nowadays interest in air-breathing plasma propulsion for very low earth orbit applications is increasing. To this end, air-breathing plasma thrusters utilize incoming air as a propellant that is ionized and then consequently accelerated to produce thrust. This talk will present a unique concept for air-breathing plasma thrusters in which ionization and acceleration occur without slowing incoming air. In addition, by varying electron energy it has been demonstrated that both positive and negative ions can be extracted. This configuration could potentially eliminate the complexity of using a collimator reducing the drag. Typically, an air-breathing plasma thruster would require an external neutralizer to inject electrons for ion beam neutralization while a self-neutralizing air-breathing plasma thruster utilizes both positive and negative ions to achieve beam neutralization. This talk focuses on the ionization aspects of air-breathing thrusters through the development of radial magnetized arc electron source. This source consists of a circular configuration of a metallic arc plasma source coupled with a positively biased grid to extract electrons and control electron energy. It was demonstrated that radial electron source leads to enhanced ionization of airflow. The effect of external parameters on the source showed that the shape and size of arcing regions/intensity varied. While the grid underwent deposition of about 600 microns, the conductance was observed to increase/saturate with time and bias voltage indicating an electrically "self-healing material