Integrating batched sparse iterative solvers for the collision operator in fusion plasma simulations on GPUs
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Kashi, Aditya (ORCID:0000000325893792)↗
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Resolving the mystery of electron perpendicular temperature spike in the plasma sheath
A large family of plasmas has collisional mean-free-path much longer than the non-neutral sheath width, which scales with the plasma Debye length. The plasmas, particularly the electrons, assume strong temperature anisotropy in the sheath. The temperature in the sheath flow direction (Te∥) is lower and drops toward the wall as a result of the decompressional cooling by the accelerating sheath flow. The electron temperature in the transverse direction of the flow field (Te⊥) not only is higher but also spikes up in the sheath. This abnormal behavior of Te⊥ spike is found to be the result of a negative gradient of the parallel heat flux of transverse degrees of freedom (qes) in the sheath. The non-zero heat flux qes is induced by pitch-angle scattering of electrons via either their interaction with self-excited electromagnetic waves in a nearly collisionless plasma or Coulomb collision in a collisional plasma, or both in the intermediate regime of plasma collisionality.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Nonmagnetized Collisional Plasma Parameter Estimation From Two Frequency Signal Interrogation Attenuation
A nonmagnetized collisional plasma parameter estimator from two frequency signal interrogation attenuation is developed. The plasma parameters that are estimated are the plasma frequency, electron neutral momentum collision frequency, and the plasma thickness. The plasma frequency and electron neutral momentum collision frequency are considered uniform across the plasma thickness. The relative permittivity is defined, and the complex index of refraction is developed. Using this definition and applying the plasma frequency, electron neutral momentum collision frequency, the radial propagation frequency, and plasma thickness, an attenuation is determined for known cases. The development of the estimator is discussed. The estimator uses a performance index where the minimum difference between the plasma frequencies and electron neutral momentum collision frequencies is determined for the two signal interrogation frequencies under the constraint of the same plasma thickness. The estimator was developed in three stages which include iterative, sequential, and adaptive. The setups of the iterative, sequential, and adaptive approaches are discussed. The impact of the interrogation frequency and the estimator setup is investigated. The estimator in the three development stages is compared with known cases and the plasma parameter estimator performance is quantified.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Extracting the speed of sound in quark–gluon plasma with ultrarelativistic lead–lead collisions at the LHC
Abstract Ultrarelativistic nuclear collisions create a strongly interacting state of hot and dense quark–gluon matter that exhibits a remarkable collective flow behavior with minimal viscous dissipation. To gain deeper insights into its intrinsic nature and fundamental degrees of freedom, we determine the speed of sound in an extended volume of quark–gluon plasma using lead–lead (PbPb) collisions at a center-of-mass energy per nucleon pair of 5.02 TeV. The data were recorded by the CMS experiment at the CERN LHC and correspond to an integrated luminosity of 0.607 nb −1 . The measurement is performed by studying the multiplicity dependence of the average transverse momentum of charged particles emitted in head-on PbPb collisions. Our findings reveal that the speed of sound in this matter is nearly half the speed of light, with a squared value of 0.241 ± 0.002 ( stat ) ± 0.016 ( syst ) in natural units. The effective medium temperature, estimated using the mean transverse momentum, is 219 ± 8 ( syst ) MeV . The measured squared speed of sound at this temperature aligns precisely with predictions from lattice quantum chromodynamic (QCD) calculations. This result provides a stringent constraint on the equation of state of the created medium and direct evidence for a deconfined QCD phase being attained in relativistic nuclear collisions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
An explicitly solvable energy-conserving algorithm for pitch-angle scattering in magnetized plasmas
In this work, we develop an Explicitly Solvable Energy-Conserving (ESEC) algorithm for the Stochastic Differential Equation (SDE) describing the pitch-angle scattering process in magnetized plasmas. The Cayley transform is used to calculate both the deterministic gyromotion and stochastic scattering, affording the algorithm to be explicitly solvable and exactly energy conserving. An unusual property of the SDE for pitch-angle scattering is that its coefficients diverge at the zero velocity and do not satisfy the global Lipschitz condition. Consequently, when standard numerical methods, such as the Euler-Maruyama (EM), are applied, numerical convergence is difficult to establish. For the proposed ESEC algorithm, its energy-preserving property enables us to overcome this obstacle. We rigorously prove that the ESEC algorithm is order 1/2 strongly convergent. This result is confirmed by detailed numerical studies. For the case of pitch-angle scattering in a magnetized plasma with a constant magnetic field, the numerical solution is benchmarked against the analytical solution, and excellent agreements are found.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Formation and Diagnostics of Collisionless Shocks in Laser-Produced Plasmas (Final Report)
Collisions of supersonic flows occur frequently in astrophysics, and the resulting shock waves are responsible for the properties of many astrophysical phenomena, such as supernova remnants, Gamma Ray Bursts and jets from Active Galactic Nuclei. Because of the low density of astrophysical plasmas, the mean free path due to Coulomb collisions is typically very large; therefore, most shock waves in astrophysics are “collisionless” and form due to plasma instabilities and self-generated magnetic fields. Laboratory experiments at DOE high energy density (HED) facilities can achieve the conditions necessary for the formation of collisionless shocks and will provide a unique avenue for studying the nonlinear physics of shock waves. This project investigates the parameters and experimental configurations needed for the creation of collisionless shocks in the laboratory experiments. This study is being performed with state of the art 3D kinetic plasma simulations. Recent advances in ab-initio particle-in-cell (PIC) simulations of astrophysical shocks enable us to simulate shock formation on timescales and in geometries relevant to the laboratory experiments. The main goal of the proposal is to ascertain which signatures of shock physics can be extracted from the realistic experiments, accounting for limitations imposed by finite spatial and time scales in the lab. To aid the interpretation of current and future experimental data, PIC simulation data have been analyzed using the same diagnostic techniques as used in the laboratory, such as proton radiography and neutronics, to unambiguously predict the experimental signatures of relevant collisionless shock phenomena.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A Performance Portable, Fully Implicit Landau Collision Operator with Batched Linear Solvers
Modern accelerators use hierarchical parallel programming models that enable massive multithreading within a processing element (PE), with multiple PEs per device driven by traditional processes. Batching is a technique for exposing PE-level parallelism in algorithms that have traditionally run on MPI processes or multiple threads within a single process. Opportunities for batching arise in, for example, kinetic discretizations of magnetized plasmas where collisions are advanced in velocity space at each spatial point independently. This paper builds on previous work on a high-performance, fully nonlinear, Landau collision operator by batching the linear solver, as well as batching the spatial point problems and adding new support for multiple grids for multiscale, multispecies problems. An anisotropic relaxation verification test that agrees well with previously published results and analytical models is presented. The performance results from NVIDIA A100 and AMD MI250X nodes are presented with hardware utilization analysis for each architecture. Finally, the entire implicit Landau operator time advance is implemented in Kokkos for performance portability, running entirely on the device and is available in the PETSc numerical library.
97 MATHEMATICS AND COMPUTING↗
Nanoparticle dynamics in the spatial afterglows of nonthermal plasma synthesis reactors
Nonthermal plasma flow tube reactors are industrially scalable systems for the production of nanocrystal (NC) based materials and coatings. One key advantage of nonthermal plasma synthesis is the ability to both synthesize NCs and deposit films in a single reactor, as at the reactor outlet, NCs can be inertially deposited onto a target substrate. The size and morphology of deposited particles can substantially influence the film structure and function. Though NCs are typically near-spherical and monodispersed as-produced in plasma synthesis reactors, NC charge and growth dynamics can be altered substantially when NCs are sampled out of the plasma and through the spatial afterglow region, affecting deposition. Experiments have demonstrated changes of NC size and charge in the spatial afterglow; however, these dynamics remain unexplored and unexplained via theory and simulation. To address this, we developed a constant number Monte Carlo (CNMC) simulation model to examine the mechanisms of NC decharging and growth in the spatial afterglow of plasma flow tube reactors. Collisions between NC and plasma species, diffusive deposition, and electron desorption from NCs are incorporated in the CNMC simulation. The simulation results are specifically compared with previous experiments on Si NCs synthesized from a low pressure Ar-SiH 4 nonthermal plasma reactor. Furthermore, the experiment-model comparison shows that CNMC models can be implemented which accurately model NC size distribution evolution in a spatial afterglow. Simultaneously, results show that improved collision models, energetic species diffusion models, and electron desorption models will be necessary to accurately depict NC dynamics in spatial afterglows.
42 ENGINEERING↗
Krash-ESL-Final report
During the period of the current Grant, the effort of the UCSD researchers was focused on: i) The application of the gyrokinetic code COGENT code to study the kinetic drift wave instability and its impact on blob dynamics, and ii) The modeling of edge plasma transport in collisional and semi-collisional regimes, and iii) Impurity transport in edge plasma and the incorporation of plasma-impurity collision operator (hereafter unlike particle collision operator) into COGENT. Over the years four UCSD graduate students (J. Angus, W. Lee, Y. Zhang, and A. Knyazev), funded under this Grant, contributed to the COGENT development/utilization and defended their PhD theses, which are based, partly, on their research related to the COGENT. Three of them (J. Angus, W. Lee, and Y. Zhang) have received “The Best MAE Graduate Student of the Year” awards. Whereas W. Lee after defending his PhD thesis returned back to his home country (South Korea), J. Angus, and Y. Zhang are continuing their research in plasma physics in the LLNL and LANL, whereas A. Knyazev currently is a postdoctoral fellow at Columbia University working on the theoretical aspects of advanced stellarators. The results obtained in our studies were disseminated in many papers published in first-class refereed scientific journals and presented on prestigious scientific meetings including the Annual APS DPP Meeting, Sherwood Fusion Theory Conference, IAEA Fusion Energy Conferences, International Conferences on Plasma-Surface Interactions in Controlled Fusion Devices, International Workshops on Edge Plasma Theory in Fusion Devices, etc. In what follows we highlight the major accomplishments of the UCSD Team in the main areas of our research.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Mechanism for the Efficient Homogeneous Nucleation of Ice in a Weakly Ionized, Ultracold Plasma
Abstract It is proposed that the rapid observed homogeneous nucleation of ice dust in a cold, weakly ionized plasma depends on the formation of hydroxide (OH − ) by fast electrons impacting water molecules. These OH − ions attract neutral water molecules because of the high dipole moment of the water molecules and so hydrates of the form (OH) − (H 2 O) n are formed. The hydrates continuously grow in the cold environment to become macroscopic ice grains. These ice grains are negatively charged as a result of electron impact and so continue to attract water molecules. Because hydroxide is a negative ion, unlike positive ions, it does not suffer recombination loss from collision with plasma electrons. Recombination with positive ions is minimal because positive ions are few in number (weak ionization) and slow-moving as result of being in thermal equilibrium with the cold background gas.
79 ASTRONOMY AND ASTROPHYSICS↗
Moments of the Boltzmann collision operator for Coulomb interactions
Exact moments of the Boltzmann collision operator are calculated in the irreducible Hermitian moment expansion written in terms of the random-velocity variable of each species. The formulas are presented in closed, algebraic form and can be straightforwardly implemented in computer algebra systems. They are valid for two arbitrary masses, temperatures, and flow velocities, and hence include all other existing results derived for distribution functions expanded with respect to reference states of one temperature and flow velocity. In comparison, the Landau collisional moments are good approximations for large Coulomb logarithm and small relative flow velocity, but they fail to predict the correct behavior of most collisional moments for large relative flow even for weakly coupled plasmas.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
2D kinetic-ion simulations of inverted corona fusion targets
Laser-driven “inverted corona” fusion targets have attracted interest as a low-convergence neutron source and platform for studying kinetic physics. The scheme consists of a hollow or gas-filled spherical shell made of deuterated plastic. The shell has one or more laser entrance holes (LEH), resembling a spherical hohlraum. The laser passes through the LEH’s and illuminates the interior surface of the shell, ablating a plasma that travels inward towards the target center. Long ion mean free paths in the converging plasma can lead to significant interpenetration, atomic mix, and other kinetic effects. Here, in this work we report on numerical simulations of inverted corona targets using the kinetic-ion, fluid–electron hybrid particle-in-cell (PIC) approach in 2D RZ geometry. 2D simulations suggest that shape effects do not have a significant impact on plasma evolution and observed yield trends are primarily the result of 1D kinetic mix mechanisms. Simulations are also compared against available experimental data recorded at the OMEGA laser facility. In particular, synthetic x-ray emission images show good qualitative agreement with experimental results, albeit with an apparent timing discrepancy for the two-sided vacuum target. More generally, we demonstrate the potential of hybrid-PIC simulations for full-system modeling and experimental design, including collisional absorption of laser energy, plasma evolution, mix, and fusion burn.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Quantitative metrics for evaluating thermonuclear design codes and physics models applied to the National Ignition Campaign
In this study, physics models and design codes for hot dense plasmas undergoing thermonuclear burn are evaluated objectively using statistical metrics that compare the difference between calculations and data relative to the experimental uncertainties. The analysis is applied to the National Ignition Campaign (NIC) because it is relevant, comprehensive, and well documented. The statistics confirm that a key process afflicting NIC performance is mix driven by hydrodynamic instabilities as approximated here using the KL model [G. Dimonte and R. Tipton, Phys. Fluids 18, 085101 (2006)]. New physics models are also presented for instability-driven magnetic fields [B. Srinivasan et al., Phys. Rev. Lett. 108, 165002 (2012)] and the Coulomb logarithm for electron–ion thermal relaxation [G. Dimonte and J. Daligault, Phys. Rev. Lett. 101, 135001 (2008)]. The plasma-generated magnetic fields improve the agreement between code and data in a statistically significant manner by reducing the electron thermal conduction in the hot-spot via the Hall term. The Coulomb logarithm is presented in a numerically practical form that incorporates recent theoretical advances. However, it does not improve the agreement between the code and data because the thermal relaxation is so fast in non-ignited NIC plasmas that the typical 20% error does not change the tight coupling between electrons and ions. Even with these improved physics models, the one-dimensional simulations presented here are not able to describe the high-convergence NIC implosions in a statistically acceptable manner. Of the heroic multi-dimensional simulations of Clark et al. [Phys. Plasmas 23, 056302 (2016)], only those in three-dimensions satisfy the statistical acceptance criterion.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Kinetic mix at gas-shell interface in inverted corona fusion targets
Gas-filled, laser-driven “inverted corona” fusion targets have attracted interest as a low-convergence neutron source and platform for studying kinetic physics. At the fill pressures under investigation, ejected particles from the shell can penetrate deeply into the gas before colliding, leading to significant mixing across the gas–shell interface. Here, we use kinetic-ion, fluid-electron hybrid particle-in-cell simulations to explore the nature of that mix. Simulations of the system demonstrate characteristics of a weakly collisional electrostatic shock, whereby a strong electric field accelerates shell ions into the rarefied gas and reflects upstream gas ions. This interpenetration is mediated by collisional processes: At higher initial gas pressure, fewer shell particles pass into the mix region and reach the hotspot. This effect is detectable through neutron yield scaling vs gas pressure. Predictions of neutron yield scaling show excellent agreement with experimental data recorded at the OMEGA laser facility, suggesting that 1D kinetic mechanisms are sufficient to capture the mix process.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A physics-constrained deep learning treatment of runaway electron dynamics
An adjoint formulation leveraging a physics-informed neural network (PINN) is employed to advance the density moment of a runaway electron (RE) distribution forward in time. A distinguishing feature of this approach is that once the adjoint problem is solved, its solution can be used to project the RE density forward in time for an arbitrary initial momentum space distribution of REs. Furthermore, by employing a PINN, a parametric solution to the adjoint problem can be learned. Thus, once trained, this adjoint-deep learning framework is able to efficiently project the RE density forward in time across various plasma conditions while still including a fully kinetic description of RE dynamics. As an example application, the temporal evolution of the density of primary electrons is studied, with particular emphasis on evaluating the decay of a RE population when below threshold. Predictions from the adjoint-deep learning framework are found to be in good agreement with a traditional relativistic electron Fokker–Planck solver, for several distinct initial conditions, and across an array of physics parameters. Once trained, the PINN thus provides a means of generating RE density time histories with exceptionally low online execution time.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Plasma hydrodynamics from mean force kinetic theory
Mean force kinetic theory is used to evaluate the electrical conductivity, thermal conductivity, electrothermal coefficient, thermoelectric coefficient, and shear viscosity of a two-component plasma. The results are compared with molecular dynamics simulations. These simulations are made possible by assuming a repulsive Coulomb force for all interactions. Good agreement is found for all coefficients up to a Coulomb coupling strength of Γ ≈ 20. This is over 100-times larger than the coupling strength at which traditional theories break down. It is concluded that mean force kinetic theory is a promising framework for extending hydrodynamics to dense plasmas.
Electrical conductivity↗
Theoretical and global simulation analysis of collisional microtearing modes
Microtearing modes (MTMs) are suggested as a candidate for anomalous thermal transport in tokamak H-mode discharges. This study investigates MTMs in tokamak plasmas, employing simulations in the BOUT++ framework. It simplifies and linearizes the governing equations in detailed linear simulations. The study meticulously evaluates various conductivity models under diverse plasma conditions and collision regimes. The research thoroughly assesses different conductivity models across a range of plasma conditions and collision regimes. A unified dispersion relation that includes both MTM and Drift-Alfvén Wave (DAW) instabilities is derived, showing that DAW and MTM instabilities occur at varying distances from the rational surface. Specifically, MTMs become unstable near the rational surface but stabilize farther away, while drift-Alfvén instability appears farther from the rational surface. The study also re-derives MTM dispersion relations using Ohm's law and the vorticity equation, providing a thorough analysis of electromagnetic and electrostatic interactions in tokamaks. Global simulations demonstrate an inverse correlation between MTM growth rates and collisionality, and a direct correlation with temperature gradients. The nonalignment of the rational surface with the peak ω*e stabilizes the MTMs. Nonlinear simulations highlight electron temperature relaxation as the primary saturation mechanism for MTMs, with magnetic flutter identified as the dominant mode of electron thermal transport.
Fan, K. (ORCID:0000000227518809)↗
Reimagining full wave rf quasilinear theory in a tokamak
The velocity dependent resonant interaction of particles with applied radio frequency (rf) waves during heating and current drive in the presence of pitch angle scattering collisions gives rise to narrow collisional velocity space boundary layers that dramatically enhance the role of collisions as recently shown by Catto (J. Plasma Phys., vol. 86, 815860302, 2020). The behavior is a generalization of the narrow collisional boundary layer that forms during Landau damping as found by Johnston (Phys. Fluids, vol. 14, 1971, pp. 2719-2726) and Auerbach (Phys. Fluids, vol. 20, 1977, pp. 1836-1844). For a wave of parallel wave number k|| interacting with weakly collisional plasma species of collision frequency ν and thermal speed vth , the effective collision frequency becomes of order ν(k_||v_th /ν)^2/3>> ν . The narrow boundary layers that arise because of the diffusive nature of the collisions allows a physically meaningful wave-particle interaction time to be defined that is the inverse of this effective collision frequency. The collisionality implied by the narrow boundary layer results in changes in the standard quasilinear treatment of applied rf fields in tokamaks while remaining consistent with causality. These changes occur because successive poloidal interactions with the rf are correlated in tokamak geometry and because the resonant velocity space dependent interactions are controlled by the spatial and temporal behavior of the perturbed full wave fields rather than just the spatially local Landau and Doppler shifted cyclotron wave-particle resonance condition associated with unperturbed motion of the particles. The correlation of successive poloidal circuits of the tokamak leads to the appearance in the quasilinear operator of transit averaged resonance conditions localized in velocity space boundary layers that maintain negative definite entropy production.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗