  Monte Carlo methods are often employed to numerically integrate kinetic
equations, such as the particle-in-cell method for the plasma kinetic equation,
but these methods suffer from the introduction of counting noise to the
solution. We report on a cautionary tale of counting noise modifying the
nonlinear saturation of kinetic instabilities driven by unstable beams of
plasma. We find a saturated magnetic field in under-resolved particle-in-cell
simulations due to the sampling error in the current density. The noise-induced
magnetic field is anomalous, as the magnetic field damps away in continuum
kinetic and increased particle count particle-in-cell simulations. This
modification of the saturated state has implications for a broad array of
astrophysical phenomena beyond the simple plasma system considered here, and it
stresses the care that must be taken when using particle methods for kinetic
equations.
