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I am currently trying to understand the theoretical frame work of diffusive shock acceleration. I am having trouble understanding a step in the derivation given by drury 1983 (http://www.oa.uj.edu.pl/user/mio/Ast-Wys-En/Literatura/drury.pdf). In the derivation of eq. 2.47 it is stated (just below the equation), that for an isotropic flux the shock crossing probability is proportional to cos(theta) and hence a factor of 2 cos(theta) is needed. I tried to tinker this together by using other literature and googling it a bit but i don't seem to find a satisfying answer for where exactly this comes from. I am sure the solution is rather simple but i don't see it. I would appreciate it if someone could explain it to me or perhaps refer me to a piece of literature where it is better described.

Thx

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# I Shock crossing probability for isotropic particle flux

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