The energy partitioning of non-thermal particles in a plasma: the Coulomb logarithm revisited

Abstract

The charged particle stopping power in a highly ionized and weakly to moderately coupled plasma has been calculated exactly to leading and next-to-leading accuracy in the plasma density by Brown, Preston and Singleton (BPS). Since the calculational techniques of BPS might be unfamiliar to some, and since the same methodology can also be used for other energy transport phenomena, we will review the main ideas behind the calculation. BPS used their stopping power calculation to derive a Fokker–Planck equation, also accurate to leading and next-to-leading orders, and we will also review this. We use this Fokker–Planck equation to compute the electron–ion energy partitioning of a charged particle traversing a plasma. The motivation for this application is ignition for inertial confinement fusion—more energy delivered to the ions means a better chance of ignition, and conversely. It is therefore important to calculate the fractional energy loss to electrons and ions as accurately as possible. One method by which one calculates the electron–ion energy splitting of a charged particle traversing a plasma involves integrating the stopping power dE/dx. However, as the charged particle slows down and becomes thermalized into the background plasma, this method of calculating the electron–ion energy splitting breaks down. As a result, it suffers a systematic error that may be as large as T/E0, where T is the plasma temperature and E0 is the initial energy of the charged particle. The formalism presented here is designed to account for the thermalization process and it provides results that are near-exact.