Vlasov fluid stability of a skin current Z pinch with finite electron pressure
- The Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom (GB)
The linear stability of a Z-pinch confined by a skin current has been studied in the collisionless regime using the Vlasov fluid model for arbitrary {ital m} number. The trajectory integrals that are normally so formidable an aspect of Vlasov fluid analyses are greatly simplified in this equilibrium and the eigenvalue equation reduces to a dispersion relation derived from the plasma edge boundary condition. For the case {ital T}{sub {ital e}}=0, an analytic solution is found in the short-wavelength limit for the growth rate, which saturates for all {ital m} at a value of {pi}{sup 1/2}{ital v}{sub {ital T}}/2{ital a}, where {ital v}{sub {ital T}} is the ion thermal velocity and {ital a} is the pinch radius. This should be compared with the ideal magnetohydrodynamic (MHD) growth rate for the same equilibrium that increases without limit as {ital k}{sup 1/2}, where {ital k} is the axial wave number. The solution with finite electron temperature is achieved by a Neumann series expansion, which is shown to converge for all finite values of {Gamma}, the ratio of specific heats. In the short-wavelength limit with {ital T}{sub {ital e}}={ital T}{sub {ital i}}, the growth rates are double those for cold electrons. The deviation from this factor of two increase is always less than 10% for longer wavelengths.
- OSTI ID:
- 5838189
- Journal Information:
- Physics of Fluids B; (USA), Journal Name: Physics of Fluids B; (USA) Vol. 3:5; ISSN 0899-8221; ISSN PFBPE
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
700107* -- Fusion Energy-- Plasma Research-- Instabilities
ANALYTICAL SOLUTION
BOLTZMANN-VLASOV EQUATION
BOUNDARY CONDITIONS
COLLISIONLESS PLASMA
CONFINEMENT
CORRELATIONS
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
EIGENVALUES
ELECTRON TEMPERATURE
EQUATIONS
EQUILIBRIUM
INSTABILITY GROWTH RATES
INTEGRALS
LINEAR PINCH DEVICES
LINEAR Z PINCH DEVICES
NEUMANN SERIES
OPEN PLASMA DEVICES
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
PINCH DEVICES
PLASMA
PLASMA CONFINEMENT
PLASMA PRESSURE
SATURATION
SERIES EXPANSION
SKIN EFFECT
SPECIFIC HEAT
STABILITY
THERMODYNAMIC PROPERTIES
THERMONUCLEAR DEVICES
TRAJECTORIES