Proton heating by pick-up proton-generated waves in the expanding solar wind: Hybrid simulations

Proton energization observed in the outer heliosphere by Voyager 2 can be attributed to the dissipation of the wave energy generated by pick-up protons. We present one-dimensional self-consistent kinetic simulation results of this kinetic phenomenon using the hybrid expanding box (HEB) model with various parameters of the solar wind and the pick-up ions. In these simulations the magnetic field is assumed to be strictly transverse and the plasma does not contain any pick-up protons initially but they are injected continuously during the expansion assuming a simple model for the charge-exchange process. The injected pick-up protons form a ring velocity distribution function in the solar wind which becomes eventually unstable and generates cyclotron waves which scatter the pick-up ions forming a shell distribution function. The generated waves also heat the solar wind protons and this cyclotron heating is able to overcome the adiabatic cooling in agreement with the Voyager 2 observations. We discuss constraints imposed by the dimensionality of the solution not allowing oblique wave modes to propagate. We propose additional one dimensional and more complex two-dimensional simulation runs.