Kinetic Simulations of the Proton-Alpha Instability in Collisionless Shocks

Abstract

The solar wind is a dynamic stream of collisionless plasma originating from the Sun. When it reaches the Earth’s magnetosphere, it abruptly slows down from super Alfvénic to sub-Alfvénic speeds, creating a bow shock. This compresses and heats the inflowing plasma. The solar wind consists primarily of electrons, protons and alpha-particles, which interact differently with the shock. A relative drift between protons and alpha particles develops, which can trigger a streaming instability, driv ing waves. Such waves have previously been identified in spacecraft observations. The dependence of the instability on the particle species temperature, density, and flow velocity has previously been investigated using the dispersion relation for an unmagnetized plasma. In this work, we investigate this proton-alpha streaming instability using two dimensional fully kinetic Particle-In-Cell simulations. This approach offers the flex ibility to freely choose the initial conditions while simulating the full non-linear dynamics. We study the parametric dependence of the instability on the flow ve locity of the alpha particles, the density ratio of the ions as well as the influence of a background magnetic field. In particular, we want to quantify the heating of different particle species due to the instability. Additionally, we aim to test the applicability of the simplified linear theory. Our simulations show that the instability mediates a strong energy exchange from the flow speed of the alphas into plasma heating of the ions. We attribute this to a Landau resonance between the proton and the alpha distribution, which produces large plateaus in velocity space. The electron dynamics do not change significantly. The wave properties are consistent with the linear theory when the external magnetic field is small. Generally, the angle between the wave and the drift direction increases with the flow speed. The fraction of energy converted to plasma heating reaches a maximum at a wave angle of 45 deg to the drift direction. Overall, the existence of a background magnetic field slightly suppresses the instability, due to the magnetization of electrons. We conclude that the proton-alpha streaming instability can play an important role in heating protons and alpha particles across collisionless shocks.