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

In hydrodynamic plasma simulations, it is necessary to have accurate but easily-computable formulas for various properties of the plasma. I present here a method for evaluating the electron-ion equilibration time arising from the Lenard-Balescu equation, which is accurate in weak coupling. The integrals are too difficult to compute directly within a hydrodynamic simulation, but I will describe the various mathematical techniques we used to derive a simple but accurate formula that holds for arbitrary electron degeneracy.