Focusing effects on waves propagating in a nonuniform plasma

The effects of ray focusing on the propagation of waves in a nonuniform plasma are considered. The treatment is based on two complementary approaches. First Bernstein’s wave energy equation is integrated numerically and studied analytically in order to gain an understanding of the singularities to which it can give rise. Second, a bundle of rays is also studied numerically and found to cross at exactly the same point in space where the energy equation produces a singularity. The particular numerical examples are done for lower hybrid waves in a tokamak.