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


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)