Vlasov-fluid theory of short-wavelength instabilities of a sharp-boundary screw pinch
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 ..gamma../sub M/(..omega..) 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 ..beta.. 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 ..beta..vertical-bar..omega../kv/sub th/vertical-barvery-much-greater-than 1 and vertical-bar..omega../kv/sub th/vertical-barvery-much-less-than 1, where v/sub th/ 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 includedexclamation 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.
- Research Organization:
- Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87545
- OSTI ID:
- 7322230
- Journal Information:
- Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 20:4; ISSN PFLDA
- Country of Publication:
- United States
- Language:
- English
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75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOLTZMANN-VLASOV EQUATION
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
DISTURBANCES
EQUATIONS
EQUILIBRIUM PLASMA
FLUID MECHANICS
HYDRODYNAMICS
INSTABILITY
INSTABILITY GROWTH RATES
LARMOR RADIUS
MAGNETOHYDRODYNAMICS
MECHANICS
PINCH EFFECT
PLASMA
PLASMA INSTABILITY
SCREW PINCH