Stochastic Ion Acceleration by the Ion-cyclotron Instability in a Growing Magnetic Field
Using 1D and 2D particle-in-cell simulations of a plasma with a growing magnetic field ${\boldsymbol{B}}$, we show herein that ions can be stochastically accelerated by the ion-cyclotron (IC) instability. As ${\boldsymbol{B}}$ grows, an ion pressure anisotropy ${p}_{\perp ,i}\gt {p}_{| | ,i}$ arises due to the adiabatic invariance of the ion magnetic moment (${p}_{| | ,i}$ and $p_{⊥,i}$ are the ion pressures parallel and perpendicular to ${\boldsymbol{B}}$). When initially $β_ i$ = 0.5 (${\beta }_{i}\equiv 8\pi {p}_{i}/| {\boldsymbol{B}}{| }^{2}$, where $p_i$ is the ion isotropic pressure), the pressure anisotropy is limited mainly by inelastic pitch-angle scattering provided by the IC instability, which in turn produces a nonthermal tail in the ion energy spectrum. After ${\boldsymbol{B}}$ is amplified by a factor of ~2.7, this tail can be approximated as a power law of index ~3.4 plus two nonthermal bumps and accounts for 2%–3% of the ions and ~18% of their kinetic energy. On the contrary, when initially $β_i$ = 2, the ion scattering is dominated by the mirror instability, and the acceleration is suppressed. This implies that efficient ion acceleration requires that initially, $β_{i} \lesssim$ 1. Although we focus on cases where ${\boldsymbol{B}}$ is amplified by plasma shear, we check that the acceleration occurs similarly if ${\boldsymbol{B}}$ grows due to plasma compression. Our results are valid in a subrelativistic regime where the ion thermal energy is ~10% of the ion rest-mass energy. This acceleration process can thus be relevant in the inner region of low-luminosity accretion flows around black holes.