Discussion of 90°stopband in low-energy superconducting linear accelerators

摘要

Superconducting linear accelerators(SCL)have a high acceleration gradient and are capable of operating in a high-duty factor mode.For high-power and high-intensity SCL,the design of beam dynamics generally follows the principle that the zero-current periodic phase advance(σ0)of each degree of freedom is less than 90°to avoid envelope instability caused by space charge.However,this principle is obtained under the condition of a completely periodic focusing channel,and it is ambiguous for pseudoperiodic structures,such as linear accelerators.Although transverse beam dynamics without acceleration have been studied by other researchers,it appears that there are some connections between pure 2D and 3D beam dynamics.Based on these two points,five focusing schemes for the solenoid and quadrupole doublet channels were designed to simulate the beam behavior with non-constantσ0.Among them,the four schemes follow the characteristics of variation in the zero-current longitudinal phase advance(σ0l)under a constant acceleration gradient and synchronous phase.The zero-current transverse phase advance(σ0t)is consistent withσ0l,based on the equipartition requirement.The initialσ0twas set to 120°,110°,100°,and 90°,and was then gradually decreased to approximately 40°at the end of the channel.The last scheme maintains the maximumσ0tof88°by reducing the acceleration gradient of the corresponding cavities,until the point at whichσ0tequals88°with a normal gradient.Using the stopbands obtained from the linearized envelope equations and multiparticle particle-in-cell(PIC)simulations,the transport properties of both continuous and 3D-bunched beams with the acceleration of the five focusing schemes were studied.It was found that for a CW beam,when tune depression>0.7,σ0tcan break through 90°when the beams were transported in both solenoid and quadrupole doublet periodic focusing channels.When tune depression<0.7,the conclusions were different.For the solenoid focusing system,σ0tcan partially break through 90°,and the beam quality is not significantly affected.For the quadrupole doublet focusing system,a partial breakthrough of 90°has a greater impact on the beam quality.The same conclusions were obtained for a bunched beam with acceleration.