3D beam-envelope approach for an asymmetric beam in a high intensity linac with a solenoid channel

Presented here is a theory model based on the beam-envelope approach to determine the global behavior of a charged beam propagating through a high intensity linac with a solenoid channel, namely, the orbital evolution of the root-mean-square beam size in the transverse and longitudinal direction. The model is applied to the Gaussian particle distribution, where the motion of an individual particle is governed by linear focusing/defocusing forces in the solenoid channel and RF fields, except for space-charge forces. In this model, highly nonlinear effects that originated from space-charge forces disappear by averaging over the harmonic motions such as the betatron motion and phase motion in the moving direction and the Gaussian distribution. All particles making up a 3D Gaussian bunch obey the same linear equations of motion where all information of nonlinearity in the space-charge forces and the particle distribution are carried in. The theory is validated using Gaussian macro-particle simulation and one of the widely used photonic integrated circuit codes, TraceWin. As an example, the model is applied to the case of an international fusion materials irradiation facility superconducting linac with solenoid guiding and half wave RF acceleration. The results are compared with results obtained by this model and other two approaches.