Evolution of the bounded magnetized jet and comparison with Helimak experiments

Abstract

Magnetized jets are important features of many systems of physical interest. To date, most interest has focused on solar and space physics and astrophysical applications, and hence the unbounded magnetized jet, and its cousin, the unbounded magnetized wake, have received the most attention. This work presents calculations of a bounded, magnetized jet for a laboratory experiments in the Helimak device [K. W. Gentle and H. He, Plasma Sci. Technol. 10, 284 (2008)]. The Helimak device has a toroidal magnetic field with a controlled velocity flow that represents jets in bounded systems. Experimental and theoretical features include three spatial dimensions, the inclusion of resistivity and viscosity, and the presence of no-slip walls. The results of the linearized model are computed with a Chebyshev-τ algorithm. The bounding walls stabilize the ideal varicose mode found in unbounded magnetized jets. The ideal sinuous mode persists in the bounded system. A comparison theorem is proved showing that two-dimensional modes are more unstable than the corresponding three-dimensional modes for any given set of system parameters. This result is a generalization of the hydrodynamic Squires theorem. An energy-stress theorem indicates that the Maxwell stress is crucial for the growth of the instability. The results of the analysis are consistent with the observed plasma fluctuations with in the limits of using a simple model for the more complex measured jet velocity flow profile. The working gas is singly ionized argon and the jet velocity profile is accurately measured with Doppler shift spectroscopy.