Classical and quantum-mechanical treatments of the energy loss of charged particles in dilute plasmas

Abstract

We calculate the energy loss of charged particles in nondegenerate plasmas using classical and quantum-mechanical approximations. First we consider classical binary collisions between the test particle and the particles in the plasma, and obtain the energy transferred as a function of the relative velocity. This is integrated over the thermal distribution of plasma-particle velocities using simple analytical approximations. Then we use the quantum-mechanical analysis of the scattering of partial waves to find the transport cross section for a screened potential, and introduce analytical approximations to calculate the phase shifts. The thermal average is also calculated analytically. The study yields simple expressions for the energy loss in terms of the velocity and charge of the particle and of the density and temperature of the plasma. In particular, we retrieve various results of previous authors, which apply as limiting cases in the classical or quantum-mechanical regimes. The transition between these cases is described by analytical expressions of excellent accuracy. The calculation is finally compared with experimental results from laboratory plasmas in the classical domain.