Heating of Magnetically Dominated Plasma by Alfvén-Wave Turbulence

Magnetic energy around astrophysical compact objects can strongly dominate over plasma rest mass. Emission observed from these systems may be fed by dissipation of Alfvén wave turbulence, which cascades to small damping scales, energizing the plasma. We use 3D kinetic simulations to investigate this process. When the cascade is excited naturally, by colliding large-scale Alfvén waves, we observe quasithermal heating with no nonthermal particle acceleration. We also find that the particles are energized along the magnetic field lines and so are poor producers of synchrotron radiation. At low plasma densities, our simulations show the transition to “charge-starved” cascades, with a distinct damping mechanism.

Figure 1

3D visualization of the onset of the wave turbulence excited by the collision of two orthogonally polarized Alfvén waves with amplitudes of $\delta B/B_0=1/4$ and obliqueness $k_{\perp ,0}/k_{\parallel ,0}=4$ at time $t/t_{\parallel }=1.5$. The magnetization parameter in this simulation is ${\sigma }_0=100$. Color shows the electric current density along the dominant magnetic field direction, $j_z$ (in units of $e{n}_{0}c$). Movie is available in Ref. [31].

Figure 2

Power spectrum ${\mathcal{P}}_j(k_{\perp },k_{\parallel })$ of the electric current $j$ (in units of $e{n}_{0}c$), averaged over time window $1<t/t_{\parallel }<1.5$, observed in two simulations with different ${\sigma }_0$ and the same fiducial parameters $\delta B/B_0=1/4$, ${\chi }_0=2$, and ${\omega }_p/c{k}_{\perp ,0}\approx 34$. The simulation with ${\sigma }_0=100$ (left) is charge surfeit, and the simulation with ${\sigma }_0=1000$ (right) is charge starved. The blue dashed line indicates the expected direction of the cascade development in the charge surfeit regime, $k_{\parallel }\propto k_{\perp }^{2/3}$.

Figure 3

Particle kinetic energy spectra (top) and mean pitch angle (bottom) at a late time $t/t_{\parallel }=3$ in the simulations with $\delta B/B_0=1/4$, ${\chi }_0=2$, and different ${\sigma }_0=30$ (green), 100 (red), and 1000 (purple). The fully kinetic PIC results are shown by the solid curves, and two RIC simulations for ${\sigma }_0=30$ and 1000 are shown by the dashed curves. Arrows indicate the mean Lorentz factor at the end of turbulence dissipation, $⟨\gamma ⟩\approx (\delta B/B_0{)}^2{\sigma }_0$. The horizontal dotted line in the bottom panel shows the mean pitch angle that would be found for an isotropic particle distribution.