A simple analytic linearized theory of the sausage mode is developed, based on resistive MHD, certain long‐wavelength assumptions, and in particular the assumption that the perturbations of the radial density profile are self‐similar. The perturbations to the magnetic field are not assumed to be self‐similar. Time dependences of the equilibrium, e.g., current rising as τα, ohmic heating, and time‐varying radius, are included quite generally. The formalism appears to provide a good representation of those modes which lead to coherent sausaging of the entire radial cross section of the pinch, but excludes modes which are localized near a particular radius. The net effect of resistivity and time variation of the equilibrium is to decrease the instability growth rate (but by no more than a factor of two) if α≲1, or to increase it if α≳1.
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Research Article|
December 01 1989
A simple analytic model of the sausage mode in a resistive Z‐pinch
Martin Lampe
Martin Lampe
Naval Research Laboratory, Washington, DC 20375–5000
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AIP Conf. Proc. 195, 252–261 (1989)
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Martin Lampe; A simple analytic model of the sausage mode in a resistive Z‐pinch. AIP Conf. Proc. 1 December 1989; 195 (1): 252–261. https://doi.org/10.1063/1.38873
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