In a fusion plasma ion cyclotron heating may be applied to a plasma in a regime where there is a population of ions whose Larmor radius is not small compared to the perpendicular wavelength. In this case the equations describing the propagation and absorption of the wave are integro-differential, describing the non-local response of the plasma to the wave field. In this paper we outline the derivation of such equations, using an extension of a technique already developed by us to obtain the differential equations appropriate to the small Larmor radius regime. We then discuss the WKB approximation and the fast wave approximation (the latter being similar to the Born approximation of scattering theory), both of which produce considerable simplification of the problem, while retaining information from the non-local response.
