Scaling of Magnetic Dissipation and Particle Acceleration in ABC Fields

TL;DR

This study uses PIC simulations to analyze how magnetic dissipation and particle acceleration efficiencies in 2D ABC magnetic fields depend on initial coherence length and system size, revealing topological constraints and scaling laws.

Contribution

It provides new insights into the scaling relations of magnetic dissipation and particle acceleration in ABC fields, highlighting topological constraints and the dependence on initial conditions.

Findings

Magnetic dissipation efficiency is limited to about 60% due to topological constraints.

Peak electric energy growth time scales with initial Alfven velocity and coherence length.

Non-thermal particle energy gain is dominant at high initial magnetization.

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 $\lambda_0$ 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.