The set of equations which determines the continuous spectrum of ideal magnetohydrodynamics (MHD) in the limit of low beta for axisymmetric toroidal equilibria is examined. It is shown that when the equilibrium pressure is set equal to zero, the cusp continuum is reduced to a single point ω = 0 in the spectrum, and a single second-order differential equation, which describes the shear Alfvén continuum, survives in this limit. This reduced equation may provide a good representation of the MHD continuum for low beta plasmas.
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Kieras et al. (1982) studied this question.
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