Spontaneous sheared flow in collisionless flux compression via inverse gyroviscosity

We identify a mechanism by which spontaneous sheared flows arise during fast adiabatic compression of a Z pinch through the magnetized pressure-strain interaction, which is the collisionless manifestation of gyroviscosity. By studying unmagnetized betatron orbits about the magnetic axis, we find that collisionless betatron heating induces an agyrotropic anisotropy in the distribution function. We then propose a phenomenological model for anisotropy in a compressing collisionless Z pinch, parameterized by the ion Budker parameter. This agyrotropic anisotropy produces shear stress via gyro-phase mixing, thus inducing an axial force on the ions and generating a sheared axial flow. We find that the net force imparted is zero, producing an oscillatory shear flow pattern. The induced current of the spontaneous flow on-axis is found to be counter the on-axis current, suggesting that the response is diamagnetic.