## 5. SummaryIn our study we presented test particle calculations for superthermal protons under the influence of large magnetic field fluctuations at supercritical quasi-parallel shock waves. Due to the presence of these structures quasi-parallel shocks show features of quasi-perpendicular shocks, i.e., protons or ions reflected off the shock transition zone are prevented from escaping into the upstream region, they return to the transition zone and may penetrate into the downstream region with a superthermal energy and can thus contribute to downstream heating. The velocity gain can be computed according to Eq. 7. In particular the following results were obtained: Describing SLAMS as reconvected simple MHD waves approaching the shock transition we found a dependence of the interacting protons on the magnetic field compression, the width, the direction and the starting position of the SLAMS. Fig. 4 showed, how far the dividing line between quasi-parallel and quasi-perpendicular shocks () is shifted to smaller angles with rising magnetic field compression of SLAMS. The location of this line seperating regions of 'return'- and 'escape'-behaviour was calculated from numerical test particle calculations. These results were compared with analytical computations using adiabatic theory (Eq. 6). For a velocity range of the deviation between numerical and analytical calculations are smaller than 30 %. In general the limits for an application of adiabatic theory depend on the ratio between the particle's gyroradius and the length scale of the reflecting structure. The magnetic moment is a constant up to the order . Furthermore, a modified critical reflection angle for non adiabatic reflection was considered (Eq. 10). In our analysis we followed closely the investigations of Fuselier et al. (1986), who made analogous studies for protons under the influence of finite amplitude, monochromatic MHD waves with a change in the magnetic field of . Doing so we broadened those results to large amplitude field fluctuations () in the upstream region. We argued that the presence of these large amplitude field fluctuations enables us to understand the observations of cold ion bunches in a supercritical, quasi-parallel shock geometry. © European Southern Observatory (ESO) 1998 Online publication: January 8, 1998 |