The shear Alfven continuum in an asymmetric MHD equilibrium

The Alfven continuum in an asymmetric plasma configuration that is an exact solution of the equilibrium equations of ideal magnetohydrodynamics is treated. The equilibrium is parallel to an infinite straight magnetic axis about which the magnetic lines of force form closed magnetic surfaces. For small plasma beta, the Alfven continuum is governed by an ordinary differential equation along the magnetic force lines. Properties of the equation are explored, and the Alfven continuous spectrum is determined. It is found that the Alfven continuum has two components: a localized component characterized by modes that decay to zero along magnetic field lines, and a non-localized component characterized by modes that approach non-zero constants at the plasma ends. The spectrum of the localized component is restricted to real frequencies; the spectrum of the non-localized component covers the entire complex frequency plane. For real and imaginary frequencies, a detailed study of the continuum is made. It is found that the non-localized modes can be joined generally with those on neighboring field lines to form modes that smoothly cover the entire magnetic surface. The localized modes, the nonsymmetry induced Alfven eigenmodes (NAE), do not occur in symmetric plasmas. (orig.)