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Fig. 4.16.3. Particle spectra for cases of shocks obtained by pitch angle treatment (PA) compared with a power-law spectrum obtained by diffusion-convection equation (DC). According to Malakit et al. (2003).

Similarly, the particle-density jump can be predicted by pitch angle treatment only. The jump is highest in the Q-Perp case, intermediate for the oblique (OB) case (d1 = 45°), and disappears for a Q-Par shock (see Fig. 4.16.4).

For compression regions, there is also a peak near the compression plane that is analogous with the jump in the case of shocks. This peak is not as high as the shock jump and the peak height decreases when the compression is wider (see Fig. 4.16.5).

In Fig. 4.16.5 compression width is expressed in terms of the ratio of b to the parallel mean free path. Malakit et al. (2003) conclude that the peak (or jump) should be owed to magnetic mirroring, which is neglected in the diffusion-convection approach. As further evidence, Fig. 4.16.6 shows equal-density contours in the p-z plane, with a density peak near the compression plane for particles mirroring back upstream.

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