Passage of Charged Particles through Plasma

TLDR

Plasma is modeled as a homogeneous dispersive medium whose dielectric constant depends on both frequency and wave number, a description valid for ionospheric and gas‑discharge plasmas but not for conduction‑band electrons in metals. The study aims to investigate how charged particles traverse such a plasma. This is achieved by applying Maxwell’s equations to a dispersive medium. For slow particles the stopping power extends the Fermi–Teller formula, an expression for the surrounding polarization density is derived, and for fast particles Debye screening vanishes while the potential falls off as an inverse cube law.

Abstract

The plasma has been treated phenomenologically as a homogeneous dispersive medium characterized by a "dielectric constant" which is a function not only of the frequency of the applied field (as in conventional dispersive media) but also on its wave number. The representation of plasma as a dispersive medium is subject to certain validity criteria which are satisfied for such typical cases as the ionosphere and electrical discharge through gases but is not satisfied for electrons in the conduction band of a metal. The passage of charged particles through plasma is investigated by means of straightforward application of Maxwell's equations for a dispersive medium. The Debye screening, which is applicable to the potential of an incident particle having velocity $V\ensuremath{\ll}{〈{v}^{2}〉}^{\frac{1}{2}}$ (where ${〈{v}^{2}〉}^{\frac{1}{2}}$ is the root mean square velocity of plasma electrons), loses its significance when $V\ensuremath{\gg}{〈{v}^{2}〉}^{\frac{1}{2}}$; and in the latter case, the potential decreases with the distance in accordance with an inverse cube law. The stopping power has been calculated for slow incident charged particles having $V\ensuremath{\ll}{〈{v}^{2}〉}^{\frac{1}{2}}$ and for fast particles having $V\ensuremath{\gg}{〈{v}^{2}〉}^{\frac{1}{2}}$ in a plasma comprising electrons distributed in accordance with Maxwell-Bolzmann and Fermi-Dirac statistics. For slow particles the results represent an extension of the formula of Fermi and Teller. An expression has been derived for the distribution of the polarization density in the space surrounding a moving particle.