The Optimum Configuration of the Periodic Quadrupole Min. \barB Field

Abstract

A variational problem with respect to a functional comprising two argument functions is solved. In this problem, the configuration of the periodic quadrupole min \barB field is optimized in a sense when the ratio of the maximum to the minimum distance of a line of force from the axis of a cylindrical geometry is kept within a limit. The two stationary functions concerned have a singular point respectively and minimize the functional only in that left side region of the singular point in which the integrand of the functional is positive.