  We propose using a directional time-varying (rotating) driving magnetic field
to suppress magneto-Rayleigh-Taylor (MRT) instability in dynamic Z-pinches. A
rotational drive magnetic field is equivalent to two magnetic-field components,
{\Theta} and Z, that alternate in time, referred to as an alternate
Theta-Z-pinch configuration. We consider the finitely thick cylindrical liner
configuration in this paper. We numerically integrate the perturbation equation
to stagnation time based on the optimal background unperturbed trajectories. We
assess the cumulative growth of the dominant mode selected by some mechanism at
the beginning of an implosion. The maximum e-folding number at stagnation of
the dominant mode of an optimized alternate Theta-Z-pinch is significantly
lower than that of the standard Theta- or Z-pinch. The directional rotation of
the magnetic field contributes to suppress the instabilities, independent of
the finite thickness. The finite thickness effect plays a role only when the
orientation of the magnetic field varies in time whereas it does not appear in
the standard Theta- or Z-pinch. The rotating frequency of the magnetic field
and the thickness of liner are both having a monotonic effect on suppression.
Their synergistic effect can enhance the suppression on MRT instability.
Because the MRT instability can be well suppressed in this way, the alternate
Theta-Z-pinch configuration has potential applications in liner inertial
fusion. This work is supported by the NSFC (Grant Nos. 11405167, 51407171,
11571293, 11605188, and 11605189) and the Foundation of the China Academy of
Engineering Physics (No. 2015B0201023).
