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 electronion 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, as this could have implications for the Laser Mégajoule (LMJ) facility in France and the National Ignition Facility (NIF) in the United States. The traditional 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, the method suffers a systematic error of order T /E 0 , where T is the plasma temperature and E 0 is the initial energy of the charged particle. In the case of DT fusion, for example, this can lead to uncertainties as high as 10% or so. The formalism presented here is designed to account for the thermalization process, and in contrast, it provides results that are near-exact.

An Exact Calculation of Electron-Ion Energy Splitting in a Hot Plasma

“…For the last several years, in collaboration with Lowell Brown and Dean Preston, I have been studying Coulomb energy exchange processes in hot multi-component but weakly coupled plasmas [1][2][3][4][5][6][7][8]. In Ref.…”

Charged Particle Motion in a Plasma: Electron-Ion Energy Partition

“…We instead focus on intermediate times when, in general, there is a significant difference between the electron and ion temperatures, but the alpha particle density has not yet become a significant fraction of the D and T ion densities. 1 The fusion rate is very sensitive to the ion temperature T I . The ion temperature is determined by competition between deposition of the alpha particle energy into the ions, which of course increases T I , and thermal equilibration with the electron distribution, which drives T I down.…”

“…This introduces additional complications, and as such merits a separate publication 2. A short preliminary account of the methods that we employ in this paper, but restricted to the case of equal ion and electron temperatures, has previously been presented in[1].…”