Scaling of Magnetic Dissipation and Particle Acceleration in ABC Fields

Abstract

Using particle-in-cell (PIC) numerical simulations with electron-positron pair plasma, we study how the efficiencies of magnetic dissipation and particle acceleration scale with the initial coherence length $\hat{I}{»}_0$ in relation to the system size $L$ of the two-dimensional (2D) `Arnold-Beltrami-Childress' (ABC) magnetic field configurations. Topological constraints on the distribution of magnetic helicity in 2D systems, identified earlier in relativistic force-free (FF) simulations, that prevent the high-$(L/\hat{I}{»}_0)$ configurations from reaching the Taylor state, limit the magnetic dissipation efficiency to about $\hat{I}{\mu }_{\mathrm{diss}}\simeq 60\%$. We find that the peak growth time scale of the electric energy $\ddot{I}{„}_{\mathrm{E},\mathrm{peak}}$ scales with the characteristic value of initial Alfven velocity ${\hat{I}}_{\mathrm{A},\mathrm{ini}}^2$ like $τ_{\rm E,peak} \propto (λ_0/L)β_{\rm A,ini}^{-3}$. The particle energy change is decomposed into non-thermal and thermal parts, with non-thermal energy gain dominant only for high initial magnetisation. The most robust description of the non-thermal high-energy part of the particle distribution is that the power-law index is a linear function of the initial magnetic energy fraction.

Published in Journal of Plasma Physics, 17 pages, 7 figures, 1 table