1. 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

2. 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

3. 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

4. Electromagnetic activity in W7-AS
(Hirsch et al, PPCF 2008)
Motivation

5. Unstable low-frequency mode in HSX
HSX Quasisymmetric Stellarator
Alfvén continuum (CONTI)
(Brower et al, 2005)
(A. Könies)
Motivation

6. Quasisymmetric operation in HSX
Case Study: HSX

7. MHD analysis: basic assumptions

8. Basic equations (MHD)
MHD Analysis

9. Continuous spectra
MHD Analysis

10. Coupling to the acoustic modes
Alfvén
acoustic
geodesic
-acoustic
modified Alfvén-acoustic
continuous spectra
unmodified Alfvén
unmodified acoustic
modified Alfvén-acoustic
MHD Analysis

11. Coupling to other Alfvén modes
MHD Analysis

12. Quasisymmetric configuration in HSX
Case Study: HSX

13. Modified continua: HSX Case
calculated
with CONTI:
Continua
calculated
with the reduced
formula:
MHD Analysis

14. Modified continua: W7-AS Case
MHD Analysis

15. Eigenmode equation (MHD)
MHD Analysis

16. Acoustic resonance
MHD Analysis

17. Eigenvalue code
MHD Analysis

18. Beta-induced gap mode (MHD)
MHD Analysis

19. Beta-induced gap mode (analysis)
MHD Analysis

20. Kinetic effects: parallel electric field

21. Weakly damped kinetic modes
Kinetic Effects

22. Heavily damped kinetic modes

23. 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

24. 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