Spectra of magnetic turbulence in a relativistic plasma

TL;DR

This paper investigates the properties of strong Alfvénic turbulence in relativistic plasmas, revealing specific energy spectra and alignment behaviors through phenomenological analysis and 2D particle-in-cell simulations.

Contribution

It provides the first detailed numerical analysis of magnetic and electric turbulence spectra in relativistic plasmas, highlighting their scaling laws and dynamic alignment.

Findings

Energy spectrum scales as k^{-3/2} for total energy.

Residual energy scales as k^{-2.4}.

At smaller scales, the spectrum steepens to k^{-3.5}.

Abstract

We present a phenomenological and numerical study of strong Alfv\'enic turbulence in a magnetically dominated collisionless relativistic plasma with a strong background magnetic field. In contrast with the non-relativistic case, the energy in such turbulence is contained in magnetic and electric fluctuations. We argue that such turbulence is analogous to turbulence in a strongly magnetized non-relativistic plasma in the regime of broken quasi-neutrality. Our 2D particle-in-cell numerical simulations of turbulence in a relativistic pair plasma find that the spectrum of the total energy has the scaling $k^{-3/2}$, while the difference between the magnetic and electric energies, the so-called residual energy, has the scaling $k^{-2.4}$. The electric and magnetic fluctuations at scale $\ell$ exhibit dynamic alignment with the alignment-angle scaling close to $\cos\phi_\ell\propto \ell^{1/4}$. At scales smaller than the (relativistic) plasma inertial scale, the energy spectrum of relativistic inertial Alfv\'en turbulence steepens to $k^{-3.5}$.