Energy spectra of accelerated proton and alpha particles at quasi-parallel shocks

*Tooru Sugiyama[1] ,Masaki Fujimoto [1],Manfred Scholer [2]
Tokyo Institute of Technology[1]
Max-Planck-Institut[2]

We have performed a number of one-dimensional hybrid simulationsof quasi-parallel shocks in order to investigate the energy spectra of non-thermal protons and alpha particles. We have investigated the dependences on a density ratio (=R) of alpha particles to protons in the upstream thermal population and on the Alfven Mach numbers (=MA). As observed in the upstream region of the earth's bow shock, the upstream differential flux spectra of these ions are well represented by exponentials in energy. The characteristic energy (=Ec) is almost identical for both ion species in the wide range of R and time. Ec is a function of the density ratio R and time. Ec increases with R and time. Since different wave spectra are obtained for different parameters of R and MA, neither proton nor alpha particle acceleration requires any special waves-length for the wave-particle interaction. A large amplitude wave is sufficient to change the direction of particle's motion.

In the region upstream of quasi-parallel bow shocks, non-thermal ions are frequently observed. One of the most characteristic features of the ions is their spectral shape. Ipavich et al. (1981) have shown that the energy spectrum observed upstream of the earth's bow shock is well described by an exponential shape. Furthermore the characteristic energy Ec is independent of ion species if represented in energy per charge (E/Q) unit. Scholer et al. (1999) have performed hybrid simulations with initially imposed upstream fluctuations and have shown that alpha particles are also accelerated at quasi-parallel shocks. The energy spectra of proton and the alpha particles have a nearly identical characteristic energy when represented in energy per charge. The acceleration process is usually described by the diffusive shock acceleration mechanism. In this mechanism, ion motion is based on the cyclotron resonance motion. However, recently a different type of wave-particle interaction from thermal to the non-thermal energy range has been proposed by Sugiyama et al. (2001a) which is based on particle interaction with large amplitude waves on both sides of the shock. In their model, the resonant motion is not essential for the injection and acceleration from the thermal population. Therefore, even in a wave field which is excited by protons, alpha particles are accelerated out of the thermal population (Sugiyama et al., 2001b). According to their results, protons and alpha particles are accelerated by the same mechanism if large amplitude waves exist near a shock. In order to confirm this, we have investigated the energy spectral shape for various upstream wave intensities/modes. By changing the density ratio (=R) of alpha particles to protons in the upstream thermal population, different waves are excited in the simulation systems. We have compared the characteristic energy for protons and alpha particles.