Ideal-magnetohydrodynamic theory of low-frequency Alfvén waves in the H-1 Heliac

A part analytical, part numerical ideal-MHD analysis of low-frequency Alfvén wave physics in the H-1 stellarator is given. The three-dimensional, compressible ideal spectrum for H-1 is presented and it is found that despite the low β of H-1 plasmas (β ≈ 10−4), significant Alfvén-acoustic interactions occur at low frequencies. Several quasi-discrete modes are found with the three-dimensional linearized ideal-MHD eigenmode solver CAS3D, including beta-induced Alfvén eigenmode-type modes in beta-induced gaps. The strongly shaped, low-aspect ratio magnetic geometry of H-1 presents a challenging numerical problem for wave-mode physics codes. For CAS3D, convergence requires the inclusion of many Fourier harmonics for the parallel component of the fluid displacement eigenvector even for shear wave motions. Finally, an explanation is offered for the measured configurational frequency dependence in terms of the scaling of the highest beta-induced gap with local temperature at the mode resonant surface. If validated it suggests a technique for temperature inference at the resonant surface of a mode, thereby extending the tools of MHD spectroscopy beyond q profile inference. (paper)