Particle Acceleration and Pitch-angle Evolution in Relativistic Turbulence

Abstract Synchrotron radiation detected from relativistic astrophysical objects such as pulsar-wind nebulae and jets from active galactic nuclei depends on the magnetic fields and the distribution functions of energetic electrons in these systems. Relativistic magnetically dominated turbulence has been recognized as an efficient mechanism for structure formation and nonthermal particle acceleration in these environments. Recent numerical simulations of relativistic turbulence have provided insights into the energy distribution functions of accelerated electrons. Much less is currently understood about their pitch angle distributions, which are crucial for accurately interpreting the spectra of synchrotron radiation. We perform a detailed case study of the pitch angle distributions formed during the process of turbulent acceleration for B 0 / δB 0 = 10 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>˜</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>40</mml:mn> </mml:math> , where B 0 is the uniform component of the magnetic field, δB 0 is the fluctuating component, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>˜</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math> is the plasma magnetization based on the magnetic fluctuations. We find that even minimal numerical noise can cause substantial pitch angle scattering, but we demonstrate techniques for overcoming the numerical challenges associated with the evolution of very small pitch angles. Our numerical results are consistent with the phenomenological considerations found in C. Vega et al. (2024a, 2025).