Properties of an axially periodic magnetic field in a betatron - Zvontsov A. A. Aleksander Akimovich (1983, 1983)
It is shown by solving an equation for the vector potential A(r, z) of the magnetic field that under appropriate conditions the focusing properties of a betatron magnetic field are periodic with respect to the z coordinate. Under these conditions there may be several equilibrium orbits lying in parallel planes z equals O, z equals z//0//1 . . . , z equals mz//0//1 in the accelerator. An equation is derived for the distance z//0//1 between the equilbrium orbit planes for a given orbit radius r//0 and field decay exponent n//0. The operation of such accelerators is described.