Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Plasma Physics
Volume 66, Number 13
Monday–Friday, November 8–12, 2021; Pittsburgh, PA
Session CO08: Fundamental: Simulation and TheoryOn Demand
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Chair: Lorin Matthews, Baylor University Room: Rooms 317-318 |
Monday, November 8, 2021 2:00PM - 2:12PM |
CO08.00001: The FARRSIGHT Vlasov-Poisson code Robert Krasny, Ryan Sandberg, Alexander G Thomas FARRSIGHT is a forward semi-Lagrangian particle method for the Vlasov-Poisson system. The particle density is represented on adaptively refined and remeshed panels in phase space, and an integral form of the Poisson equation is solved using a regularized electric field kernel and a GPU-accelerated hierarchical treecode. The talk will summarize the ongoing development of the method and present numerical results. |
Monday, November 8, 2021 2:12PM - 2:24PM |
CO08.00002: Hamiltonian structure of the guiding-center Vlasov-Maxwell equations Alain J Brizard The Hamiltonian structure of the guiding-center Vlasov-Maxwell equations is presented in terms of a Hamiltonian functional and a guiding-center Vlasov-Maxwell bracket, which explicitly satisfies the Jacobi property. The bracket is used to show that the guiding-center momentum and angular-momentum conservation laws can also be expressed in Hamiltonian form. |
Monday, November 8, 2021 2:24PM - 2:36PM |
CO08.00003: Quadrature-based moment methods for kinetic plasma simulations Pierre-Yves Taunay, Michael E Mueller Quadrature-based moment methods (QBMM) are applied to plasma physics problems represented by the Vlasov-Poisson system of equations. QBMM are a computationally advantageous alternative to both direct and Lagrangian particle solvers, able to provide a noise-free solution to the Vlasov-Poisson system of equations and capture non-equilibrium velocity distribution functions (VDF) without excessive computational cost. To provide a closure of the moment equations, the VDF is assumed to be represented by the sum of weighted kernel functions that are placed at given velocity abscissas. The weights and abscissas on which the VDF depend are retrieved through a non-linear inversion procedure that relies on the transported moments. Two QBMM approaches, QMOM1 (Dirac delta kernels) and EQMOM2 (Gaussian kernels) are applied to canonical one-dimensional plasma physics problems. The results of QBMM compare favorably to that of a direct solver but at a lower computational cost. The proposed methods appear to be a promising alternative to existing solvers for multi-fluid kinetic plasma simulations. |
Monday, November 8, 2021 2:36PM - 2:48PM |
CO08.00004: Grid instability growth rates of electrostatic particle-in-cell simulation algorithms Luke C Adams, Gregory R Werner, John R Cary An exhaustive study of grid-instability behavior in uniform drifting Maxwellian plasmas is presented for several explicit electrostatic particle-in-cell algorithms. Studied are the standard momentum conserving algorithm (MPIC), an energy conserving algorithm (EPIC), the Precise-Particle-in-Fourier method (PPIF), and a new cubic-spline based method (Particle-in-Cubic-Spline, PICS). The new PICS method has computational effort with ``PIC scaling'', while PPIF does not. MPIC and EPIC are studied for the three lowest-order shape functions. These methods are compared on the basis of accuracy, region of instability in the drift-velocity/temperature plane, instability growth rate, and particle noise. It is found that PPIF is stable throughout the plane and that MPIC is unstable near the origin and for vanishing temperature (i.e. Debye length is less than cell size), regardless of shape function. EPIC and PICS are stable for vanishing drift velocity. PICS is shown to have error that is fourth-order in the cell size, while MPIC and EPIC have second-order error, regardless of the shape function. Thermal noise is also lower for PICS, compared with MPIC and EPIC, but all methods have Monte Carlo noise scaling, $1/\sqrt{N_p}$, with particle number, $N_p$. |
Monday, November 8, 2021 2:48PM - 3:00PM |
CO08.00005: An adaptive sparse grids scheme for reducing noise in Particle-In-Cell simulations Antoine Cerfon, Lee Ricketson, Matthias Frey, Sriramkrishnan Muralikrishnan, Andreas Adelmann The computational complexity of grid based numerical schemes grows exponentially with the number of dimensions. This is the curse of dimensionality, which is the source of the high computational cost of grid based solvers for kinetic equations. The Particle-In-Cell (PIC) scheme partially avoids this curse by combining a grid-based approach for the computation of the electromagnetic fields with a particle approach for the evolution of the distribution function. However, the slow decay of the intrinsic numerical noise in PIC with the number of simulated particles leads to codes which may be more computationally intensive than grid based codes when a high level of accuracy is required. |
Monday, November 8, 2021 3:00PM - 3:12PM |
CO08.00006: Deterministic verification for electrostatic particle-in-cell algorithms using the method of manufactured solutions. Paul Tranquilli, Lee F Ricketson, Luis Chacon As simulations of kinetic plasmas continue to increase in scope and complexity, a rigorous and straightforward method for verifying particle-in-cell implementations is necessary to ensure their correctness. In this talk we present a deterministic method for the rigorous verification of multidimensional, multispecies electrostatic particle-in-cell codes based on the method of manufactured solutions. We show that rigorous verification is possible through the exclusive examination of errors of grid quantities, allowing for a very light-weight and non-intrusive implementation in existing particle-in-cell codes. We further show that different grid quantities feature different rates of convergence with the number of particles, as well as numerical results of a 2D-2V multi-species particle-in-cell code which confirm our theoretical claims. Additionally, we report on ongoing work extending the method to electromagnetic and gyrokinetic systems. |
Monday, November 8, 2021 3:12PM - 3:24PM |
CO08.00007: Extended Magnetohydrodynamics in the FLASH Code Edward C Hansen, Adam Reyes, Jonathan R Davies, Benjamin Khiar, Marissa B Adams, Abigail Armstrong, Periklis Farmakis, Yingchao Lu, David Michta, Kasper Moczulski, Don Q Lamb, Petros Tzeferacos The FLASH code’s extended magnetohydrodynamic (MHD) capabilities have been greatly expanded recently. Improvements have been made to the Biermann battery and Hall terms in the induction equation, and several transport processes have been added to the code including anisotropic thermal conductivity, anisotropic magnetic resistivity, and thermoelectric effects. The implicit thermal diffusion solver was adapted to handle magnetic field dependent anisotropic conduction terms, while the implicit magnetic diffusion solver is a separate, new implementation. Seebeck, Righi–Leduc, and Nernst thermoelectric effects are solved with a flux-based explicit method. New resistivity and thermoelectric transport coefficients resulting from work with the Fokker–Planck code OSHUN (J. R. Davies et al., Phys. Plasmas 28, 012305 (2021)) have been incorporated into FLASH, and new thermal conductivity coefficients were also added (J.-Y. Ji and E. D. Held, Phys. Plasmas 20, 042114 (2013)). These new implementations enhance FLASH’s ability to model important magnetized plasma phenomena and problems such as Z-pinches. |
Monday, November 8, 2021 3:24PM - 3:36PM |
CO08.00008: Finite Element Simulation of Magnetized Edge Plasma Turbulence Ilon Joseph, Ben Zhu, Milan Holec, Chris J Vogl, Alejandro Campos, Andris M Dimits, Tzanio Kolev, Mark L Stowell We explore the use of the MFEM framework, a highly scalable finite element library, for addressing the challenging physical, geometric, and numerical issues associated with high-performance simulation of fusion edge plasmas. Adaptive mesh refinement, mesh optimization, high-order discretization, and high-order curved meshes can reduce numerical discretization error by orders of magnitude for cases of interest that correspond to divertors, magnetic islands, and external walls. Several reduced MHD models have been developed that describe magnetized plasma dynamics in 2D: the Navier-Stokes, Hasegawa-Mima, and Hasegawa-Wakatani models. We have developed both linear and nonlinear solvers for the plasma fluid equations, including preconditioning strategies and block preconditioning strategies that address the combination of the ExB flow and anisotropic diffusion. In addition, an antisymmetric form of the advection operator conserves both energy and enstrophy for arbitrary polynomial order elements, like the Arakawa bracket. The numerical models have been validated by comparing the linear growth rates with predictions of a semi-analytical eigensolver for various conditions and benchmarked with Global Drift Ballooning (GDB) finite difference code. |
Monday, November 8, 2021 3:36PM - 3:48PM Not Participating |
CO08.00009: A deterministic Gaussian-Mixtures Coulomb-collision algorithm for particle-in-cell methods Truong Nguyen, Luis Chacon, Guangye Chen, William T Taitano Coulomb-collision modules in PIC simulations are typically Monte-Carlo-based. Monte Carlo (MC) is attractive for its simplicity, efficiency in high dimensions, and conservation properties. However, it is noisy, of low temporal order (typically O(√∆t), and has to resolve the collision frequency for accuracy [1]. In this study, we explore a machine-learning- based, multiscale alternative to MC for PIC. The approach is based on the reconstruction of the particles’ velocity distribution function (VDF) using a Gaussian Mixtures Model (GMM) via the Maximum Likelihood Estimation principle [2,3]. A key element of our algorithm is to decompose each Gaussian in the GMM into a convex linear combination of isotropic Maxwellians for which an exact set of evolution equations can be de- rived according to the Landau-Fokker-Planck collision operator [4]. The proposed method is deterministic, free of instability, positivity-preserving, and strictly conservative, and is orders of magnitude faster than either MC or Eulerian Fokker-Planck solvers. We will illustrate the accuracy and performance of the proposed method with several examples of varying complexity. |
Monday, November 8, 2021 3:48PM - 4:00PM |
CO08.00010: Investigation of Optical Smoothing Techniques on Multiple Beams Joshua Ludwig, Pierre A Michel Intense laser hotspots/speckles are a concern on high power laser facilities due to their role in seeding unwanted instabilities such as SBS (Stimulated Brillouin Scattering). Optical smoothing techniques such as SSD1,2 (Smoothing by Spectral Dispersion) are used to better homogenize the laser focal spot intensity pattern on the time scale of the instabilities. Here we report on a project that examines the combined laser electric fields of overlapping NIF beams including the effects of SSD, polarization rotation, and beat waves3. An overview of the simulation technique will be presented with updates on characterizing various optical smoothing techniques. |
Monday, November 8, 2021 4:00PM - 4:12PM |
CO08.00011: Self-similar rotating magnetized implosions Andrey Beresnyak, Alexander L Velikovich, John L Giuliani, Arati Dasgupta NRL Mag Noh problem is a self-similar cylindrical implosion flow, with a fast MHD outward propagating shock of constant velocity. Inspired by the Noh shock, this solution includes magnetic field and rotation, making our family of ideal exact Mag Noh solutions five-parametric, each solution having its own self- similarity index, gas gamma, magnetization, ratio of axial to azimuthal field and rotation. While classic Noh problem must have a supersonic implosion velocity to create a shock, our solution has an interesting special case with zero initial velocity, which creates the shock instantaneously. Our self-similar solutions are indeed realized when we solve initial condition problem with finite volume MHD code Athena. We found our solutions can be stable or unstable to azimuthal perturbations. It is important to check how numerical codes handle instabilities, transition to turbulence and mixing because in high energy density physics we often deal with unstable plasmas. Our analytic test solution features all elements relevant to magnetically driven implosions: convergent flow, magnetic field and the shock. A subset of our solutions has singular azimuthal current at the origin. Such singularity may help to create a hot spot in magnetically driven implosions. |
Monday, November 8, 2021 4:12PM - 4:24PM |
CO08.00012: Effective Static Approximation: A Fast and Reliable Tool for Warm-Dense Matter Theory Tobias Dornheim Warm dense matter is of high current interest for many applications, including astrophysics and fusion research. Yet, the accurate description of electronic correlation effects at these conditions is most difficult, and often computationally intensive ab-initio methods have to be used. Here we present the effective static approximation (ESA) [1] to the local field correction (LFC) of the electron gas, which enables highly accurate calculations of electronic properties like the dynamic structure factor S(q,ω), the static structure factor S(q), and the interaction energy v with no computational extra cost compared to the random phase approximation (RPA). |
Monday, November 8, 2021 4:24PM - 4:36PM |
CO08.00013: Using chaotic quantum maps as a test of current quantum computing hardware fidelity Max D Porter, Ilon Joseph, Alessandro R Castelli, Vasily I Geyko, Frank R Graziani, Stephen B Libby, Yuan Shi, Jonathan L DuBois Quantum computers promise to deliver large gains in computational power that can potentially be used to benefit the Fusion Energy Sciences (FES) program. Through the quantum-classical correspondence principle, future error-corrected quantum computers should eventually be able to simulate classical dynamical systems. The quantum dynamics also efficiently encodes classical dynamical information in the decay of the fidelity. However, if the effective Planck’s constant is too large, the quantum system will display dynamical Anderson localization rather than classically chaotic diffusion. |
Monday, November 8, 2021 4:36PM - 4:48PM |
CO08.00014: Density Limit for Electrostatic Ion Confinement Using the Space-Charge of an Electron Plasma Kelly S Wood, Carlos Ordonez The density limit for ions electrically trapped by the space charge of an electron plasma is studied numerically and reported. A non-neutral plasma with a Boltzmann distribution is considered via a self-consistent finite-difference evaluation. A constraint on the maximum electric field at the plasma’s edge is expected to limit the ion density. The functional dependence of the normalized electric field on the following parameters is evaluated using a parameter study by varying: the charge density of the positive plasma species at the system’s center normalized by the electron charge density at the system’s edge, the average of the positive plasma species’ charge state multiplied by the ratio of the electron temperature to the temperature of the positive plasma, and the normalized distance from the center of the system to the system’s edge. This dependence is fit with a function that is used to determine the ideal parameters for ion density maximization. |
Monday, November 8, 2021 4:48PM - 5:00PM |
CO08.00015: Collisional-radiative rate coefficient function estimation using Gaussian process regression Richard June E Abrantes, Yun-Wen Mao, David D. W. Ren Calculating rate coefficients for atomic kinetics simulations can require prolonged computational times and additional memory reserves whenever a large number of atomic levels and transitions must be resolved. These requirements are amplified when strong multifluid phenomena are observed such that multifluid rate coefficients must be employed, thereby expanding the precomputed, 1D rate coefficient profile into a 2D map due to the additional relative kinetic energy axis. This work explores using Gaussian process regression (GPR) to model any general atomic transition's rate coefficient profile or map. Through a sparse set of training data points, this nonparametric, Bayesian approach can provide an estimation of the entire transition profile and map over prescribed test data points. Preliminary results will show the set of parameters and features used to generalize GPR to a variety of transitions, along with the performance improvements attained when compared to an exhaustive, point-by-point calculation of the rate coefficient field. |
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