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nONLINEAR cOSMIC rAY eFFECTS IN sPACE pLASMAS

Fig. 3.10.3. CR pressure (solid line) compared to the ram (dashed line) and the thermal pressure (dash-dotted line) for (a) n = 0.0003 and (b) n = 0.9. All pressures are in eV cm-3. According to Le Roux and Fichtner (1997b).

From Fig. 3.10.3 it can be seen that for n = 0.0003, the contribution from anomalous CR is negligible and the CR pressure profile is rather flat. Also the CR pressure is everywhere smaller than that of the thermal plasma; its ram pressure dominates upstream, its thermal pressure downstream. For n = 0.9, however, the acceleration of anomalous CR results in a significant CR pressure at and downstream of the heliospheric shock.

According to Le Roux and Fichtner (1997a,b) the strong modification of the heliospheric shock shown in Fig. 3.10.2b and given in Table 3.10.1 can be understood in view of the large CR pressure gradient close to the heliospheric shock seen in Fig. 3.10.36. This gradient forces the solar wind to decelerate strongly. It is also evident why both the high- and the low-injection case result in similar flux levels for distances smaller than ~ 60 AU: the production of anomalous CR leads to a pressure buildup close to, at, and beyond the heliospheric shock, but not very far upstream. If only a small fraction of the pickup ion population is injected, the sub-shock strength remains relatively high (5 = 3.4) and the acceleration remains sufficiently efficient to produce the observed flux levels. If, on the other hand, a larger fraction of pickup ions becomes injected, the heliospheric shock is strongly modified (5 = 1.5) and its acceleration is efficiency reduced, accompanied by stronger modulation, i.e., larger radial gradients gr = Cujk, particularly beyond ~ 60 AU. These effects occur because the steeper spectral gradient dJ(Ek )/d at the heliospheric shock (see Fig. 3.10.1) implies a larger Compton-Getting factor

d ln Ek

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