Ion cyclotron electromagnetic wave structure in Elmo bumpy torus

The problem of ion cyclotron wave structure in EBT has been analyzed using the smallness of the inverse aspect ratio ɛ = a/R₀ and of the inverse cavity number ɛ' = 1/N. The procedure is to expand in these two parameters, reducing the complete toroidal problem to a system of equations to be solved in sequence. To second order in ɛ and ɛ', this system contains two ordinary differential equations of second order and one partial differential equation with periodic coefficients in a magnetically adapted system of co-ordinates. The smallness of the mean bumpiness parameter ɛ_B reduces the problem to a single second-order differential equation which, for a parabolic density profile, is a Whittaker equation. The EM wave structure corresponds to a simple mode with only a few wavelengths across the plasma radius, permitting multi-harmonic ion cyclotron heating with interesting efficiency, as observed in experiments.