Transmission line model of beam loading in a high-current accelerating gap

Recently high-current accelerators have attracted considerable attention because of their potential applications in diverse area. Unlike in the conventional low current accelerators, substantial amount of field energy is accompanied by the high current beam. Thus, the energy gained by such a high current beam after passing through the gap is not necessarily the same as the source voltage. Typical high current accelerating gap is powered by a relatively low impedance voltage source through a transmission line. We modeled such a system with a transmission line and a beam load. The beam current is treated as a load satisfying the boundary conditions. It is found from this model that there exists a matching condition that the source voltage is equal to the characteristic impedance of the transmission line times the beam current, V
₀
= Z
₀
I
_B
, Under only this condition, the beam energy gained is equal to the full source voltage. For a general case, a simple expression is found for the beam energy gained in terms of the ratio of the source voltage to the matching voltage. Interesting other special cases include 1) the source voltage equal to one half of the matching voltage results in zero beam energy gain, and 2) zero source voltage results in beam energy loss of the matching voltage.