Experimental observation of discrete helical modes in imploding cylindrical liners*

The 1-MA Linear Transformer Driver at the University of Michigan was used to implode ultrathin (400 nm thick) cylindrical aluminum liners$^{1}$ that were pre-embedded with externally applied, axial magnetic fields of $B_{z} \quad =$ 0.2-2.0 T. Using 12-frame laser shadowgraphy and visible self-emission, helical striations were found that \textit{increased} in pitch angle during the implosion and \textit{decreased} in angle during the later time explosion, despite the relatively large, peak azimuthal magnetic field exceeding 40 T. The results are interpreted as a discrete, non-axisymmetric eigenmode of a helical instability that persists from implosion to explosion. The helical pitch angle $\varphi $ was found to obey the simple relation $\varphi \quad =$ \textit{m/kR}, where $m$, $k$, and $R$ are the azimuthal mode number, axial wavenumber, and radius of the helical instability. Analytic growth rates$^{2}$ for experimental parameters are presented, and show that early in the current pulse, axisymmetric modes ($m$ $=$ 0) are completely stabilized while non-axisymmetric modes ($m$ \underline {\textgreater } 1) are found to be unstable. [1] D. A. Yager-Elorriaga, et al., \textit{Rev. Sci. Instrum.} \textbf{86}, 113506 (2015). [2] M. R. Weis, P. Zhang, et al., \textit{Phys. Plasmas} \textbf{22}, 032706 (2015).