Stability of a Rotating Theta-Pinch Plasma

The bounce model has been used to calculate the growth rate of the m = 1 mode of a linear θ pinch having an isotropic Maxwellian ion distribution function rotating with angular velocity ω. For short wavelength, the perturbation rotates with the ions; for longer wavelength it rotates more slowly. The plasma is unstable above a critical wavelength, with growth times τ ≈ 25 μsec for typical values of ω. This result falls between the magnetohydrodynamic result of τ = ∞ (stable) and the rigid body limit of τ ≈ ω−1. Consideration of the m = 2 mode is also included.