Contribution to the use of superconducting shields for magnetic field shaping

The low-field diamagnetism of superconductors has often been used to design quasi-ideal magnetic circuits, especially for traveling wave maser (TWM) magnets. An analogical approach to the calculation of the efficiency of such nonideal cylindrical superconducting shields is presented. In most cases, the problem reduces to a 2-dimensional Laplace equation with given boundary conditions. The logarithmic complex potential
\log (Bx - iBy)
has been used to obtain the field homogeneity and disorientation. Partially penetrated shields may be replaced by perfect equivalent ones. The analog measurements on conducting paper permit quick iterations of the solution. Various field component measurements have been done on TWM magnets using bismuth thin film Hall probes and found to be in good agreement with the analog measurements.