Motion of charged particles in curved planar channels: Effects of dislocations

A simple model to discuss the motion of charged particles in curved channels, such as those around a dislocation, is presented. The curvature in the channel produced by a dislocaiton is approximated by an are of constant radius $R$, which is determined by using the displacement equations for the case of screw dislocation. The equations of motion for the planar channeling case have been written by approximating the effects of curvature on the particle motion by an average constant centrifugal force $\frac{2E}{R}$, $E$ being the average energy in the curved part of the channel. These equations are solved in the limit of small curvatures (i.e., for channels not very near to the dislocation) and an analytical expression for the change in energy loss of an initially well-channeled particle is obtained.