Giacalone (2005b) performed massive-scale two-dimensional hybrid simulations of perpendicular shocks propagating into a turbulent upstream magnetic field. It was shown that a fraction of thermal particles encountering the shock are accelerated to high energies. The physics of this process is similar to that which we have already described above. However, the source of the high-energy particles
10° 101 102 103 10" 10s 106 107 Energy (m U j~ / 2)
comes directly from the thermal population, which had not been seen in previous self-consistent plasma simulations. It has been long known that a fraction of thermal ions are assumed to be reflected by the shock and begin to gyrate within the shock ramp before becoming thermalized downstream. For the case in which the shock moves into an upstream region containing large-scale magnetic fluctuations, some of these ions can move upstream along these lines of force before returning to the shock. These ions can gain considerable energy because they can achieve multiple interactions with the shock. The efficiency for the acceleration in these large-scale hybrid simulations is difficult to estimate because the spatial domain is still rather limited by computation resources. However, it was estimated that the efficiency is probably comparable to that obtained for a parallel shock, or about 10-20% (Giacalone et al., 1997).
Giacalone and Jokipii (2005) have shown that the perpendicular shocks are as efficient as parallel shocks in accelerating particles to high energies using reasonable parameters. For these same parameters, perpendicular shocks are much more rapid accelerators. Thus, they conclude that perpendicular shocks are important sites of acceleration and can produce high-energy CR in a wide variety of astrophysical plasmas.
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