On test charge potentials in collisional plasmas

Abstract

The effect of electron-electron collisions on the potential of a slowly moving test charge in a plasma is considered. A new dipole-like term is found. IntroductionThe electric field of a moving test charge in a uniform plasma has recently received increased attention. Thus, Montgomery and others [1,2] considered the far-field potential of a test charge in a collisionless plasma and found that it can decrease as the inverse cube of the distance. The effect of collisions has been considered recently [3,4] using simple models. It was found that an inverse-square distance dependence can appear. This conclusion is clearly of sufficient interest to justify further investigations of collisional effects. In this paper we reconsider the problem by means of a full BGK model collision operator [5]. In addition we show explicitly that some of the results [c.f. (18)] can be demonstrated to be valid for arbitrary collision processes.The full BGK collision term [5] conserves number density, momentum and energy. Thus it describes electron-electron scattering which cannot be accounted for by the simple BGK model [3] in which momentum is not conserved. For the same reason the present model does not correspond to any collisional contributions within a conventional macroscopic analysis [4]. The results in this paper are thus complementary to those of Refs.[3] and [4] in which electron-ion and electron-molecule collisions are treated. Finally we demonstrate that ion motion can be significant if the test charge velocity is very small. Basic FormulationWe consider a homogeneous, isotropic electron plasma in the absence of external fields. The test particle is not affected by collisions in our model and it travels at a constant velocity Vo. where -qNo and qt6 (X-Vot) are the charge densities of the positive background and the test charge, respectively, and r is the potential due to the presence of the latter. The distribution function for the electrons is denoted by f, and C is the collision term [5]. The constant parameter v represents the electron-electron collision frequency. The density, mean velocity and normalized temperature are given by the following moments of the distribution function,

Novel Attractive Force between Ions in Quantum Plasmas

“…In a classical electronion plasma [1,2], an isolated ion is shielded by nondegenerate Boltzmann distributed electrons, and hence one [3] replaces Q by Z i e and λ by the electron Debye radius λ De = (k B T e /4πn 0 e 2 ) 1/2 , where Z i is the ion charge state, e the magnitude of the electron charge, k B the Boltzmann constant, T e the electron temperature, and n 0 the unperturbed electron number density. For a slowly moving test charge in collisionless [4] and collisional [5,6] plasmas, there appear additional far-field potentials decreasing as inverse cube and inverse square of the distance between the test charge and the observer. In a collisionless dusty plasma [7][8][9] with Boltzmann distributed electrons and ions, a micron-sized negatively charged isolated dust is shielded by both positive ions and electrons.…”

Connecting the very large and the very small: effective particle mass in curved-space cosmological models

“…Surprisingly, however, starting in the 1950's several authors (Neufeld & Ritchie 1955; Tappert 1967; Montgomery, Joyce & Sugihara 1968) discovered that a test charge moving uniformly is not exponentially screened, but generates the field of a quadrupole in a collisionless plasma. The restriction to a collisionless plasma was lifted in later papers (Yu, Tegeback & Stenflo 1973; Schroeder 1975), where it was shown that the far field of a moving test charge is that of a dipole with strength of order q τ t V , where q is the charge, τ t the collision time as measured by t and V the velocity. This dipole form ensures that in Minkowski space the contribution of particles to the effective mass falls off rapidly with distance beyond the Debye radius.…”

Quasistationary wake plasma wave excited by a comoving charged pulse

“…[13][14][15][16][17][18][19][20][21][22][23] Electrostatic shielding of a moving charge is a fundamental problem in plasma physics. [13][14][15][16][17][18][19][20][21][22][23] Electrostatic shielding of a moving charge is a fundamental problem in plasma physics.…”

“…In a thermal plasma the far-field electrostatic potential of a freely moving test charge is not Debyeshielded like that of a stationary charge because the motion of the test charge introduces in the expression for potential a relatively slowly decaying inertial term that does not contain the characteristic exponential shielding. [18][19][20] In the classical moving test-charge problem, one is concerned with the linear kinetic response of the background plasma to a moving point charge. [14][15][16][17] When the test charge is suprathermal, there also appears behind it potential oscillations.…”