Focusing and guiding charged particles using a superconducting tube: An analytical nonlinear approach

We present an analytical solution for the nonlinear equation of motion of a n electron beam in the radial direction of a superconducting tube, for the case of elections moving close to the tube axis. Accordingly, we deduce a g eneral expression for the focusing length dependence on the parameters of t he superconducting tube and the electron stream. Our calculated focusing le ngth is in good agreement with the experimental data.