Matrix method for the solution of RF field perturbations due to local frequency shifts

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SUN Zhi-Rui, PENG Jun and FU Shi-Nian. Matrix method for the solution of RF field perturbations due to local frequency shifts[J]. Chinese Physics C, 2009, 33(9): 798-803. doi: 10.1088/1674-1137/33/9/018
SUN Zhi-Rui, PENG Jun and FU Shi-Nian. Matrix method for the solution of RF field perturbations due to local frequency shifts[J]. Chinese Physics C, 2009, 33(9): 798-803.  doi: 10.1088/1674-1137/33/9/018 shu
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Received: 2008-11-28
Revised: 2009-04-09
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Matrix method for the solution of RF field perturbations due to local frequency shifts

    Corresponding author: SUN Zhi-Rui,

Abstract: 

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.

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