Heavy ion acceleration at parallel shocks

A study of alpha particle acceleration at parallel shock due to an interaction with Alfvén waves self-consistently excited in both upstream and downstream regions was conducted using a scale-separation model (Galinsky and Shevchenko, 2000, 2007). The model uses conservation laws and resonance conditions to find where waves will be generated or damped and hence where particles will be pitch-angle scattered. It considers the total distribution function (for the bulk plasma and high energy tail), so no standard assumptions (e.g. seed populations, or some ad-hoc escape rate of accelerated particles) are required. The heavy ion scattering on hydromagnetic turbulence generated by both protons and ions themselves is considered. The contribution of alpha particles to turbulence generation is important because of their relatively large mass-loading parameter P_α= n_αm_α/ n_pm_p ( m_p, n_p and m_α, n_α are proton and alpha particle mass and density) that defines efficiency of wave excitation. The energy spectra of alpha particles are found and compared with those obtained in test particle approximation.