Lumped-circuit model of four vane RFQ resonator

The RF cavity code SUPERFISH is a necessary tool in designing RF cavities and it is often used it for approximate analytic formulas of electromagnetic properties of a cavity. One approach for the RFQ four vane cavity is the use of analytic solutions associated with an inclined plane waveguide. The large capacity vane loading in the four vane RFQ resonator give a convenient representation by a simple lumped circuit model. Formulas are derived which depend on a single unknown parameter: the vane capacitance per unit length, which can be calculated for different vane geometries using SUPERFISH. The formulas from the model are useful for estimating the RFQ's electromagnetic properties.