To tune the accelerating field to the design value in a periodical radio frequency accelerating structure, Slater＇s perturbation theorem is commonly used. This theorem solves a second-order differential equation to o...To tune the accelerating field to the design value in a periodical radio frequency accelerating structure, Slater＇s perturbation theorem is commonly used. This theorem solves a second-order differential equation to obtain the electrical field variation due to a local frequency shift. The solution becomes very difficult for a complex distribution of the local frequency shifts. Noticing the similarity between the field perturbation equation and the equation describing the transverse motion of a particle in a quadrupole channel, we propose in this paper a new method in which the transfer matrix method is applied to the field calculation instead of directly solving the differential equation. The advantage of the matrix method is illustrated in examples.展开更多
In the construction of a drift tube LINAC （DTL）, many factors caused during the fabrication and assembly of the structure cells cause the electric field distribution not as the same as the design curve. To solve thi...In the construction of a drift tube LINAC （DTL）, many factors caused during the fabrication and assembly of the structure cells cause the electric field distribution not as the same as the design curve. To solve this problem, the traditional way is to solve the equation of Slater＇s perturbation theorem to obtain the electrical field variation due to local frequency shift. However, that is very difficult under complicated conditions. Since the field perturbation equation is similar to the particle＇s transverse motion equation, which can be simply solved by using the transfer matrix method, we thus propose to apply a transfer matrix method in tuning the DTL. We demonstrate the availability and advantages of this method with 3D microwave code simulation and the LabVIEW calculation program. After two iterations, the initial error of the electric field of 19.5% has been improved greatly down to 1.3%- -4.5%. This indicates that the transfer matrix method is very useful and convenient for the simplification of tuning procedures.展开更多
文摘To tune the accelerating field to the design value in a periodical radio frequency accelerating structure, Slater＇s perturbation theorem is commonly used. This theorem solves a second-order differential equation to obtain the electrical field variation due to a local frequency shift. The solution becomes very difficult for a complex distribution of the local frequency shifts. Noticing the similarity between the field perturbation equation and the equation describing the transverse motion of a particle in a quadrupole channel, we propose in this paper a new method in which the transfer matrix method is applied to the field calculation instead of directly solving the differential equation. The advantage of the matrix method is illustrated in examples.
文摘In the construction of a drift tube LINAC （DTL）, many factors caused during the fabrication and assembly of the structure cells cause the electric field distribution not as the same as the design curve. To solve this problem, the traditional way is to solve the equation of Slater＇s perturbation theorem to obtain the electrical field variation due to local frequency shift. However, that is very difficult under complicated conditions. Since the field perturbation equation is similar to the particle＇s transverse motion equation, which can be simply solved by using the transfer matrix method, we thus propose to apply a transfer matrix method in tuning the DTL. We demonstrate the availability and advantages of this method with 3D microwave code simulation and the LabVIEW calculation program. After two iterations, the initial error of the electric field of 19.5% has been improved greatly down to 1.3%- -4.5%. This indicates that the transfer matrix method is very useful and convenient for the simplification of tuning procedures.
