| Autor: |
Lavi, Assaf, Arad, Ofir, Nagar, Yotam, Keshet, Uri |
| Předmět: |
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| Zdroj: |
Astrophysical Journal; 6/1/2020, Vol. 895 Issue 2, p1-14, 14p |
| Abstrakt: |
Collisionless shocks are often studied in two spatial dimensions (2D) to gain insights into the 3D case. We analyze diffusive shock acceleration for an arbitrary number of dimensions. For a nonrelativistic shock of compression ratio , the spectral index of the accelerated particles is this curiously yields, for any N, the familiar (i.e., equal energy per logarithmic particle energy bin) for a strong shock in a monatomic gas. A precise relation between and the anisotropy along an arbitrary relativistic shock is derived and is used to obtain an analytic expression for in the case of isotropic angular diffusion, affirming an analogous result in 3D. In particular, this approach yields in the ultrarelativistic shock limit for N = 2, and for any strong shock. The angular eigenfunctions of the isotropic-diffusion transport equation reduce in 2D to elliptic cosine functions, providing a rigorous solution to the problem; the first function upstream already yields a remarkably accurate approximation. We show how these and additional results can be used to promote the study of shocks in 3D. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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