An analytical solution for the electrical properties of a Radio Frequency Quadrupole (RFQ) with simple vanes

Although the SUPERFISH program is used for calculating the design parameters of an radio frequency quadrupole (RFQ) structure with complex vanes, an analytical solution for electrical properties of an RFQ with simple vanes provides insight into the parametric behavior of these more complicated resonators. The fields in an inclined plane wave guide with proper boundary conditions match those in one quadrant of an RFQ. The principle of duality is used to exploit the solutions to a radial transmission line in solving the field equations. Calculated are the frequency equation, frequency sensitivity factors (5), electric field (E), magnetic field (H), stored energy (U), power dissipation (P), and quality factor (Q).