A Method to Determine the Electron-Ion Thermal Exchange Rate from Force Distributions of Test Ions

Temperature relaxation between species, e.g. electrons and ions, is an important transport process in plasma applications such as fusion experiments. However, these relaxation rates can be difficult to measure in the laboratory. A sparse population of test particles, e.g. fusion products, is often present and may be used as a diagnostic. Here, we demonstrate that the velocity distributions and distribution of forces on these test particles can be used to measure electron-ion energy exchange densities, which are directly proportional to temperature relaxation rates. It is well known that the average force on test particles is the friction force, which is essentially the stopping power. Here, we show that the thermal energy exchange is related to the covariance between the test particle velocity and force distributions. First-principles molecular dynamics (MD) simulations are used to test this under a range of conditions: when the background species with which the test particles interact is strongly coupled (the average inter-particle potential energy exceeds the average thermal energy), when the background species is strongly magnetized (particle gyroradii are smaller than length scales associated with collisions), and when the test particle has opposite charge as that of the background particles. These conditions are known to significantly affect the friction, and their effects on the energy exchange density are assessed with the proposed covariance method.