Magnetic Field Simulation of Serpentine Quadrupole Coil

Based on the line current approximation, a semi-analytical method for 3D magnetic field computation of the serpentine quadrupole coil is presented. Using the Biot-Savart law, the integral field of a line current with finite length located at an arbitrary position is derived. By dividing the coil into many line current segments, and summing up the integral field of each segment, the total integral field strength and field quality are obtained. The traditional line current theory is extended to 3D. This method is applied to an example of BEPCII serpentine quadrupole coil, and the magnetic field calculation results are in good agreement with the results of OPERA-3D. Harmonic correction is introduced by changing the coil geometry to compensate the unwanted multipole field. In addition, the influence of the increased reference radius on the computation accuracy of higher order multipole field is presented.