The physical characteristics of an annular Pierce-type electron gun are investigated
analytically. The electron gun is used in conjunction with a nonadiabatic magnetic reversal
and adiabatic compression region to produce an axis-encircling beam. Typical magnetic
field profiles that can generate zero velocity spreads are obtained from the analytical
calculation, taking into account initial canonical angular momentum spreads at the cathode
and the crossing of the beam trajectory and magnetic flux line before the magnetic cusp …