Spatial Intermittency of Particle Distribution in Relativistic Plasma Turbulence

Abstract

Relativistic magnetically dominated turbulence is an efficient engine for particle acceleration in a collisionless plasma. Ultrarelativistic particles accelerated by interactions with turbulent fluctuations form nonthermal power-law distribution functions in the momentum (or energy) space, f(γ)d γ ∝ γ −α d γ, where γ is the Lorenz factor. We argue that in addition to exhibiting non-Gaussian distributions over energies, particles energized by relativistic turbulence also become highly intermittent in space. Based on particle-in-cell numerical simulations and phenomenological modeling, we propose that the bulk plasma density has lognormal statistics, while the density of the accelerated particles, n, has a power-law distribution function, P ( n ) dn ∝ n − β dn . We argue that the scaling exponents are related as β ≈ α + 1, which is broadly consistent with numerical simulations. Non-space-filling, intermittent distributions of plasma density and energy fluctuations may have implications for plasma heating and for radiation produced by relativistic turbulence.

Relativistic Alfvén Turbulence at Kinetic Scales

“…Since all the vector components of the electromagnetic field and particle momenta are preserved, it is expected to capture some essential nonlinear interactions existing in the 3D case. Previous numerical studies involving 2.5D and 3D runs seem to produce similar energy spectra of fields and particles (e.g., Zhdankin et al 2017Zhdankin et al , 2018Comisso & Sironi 2018Vega et al 2023).…”

“…We found that in both cases of the large and small boxes, the resulting particle distribution functions are qualitatively the same; they are well approximated by a universal log-normal distribution. This is in contrast with particle acceleration in weak guide-field turbulence, where energetic particles develop power-law energy distribution functions (e.g., Comisso & Sironi 2019;Zhdankin et al 2019;Wong et al 2020;Vega et al 2022bVega et al , 2023, which may indicate different acceleration mechanisms in these two cases.…”

“…However, as turbulence evolves, turbulent fluctuations efficiently heat the plasma, so plasma temperature becomes ultrarelativistic while simultaneously s ˜decreases. This reflects the fact that relativistic turbulent motion is inherently compressible, which allows colliding fluid elements to convert their kinetic energy into heat rapidly (Zhdankin et al 2018;Nättilä & Beloborodov 2021;Vega et al 2022bVega et al , 2023). We will therefore analyze the case when plasma bulk fluctuations are nonrelativistic (or mildly relativistic), while plasma temperature is ultrarelativistic.…”

“…In a weakly collisional plasma, the dissipated turbulent energy is converted into heat or nonthermally accelerated particles. The particle distribution functions can significantly deviate from a Maxwellian, which affects plasma dynamics and thermodynamics, as well as the radiative signatures of astrophysical objects (e.g., Drake et al 2013;Sironi & Spitkovsky 2014;Zhdankin et al 2017;Comisso & Sironi 2019;Demidem et al 2020;Trotta et al 2020;Wong et al 2020;Nättilä & Beloborodov 2021;Vega et al 2022aVega et al , 2023Bresci et al 2022;Comisso & Sironi 2022;Pezzi et al 2022).…”

“…Energy cascade in the kinetic range arguably governs the energy dissipation and particle heating in a collisionless turbulent plasma, and it may be relevant for nonthermal particle acceleration. Kinetic-range modes play an important role in space and astrophysical plasmas, where they have been studied analytically, numerically, and, where possible, in in situ spacecraft measurements (e.g., Chen et al 2013;Sahraoui et al 2013;Chen & Sorriso-Valvo 2014;Told et al 2015;Chen & Boldyrev 2017;Roytershteyn et al 2019;He et al 2020;Mallet et al 2023;Vega et al 2023;Zhou et al 2023).…”