Stochastic acceleration by the ion-cyclotron instability in a growing magnetic field

Using 1D and 2D particle-in-cell (PIC) simulations of a plasma with a growing magnetic field $\vec{B}$, we show that ions can be stochastically accelerated by the ion-cyclotron (IC) instability. As $\vec{B}$ grows, an ion pressure anisotropy $p_{\perp,i} > p_{||,i}$ arises, due to the adiabatic invariance of the ion magnetic moment ($p_{||,i}$ and $p_{\perp,i}$ are the ion pressures parallel and perpendicular to $\vec{B}$). When initially $\beta_i = 0.5$ ($\beta_i \equiv 8\pi p_i/|\vec{B}|^2$, 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 non-thermal tail in the ion energy spectrum. After $\vec{B}$ is amplified by a factor $\sim 2.7$, this tail can be approximated as a power-law of index $\sim 3.4$ plus two non-thermal bumps, and accounts for $2-3\%$ of the ions and $\sim 18\%$ of their kinetic energy.Although we focus on cases where $\vec{B}$ is amplified by plasma shear, we check that the acceleration occurs similarly if $\vec{B}$ grows due to plasma compression. Our results are valid in sub-relativistic regimes where the ion thermal energy is $\sim 10\%$ of the ion rest mass energy. This mechanism can be relevant in low-luminosity accretion disks