Solution of the Nonlinear Equation of Motion of Relativistic Positrons under Planar Channeling Conditions

In earlier publications the positron planar channeling at relativistic energies was often described by a harmonic potential. In this paper a system of differential equations describing the channeled positron motion in an anharmonic potential is derived. It is shown that at such small depths, where the statistical equilibrium is not established, the radiation energy loss may be neglected. The obtained simplified equations are equivalent to corresponding expressions for ion channeling at small depths. Therefore, these earlier results can also be extended to the positron case.