Scaling of Magnetic Dissipation and Particle Acceleration in ABC Fields

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 $lambda_0$ 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-$(L/lambda_0)$ configurations from reaching the Taylor state, limit the magnetic dissipation efficiency to about $epsilon_{rm diss} simeq 60%$. We find that the peak growth time scale of the electric energy $tau_{rm E,peak}$ scales with the characteristic value of initial Alfven velocity $beta_{rm A,ini}$ like $tau_{rm E,peak} propto (lambda_0/L)beta_{rm A,ini}^{-3}$. 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.