© 2018 American Physical Society. 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 analytic 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.
Scullard, C. R., Serna, S., Benedict, L. X., Ellison, C. L., & Graziani, F. R. (2018). Analytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation. Physical Review E, 97(1), . https://doi.org/10.1103/PhysRevE.97.013205