Modification of classical electron transport due to collisions between electrons and fast ions

A Fokker-Planck model for the interaction of fast ions with the thermal electrons in a quasi-neutral plasma is developed. When the fast ion population has a net flux (i.e. the distribution of the fast ions is anisotropic in velocity space) the electron distribution function is significantly perturbed from Maxwellian by collisions with the fast ions, even if the fast ion density is orders of magnitude smaller than the electron density. The Fokker-Planck model is used to derive classical electron transport equations (a generalized Ohm's law and a heat flow equation) that include the effects of the electron-fast ion collisions. It is found that these collisions result in a current term in the transport equations which can be significant even when total current is zero. The new transport equations are analyzed in the context of a number of scenarios including $\alpha$ particle heating in ICF and MIF plasmas and ion beam heating of dense plasmas

Kinetic properties of particle-in-cell simulations compromised by Monte Carlo collisions

he particle-in-cell method with Monte Carlo collisions is frequently used when a detailed kinetic simulation of a weakly collisional plasma is required. In such cases, one usually desires, inter alia, an accurate calculation of the particle distribution functions in velocity space. However, velocity space diffusion affects most, perhaps all, kinetic simulations to some degree, leading to numerical thermalization (i.e., relaxation of the velocity distribution toward a Maxwellian), and consequently distortion of the true velocity distribution functions, among other undesirable effects. The rate of such thermalization can be considered a figure of merit for kinetic simulations. This article shows that, contrary to previous assumption, the addition of Monte Carlo collisions to a one-dimensional particle-in-cell simulation seriously degrades certain properties of the simulation. In particular, the thermalization time can be reduced by as much as three orders of magnitude. This effect makes obtaining strictly converged simulation results difficult in many cases of practical interest

Bernstein modes in a weakly relativistic electron-positron plasma

The kinetic theory of weakly relativistic electron-positron plasmas, producing dispersion relations for the electrostatic Bernstein modes was addressed. The treatment presented preserves the full momentum dependence of the cyclotron frequency, albeit with a relaxation on the true relativistic form of the distribution function. The implications of this new treatment were confined largely to astrophysical plasmas, where relativistic electronpositron plasmas occur naturally

Index

The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell–Jüttner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.Original Publication: Antoine Bret, Laurent Gremillet and Mark Eric Dieckmann, Multidimensional electron beam-plasma instabilities in the relativistic regime, 2010, Physics of Plasmas, (17), 12, 120501-1-120501-36. http://dx.doi.org/10.1063/1.3514586 Copyright: American Institute of Physics http://www.aip.org/</p

Deviations from the local field approximation in negative streamer heads

Negative streamer ionization fronts in nitrogen under normal conditions are investigated both in a particle model and in a fluid model in local field approximation. The parameter functions for the fluid model are derived from swarm experiments in the particle model. The front structure on the inner scale is investigated in a 1D setting, allowing reasonable run-time and memory consumption and high numerical accuracy without introducing super-particles. If the reduced electric field immediately before the front is >= 50kV/(cm bar), solutions of fluid and particle model agree very well. If the field increases up to 200kV/(cm bar), the solutions of particle and fluid model deviate, in particular, the ionization level behind the front becomes up to 60% higher in the particle model while the velocity is rather insensitive. Particle and fluid model deviate because electrons with high energies do not yet fully run away from the front, but are somewhat ahead. This leads to increasing ionization rates in the particle model at the very tip of the front. The energy overshoot of electrons in the leading edge of the front actually agrees quantitatively with the energy overshoot in the leading edge of an electron swarm or avalanche in the same electric field.Comment: The paper has 17 pages, including 15 figures and 3 table

On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials

The paper concerns $L^1$- convergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials (-4\le \gm<0), with and without angular cutoff. We prove the time-averaged $L^1$-convergence to equilibrium for all weak solutions whose initial data have finite entropy and finite moments up to order greater than 2+|\gm|. For the usual $L^1$-convergence we prove that the convergence rate can be controlled from below by the initial energy tails, and hence, for initial data with long energy tails, the convergence can be arbitrarily slow. We also show that under the integrable angular cutoff on the collision kernel with -1\le \gm<0, there are algebraic upper and lower bounds on the rate of $L^1$-convergence to equilibrium. Our methods of proof are based on entropy inequalities and moment estimates.Comment: This version contains a strengthened theorem 3, on rate of convergence, considerably relaxing the hypotheses on the initial data, and introducing a new method for avoiding use of poitwise lower bounds in applications of entropy production to convergence problem

Duration of cyclotron harmonic resonances observed by satellites

Cyclotron harmonic waves travelling at group velocity equal to satellite velocit

Formation of plasma around a small meteoroid: 1. Kinetic theory

This article is a companion to Dimant and Oppenheim [2017] https://doi.org/10.1002/2017JA023963.This paper calculates the spatial distribution of the plasma responsible for radar head echoes by applying the kinetic theory developed in the companion paper. This results in a set of analytic expressions for the plasma density as a function of distance from the meteoroid. It shows that at distances less than a collisional mean free path from the meteoroid surface, the plasma density drops in proportion to 1/R where R is the distance from the meteoroid center; and, at distances much longer than the mean‐free‐path behind the meteoroid, the density diminishes at a rate proportional to 1/R2. The results of this paper should be used for modeling and analysis of radar head echoes.This work was supported by NSF grant AGS-1244842. (AGS-1244842 - NSF

Spatially hybrid computations for streamer discharges: II. Fully 3D simulations

We recently have presented first physical predictions of a spatially hybrid model that follows the evolution of a negative streamer discharge in full three spatial dimensions; our spatially hybrid model couples a particle model in the high field region ahead of the streamer with a fluid model in the streamer interior where electron densities are high and fields are low. Therefore the model is computationally efficient, while it also follows the dynamics of single electrons including their possible run-away. Here we describe the technical details of our computations, and present the next step in a systematic development of the simulation code. First, new sets of transport coefficients and reaction rates are obtained from particle swarm simulations in air, nitrogen, oxygen and argon. These coefficients are implemented in an extended fluid model to make the fluid approximation as consistent as possible with the particle model, and to avoid discontinuities at the interface between fluid and particle regions. Then two splitting methods are introduced and compared for the location and motion of the fluid-particle-interface in three spatial dimensions. Finally, we present first results of the 3D spatially hybrid model for a negative streamer in air

Sagittarius A* Accretion Flow and Black Hole Parameters from General Relativistic Dynamical and Polarized Radiative Modeling

We obtain estimates of Sgr A* accretion flow and black hole parameters by fitting polarized sub-mm observations with spectra computed using three-dimensional (3D) general relativistic (GR) magnetohydrodynamical (MHD) (GRMHD) simulations. Observations are compiled from averages over many epochs from reports in 29 papers for estimating the mean fluxes Fnu, linear polarization (LP) fractions, circular polarization (CP) fractions, and electric vector position angles (EVPAs). GRMHD simulations are computed with dimensionless spins a_*=0,0.5,0.7,0.9,0.98 over a 20,000M time interval. We perform fully self-consistent GR polarized radiative transfer using our new code to explore the effects of spin a_*, inclination angle \theta, position angle (PA), accretion rate Mdot, and electron temperature Te (Te is reported for radius 6M). By fitting the mean sub-mm fluxes and LP/CP fractions, we obtain estimates for these model parameters and determine the physical effects that could produce polarization signatures. Our best bet model has a_*=0.5, \theta=75deg, PA=115deg, Mdot=4.6*10^{-8}M_Sun/year, and Te=3.1*10^10K at 6M. The sub-mm CP is mainly produced by Faraday conversion as modified by Faraday rotation, and the emission region size at 230GHz is consistent with the VLBI size of 37microas. Across all spins, model parameters are in the ranges \theta=42deg-75deg, Mdot=(1.4-7.0)*10^{-8}M_Sun/year, and Te=(3-4)*10^10K. Polarization is found both to help differentiate models and to introduce new observational constraints on the effects of the magnetic field that might not be fit by accretion models so-far considered.Comment: 19 pages, 11 figures, accepted to Ap