Excitation of contained interacting modes by fusion products

Summary form only given. We investigate modes that can interact with high energy reaction products in fusion burning plasmas giving rise to instability for frequencies that correspond to harmonics of the energetic particles\´ cyclotron frequency. The corresponding modes in a homogeneous plasma would be classified as magnetosonic-whistler modes. It is known that in a configuration with inhomogeneous magnetic field, density, and temperature, it is possible to find radially localized solutions, that we call "contained modes," for the perturbed field. We study new localized solutions for the perturbed fields by solving the equations obtained by linearizing the extended MHD equations, including the Hall term. The main effects associated with this term are to break the symmetry in /spl plusmn/k/sub /spl perp// and to include a (Whistler type) term in the dispersion equation related to propagation in the direction of the equilibrium magnetic field. We point out how the existence of this solution is essential to make it possible that the resonant interaction of the considered modes with relatively few fusion products will yield a positive growth rate.