Proton heating by pick-up ion driven cyclotron waves in the outer   heliosphere: Hybrid expanding box simulations
  Using one-dimensional hybrid expanding box model we investigate properties of the solar wind in the outer heliosphere. We assume a proton-electron plasma with a strictly transverse ambient magnetic field and, beside the expansion, we take into account influence of a continuous injection of cold pick-up protons through the charge-exchange process between the solar wind protons and hydrogen of interstellar origin. The injected cold pick-up protons form a ring distribution function that rapidly becomes unstable and generate Alfv\'en cyclotron waves. The Alfv\'en cyclotron waves scatter pick-up protons to a spherical shell distribution function that thickens over that time owing to the expansion-driven cooling. The Alf\'ven cyclotron waves heat solar wind protons in the perpendicular direction (with respect to the ambient magnetic field) through the cyclotron resonance. At later times, the Alfv\'en cyclotron waves become parametrically unstable and the generated ion acoustic waves heat protons in the parallel direction through the Landau resonance. The resulting heating of the solar wind protons is efficient on the expansion time scale. 
Petr Hellinger and Pavel M. Travnicek
astro-ph.SR physics.space-ph