A new normal form for multidimensional mode conversion

Linear conversion occurs when two wave types are locally resonant in a nonuniform plasma [1]. In recent work, we have shown how to incorporate a ray-based approach to mode conversion in numerical algorithms [2,3] for the most common type of conversion. Here, we present a new formulation that can deal with more general cases [4]. We exploit a new normal form for the 2X2 dispersion matrix defined such that the diagonals Poisson- commute with the off-diagonals (at leading order). Therefore, if we use the diagonals as ray Hamiltonians, the off- diagonals will be constant. Thus, the 2X2 dispersion matrix in normal form has a very natural physical interpretation: the diagonals are the uncoupled ray Hamiltonians and the off-diagonals are the coupling. We further discuss how to incorporate the normal form into ray tracing algorithms. 1] E. Tracy, A. Kaufman and A. Brizard, Phys. Plasmas {\bf 10} (2003) 2147. 2] A. Jaun, E. Tracy and A. Kaufman, Plasma Phys. Control. Fusion {\bf 49} (2006) 43. 3] E. Tracy, A. Kaufman and A. Jaun, to appear in Phys. Plasmas. 4] A. Kaufman, E. Tracy and A. Brizard, Phys. Plasmas {\bf 12} (2005) 022101. 5] E. Tracy and A. Kaufman, PRL {\bf 91} (2003) 130402.