Experiments on helical modes in magnetized thin foil-plasmas*

This paper gives an in-depth experimental study of helical features on magnetized, ultrathin foil-plasmas driven by the 1-MA linear transformer driver at University of Michigan. Three types of cylindrical liner loads were designed to produce: (a) pure magneto-hydrodynamic (MHD) modes (defined as being void of the acceleration-driven magneto-Rayleigh-Taylor instability, MRT) using a non-imploding geometry, (b) pure kink modes using a non-imploding, kink-seeded geometry, and (c) MRT-MHD coupled modes in an unseeded, imploding geometry. For each configuration, we applied relatively small axial magnetic fields of $B_{z} =$ 0.2-2.0 T (compared to peak azimuthal fields of 30-40 T). The resulting liner-plasmas and instabilities were imaged using 12-frame laser shadowgraphy and visible self-emission on a fast framing camera. The azimuthal mode number was carefully identified with a tracking algorithm of self-emission minima. Our experiments show that the helical structures are a manifestation of discrete eigenmodes. The pitch angle of the helix is simply $m/kR$, from implosion to explosion, where $m$, $k$, and $R$ are the azimuthal mode number, axial wavenumber, and radius of the helical instability. Thus, the pitch angle increases (decreases) during implosion (explosion) as $R$ becomes smaller (larger). We found that there are one, or at most two, discrete helical modes that arise for magnetized liners, with no apparent threshold on the applied $B_{z} $ for the appearance of helical modes; increasing the axial magnetic field from zero to 0.5 T changes the relative weight between the $m=0$ and $m=1$ modes. Further increasing the applied axial magnetic fields yield higher $m$ modes. Finally, the seeded kink instability overwhelms the intrinsic instability modes of the plasma. These results are corroborated with our analytic theory on the effects of radial acceleration on the classical sausage, kink, and higher $m$ modes. \\ \par*Work supported by US DOE award DE-SC0012328, Sandia National Laboratories, and the National Science Foundation. D.Y.E. was supported by NSF fellowship grant number DGE 1256260. The fast framing camera was supported by a DURIP, AFOSR Grant FA9550-15-1-0419.