Effect of spin on the electron-ion scattering and the heating rate of a plasma in very intense laser light.

Abstract

An exact Volkov state solution of the minimally coupled Dirac equation is used to calculate the transition rate dR of an electron scattering via a stationary ion in the presence of a very intense laser field. A consistent picture of the scattering is presented in which the electrons' initial and final states are quasifree states. Accordingly, a modified transition rate ${\mathrm{dR}}^{\mathrm{*}}$ and a modified Maxwell-Boltzmann distribution are developed. They are used to calculate the heating rate W of the isotropic part of a quasifree neutral plasma in the presence of very intense laser light. In order to simplify the expression for the heating rate W, an important transformation, which changes an infinite sum over Bessel functions into a finite integral, is introduced. It is then shown that the leading term of the heating rate W is similar to the expression of Osborn (with corrections) for intensity I${<10}^{16}$ W/${\mathrm{cm}}^{2}$ and ${k}_{B}$T1 keV. A new correction factor is defined to show the effect of a very intense laser field when the intensity I${10}^{16}$ W/${\mathrm{cm}}^{2}$. For ${k}_{B}$T>1 keV, a spin-dependent term of order ${k}_{B}$T/${\mathrm{mc}}^{2}$ is also discovered. This represents a new term not previously known. We show that the effect of this term on the heating rate is substantial and it would be possible to measure its effect with present-day laser systems.