A modified low-frequency electrostatic instability is found for the Bennett equilibrium. The instability is of the ion-acoustic type and is primarily driven by the equilibrium electron drift. For large wavelengths the ion betatron motion has a stabilizing influence and causes a significant shift in the real frequency. A simplified dispersion relation is obtained from general non-local kinetic stability analysis. Both numerical and analytic results are presented.
The kinetic theory of the m = 1 kink instability of a Z-pinch with Bennett profile is presented. The dominant particle trajectories in the equilibrium field are the large excursion betatron orbits. To deal with these orbits, an integral formulation of the stability analysis is adopted. In this case, the dispersion relation is expressed as the determinant of a matrix. In the limit where the electrostatic perturbation is neglected, the eigenmodes are computed numerically from this dispersion relation. Two methods are used to obtain the growth rates, and the computed values agree very well. The Landau damping of the mode is found to be strong enough to stabilize the mode at shorter wavelengths. This may explain the stability of the kink mode in some experiments.
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