Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner

Abstract

This paper analyzes the coupling of magneto-Rayleigh-Taylor (MRT), sausage, and kink modes in an imploding cylindrical liner, using ideal MHD. A uniform axial magnetic field of arbitrary value is included in each region: liner, its interior, and its exterior. The dispersion relation is solved exactly, for arbitrary radial acceleration (-g), axial wavenumber (k), azimuthal mode number (m), liner aspect ratio, and equilibrium quantities in each region. For small k, a positive g (inward radial acceleration in the lab frame) tends to stabilize the sausage mode, but destabilize the kink mode. For large k, a positive g destabilizes both the kink and sausage mode. Using the 1D-HYDRA simulation results for an equilibrium model that includes a pre-existing axial magnetic field and a preheated fuel, we identify several stages of MRT-sausage-kink mode evolution. We find that the m ¼ 1 kink-MRT mode has a higher growth rate at the initial stage and stagnation stage of the implosion, and that the m ¼ 0 sausage-MRT mode dominates at the main part of implosion. This analysis also sheds light on a puzzling feature in Harris' classic paper of MRT [E. G. Harris, Phys. Fluids 5, 1057(1962]. An attempt is made to interpret the persistence of the observed helical structures [Awe et al., Phys. Rev. Lett. 111, 235005 (2013)] in terms of non-axisymmetric eigenmode. V C 2015 AIP Publishing LLC. [http://dx.

Characterizing the Plasmas of Dense $Z$ -Pinches

“…In general, the physics of Z -pinch plasmas is a rich and rapidly advancing area of plasma physics (in particular, some interesting and important studies [94]- [99] appeared already after this paper had been submitted and reviewed). Given the fundamental value and numerous applications of Z -pinches, they certainly deserve more attention of a broader plasma physics community.…”

Sausage instabilities on top of kinking lengthening current-carrying magnetic flux tubes

“…A sausage instability in a screw pinch plasma may be unfamiliar because classical analyses consider diffuse or skin currents separately; however, evidence for sausage instabilities has been observed in coronal loops 30 and predicted in magnetospheric current sheets 31 and cylindrical liner compression experiments with axial fields. 32 We note that in ideal MHD, a linear configuration without magnetic field reversal is never sausage unstable without also being unstable to the kink. Sausage instabilities are commonly observed in Zpinches, 33 which are always unstable to the kink.…”

Evolution of sausage and helical modes in magnetized thin-foil cylindrical liners driven by a Z-pinch

“…We first show that the applied axial magnetic field, irrespective of its direction (e.g., parallel or anti-parallel to the flow of current), reduces the instability amplitude for pure MHD modes (i.e., modes devoid of the MRT instability 8 ). We then show that liners with applied fields of B z ¼ 0.5 -0.8 T generate an m ¼ 1 helical mode that persists not only during the implosion phase but also during the subsequent stagnation and explosion phases; additionally, these data are compared with the m ¼ 2 helical mode that was previously found to persist for applied fields of B z ¼ 1.1 -2.0 T. 2 Finally, using a 12frame shadowgraphy system, we track individual instability bumps during the evolution of a single shot and demonstrate two important effects of mode merging: (1) we show that the merging of adjacent instability bumps may be used to explain an unexpected recurrence of exponential instability growth at late times and (2) we discuss how the mode merging of helical features may explain why an m ¼ 2 mode is observed in the experiments when higher order modes (m > 2) are the first to destabilize in an analytical, ideal MHD, linear theory; 8 here, we also present new experimental evidence of helical mode merging.…”

“…1) MHD modes; moreover, the MHD modes are likely coupled to the MRT instability. 8 Previous investigations on the stability of MagLIF liners observed azimuthally correlated structures when no axial magnetic field was applied 9,10 and helically oriented structures when an axial magnetic field of 7-10 T was pre-imposed. 11,12 Furthermore, the magnetized stagnation column within the fuel develops a helical structure, 6,7 suggesting that the helical instabilities in the liner may feed through to the fuel 13,14 and/or that the magnetized plasma in the fuel itself is unstable to helical modes during the strong deceleration phase, when the liner's inner surface becomes MRT unstable.…”

“…11,12 Furthermore, the magnetized stagnation column within the fuel develops a helical structure, 6,7 suggesting that the helical instabilities in the liner may feed through to the fuel 13,14 and/or that the magnetized plasma in the fuel itself is unstable to helical modes during the strong deceleration phase, when the liner's inner surface becomes MRT unstable. 8 Relative to the large 27-MA Z facility, investigating these instabilities at $1 MA on university-scale pulsed power machines like MAIZE 15 offers several advantages, including reduced costs, higher shot rates, and a less destructive debris environment for developing new diagnostic techniques. However, because of the reduced driver current, imploding an initially solid liner on MAIZE requires a sub-micron wall thickness (the MagLIF liners on Z have a wall thickness of approximately 500 lm).…”