Abstract
Using finite Larmor radius equations developed in an earlier paper the stability of an arbitrary β rotating θ pinch with straight lines of force in equilibrium is worked out in detail. The resulting differential equation together with boundary conditions and the specification of radial density profiles yields an eigenvalue problem which is solved with the aid of a computer. The results obtained show that an m = 1 rotational instability can occur in a θ pinch and that finite Larmor radius stabilization of this mode is present. It is also found that the rotating plasma should be stable to perturbations with an axial wavelength ≲ 1 m. This provides an explanation of why long θ pinches tend to go unstable uniformly along their length. Finite Larmor radius stabilization is critically dependent on the radial density profile, the steeper gradient favoring stability. Results are also presented showing how a large parallel temperature and shear in the axial flow can modify the rotational instability.
Published Version
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