EXACT ORDER REDUCTION METHOD IN MODE CONVERSION PROBLEMS

The exact order reduction method solves the fourth-order system of equ ations from the Vlasov equations that describe mode conversion by brea king the solution into two steps. The first step is to find the numeri cal solutions of a pair of second-order equations for the fast waves a nd slow waves, respectively, which are easily obtained. The second ste p uses an associated integral equation to obtain the coupling between the fast and slow waves. Potential difficulties due to singularities i n the kernel of the integral equations near the axis are resolved by a ltering the integration path. This allows accurate estimates for mode conversion efficiencies in realistic geometries as the integral equati on is solved only in a narrow region near resonance, while the global fast wave solution of the reduced second-order equation covers the ent ire cross section. The method makes virtually no approximations except that it keeps only the lowest nontrivial order terms in the Larmor ra dius expansion. (C) 1997 American Institute of Physics.