We analyze the supertron experiments (the superconducting-cone focusin
g of electron beams). As the distinct features of superconductors from
metals are concerned, the Meissner effect is considered as an alterna
tive mechanism to explain the focusing function of the supertron. As a
model study, we consider the system of a charged point particle movin
g in an infinite square cross-section hole through a superconductor. U
sing the method of images, we have studied the confined motion of the
charged particle due to the self-induced magnetic field in the nonrela
tivistic regime. The relevant applications, in particular the focusing
of electron and positron beams, are discussed.