2-DIMENSIONAL ANALYTIC THEORY FOR TOROIDAL ALFVEN EIGENMODES

A two-dimensional analysis of the toroidal Alfven eigenmodes (TAE) is presented, based on an integrodifferential equation describing the she ar Alfven perturbation of a toroidal plasma equilibrium in terms of co upling among the toroidal Alfven continua with the usual gap structure . Using a method similar to the Van Kampen-Case analysis for the Vlaso v equation, exact analytic expressions are derived for the dispersion function and the two-dimensional eigenmode structure. The dispersion f unction is expressed in terms of Cauchy-type integrals, which explicit ly expresses the global character of TAE modes and facilitates the cal culation of their damping. The continuum-damped TAE modes are shown to be, in general, not true eigenmodes of the toroidal plasma equilibriu m, but rather resonances corresponding to zeros of the analytic contin uation of the dispersion function onto unphysical sheets of its Rieman n surface. Approximate but explicit expressions for the dispersion rel ation and the eigenfunction are also obtained in the limit of vanishin g inverse aspect ratio.