Weak Alfvénic turbulence in relativistic plasmas. Part 1. Dynamical equations and basic dynamics of interacting resonant triads

Creators: TenBarge, J. M.; Ripperda, B.; Chernoglazov, A.; Bhattacharjee, A.; Mahlmann, J. F.; Most, E. R.; Juno, J.; Yuan, Y.; Philippov, A. A.

Abstract

Alfvén wave collisions are the primary building blocks of the non-relativistic turbulence that permeates the heliosphere and low- to moderate-energy astrophysical systems. However, many astrophysical systems such as gamma-ray bursts, pulsar and magnetar magnetospheres and active galactic nuclei have relativistic flows or energy densities. To better understand these high-energy systems, we derive reduced relativistic magnetohydrodynamics equations and employ them to examine weak Alfvénic turbulence, dominated by three-wave interactions, in reduced relativistic magnetohydrodynamics, including the force-free, infinitely magnetized limit. We compare both numerical and analytical solutions to demonstrate that many of the findings from non-relativistic weak turbulence are retained in relativistic systems. But, an important distinction in the relativistic limit is the inapplicability of a formally incompressible limit, i.e. there exists finite coupling to the compressible fast mode regardless of the strength of the magnetic field. Since fast modes can propagate across field lines, this mechanism provides a route for energy to escape strongly magnetized systems, e.g. magnetar magnetospheres. However, we find that the fast-Alfvén coupling is diminished in the limit of oblique propagation.

Additional Information

Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited. We thank G. Howes and B. Chandran for helpful discussions. We acknowledge the Flatiron's Center for Computational Astrophysics (CCA) and the Princeton Plasma Physics Laboratory (PPPL) for support of collaborative CCA-PPPL meetings on plasma-astrophysics where the ideas presented in this paper have been initiated. The computational resources and services used in this work were provided by facilities supported by the Scientific Computing Core at the Flatiron Institute, a division of the Simons Foundation; and by the VSC (Flemish Supercomputer Center), funded by the Research Foundation Flanders (FWO) and the Flemish Government – department EWI. This work was supported by the Simons Foundation (J.M.T., A.B. and A.C.); a Flatiron Research Fellowship (Y.Y.); a Joint Princeton/Flatiron Postdoctoral Fellowship (B.R.); the National Science Foundation (A.P. and J.F.M., Grant No. AST-1909458); Atmospheric and Geospace Science Postdoctoral Fellowship (J.J., Grant No. AGS-2019828); a joint fellowship at the Princeton Center for Theoretical Science, the Princeton Gravity Initiative and the Institute for Advanced Study (E.R.M.). The authors report no conflict of interest.

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