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

Abstract

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 linearised ideal MHD eigenmode solver CAS3D, including beta-induced Alfvén eigenmode (BAE)type modes in beta-induced gaps. The strongly shaped, low-aspect ratio magnetic geometry of H-1 causes CAS3D convergence difficulties requiring the inclusion of many Fourier harmonics for the parallel component of the fluid displacement eigenvector even for shear wave motions. The highest beta-induced gap reproduces large parts of the observed configurational frequency dependencies in the presence of hollow temperature profiles. *

Global Alfvén eigenmodes in the H-1 heliac

“…Overlaid on both figures is the predicted evolution of the GAE frequency computed in Sec. 3, as well as the lowest BAE geodesic solution computed for κ h = 0.30 in Bertram et al [4], at 9.4 kHz. In both cases the mode numbers are assumed to be (m, n) = (4, −5) and the mode frequency is computed at 20 ms. For the higher frequency GAE mode, the time evolution of the mode is computed from the 1/ (n e (0)) scaling, where n e (0) is the core electron density chord.…”

“…For the low frequency branch at approximately 10 kHz, a mode analysis computes the poloidal (m) and toroidal (n) mode numbers (m, n) = (4, −5). This is the mode that has systematically been studied in a range of experiments [6,7,9,14,4,15]. The 40 kHz mode that appears at 20 ms has a mode number that is indeterminate, and there is evidence for a mixture of multiple modes, including (m, n) = (4, −5).…”

“…Another motivation for the study of Alfvén eigenmodes is their potential use as a diagnostic for the plasma, particularly through the tool of magnetohydrodynamic (MHD) spectroscopy. In recent years this has been expanded beyond safety factor or q profile inference to include temperature profile [3,4].…”

“…Bertram et al [14] extended a reduceddimension cylindrical stellarator ideal-MHD normal-mode model to include a vacuum region, and describe magnetic fluctuations in the H-1 heliac. Analysis focused on the two lowest frequency global Alfvén Eigenmodes (GAEs) at κ h = 0.54, the (m, n) = (4, 5) and (7,9) modes, and showed that for the low temperature T i = T e = 20 eV and low density n e (0) = 2.5 × 10 18 m −3 plasma conditions assumed for mixed helium/hydrogen plasmas, the (7,9) and (4,5) modes have a frequency of 20.3 kHz and 114.1 kHz, respectively, with the measured frequency of approximately 40 kHz. Mirnov coil data suggested the (4, 5) mode a better phase fit to the data, with the (7,9) a closer amplitude profile fit.…”

“…Mirnov coil data suggested the (4, 5) mode a better phase fit to the data, with the (7,9) a closer amplitude profile fit. Building on this work, Bertram et al [4] developed a part-analytical, part-numerical ideal MHD analysis of low frequency compressible modes. Using ideal MHD codes CAS3D [16] and CONTI [17] the compressible ideal MHD spectrum for H-1 plasmas with κ h = 0.30 was computed, and low frequency modes lying within the acoustic-Alfvén gap studied.…”