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arXiv · 1710.00972

Analytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation

Christian R. Scullard·Susana Serna·Lorin X. Benedict·C. Leland Ellison·Frank Graziani
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Abstract

In this work, we elucidate the mathematical structure of the integral that arises when computing the electron-ion temperature equilibration time for a homogeneous weakly-coupled plasma from the Lenard-Balescu equation. With some minor approximations, we derive an exact formula, requiring no input Coulomb logarithm, for the equilibration rate that is valid for moderate electron-ion temperature ratios and arbitrary electron degeneracy. For large temperature ratios, we derive the necessary correction to account for the coupled-mode effect, which can be evaluated very efficiently using ordinary Gaussian quadrature.

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Christian R. Scullard, Susana Serna, Lorin X. Benedict, C. Leland Ellison, Frank Graziani. 2017-10-03. Analytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation. https://doi.org/10.1103/physreve.97.013205

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