DC magnetic field generation in unmagnetized shear flows

The generation of DC magnetic fields in unmagnetized plasmas with velocity shear is predicted for non relativistic and relativistic scenarios either due to thermal effects or due to the onset of the Kelvin-Helmholtz instability (KHI). A kinetic model describes the growth and the saturation of the DC field. The predictions of the theory are confirmed by multidimensional particle-in-cell simulations, demonstrating the formation of long lived magnetic fields ($t\sim 100s{\omega }_{pi}^{-1}$) along the full longitudinal extent of the shear layer, with transverse width on the electron length scale ($\sqrt{{\gamma }_0}c\mathrm{/}{\omega }_{pe}$), reaching magnitudes $e{B}_{\mathrm{D}\mathrm{C}}\mathrm{/}{m}_{e}c{\omega }_{pe}\sim {\beta }_0\sqrt{{\gamma }_0}$.