Scaling of rise time of drive current on development of magneto-Rayleigh-Taylor instabilities for single-shell Z-pinches

In fast Z-pinches, rise time of drive current plays an important role in development of magneto-Rayleigh-Taylor (MRT) instabilities. It is essential for applications of Z-pinch dynamic hohlraum (ZPDH), which could be used for driving inertial confinement fusion (ICF), to understand the scaling of rise time on MRTs. Therefore, a theoretical model for nonlinear development of MRTs is developed according to the numerical analysis. It is found from the model that the implosion distance L=r₀-r_mc determines the development of MRTs, where r₀ is the initial radius and r_mc is the position of the accelerating shell. The current rise time τ would affect the MRT development because of its strong coupling with the r₀. The amplitude of MRTs would increase with the rise time linearly if an implosion velocity is specified. The effects of the rise time on MRT, in addition, are studied by numerical simulation. The results are consistent with those of the theoretical model very well. Finally, the scaling of the rise time on amplitude of MRTs is obtained for a specified implosion velocity by the theoretical model and numerical simulations.