BPS Explained I: Temperature Relaxation in a Plasma

TL;DR

This paper introduces a novel technique based on dimensional continuation for calculating plasma transport properties, specifically the temperature relaxation rate, with exact leading and subleading order results.

Contribution

It presents a new exact calculation method for plasma transport quantities using dimensional continuation, improving upon previous models and approximations.

Findings

Calculated temperature equilibration rate to leading and next-to-leading order.

Provided an exact perturbative calculation, not a model.

Applied the method to electron-ion temperature relaxation.

Abstract

This is the first of two lectures on a new powerful technique employed by Brown, Preston, and Singleton (BPS) to calculate transport quantities in a plasma. This exposition will be self-contained and intended for those who are not specialists in quantum field theory, where the technique of dimensional continuation exploited by BPS first arose. The method is highlighted by the interesting analogy between the Coulomb logarithm of Lyman Spitzer on the one hand, and the Lamb shift as calculated by Hans Bethe on the other. BPS employed the method in a novel way that provides the leading and subleading behavior for processes with competing disparate length or energy scales. They calculated the temperature equilibration rate to leading and next-to-leading order in the plasma number density for any two species in a plasma that are in thermal equilibrium with themselves, but not necessarily with each other. A special case of this calculation is the electron-ion temperature equilibration rate. It should be emphasized that the BPS result is not a model, but rather it is an exact calculation of the leading terms in a well-defined perturbation theory. This exact result differs from approximations and models given in the literature.