Analytical solution for the mode conversion equations with steep exponential density profiles

A general analytical solution for the converted power from the fast magnetosonic wave to an ion Bernstein wave in a magnetized plasma with an exponential steeply increasing density profile is given in the closed form. The solution covers both the conversion at the lower-hybrid resonance and the conversion through the density gradient for small parallel wave numbers. As an application, the conversion coefficients at the scrape-off layer plasma are estimated in the context of ion cyclotron heating of a tokamak plasma