A charge-flow instability in plasmas with charge fluctuations

We present a linear instability in magnetized plasmas with charge fluctuations. It is driven by an electric current proportional to the charge chemical potential $\mu$ and the bulk velocity. This charge-flow (C-flow) instability has hitherto not been considered in standard magnetohydrodynamics or its chiral extensions. We derive its dispersion relation and maximum growth rate, and confirm them with direct numerical simulations. We also show that the C-flow instability persists even for zero-mean fluctuations of $\mu$, vanishing resistivity, and a magnetic Prandtl number of unity.