Modified Budden problem associated with energetic particles in fusion plasmas

The classic Budden problem is a double-conversion process, whereby a primary incoming wave is converted to a localized secondary wave which then converts to an outgoing (reflected) primary wave. Using ray phase-space methods [1], we investigate the modification of the Budden problem associated with the presence of a localized tertiary wave supported by an energetic-particle population in an inhomogeneous magnetized plasma.~The calculation of the reflection coefficient for this modified Budden problem is based on a simple one-dimensional model where the tertiary wave is parameterized by the energetic-particle density and its separation from the localized secondary wave. Note that, since an energetic-particle population can support waves of either positive or negative energy, interference effects are taken into account for each case by using~a modular-eikonal approach [2]. \newline ~ \newline [1] E.R. Tracy, A.N. Kaufman, and A.J. Brizard, Phys. Plasmas\underline { 10}, 2147 (2003). \newline ~ \newline [2] A.J. Brizard, J.J. Morehead, A.N. Kaufman, and E.R. Tracy, Phys. Plasmas\underline { 5}, 45 (1998).