Controlling hollow relativistic electron beam orbits with an inductive current divider

A passive method for controlling the trajectory of an intense, hollow electron beam is proposed using a vacuum structure that inductively splits the beam's return current. A central post carries a portion of the return current (I{sub 1}), while the outer conductor carries the remainder (I{sub 2}). An envelope equation appropriate for a hollow electron beam is derived and applied to the current divider. The force on the beam trajectory is shown to be proportional to (I{sub 2}-I{sub 1}), while the average force on the envelope (the beam width) is proportional to the beam current I{sub b} = (I{sub 2} + I{sub 1}). The values of I{sub 1} and I{sub 2} depend on the inductances in the return-current path geometries. Proper choice of the return-current geometries determines these inductances and offers control over the beam trajectory. Solutions using realistic beam parameters show that, for appropriate choices of the return-current-path geometry, the inductive current divider can produce a beam that is both pinched and straightened so that it approaches a target at near-normal incidence with a beam diameter that is on the order of a few mm.