Distortion of Maxwellian distribution in an inhomogeneous magnetized plasma

A theory is derived for the enhancement of the high-energy part of the ion distribution function because of the finite transverse dimension of the orbits. Cyclotron rotation in a straight magnetic field is taken into account, as is a banana drift motion in a toroidal system. In contrast with previous theoretical papers, the kinetic equation for the tail of the ion distribution is found by a systematic method of averaging over a rapidly oscillating variable. The kinetic equation is solved by analytic methods. It is shown that the broadening of the profile of the ion temperature and the pronounced enrichment of the tail of the ion distribution which have been observed in tokamak experiments can be explained on the basis of the finite thickness of the banana orbits. In the process it is demonstrated that the previous theoretical models lead to a significant error in a determination of the temperature of the high-energy component, especially at high energies