Assessing the Validity of the Staged Z-Pinch with FLASH: Preliminary Simulations

In the last decade, the staged Z-pinch (SZP)[1] has emerged as a potential high-gain magneto-inertial fusion energy concept. Its attractiveness lies in its simplicity that neither an external preheat mechanism nor fuel magnetization is required. Instead, shock preheat and enough magnetic-field diffusion through the high atomic number liner are predicted to adequately magnetize the fuel. Calculations using the MACH2 code computed high gains (84 to 400 MJ)[2]^–[4] for different liner materials using a pulsed-power machine comparable to Sandia’s Z facility. The validity of these simulations, however, has been put in question recently[5] when a potential verification issue concerning the use of the MACH2 code was suggested. The counter-arguments opposed to this criticism[6] have brought up a thrilling and enriching discussion in the community. In this talk, we discuss the first steps of an independent evaluation of the SZP using the radiation magnetohydrodynamic code FLASH. We focus on the main issue highlighted in the critique—adequately capturing the dynamics of the shock waves. For this purpose, we first present MACH2–FLASH comparisons of test problems and analytical solutions (magnetized Noh Z-pinch[7] and nonequilibrium radiative shock[8]) to subsequently address ideal gas simulations of the SZP2 scheme (silver liner). From an implosion perspective, this scheme is essentially a shock problem because Ohmic heating plays a secondary role.

[1] H. U. Rahman et al., Phys. Plasmas 26, 052706 (2019).

[2] H. U. Rahman et al., J. Plasma Phys. 75, 749 (2009).

[3] F. J. Wessel et al., IEEE Trans. Plasma Sci. 43, 2463 (2015).

[4] F. J. Wessel et al., AIP Conf. Proc. 1721, 060002 (2016).

[5] I. R. Lindemuth, M. R. Weis, and W. L. Atchison, Phys. Plasmas 25, 102707 (2018).

[6] E. Ruskov, P. Ney, and H. U. Rahman, Phys. Plasmas 27, 042709 (2020).

[7] A. L. Velikovich et al., Phys. Plasmas 19, 012707 (2012).

[8] R. B. Lowrie, and J. D. Edwards, Shock Waves 18, 129 (2008).