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 pseudo-periodic 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-constant σ0.Among them,the four schemes follow the characteristics of vari-ation in the zero-current longitudinal phase advance(σ01)under a constant acceleration gradient and synchronous phase.The zero-current transverse phase advance(σ0t)is consistent with σ01,based on the equipartition requirement.The initial σ0t was 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 maximum σ0t of 88° by reducing the acceleration gradient of the corresponding cavities,until the point at which σ0t equals 88° 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 depres-sion＞0.7,σ0t can break through 90° when the beams were transported in both solenoid and quadrupole doublet peri-odic focusing channels.When tune depression＜0.7,the conclusions were different.For the solenoid focusing sys-tem,σ0t can 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 conclu-sions were obtained for a bunched beam with acceleration.

Xin-Miao Wan;Xue-Jiang Pu;Zhi-Qiang Ren;Wei-Hong Huang;Yu-Fei Yang;Zhi-Hui Li

The Key Laboratory of Radiation Physics and Technology of Ministry of Education,Institute of Nuclear Science and Technology,Sichuan University,Chengdu 610065,China

核技术（英文版）

[1]Xin-Miao Wan;Xue-Jiang Pu;Zhi-Qiang Ren;Wei-Hong Huang;Yu-Fei Yang;Zhi-Hui Li-.Discussion of 90° stopband in low-energy superconducting linear accelerators)[J].核技术（英文版）,2022(09):137-147

stopband,stopbands

Discussion,energy,superconducting,accelerators,Superconducting,SCL,have,high,acceleration,gradient,are,capable,operating,duty,mode,For,power,intensity,dynamics,generally,follows,principle,that,zero,current,periodic,phase,advance,each,degree,freedom,less,than,avoid,envelope,instability,caused,by,space,charge,However,this,obtained,under,condition,completely,focusing,ambiguous,pseudo,structures,such,Although,transverse,without,been,studied,other,researchers,appears,there,some,connections,between,pure,2D,Based,these,two,points,five,schemes,solenoid,quadrupole,doublet,channels,were,designed,simulate,behavior,constant,Among,them,four,characteristics,vari,longitudinal,synchronous,0t,consistent,equipartition,requirement,initial,was,set,then,gradually,decreased,approximately,end,last,maintains,maximum,reducing,corresponding,cavities,until,which,equals,normal,Using,from,linearized,equations,multiparticle,cell,PIC,simulations,properties,both,continuous,bunched,beams,It,found,CW,when,tune,transported,When,depression,conclusions,different,partially,quality,not,significantly,affected,system,breakthrough,greater,impact,same

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