Relativistic Alfvén Turbulence at Kinetic Scales

Abstract

In a strongly magnetized, magnetically dominated relativistic plasma, Alfvénic turbulence can extend to scales much smaller than the particle inertial scales. It leads to an energy cascade somewhat analogous to inertial- or kinetic-Alfvén turbulent cascades existing in nonrelativistic space and astrophysical plasmas. Based on phenomenological modeling and particle-in-cell numerical simulations, we propose that the energy spectrum of such relativistic kinetic-scale Alfvénic turbulence is close to k −3 or slightly steeper than that due to intermittency corrections or Landau damping. We note the analogy of this spectrum with the Kraichnan spectrum corresponding to the enstrophy cascade in 2D incompressible fluid turbulence. Such turbulence strongly energizes particles in the direction parallel to the background magnetic field, leading to nearly one-dimensional particle momentum distributions. We find that these distributions have universal log-normal statistics.

Particle Acceleration in Relativistic Alfvénic Turbulence

“…Due to the quadratic dependence of the acceleration rate on the intensity of turbulent fluctuations, the acceleration time increases significantly when δB 0 /B 0 decreases. These results are consistent with the numerical observations in Vega et al (2024). In Section 2.4, we will discuss the mirror acceleration mechanism.…”

“…When s is initially large, which is the case in some numerical setups of decaying turbulence (e.g., Comisso & Sironi 2018Vega et al 2022aVega et al , 2022bVega et al , 2023Vega et al , 2024, the parallel particle heating and acceleration are initially strong. However, as the magnetic perturbations relax and release energy to plasma particles, plasma magnetization s decreases while (in the absence of significant radiative cooling) the particle enthalpy w 0 increases.…”

“…The parallel electric field fluctuations are relatively weak in Alfvénic turbulence with a strong guide field. For instance, in a magnetically dominated ultrarelativistic plasma with onedimensional momentum distribution of particles, 4 the linear wave analysis in (Vega et al 2024) yields for the parallel and perpendicular electric fluctuations at scales λ  d rel :…”

“…The table also shows the initial value of B 0 /δB 0 and the initial value of the magnetization s defined by Equation (1). Some results of these simulations were also analyzed in Vega et al (2022bVega et al ( , 2024, where more specific details of the initial setup can be found.…”

“…Therefore, turbulent fluctuations at large hydrodynamic scales can be described, to the leading order, in the framework of nonrelativistic MHD.4 This is certainly an idealization, since in reality (and in numerical simulations) the particle distributions are not strictly one-dimensional. Moreover, turbulence may contain a small admixture of ordinary and extraordinary modes (e.g.,Vega et al 2024).…”