Dispersion Relation and Frequency Characteristics of Alternating Periodic Structure for Linear Accelerators

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Abstract
For linear acceleration of high energy protons an alternating periodic structure operated in a ½π standing wave mode has the advantage of relative immunity from beam loading and detuning effects while sacrificing little in shunt impedance when compared to π mode operation in a uniform periodic structure. The dispersion curve of the alternating periodic structure is derived from an analysis of a chain of coupled cavities, in each of which the fields are expanded in normal modes. By introducing the effect of coupling between alternate cells in addition to adjacent cell coupling, the passband of any one cavity mode is then found to split into two unequal passbands separated by a stop band, the width of which depends on the structure's geometrical parameters. The relative distribution of energy between cells is also found as a function of frequency. Measured dispersion curves were used to check the theory and the dependence of theoretical parameters on structure geometry. It is shown that the stop band may be reduced or eliminated simply by introducing a fixed detuning of one of the two different alternating periodic cells. It is also shown that the advantages of reduced beam loading and detuning effects resulting from operation in the ½π mode is obtained even when the group velocity vanishes, as occurs in a split passband.

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