Injection and acceleration of H+ and He2+ at Earth's bow shock

We have performed a number of one-dimensional hybrid simulations (particle ions, massless electron fluid) of quasi-parallel collisionless shocks in or der to investigate the injection and subsequent acceleration of part of the solar wind ions at the Earth's bow shock. The shocks propagate into a medi um containing magnetic fluctuations, which are initially superimposed on th e background field, as well as generated or enhanced by the electromagnetic ion/ion beam instability between the solar wind and backstreaming ions. In order to study the mass (M) and charge (Q) dependence of the acceleration process He2+ is included self-consistently. The upstream differential inten sity spectra of H+ and He2+ can be well represented by exponentials in ener gy. The e-folding energy E-c is a function of time: E-c increases with time . Furthermore the e-folding energy (normalized to the shock ramming energy E-p) increases with increasing Alfven Mach number of the shock and with inc reasing fluctuation level of the initially superimposed turbulence. When ba ckstreaming ions leave the shock after their first encounter they exhibit a lready a spectrum which extends to more than ten times the shock ramming en ergy and which is ordered in energy per charge. From the injection spectrum it is concluded that leakage of heated downstream particles does not contr ibute to ion injection. Acceleration models that permit thermal particles t o scatter like the non-thermal population do not describe the correct physi cs.