Sherwood 2015

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Nonlinear theory of Alfven resonances

Author: Francois L Waelbroeck
Requested Type: Poster Only
Submitted: 2015-01-20 09:02:54

Co-authors: H.L.Berk, B.Breizman, M.Idouakass

Contact Info:
Inst. Fusion Studies, Univ. Texas Austin
2515 Speedway
Austin, Texas   78712-1

Abstract Text:
Slowly growing electromagnetic disturbances are subject to resonances near surfaces where |w|=|k.c|, where w is the frequency, k is the wavevector and c is the Alfven velocity. In linear theory, these resonances can be resolved by inertia if the mode is growing, or by viscosity otherwise. If, however, the plasma displacement is larger than the visco-inertial layer width, nonlinear effects become important near the resonance.[1] In fusion experiments, this situation is encountered for fishbone oscillations as well as for resonant magnetic perturbation when the plasma rotation frequency is sufficiently large. For moderate frequency, the Alfvén resonances occur in pairs straddling the mode-rational surface where the wavefronts are parallel to the magnetic field (k.c=0).

An extension of the saturated kink theory of Rosenbluth et al.[2] to describe Alfvén resonances is presented. The results show that for a given wave amplitude and mode frequency, there is a family of saturated solutions exhibiting superposed current and vortex singularities and parametrized by the driving energy and the phase velocity of the mode in the plasma frame. The perpendicular component of the plasma velocity in the wave frame is everywhere proportional to the ratio of the helical magnetic field and its average on flux-surfaces. A similarity property shows that the plasma displacement normalized to the driving energy is a function of the square of the phase velocity, also normalized to the driving energy. The implications for fishbone and RMP experiments will be discussed.

This work was funded by the U.S. DOE Contract No. DE-FG03-96ER-54346.

[1] A. Odblom, B. N. Breizman, S. E. Sharapov, T. C. Hender, and V. P. Pastukhov,, Phys. Plasmas 9, 155 (2002).
[2] M. N. Rosenbluth, R. Y. Dagazian, and P. H. Rutherford, Phys. Fluids 16, 1894 (1973).

Plasma Properties, Equilibrium, Stability, and Transport

March 16-18, 2015
The Courant Institute, New York University