Analytic Evaluaiion of the LAMPF II Booster Cavity Design

Through the past few decades, a great deal of sophistication has evolved in the numeric codes used to evaluate electromagnetically resonant structures. The numeric methods are extremely precise, even for complicated geometries, whereas analytic methods require a simple uniform geometry and a simple, known mode configuration if the same precision is to be obtained. The code SUPERFISH, which is near the present state of the art of numeric methods, does have the following limitations: No circumferential geometry variations are permissible; there are no provisions for magnetic or dielectric losses; and finally, it is impractical (because of the complexity of the code) to modify it to extract particular bits of data one might want that are not provided by the code as written. This paper describes how SUPERFISH was used as an aid in derivating an analytic model of the LAMPF II Booster Cavity. Once a satisfactory model was derived, simple FORTRAN codes were generated to provide whatever data was required. The analytic model is made up of TEM- and radial-mode transmission-line sections, as well as lumped elements where appropriate. Radial transmission-line equations, which include losses, were not found in any literature, and the extension of the lossless equations1 to include magnetic and dielectric losses are included in this paper.