Motion of charged particles in curved axial channels—effects of dislocations

A simple model to calculate the effects of dislocations on the energy loss of charged particles in proper axial channeling (hyperchanneling) is presented. The cylindrically symmetric potential around the channel axis is obtained in the continuum approximation for the axial channel in diamond-structure crystals and the axial channels in fcc and bcc crystals. As in recent work on planar channeling, the channel curvature due to dislocations is approximated by an arc of constant radius $R$ which is determined from the displacement equations for dislocations. The effects of this curvature on the particle motion are approximated by an average constant centrifugal force $\frac{2E}{R}$, $E$ being the average energy in the curved parts of the channel. Thus, solving the relevant equations of motion for initially well-channeled particles, we derive an analytical expression for the change in energy loss of these particles due to their passage through channels with small curvature (i.e., for channels situated at a distance from 100 to 1000 Å from the dislocation axis). The results obtained are thus expected to be valid for a concentration in the region of ${10}^9$ to ${10}^{10}$ dislocations per ${\mathrm{cm}}^2$.