The skin effect in anomalous transport of charged particles in plasma with a microturbulent magnetic field. I. Isotropic plasma

TL;DR

This work investigates how the electromagnetic skin effect alters anomalous transport of charged particles in dense, non-relativistic, collisionless plasma with microturbulent magnetic fields by developing a quasi-linear FP framework. It derives the diffusion-tensor components $\\hat{\\mu}_{\\alpha\\beta}$, including the influence of the screening factor $|\\Lambda(\\omega,\\mathbf{k})|^2$, and analyzes isotropic magnetostatic turbulence to reveal elastic scattering in the magnetostatic limit and the emergence of anisotropy due to a finite screening length. The study provides analytic expressions for the effective mobility and conductivity in isotropic turbulence and confirms, via numerical FP solutions, that screening increases the mean free path and induces a strong anisotropy in the stationary velocity distribution that grows roughly as $\\xi^4$ with screening parameter $\\xi$. These results illuminate how screening modulates anomalous transport and conductivity in dense plasmas, with potential relevance to current layers and turbulence-driven heating, while highlighting the need for self-consistent turbulence spectra and non-stationary-field analyses in future work.

Abstract

The influence of electromagnetic skin effect on anomalous charged particle transport in dense, non-relativistic, collisionless plasma with a small-scale turbulent magnetic field was investigated using quasi-linear kinetic equations, through both analytical and numerical methods. Analytical expressions for the diffusion tensor components in the Fokker-Planck equation that take this effect into account have been found. The equation was solved numerically in the case of magnetostatic turbulence. It has been demonstrated that the skin effect increases the mean free path of particles in turbulent plasma, thereby reducing its anomalous resistance. It also leads to anisotropy in particle scattering, resulting in anisotropy in their stationary velocity distribution, which increases as the screening parameter grows. Approximate analytical formulas for the effective mobility of charged particles and the electric conductivity of plasma with isotropic magnetostatic turbulence have been obtained.

Figures (3)

• Figure 1: a) Schematic representation of a laboratory reference frame with guide axes $\mathbf{e}_{\alpha,\beta,\gamma}$ and the direction of motion of a single particle with velocity $\mathbf{v}$ and a particle beam with drift velocity $\mathbf{u}$. The shaded area shows the resonance plane of the wave vectors of the turbulent magnetic field $\mathbf{k}_{\perp}$ that contribute non-zero to particle scattering. b) Schematic representation of the averaged distribution function of scattered beam particles by velocity. The average values of the drift and double thermal velocities ($u$ and $v_{T}$) are marked. c) Symbolic two-dimensional picture of the propagation of a particle beam in plasma with a turbulent magnetic field.
• Figure 2: Dependence of (a) dimensionless mobility $b$ and (b) anisotropy of the particle velocity distribution function $A$ on the screening parameter $\xi$. Numerical calculation - blue dashed-dotted curve, analytical approximation - red dotted curve.
• Figure 3: a) Time dependence of the normalized average particle velocity $u$ during free relaxation of its initial value for different values of the screening parameter $\xi$. b) Dependence of the normalized effective conductivity of turbulent plasma $\sigma_{B}$ on the characteristic scale of magnetic perturbations $\lambda_{cor}$. The parameter $\lambda_{cor}^{0}$ is equal to the screening length $l_s$ at $\xi=1$.