Demarcating the classical and quantum approaches for the Coulomb logarithm in plasmas

TL;DR

This paper compares classical and quantum models for calculating the Coulomb logarithm in plasmas, establishing criteria for when classical descriptions are valid based on electron wavelength and screening length.

Contribution

It provides a detailed analysis of the applicability of classical versus quantum approaches for electron-ion collisions in plasmas across various conditions.

Findings

Classical scattering is valid when electron de Broglie wavelength is smaller than the ion screening length.

Quantum first-order Born approximation aligns with classical results only in the classical regime.

The study covers a wide range of temperatures and densities relevant to inertial confinement fusion.

Abstract

The Coulomb logarithm often enters various plasma models and simulation methods for computing the transport and relaxation properties of plasmas. Traditionally, a classical pair collision picture was used to calculate the Coulomb logarithm for different plasma parameters. With the recent emergence of the high interest in dense plasmas with partially degenerate electrons, new approaches have been developed to treat electron-ion collisions in a quantum-mechanical way. In this context, gaining a deeper physical understanding of the criteria for the applicability of classical plasma models is crucial. We have analyzed the Coulomb logarithm describing the electron-ion collisions in hydrogen plasmas in a wide range of temperatures and densities relevant to inertial confinement fusion experiments. The electron-ion collision cross-sections were computed using both quantum and classical scattering theories. We found that the classical description of the electron-ion scattering in plasmas and related plasma models is applicable if the de Broglie wavelength of electrons is smaller than the ion charge screening length in plasmas. Additionally, we show that the quantum first-order Born approximation for describing the electron-ion collision is accurate only in the regime where classical scattering theory is accurate.