Plasma Astrophysicist | HAPI Research Associate
Using fully kinetic particle-in-cell (PIC) simulations, we show that the cosmic-ray (CR) streaming instability driven by CRs with a shell momentum distribution saturates through gyro-phase bunching around the resonantly driven Alfvén waves. Fluid-PIC (FPIC) simulations with both ideal and Landau closures reproduce the same saturation amplitude, \(\delta B/B_0 \approx 0.25\), and the same bunching mechanism — including the ideal-closure run, in which nonlinear Landau damping (NLLD) is entirely absent by construction. This indicates that NLLD is not the dominant saturation channel at our parameters (\(v_A = 0.01c\), \(n_{\rm CR}/n_i = 0.01\)), in tension with common assumptions in subgrid CR-transport models.
Below, for each of the four simulations shown in Figures 2 and 4 of the paper, we show two animations: (1) the evolution of the CR ion phase-space distribution together with the helicity-resolved magnetic-field Fourier amplitudes, and (2) the gyro-phase bunching of CR ions at resonant pitch angles (\(\mu \in [0.9,1.0]\) driving right-handed modes, and \(\mu \in [-1.0,-0.9]\) driving left-handed modes) around the driven waves.
Fully kinetic PIC simulation, domain \(L \simeq 5.42\,\lambda_m\). Background electrons and ions are evolved kinetically, so NLLD is included self-consistently with no approximation.
FPIC simulation with an ideal-fluid closure for the background, domain \(L \simeq 5.42\,\lambda_m\). This closure omits NLLD (and any other background damping channel) entirely by construction.
FPIC simulation with a Landau-fluid closure (the \(R_{31}\) closure of Hunana et al. 2018) for the background, domain \(L \simeq 5.42\,\lambda_m\). This closure approximates linear and nonlinear Landau damping.
FPIC simulation with an ideal-fluid closure, extended domain \(L \simeq 54.2\,\lambda_m\) (\(6000\,c/\omega_{pi}\)). Used to demonstrate that the saturation amplitude and gyro-phase-bunching mechanism are local and independent of domain size.