## Diffusive shock acceleration in N dimensions

#### by Mr. Assaf Lavi

##### at Astrophysics and Cosmology Seminar

Wed, 17 Jun 2020, 11:10
Sacta-Rashi Building for Physics (54), room 207

#### Abstract

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 $N\in\mathbb{N}$ of dimensions.
For a non-relativistic shock of compression ratio $r$, the spectral index of the accelerated particles is $s_{\text{E}}=1+N/(r-1)$; this curiously yields, for any $N$, the familiar $s_{\text{E}}=2$ (\ie equal energy per logarithmic particle energy bin) for a strong shock in a monatomic gas.
A precise relation between $s_{\text{E}}$ and the anisotropy along an arbitrary relativistic shock is derived, and is used to obtain an analytic expression for $s_{\text{E}}$ in the case of isotropic angular diffusion, affirming an analogous result in 3D.
In particular, this approach yields $s_{\text{E}} = (1+\sqrt{13})/2 \simeq 2.30$ in the ultra-relativistic shock limit for $N=2$, and $s_{\text{E}}(N\to\infty)=2$ 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.
Zoom link for talk: https://zoom.us/j/99798652587?pwd=aTlUS05XQ1lNWHFYMkwwQXVpbFNBdz09
We show how these and additional results can be used to promote the study of shocks in 3D.

Created on 14-06-2020 by Zitrin, Adi (zitrin)
Updaded on 14-06-2020 by Zitrin, Adi (zitrin)