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

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.

Spectra of Magnetic Turbulence in a Relativistic Plasma

“…We see that it also holds in relativistic collisionless plasma turbulence dominated by magnetic and electric fields. Our result is also consistent with the recent relativistic MHD studies (Chernoglazov et al 2021;TenBarge et al 2021).…”

“…In our relativistic case, these two corrections are necessarily on the same order. We also note that, similarly to the previous study (TenBarge et al 2021) , Equations ( 9) and (10) describe the shear Alfvén waves in a relativistically hot plasma, and they are mathematically analogous to the equations of reduced MHD.…”

“…Recent numerical and analytical studies of relativistic plasma turbulence using magnetohydrodynamic (MHD) approximation suggested analogies with the nonrelativistic case, such as the description in terms of the Elsässer fields, the similarities in the power-law exponents of the spectra of magnetic fluctuations, and the existence of dynamic alignment between magnetic and velocity fields (Chernoglazov et al 2021;TenBarge et al 2021). It was also noted that the relative magnitude of the electric field fluctuations in this case exceeds that of the kinetic fluctuations (Chernoglazov et al 2021;Vega et al 2021).…”

Hall magnetohydrodynamics in a relativistically strong mean magnetic field

“…2022), relativistic RMHD was formulated only recently (Chandran, Foucart & Tchekhovskoy 2018; TenBarge et al. 2021). Remarkably, relativistic RMHD and non-relativistic RMHD are formally identical except for the definition of Alfvén speed which is modified such that it never exceeds the speed of light.…”

Simulating Three-Wave Interactions and the Resulting Particle Transport Coefficients in a Magnetic Loop

“…Thus, wave-wave interactions between counter-propagating waves become a topic of investigation to find out how the spectral energy density of the waves is evolving beyond the WKB approximation. Three-wave interactions have been studied theoretically (see, e.g., [7][8][9]), numerically (see, e.g., [10][11][12]), and experimentally (see, e.g., [13,14]). Their descriptions in coronal (see, e.g., [15]), and solar-wind (see, e.g., [16,17]) plasmas, have been a topic of recent research.…”