Tearing-mediated Alfvénic Turbulence in a Relativistic Plasma - Stanislav Boldyrev; Nuno F. Loureiro (The Astrophysical Journal)
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 ${a}_{t}\sim {d}_{rel}{\left(L_{\perp }/{d}_{rel}\right)}^{n/(4+5n)}$ , 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 $\tilde{σ }\ll {\left(L_{\perp }/{d}_{rel}\right)}^{(2+4n)/(4+5n)}$ , where $\tilde{σ }$ 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 ${a}_{ch}\sim {d}_{rel}{\left({d}_{rel}/L_{\perp }\right)}^{1/3}{\tilde{σ }}^{2/3}$ , 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.