Simulations of plasma obeying Coulomb's law and the formation of suprathermal ion tails in the solar wind

Abstract

We present a model for the velocity distribution function (VDF) of the suprathermal ion tail in the solar wind and its commonly observed spectrum, a power law in velocity of index -5. The mechanism for our model is acceleration from extremely small scale electric fields caused by the finite number of particles in the solar wind (or any plasma). The simulations produce a VDF with a broken power law at short times and a type of κ distribution VDF at later times. The simulation uses very few assumptions as it is based solely on Coulomb's law, and the results are robust to a range of parameters that, although outside the range of the solar wind at 1 AU, are close to those in the lower solar atmosphere. Furthermore, we provide predictions based on the following mechanism: the probability distribution function for the electric field (the electric field distribution function or EDF) dictates the final state of the plasma, which means that the VDF at any time is a convolution of the initial VDF and the EDF. We have also shown that by varying the power law index of the electrostatic force law, the relationship between the two is such that the EDF power law index is exactly 5 for Coulomb's law, harder for shorter-range forces, and softer for longer-range forces, converging to a power law of index 3 in the former limit and to a Maxwellian in the latter.