Development of the technique for improving the structure of a magnetic field in the aperture of a quadrupole electromagnet with a superconducting winding

It is of practical interest to construct models for a magnetic field of the quadrupole electromagnet that would make it possible to adjust the medium-integral coefficients of magnetic flux density by changing the geometrical parameters of magnet design. The aim of this work is to develop a method for the optimization of a quadrupole electromagnet's structure with a superconducting winding based on the criterion for a minimum of magnitudes of the non-quadrupole medium-integral coefficients of magnetic flux density in the aperture. Practical application of the technique makes it possible to optimize the design of a quadrupole electromagnet to minimize coefficients of magnetic flux density, medium-integral in length, based on the calculation of geometrical parameters for the yoke and winding. The derived analytical expressions to calculate the minimized magnetic flux density coefficients, medium-integral in length, generated inside the aperture of a quadrupole electromagnet, are based on their proportionality to the contributions from the current winding and the dependence on its position relative to the yoke. The relationships between the coefficients of magnetic flux density, medium-integral in length, and design parameters, established empirically, underlie the procedure for practical application of the technique for improving the uniformity of a gradient of magnetic flux density of a quadrupole electromagnet. The expressions obtained allow the calculation of the required correction of geometrical parameters in the already existing structure in order to optimize magnetic field inside the aperture of quadrupole electromagnets based on the assigned medium-integral coefficients.The paper reports results of the optimization of design of a magnetoactive part of the triplet of quadrupole electromagnets at an accelerator complex for the project NICA. Optimization was carried out based on the proposed technique with the minimization to a level of 10-5 of the non-quadrupole medium-integral coefficients for the transverse components of magnetic flux density generated in the aperture of an electromagnet with a superconducting winding