A novel rectangular aperture quadrupole electromagnet

An analytical model of a square or a rectangular aperture iron dominated quadrupole electromagnet is presented with a fixed core aperture for any coil size, with a strength ∼70% of hyperbolic iron pole quadrupoles for the same excitation and current density. It is up to four times stronger than the Panofsky quadrupole electromagnet with better field quality for square aperture, same excitation, and low current density with ambient air cooled coils. Similar to the gap tuning in Halbach quadrupoles, the presented model can reduce the first harmonic 12th pole field, by fine-tuning the coil and core geometry with an air gap. For the square aperture Panofsky quadrupole too, a coil design is presented to cancel the 12th pole. For rectangular aperture, up to the aspect ratio of 1:4, the model is 40% stronger but with more octupoles. The presented model is a stronger alternative to the Panofsky quadrupole electromagnet using thick air cooled coils with low current density and compares better with conventional hyperbolic iron pole quadrupoles.