Exact order reduction method in mode conversion problems

Abstract

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. The second step uses an associated integral equation to obtain the coupling between the fast and slow waves. The method makes virtually no approximations except that it keeps only the lowest nontrivial order terms in the Larmor radius expansion.