An Equivalent Circuit Model of the General 3-Dimensional RFQ

An equivalent circuit model has been developed, based on the description of the RFQ as a terminated waveguide. The RFQ is modeled as a length of inductively loaded square waveguide operating in "TE10-and TE11- like" modes in the dipole and quadrupole configurations respectively. This is described by 6 coupled first order differential equations using distributed values for the four quadrant shunt admittances and series impedances. The end terminations are represented by lumped terminating reactances. The first few orders of both dipole and quadrupole modes are described by the model. By relating the equivalent circuit values to physical dimnensions, the effects on frequency and field distributions of vane movement, tube distortion, individual end tuner movement and vane strapping were determined. Agreement with measured properties is reasonable, and some new insights on RFQ operation have been gained.