Symbolic vector analysis in plasma physics

A Three-Dimensional Finite Volume Arbitrary Lagrangian-Eulerian simulation code was developed to study different plasma physics problems in 3D+t. The code is based on a complex multi-component species program with transport and radiation terms written and applied to plasma and fusion physics problems. The integration domain is represented with a structured irregular mesh, with fixed connectivity made of hexahedral cells. Coordinates and velocities are assigned to cell vertices. After each calculation cycle, mesh vertices are moved arbitrary over the fluid. The adaptive method consists of shifting mesh vertices over the fluid in order to keep a reasonable mesh structure and increase the spatial resolution where the physical solution demands. The code was a valuable tool for parametric study of different physical problems, mainly optimization of Plasma Focus Machine, detonation and propagation of thermonuclear reactions, and Kelvin-Helmholtz instabilities in the boundary layer of the terrestrial magnetopause.

Dynamic load balancing with enhanced shared-memory parallelism for particle-in-cell codes

The impedance technique, also known as a particular case of the invariant embedding approach, is generalized for modeling electromagnetic wave propagation in anisotropic and gyrotropic media with spatial dispersion such as hot magnetized plasmas. That provides a new way for analytical and numerical studies of ‘full-wave’ problems in plasma physics that require exact solutions of Maxwell equations. Several examples of such a treatment are considered to demonstrate the flexibility and computational robustness of the proposed technique.

A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields.

Some new soliton solutions to the (3 + 1)-dimensional generalized KdV-ZK equation via enhanced modified extended tanh-expansion approach

One of the fundamental problems of lunar astronomy is the reduction of the coordinates of the Moon's surface, found by astronomical methods, to its mean pole. The instantaneous poles of the rotation axis and the instantaneous equator move in the Moon's body. The unstable position of this equator does not allow one to use in selenodesy the instantaneous spherical coordinates which have not been preliminarily transformed into some unified system of coordinates. Such a reduction can be made to the system of coordinates connected with the mean pole—to be definite, we shall speak about the Moon's North pole.

Publication in the conference proceedings of EUSIPCO, Rhodes, Greece, 1998

A 3-D Navier-Stokes analysis for turbomachinery flows on C- or O-type grids is presented. The analysis is based on the Beam and Warming implicit algorithm for solution of the unsteady Navier-Stokes equations and is derived from an early version of the ARC3D flow code developed at NASA Ames Research Center. The Navier-Stokes equations are written in a Cartesian coordinate system rotating about the z-axis, and then mapped to a general body-fitted coordinate system. All viscous terms are calculated and the turbulence effects are modelled using the Baldwin-Lomax turbulence model. The equations are discretized using finite differences on stacked body-conforming grids. Modifications made to convert ARC3D from external flow to internal turbomachinery flows and to improve solution accuracy are given in detail. The body-conforming grid construction procedure is also presented. Calculations for several rotor flows have been made, and results of code experimental verification studies are presented. Comparisons of the solutions obtained on the C- and O-type grids are also presented, with particular attention to shock resolution.

Starting from the action of the massive charged particles, we have firstlyapplied the Euler-Lagranges variation method to give a new derivation of the time-likeand null geodesic equations of the rotating Kerr-Sen black hole in a general (non-dragging)coordinate system. Adopting the semi-classical tunneling method proposed by Parikh andWilczek, we then reinvestigate the tunneling radiation of a massive charged particle fromthe event horizon of the Kerr-Sen black holes, and present the tunneling probability also.This work demonstrates that the study of tunneling radiation from this rotation black holemay not be limited in using a dragging coordinate system.

An interesting problem in plasma physics, when approached from the point of view of Statistical Mechanics is to obtain properties of collisionless plasmas, which are described by the Vlasov equation. Through what we call the Ehrenfest procedure, which uses statistical mechanical relations we obtain expectation value relations for arbitrary observables, which allows us to study the dynamics of the Earth's Outer Radiation Belt. Focusing on the velocity fluctuations, the width of the distribution function and the pitch angle, a computer simulation was performed to describe the system in order to compare and test the Ehrenfest approach. Our results show that the change in the average width of the distribution follows the analytical relation. However, for the velocity fluctuation results are not conclusive yet and require more exploration. It remains as future work to verify the relation for the pitch angle.

In these lectures we present several areas of plasma physics research where computation has been of importance. We have taken these problems primarily from controlled thermonuclear research, because this programme has provided the impetus for most of the theoretical development of the subject and because only numerical methods could give the answers to specific questions in the design and analysis of experiments.

Inverse problems in plasma physics commonly face a tradeoff between approximated real-time schemes or post-processed rigorous uncertainty handling. Bayesian analysis allows parameter and uncertainty estimation as well as joint analysis of multiple diagnostics in a strict mathematical way. It also improves the inference from correlated measurements but with long processing times. For linear and non-linear problems, many optimal and sub-optimal Bayesian online algorithms are available but generally targeted at dynamic systems and introducing some level of approximation. Given plasma physics time-independent non-linear inverse problems, several Wendelstein 7-X diagnostics use a Bayesian inference framework. This research focuses on accelerating this type of mathematically intense standard Bayesian analysis for such inverse problems. We show a significant acceleration for the estimation of electron density and temperature profiles. The approach maintains a floating-point double precision while reducing the processing time useful in applications where a reliable error estimation is required together with a fast processing time.

Kinetic approaches are generally accurate in dealing with microscale plasma physics problems but are computationally expensive for large-scale or multiscale systems. One of the long-standing problems in plasma physics is the integration of kinetic physics into fluid models, which is often achieved through sophisticated analytical closure terms. In this paper, we successfully construct a multimoment fluid model with an implicit fluid closure included in the neural network using machine learning. The multimoment fluid model is trained with a small fraction of sparsely sampled data from kinetic simulations of Landau damping, using the physics-informed neural network (PINN) and the gradient-enhanced physics-informed neural network (gPINN). The multimoment fluid model constructed using either PINN or gPINN reproduces the time evolution of the electric field energy, including its damping rate, and the plasma dynamics from the kinetic simulations. In addition, we introduce a variant of the gPINN architecture, namely, $\mathrm{gPINN}p$, to capture the Landau damping process. Instead of including the gradients of all the equation residuals, $\mathrm{gPINN}p$ only adds the gradient of the pressure equation residual as one additional constraint. Among the three approaches, the $\mathrm{gPINN}p$-constructed multimoment fluid model offers the most accurate results. This work sheds light on the accurate and efficient modeling of large-scale systems, which can be extended to complex multiscale laboratory, space, and astrophysical plasma physics problems.

An energy–momentum tensor for the microscopic plasma model is constructed from the action integral by allowing for dynamics of special relativity. The energy density is then identified with the 44-component of the energy–momentum tensor. The result is compared with that obtained from an ad hoc method with the Legendre transformation. The Hamiltonian obtained can be used to tackle nonlinear problems in plasma physics.

Cross‐scale energy transfer is a fundamental problem in plasma physics but is poorly understood. Based on Magnetospheric Multiscale satellite (MMS) data, we present the evidence of the energy transfer between ion‐scale and electron‐scale waves in the Earth's foreshock region. Low‐frequency fast‐magnetosonic waves (LFWs, ∼0.2 Hz; ion‐gyration scales) are observed in the solar wind upstream of the Earth's bow shock. Due to the magnetic compression of LFWs, suprathermal electrons (∼10–100s eV) are adiabatically heated in the perpendicular direction, which leads to the high anisotropy in the high‐magnetic‐field region. Then high‐frequency whistler mode waves (HFWs, 0.1–0.5 fce; electron‐gyration scales) are excited by those anisotropic electrons through cyclotron resonance. Therefore, this study reveals how energy is transported from LFWs to HFWs, suggesting that wave‐particle interactions have played a key role in cross‐scale energy transfer in collisionless plasmas.