Finite-Larmor-radius stabilization in a sharp-boundary Vlasov-fluid screw pinch

Journal Article · Fri Apr 01 04:00:00 EST 1977 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.861925· OSTI ID:7308523

Turner, L

Starting from the basic equations of the Vlasov-fluid model, assuming small ion Larmor radii, and assuming unstable, long-wavelength perturbations in a sharp-boundary screw pinch whose equilibrium distribution of ion velocities is isotropic, a derivation is presented of the dependence upon xi/sub perpendicular/(r) and its derivatives of the dominant terms in perturbations of the ion distribution, the ion number density, the ion fluid velocity, the pressure tensor, and the heat flux vector. A differential equation governing xi/sub perpendicular/(r) is derived and solved. A dispersion relation for a perturbation with arbitrary azimuthal mode number is derived by application of boundary conditions appropriate for a sharp-boundary screw pinch. It is found that ideal magnetohydrodynamics and the Vlasov-fluid model yield identical dispersion relations only for an m=1 mode. For m> or =2, the Vlasov-fluid model yields a damping of the ideal magnetohydrodynamic growth rate with increasing ion temperature. The m=2 instability is extinguished at an ion temperature equal to one-fourth of that given by Freidberg's analysis. This result allows greater leeway for wall stabilization of m=1 modes while maintaining finite-Larmor-radius stabilization of m=2 modes in theta-pinch machines, such as scyllac.

• Research Organization: Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87545
• OSTI ID: 7308523
• 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
DISPERSION RELATIONS
DISTURBANCES
EQUATIONS
EQUILIBRIUM PLASMA
FLUID MECHANICS
HYDRODYNAMICS
INSTABILITY
INSTABILITY GROWTH RATES
LARMOR RADIUS
MAGNETOHYDRODYNAMICS
MECHANICS
PINCH EFFECT
PLASMA
PLASMA INSTABILITY
SCREW PINCH