Garching-Greifswald Ringberg Theory Meeting

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Presentation transcript:

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