Two-dimensional analytic theory for toroidal Alfven eigenmodes
- Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)
A two-dimensional analysis of the toroidal Alfven eigenmodes (TAE) is presented, based on an integrodifferential equation describing the shear Alfven perturbation of a toroidal plasma equilibrium in terms of coupling among the toroidal Alfven continua with the usual gap structure. Using a method similar to the Van Kampen--Case analysis for the Vlasov equation, exact analytic expressions are derived for the dispersion function and the two-dimensional eigenmode structure. The dispersion function is expressed in terms of Cauchy-type integrals, which explicitly expresses the global character of TAE modes and facilitates the calculation of their damping. The continuum-damped TAE modes are shown to be, in general, not true eigenmodes of the toroidal plasma equilibrium, but rather resonances corresponding to zeros of the analytic continuation of the dispersion function onto unphysical sheets of its Riemann surface. Approximate but explicit expressions for the dispersion relation and the eigenfunction are also obtained in the limit of vanishing inverse aspect ratio.
- DOE Contract Number:
- FG05-80ET53088
- OSTI ID:
- 6071992
- Journal Information:
- Physics of Fluids B; (United States), Vol. 5:8; ISSN 0899-8221
- Country of Publication:
- United States
- Language:
- English
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ALFVEN WAVES
DISPERSION RELATIONS
ALPHA PARTICLES
ANALYTIC FUNCTIONS
ASPECT RATIO
EIGENFUNCTIONS
INTEGRAL EQUATIONS
MHD EQUILIBRIUM
PLASMA CONFINEMENT
RECURSION RELATIONS
THERMONUCLEAR REACTORS
TOKAMAK DEVICES
TOROIDAL CONFIGURATION
WAVE FUNCTIONS
ANNULAR SPACE
CHARGED PARTICLES
CLOSED CONFIGURATIONS
CLOSED PLASMA DEVICES
CONFIGURATION
CONFINEMENT
EQUATIONS
EQUILIBRIUM
FUNCTIONS
HYDROMAGNETIC WAVES
MAGNETIC FIELD CONFIGURATIONS
SPACE
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700340* - Plasma Waves
Oscillations
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