Analytic feedback optimization for dipole fields

It has been shown that the method of using a simple analytic model, such as a Fourier function, within the iterative optimization cycle, for magnetic field configurations which have aperture aspect ratios near unity, (e.g. quadrupoles) is very effective. The desired field configuration is typically reached within two or three iterations. However for magnets with gap aspect ratios far from unity, such as most dipoles, the Fourier function is inappropriate. Here it is shown that a simpler model is effective for dipoles. It assumes that the field is proportional to the gap height. Then the field distribution and the pole profile can be modeled using a polynomial function, where for a uniform field, the terms higher than the first are zero. Several examples are given for different types of dipole field configurations