Exact order reduction method in mode conversion problems

The exact order reduction method solves the fourth-order system of equations from the Vlasov equations that describe mode conversion by breaking the solution into two steps. The first step is to find the numerical solutions of a pair of second-order equations for the fast waves and slow waves, respectively, which are easily obtained. The second step uses an associated integral equation to obtain the coupling between the fast and slow waves. Potential difficulties due to singularities in the kernel of the integral equations near the axis are resolved by altering the integration path. This allows accurate estimates for mode conversion efficiencies in realistic geometries as the integral equation is solved only in a narrow region near resonance, while the global fast wave solution of the reduced second-order equation covers the entire cross section. The method makes virtually no approximations except that it keeps only the lowest nontrivial order terms in the Larmor radius expansion. copyright 1997 American Institute of Physics