Focusing and guiding charged particles by a superconducting tube

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Abstract
Electrons traveling through a superconducting tube are studied. Two simple models are proposed to describe the interaction of the magnetic self‐field of the electron stream with the superconducting tube. In the first model A, a complete expulsion of the magnetic flux from the superconductor due to the Meissner effect is assumed. On the contrary, a complete flux penetration through vortices is supposed in the second model B. Both models indicate an electron focusing when the space‐charge effect is compensated. The focusing length is estimated. For electrons traveling in the vicinity of the tube axis, the focusing length determined according to model A is nearly independent on the distance of the electrons from the tube axis, while the focusing length according to model B increases at increasing distance of the electrons from the tube axis. Similar focusing effects are obtained by a superconducting cone.