Tearing-mediated Alfvénic Turbulence in a Relativistic Plasma

Journal Article · Wed Jan 29 00:00:00 EST 2025 · The Astrophysical Journal

DOI:https://doi.org/10.3847/1538-4357/ada28a· OSTI ID:2507366

Boldyrev, Stanislav; Loureiro, Nuno F.

Abstract In astrophysical relativistic plasmas, Alfvénic turbulence exists across a wide range of scales. Similar to a nonrelativistic case, this turbulence can be influenced by the tearing instability. We argue that in an ultrarelativistic pair plasma the tearing effects become significant at the critical scale given by $a_t\sim d_{\mathrm{rel}}{\left(L_{\perp }/d_{\mathrm{rel}}\right)}^{n/(4+5n)}$ , where L _⊥ represents the outer scale of the turbulence and d _rel the relativistic electron inertial scale. Here n = 1 corresponds to the Harris magnetic configurations, while n = 2 applies to localized (non-Harris) magnetic profiles of turbulence-generated current sheets. Below the critical scale, the energy spectrum of magnetic fluctuations steepens to W ( k ) dk ∝ k ^{−(7 n +2)/3 n} dk . However, this happens only when $\tilde{\sigma }\ll {\left(L_{\perp }/d_{\mathrm{rel}}\right)}^{(2+4n)/(4+5n)}$ , where $\tilde{\sigma }$ is the magnetization parameter based on the magnetic fluctuations. If the opposite inequality holds, the Alfvénic cascade is instead affected by charge starvation at scales below $a_{\mathrm{ch}}\sim d_{\mathrm{rel}}{\left(d_{\mathrm{rel}}/L_{\perp }\right)}^{1/3}{\tilde{\sigma }}^{2/3}$ , and the energy spectrum becomes steeper than W ( k ) dk ∝ k ⁻³ dk . When d _rel is replaced by its nonrelativistic equivalent, our results agree with the nonrelativistic analysis of N. F. Loureiro & S. Boldyrev (2018). In the Harris case n = 1, they agree with the recent relativistic studies by I. Demidov & Y. Lyubarsky.

• Sponsoring Organization: USDOE
• OSTI ID: 2507366
• Journal Information: The Astrophysical Journal, Journal Name: The Astrophysical Journal Vol. 979 Journal Issue: 2; ISSN 0004-637X
• Publisher: American Astronomical Society
• Country of Publication: United States
• Language: English