We use particle-in-cell ( PIC ) simulations to study the nonlinear evolution of ion velocity space instabilities in an idealized problem in which a background velocity shear continuously amplifies the magnetic field .
We simulate the astrophysically relevant regime where the shear timescale is long compared to the ion cyclotron period , and the plasma beta is \beta \sim 1 - 100 .
The background field amplification in our calculation is meant to mimic processes such as turbulent fluctuations or MHD-scale instabilities .
The field amplification continuously drives a pressure anisotropy with p _ { \perp } > p _ { \parallel } and the plasma becomes unstable to the mirror and ion cyclotron instabilities .
In all cases , the nonlinear state is dominated by the mirror instability , not the ion cyclotron instability , and the plasma pressure anisotropy saturates near the threshold for the linear mirror instability .
The magnetic field fluctuations initially undergo exponential growth but saturate in a secular phase in which the fluctuations grow on the same timescale as the background magnetic field ( with \delta B \sim 0.3 \langle B \rangle in the secular phase ) .
At early times , the ion magnetic moment is well-conserved but once the fluctuation amplitudes exceed \delta B \sim 0.1 \langle B \rangle , the magnetic moment is no longer conserved but instead changes on a timescale comparable to that of the mean magnetic field .
We discuss the implications of our results for low-collisionality astrophysical plasmas , including the near-Earth solar wind and low-luminosity accretion disks around black holes .