Computational Plasmadynamics applied to parametric studies

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.

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

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.

Symbolic vector analysis in plasma physics

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.

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

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.

This paper deals with the numerical identification of the plasma current density in a Tokamak, from experimental measurements. This problem consists in the identification of a non-linearity in a semi-linear 2D elliptic equation from Cauchy boundary measurements and from integrals of the magnetic field over several chords. A simplified problem, corresponding to the cylindrical approximation, is first solved by a SQP algorithm, where the non-linearity is decomposed in a basis of B-splines and where Tikhonov regularization is used, the regularizing parameter being determined by a cross-validation procedure. An alternative approach based on the decomposition of the non-linearity in a basis of compactly supported wavelets and the use of a new scalar product in the HH2 space has enabled to solve the identification problem in a robust way, without using Tikhonov regularization Finally several test-cases are presented for the determination of the current density in the real toroidal configuration from magnetic, interferometric and polarimetric measurements.KeywordsInverse ProblemSequential Quadratic ProgrammingTikhonov RegularizationMagnetic SurfaceFlux LineThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The problem of analytic continuation is considered for the Lauricella function , a generalized hypergeometric functions of complex variables. For an arbitrary a complete set of formulae is given for its analytic continuation outside the boundary of the unit polydisk, where it is defined originally by an -variate hypergeometric series. Such formulae represent in suitable subdomains of in terms of other generalized hypergeometric series, which solve the same system of partial differential equations as . These hypergeometric series are the -dimensional analogue of Kummer’s solutions in the theory of Gauss’s classical hypergeometric equation. The use of this function in the theory of the Riemann–Hilbert problem and its applications to the Schwarz–Christoffel parameter problem and problems in plasma physics are also discussed. Bibliography: 163 titles.

Simplicity and boundary behavior of spike sequences for a superlinear problem in plasma physics

Simulation of nonlinear reaction-diffusion equations