Dynamic Stabilization of the m = 1 Instability in a Bumpy Theta Pinch

Both theoretically and experimentally a bumpy theta pinch is known to be hydromagnetically unstable. The possibility of dynamic stabilization of this configuration is discussed. The results show that stability can be achieved in this way. The plasma column is assumed to be separated from a vacuum magnetic field by a sharp boundary. The analysis is based on a generalization of the hydromagnetic energy principle. Within the framework of this theory a sufficient condition for stability is obtained for the m = 1 mode. This condition contains the amplitude of the unstable bulge, the frequency and amplitude of the forced oscillations, and the characteristic lengths and speeds in the system. The condition shows that stability is obtained for sufficiently large amplitude in the oscillatory magnetic field. The case of β = 1 and “arbitrary” m numbers is also briefly reviewed.