Emittance growth due to radial density variations of an emittance-dominated electron beam in a channel with continuous acceleration and focusing

摘要

Simulations have identified charge-density variations as driving the dominant emittance growth mechanism for high-current, low-emittance induction linacs using solenoidal focusing, once the beam enters the emittance-dominated regime. In this paper, we use the radial equation of motion, including the nonlinearities resulting from radial density variations, to understand this effect. Nonlinearities in the beam's radial motion while in a solenoid arise from the noncancellation of the effects from the diamagnetic axial magnetic field and the potential depression of the beam, if the beam density is nonuniform. Any initial density variation drives a logarithmic increase in additional higher-order density variations (through the differential betatron motion), and an emittance growth that scales logarithmically, or greater (even potentially faster than linear), with the axial distance along the accelerator. The growth rate depends on the beam current, the focusing force, and the accelerating gradient, and for typical machine parameters, the growth rate can be faster than linear with distance. The magnitude of the emittance growth depends critically on the matching of the beam from the injector to the beamline. This formalism leads to a criterion of how uniform the beam density has to be and how well the beam needs to be matched in order not to have an unacceptable emittance growth. (C) 1998 American Institute of Physics. [References: 14]