On equations for ion cyclotron modes in `warm' bounded plasmas

An equation describing eigenmodes in the ion cyclotron frequency range in `warm' bounded plasmas, i.e. eigenmodes which are absent in the two-fluid model but exist in kinetic theory due to finite Larmor radius of the ions, is derived for the first time. It is valid for electrostatic modes but the developed approach is generic. Calculations are carried out for two cases: first, for a homogeneous magnetic field; second, taking into account the effects of toroidicity in tokamaks. It is found that, in general, equations for eigenmodes in warm plasmas do not reduce to second-order differential equations (in contrast to those which are usually used to describe the radial structure of eigenmodes in fusion devices). The study of modes in warm plasmas is of interest, in particular, in connection with the recent observations of superthermal ion cyclotron emission in the NSTX-U spherical torus and DIII-D tokamak, which can be hardly explained by conventional theories employing fast magnetoacoustic modes.