Snowplow shocks are supersonic flows in plasmas driven by a magnetic piston, in which the material impacted by the piston ‘‘sticks’’ to it, resulting in accretion of the plasma near the piston.The density front and the magnetic piston move together as a single structure. A typical example ofa snowplow shock is the plasma focus sheath. When normally neglected electron-inertia (EI) Terms in the fluid model of the plasma are taken into account, a time scale ω_p^-1 and a space scale cω_p^-1are introduced which are negligible in the bulk of the plasma but are non-negligible in a transition region between the no-plasma region and the dense plasma. As a result ‘‘no-plasma’’ initial conditions are not valid for the fluid equations obtained by neglecting EI. A resonant coupling between two electron plasma modes via the Hall term is shown to result in spontaneous generation of axial magnetic field and rotation even in the presence of perfect azimuthal symmetry in the low density precursor plasma formed before the ideal plasma phase. Related physics issues such as spontaneous symmetry breaking mechanism are discussed.