A solvable model is developed for the linearized sausage mode within the context of resistive magnetohydrodynamics. The model is based on the assumption that the fluid motion of the plasma is self‐similar, as well as several assumptions pertinent to the limit of wavelength long compared to the pinch radius. The perturbations to the magnetic field are not assumed to be self‐similar, but rather are calculated. Effects arising from time dependences of the z‐independent perturbed state, e.g., current rising as tα, Ohmic heating, and time variation of the pinch radius, are included in the analysis. The formalism appears to provide a good representation of ‘‘global’’ modes that involve coherent sausage distortion of the entire cross section of the pinch, but excludes modes that are localized radially, and higher radial eigenmodes. For this and other reasons, it is expected that the model underestimates the maximum instability growth rates, but is reasonable for global sausage modes. The net effect of resistivity and time variation of the unperturbed state is to decrease the growth rate if α≲1, but never by more than a factor of about 2. The effect is to increase the growth rate if α≳1.
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July 1991
Research Article|
July 01 1991
A solvable self‐similar model of the sausage instability in a resistive Z pinch
Martin Lampe
Martin Lampe
Beam Physics Branch, Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375‐5000
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Phys. Fluids B 3, 1521–1531 (1991)
Article history
Received:
June 27 1989
Accepted:
February 25 1991
Citation
Martin Lampe; A solvable self‐similar model of the sausage instability in a resistive Z pinch. Phys. Fluids B 1 July 1991; 3 (7): 1521–1531. https://doi.org/10.1063/1.859723
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