摘要
The particle motion equation for a Radio Frequency(RF) quadrupole is derived. The motion equation shows that the general transform matrix of a RF quadrupole with length less than or equal to 0.5βλ(β is the relativistic velocity of particles and λ is wavelength of radio frequency electromagnetic field) can describe the particle motion in an arbitrarily long RF quadrupole. By iterative integration, the general transform matrix of a discrete RF quadrupole is derived from the motion equation. The transform matrix is in form of a power series of focusing parameter B. It shows that for length less than βλ, the series up to the 2ndorder of B agrees well with the direct integration results for B up to 30, while for length less than 0.5βλ, the series up to 1storder is already a good approximation of the real solution for B less than 30. The formula of the transform matrix can be integrated into linac or beam line design code to deal with the focusing of discrete RF quadrupoles.
The particle motion equation for a Radio Frequency(RF) quadrupole is derived. The motion equation shows that the general transform matrix of a RF quadrupole with length less than or equal to 0.5βλ(β is the relativistic velocity of particles and λ is wavelength of radio frequency electromagnetic field) can describe the particle motion in an arbitrarily long RF quadrupole. By iterative integration, the general transform matrix of a discrete RF quadrupole is derived from the motion equation. The transform matrix is in form of a power series of focusing parameter B. It shows that for length less than βλ, the series up to the 2ndorder of B agrees well with the direct integration results for B up to 30, while for length less than 0.5βλ, the series up to 1storder is already a good approximation of the real solution for B less than 30. The formula of the transform matrix can be integrated into linac or beam line design code to deal with the focusing of discrete RF quadrupoles.
基金
Supported by National Natural Science Foundation of China(11375122,11511140277)
Strategic Priority Research Program of the Chinese Academy of Sciences(XDA03020705)