dc-Magnetic-Field Generation in Unmagnetized Shear Flows

Abstract

The generation of dc magnetic fields in unmagnetized electron-ion shear flows is shown to be associated to either initial thermal effects or the onset of electron-scale shear instabilities, in particular the cold Kelvin-Helmholtz instability. This mechanism, intrinsic to shear gradients on the electron scale, is described through a kinetic model that predicts the growth and the saturation of the dc field in both scenarios. The theoretical results are confirmed by multidimensional particle-in-cell simulations, demonstrating the formation of long-lived magnetic fields ($t\ensuremath{\sim}100'\mathrm{s}\text{ }\text{ }{\ensuremath{\omega}}_{pi}^{\ensuremath{-}1}$) along the full longitudinal extent of the shear layer, with a typical transverse width of $\sqrt{{\ensuremath{\gamma}}_{0}}c/{\ensuremath{\omega}}_{pe}$, reaching magnitudes $e{B}_{\mathrm{dc}}/{m}_{e}c{\ensuremath{\omega}}_{pe}\ensuremath{\sim}{\ensuremath{\beta}}_{0}\sqrt{{\ensuremath{\gamma}}_{0}}$ for an initial sharp shear. The case of an initial smooth shear is also discussed.