Vlasov-fluid theory of short-wavelength instabilities of a sharp-boundary screw pinch

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Abstract
The physics of instabilities of a sharp-boundary screw pinch is analyzed using the Vlasov-fluid model of Freidberg. An ordering especially applicable to the study of stabilized Z pinches is used. The equations of the Vlasov-fluid screw pinch differ from those of an ideal magnetohydrodynamic screw pinch in two crucial respects: a frequency-dependent compressibility function γM(ω) and a magnetoviscosity term that can induce finite-Larmor-radius stabilization. The domain of marginal stability of the Vlasov-fluid screw pinch is identical to that of the ideal magnetohydrodynamic screw pinch, in agreement with the results of Freidberg. Even when finite-Larmor-radius effects are ignored, the ratio (Vlasov-fluid growth rate)/(ideal magnetohydrodynamic growth rate) is less than unity in all cases studied. When β is finite, this ratio must approach zero as marginal stability is approached. In addition, for unstable modes with m≳1, finite-Larmor-radius stabilization effects in the Vlasov-fluid model can be significant when β‖ω/kvth‖≫ 1 and ‖ω/kvth‖≪ 1, where vth is the ion thermal speed and k is the wavenumber. In contrast, these effects are always insignificant in a magnetohydrodynamic model even when a phenomenological magnetoviscosity term is included! Numerical results are presented for m=1 and m=2 instabilities of a stabilized Z pinch. This analysis may help to explain the apparent stability of the Kurchatov reversed-field experiment.