Plasma Stability in an Inhomogeneous Magnetic Field

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Abstract
The problem of flute instabilities earlier discussed by Rosenbluth and Longmire and by the author is reconsidered. The theory is extended to include the influence of a mass velocity in the unperturbed state as well as compression and expansion effects arising from the inhomogeneity of the magnetic field. According to the latter effects, surfaces of constant density will not move with the fluid velocity. A description of the dynamics of density perturbations is made in terms of the fluid equations under the assumption of negligible Ohmic and viscous dissipation. Adiabatic and isothermal changes of state are discussed for a plasma with adiabatic and isothermal distributions of pressure and density in the unperturbed state. The plasma is found to be stable against flute disturbances of any wavelength, not only for cusped geometry, but also for mirror geometry under certain conditions. This is the case when the characteristic length B/|∇B| of the magnetic field is less than twice the characteristic length N/|∇N| of the unperturbed density distribution. The approximations of the present theory exclude a treatment of perturbations which extend across the whole plasma body. The compression mechanism which is responsible for the stabilization is a zero‐order effect which is independent of the assumptions of isotropy and of the special forms of the unperturbed density and pressure distributions.