The ion acceleration by a sausage instability in a z-pinch is modeled using Hall-magnetohydrodynamic theory taking into account the axial plasma velocity that necessarily develops during the instability. The instability grows, shrinking the neck, until it is stopped by increased pressure. The axial velocity influences ion acceleration through the radial electric field. An axial left–right asymmetry arises due to the contribution of the Hall term. The total electric field reverses its axial direction always on the anode side of the neck. The resulting electromagnetic fields are used to compute ion trajectories. Two classes of particle motion arise: singular ions that cross the cylinder axis and off-axis regular ions, and for both the acceleration by the electric fields is always toward the cathode. The energy gain of singular-orbit ions is larger, reaching values of up to 60. Most off-axis ions drift toward the axis due to the axial electric field, where they experience large energy gains. When the column radius is of the order of the Larmor radius the orbits are complex but the energy gain is still large.
Effect of a dynamic axial magnetic field on a preconditioned single-wire Z-pinch