Ion Beam Instabilities during Solar Flare Energy Release

Abstract: The linear stability of waves driven by ion beams produced during solar flare energy release are explored to assess their role in driving abundance enhancements in minority species such as $^3$He and in controlling, through pitch-angle scattering, proton/alpha confinement during energy release. The Arbitrary Linear Plasma Solver (ALPS) is used to solve the linear dispersion relation for a population of energetic, reconnection-accelerated protons streaming into a cold background plasma. We assume equal densities of the two populations, using an anisotropic ($T_\parallel/T_\perp = 10$), one-sided kappa distribution for the energetic streaming population and a cold Maxwellian for the background. We find two unstable modes with parallel propagation: a right-handed wave with a frequency of the order of the proton cyclotron frequency ($\Omega_{cp}$) and a left-handed, lower frequency mode. We also find highly oblique modes with frequencies below $\Omega_{cp}$ that are unstable for higher beam energies. Through resonant interactions, all three modes will contribute to the scattering of the high-energy protons, thereby limiting their transport out of the flare-acceleration region. The higher-frequency oblique mode, which can be characterized as a kinetic Alfv\'en wave, will preferentially heat $^3$He, making it a good candidate for the driver of the abundance enhancements commonly observed for this species in impulsive events.