Coupling of Alfvén and sound waves in stellarator plasmas

Abstract

Recently, a low frequency mode possibly driven unstable by hot electrons ͓J. M. Canik et al., 21st IAEA Fusion Energy Conference, Chengdu ͑China͒ ͑IAEA, Vienna, 2006͒, CN-149EX/5-2͔ has been observed in the Helically Symmetric Experiment ͓F. S. B. Anderson et al., Fusion Technol. 27, 273 ͑1995͔͒.The emergence of such a mode has been investigated within the framework of computational three-dimensional magnetohydrodynamics ͑MHD͒. A three-dimensional MHD continuum code CONTI has been developed for a fast computation of the continuous Alfvén and sound spectrum. The global modes have been calculated using the CAS3D code. A possibly new class of modes has been identified which is generated by the interaction between sound and Alfvén waves. The respective gap still contains a continuum branch, so that because of the continuum interaction, a conclusive answer if these modes really exist cannot be achieved within the computational ideal MHD picture. Additionally, continuum gaps of similar type have been investigated also for other stellarators.

A computational approach to continuum damping of Alfvén waves in two and three-dimensional geometry

“…Figure 4 shows the spectrum of the modulus of the normalized magnetic field (top) and that of the g ss component of the metric tensor (bottom). Figure 5 shows the Alfv en continuum for this configuration, calculated with the CONTI code, 33 which uses the full numerical information available for this equilibrium and the 19 for a numerical stellarator equilibrium using a Fourier decomposition of the perturbation. As the continuous spectrum is a local property of each flux surface, the spectrum is constructed from the solution on many flux surfaces.…”

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

“…The continuous ideal MHD spectrum for a general three-dimensional toroid can be obtained by CONTI [11] which solves the coupled continuum equations [21]…”

“…[8] However, ideal MHD has the important advantage that it is simple enough to allow for an accurate treatment of the geometry, providing a good first model for understanding the low-frequency domain. [8,9,10] In this work we present the three-dimensional, compressible ideal spectrum for H-1, based on numerical simulations with the three-dimensional continuous spectrum code CONTI [11] in combination with the three-dimensional ideal MHD linear eigenmode solver CAS3D. [12,13] Significant coupling of eigenmode Fourier harmonics in both toroidal and poloidal directions are induced by a substantial mirror term (inherent in a helical axis, low aspect-ratio configuration) in combination with a variety of strong field-strength modulations within a cross-section.…”

Energetic‐Particle‐Driven Instabilities in General Toroidal Configurations

“…A number of models have been developed for the calculation of such continua in stellarators [6][7][8] and generally provide reasonable agreement with frequency lines that are measured in experiments, to within uncertainties related to imprecise knowledge of the i --and density profiles, average ion mass and Doppler shifts related to plasma flows. A topic of recent interest both for tokamaks [9,10] and stellarators [4,6,8,11] has been the inclusion of sound wave couplings to the shear Alfvén continua. In a three-dimensional system these couplings might be expected to become of importance when k 2 m,n v 2 A ≈ k 2 m±Δm,n±Δn C 2 s where Δm, Δn are the coupling intervals in the poloidal and toroidal mode numbers, v A = B 2 /μ 0 n ion m ion 1/2 is the Alfvén velocity and…”