Emittance Compensation of Compact Superconducting Guns and Booster Linac System

We discuss the mechanics of emittance compensation for a compact superconducting rf gun with a solenoid, a drift space, and a linac system, and give general rules for designing such a system. It is preferable to ensure that the cathode is recessed and that the solenoid is close to it. The drift length, the solenoid's strength, the size of the waist spot, and the linac's accelerating gradient can be determined from the size of the beam's spot at the gun exit, all of which are easily obtained from simulations. Chromaticity effects generally start at the solenoid but can be ignored in the gun. The energy spread extends the spread of the slices' waist positions, and therefore degrades the emittance compensation. The gun cavity should be designed to minimize energy spread at the gun's exit; this can be achieved by shortening the effective length of the cavity cell. The linac gradient required to minimize chromaticity by focusing at the linac entrance is larger than the gradient required for matching the linac's invariant envelope. The applied solution must be a compromise between these two parameters. For a beam with limited energy spread, its waist must be in front of the linac's entrance.