Garching-Greifswald Ringberg Theory Meeting 17 November 2008 Compressional and Kinetic Effects on the Lowest Part of the Alfvén Spectrum in Stellarators with Weak Shear D. Eremin, A. Könies Max-Planck-Institut für Plasmaphysik, EURATOM Association, Teilinstitut Greifswald
Outline Motivation Case study: unstable Alfvénic mode in quasisymmetric HSX MHD Analysis: coupling of the Alfvén and acoustic modes Kinetic Effects: parallel electric field Further Work Conclusions
Motivation Low-frequency electromagnetic activity in experiment, often no adequate explanation within the purely shear Alfvén physics Direct analysis of the numerical data for stellarators can be extremely complicated. Reduced models needed Alfvén modes can couple with acoustic modes through the curvature of magnetic field lines leading to modified continua (e.g., beta-induced gaps) and new eigenmodes The mode with the helicity close to the rotational transform is particularly sensitive to the interaction with acoustic modes as it has very low frequency Kinetic effects, such as the parallel electric field, are an essential part of the problem Motivation
Electromagnetic activity in W7-AS (Hirsch et al, PPCF 2008) Motivation
Unstable low-frequency mode in HSX HSX Quasisymmetric Stellarator Alfvén continuum (CONTI) (Brower et al, 2005) (A. Könies) Motivation
Quasisymmetric operation in HSX Case Study: HSX
MHD analysis: basic assumptions
Basic equations (MHD) MHD Analysis
Continuous spectra MHD Analysis
Coupling to the acoustic modes Alfvén acoustic geodesic -acoustic modified Alfvén-acoustic continuous spectra unmodified Alfvén unmodified acoustic modified Alfvén-acoustic MHD Analysis
Coupling to other Alfvén modes MHD Analysis
Quasisymmetric configuration in HSX Case Study: HSX
Modified continua: HSX Case calculated with CONTI: Continua calculated with the reduced formula: MHD Analysis
Modified continua: W7-AS Case MHD Analysis
Eigenmode equation (MHD) MHD Analysis
Acoustic resonance MHD Analysis
Eigenvalue code MHD Analysis
Beta-induced gap mode (MHD) MHD Analysis
Beta-induced gap mode (analysis) MHD Analysis
Kinetic effects: parallel electric field
Weakly damped kinetic modes Kinetic Effects
Heavily damped kinetic modes
To do Investigate damping vs magnitude of the magnetic field strength Fourier harmonics Conduct analytical research as to why there are undamped modes despite the strong parallel Landau damping in the kinetic case Study dependence of the continuum damping on the acoustic branches separation Study interaction of Alfvén and acoustic modes in W7-X and W7-AS New physics: - more dominant harmonics of the field strength than in HSX - large ion damping in isothermal plasmas - finite Larmor radius effects Further Work
Conclusions A reduced model for treatment of the coupled Alfvén-acoustic modes in low part of the frequency spectrum is derived Case of the Alfvénic mode with helicity close to the rotational transform as an example of such mode is studied for HSX parameters Alfvén continuum exhibits drastic change of topology as long at the locations where the acoustic frequencies and the Alfvén continuum cross. A gap and a “crossing continuum” are formed MHD eigenfunctions have global character and seem to have no continuum damping Kinetic effects lead to generation of KAWs, which significantly enhances damping of the global gap mode Present research provides a knowledge base for exploring more sophisticated stellarators, such as W7-AS or W7-X