Turbulence and Particle Acceleration in a Relativistic Plasma

Abstract

In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a nonthermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameter σ ≫ 1) quickly evolves into a state with ultrarelativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponent α in the power-law particle-energy distribution function, f(γ)d γ ∝ γ −α d γ, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponent α is in good agreement with the numerical results.

MHD turbulence: a biased review

“…Of this, relativistic turbulence has indeed been found guilty, provided it was stirred up with δB ∼ B 0 (Zhdankin et al 2017;Comisso & Sironi 2018). The most recent spate of papers on this topic, which represent the state of the art and from which the historical paper trail can be followed, are Comisso & Sironi (2021), Vega et al (2022b); Vega, Boldyrev & Roytershteyn (2022a), Hankla et al (2022) (imbalanced turbulence), Nättilä & Beloborodov (2022) (small δB/B 0 , no non-thermal acceleration), Zhdankin, Uzdensky & Kunz (2021) (non-unity mass ratio, ion vs. electron heating), and Chernoglazov, Ripperda & Philippov (2021) (alignment and current sheets in fluid but relativistic MHD turbulence). It is interesting that in this context again, reconnecting structures spontaneously generated by turbulence appear to play a prominent rolethis time as sites of particle acceleration.…”

“…The firehose corresponds to the Alfvén speed (14.1) turning imaginary, i.e., it is an instability caused by negative tension; the mirror is not quite as simple to 91 Of course, collisionless equilibrium distributions do not have to be 'thermal', i.e., they can have extended tails at high energies -such tails are indeed observed by astronomers and so non-thermal particle acceleration by turbulence is an object of intense interest to astrophysicists: see references in footnote 90. Mathematically, distribution functions with non-thermal, power-law tails can be derived as solutions of kinetic equations containing phase-space advection and diffusion with velocity-dependent coefficients (see, e.g., Wong et al 2020;Vega et al 2022b;Uzdensky 2022, and references therein) or as maximisers of a judiciously chosen entropy (e.g., Zhdankin 2022b; Ewart et al 2022). In a complete theory, they should appear as fixed points of the 'collisionless collision integrals'.…”

“…The most recent spate of papers on this topic, which represent the state of the art and from which the historical paper trail can be followed, are Comisso & Sironi (2021), Vega et al. (2022 b ); Vega, Boldyrev & Roytershteyn (2022 a ), Hankla et al. (2022) (imbalanced turbulence), Nättilä & Beloborodov (2022) (small , no non-thermal acceleration), Zhdankin, Uzdensky & Kunz (2021) (non-unity mass ratio, ion vs. electron heating), and Chernoglazov, Ripperda & Philippov (2021) (alignment and current sheets in fluid but relativistic MHD turbulence).…”

Non-thermal particle acceleration from maximum entropy in collisionless plasmas

“…Non-thermal particle acceleration is usually modelled in the language of quasilinear theory, involving concepts such as the Fokker-Planck equation (or its extensions), pitch angle scattering and trapping (or escape) mechanisms (see, e.g. Kulsrud & Ferrari 1971;Blandford & Eichler 1987;Schlickeiser 1989;Chandran 2000;Isliker, Vlahos & Constantinescu 2017;Demidem, Lemoine & Casse 2020;Lemoine & Malkov 2020;Lemoine 2021;Vega et al 2022). The maximum-entropy model proposed in this Letter stands in stark contrast to these conventional approaches, being only weakly dependent on the physical ingredients responsible for enabling the GME state.…”

“…Kulsrud & Ferrari 1971; Blandford & Eichler 1987; Schlickeiser 1989; Chandran 2000; Isliker, Vlahos & Constantinescu 2017; Demidem, Lemoine & Casse 2020; Lemoine & Malkov 2020; Lemoine 2021; Vega et al. 2022). The maximum-entropy model proposed in this Letter stands in stark contrast to these conventional approaches, being only weakly dependent on the physical ingredients responsible for enabling the GME state.…”