Development of a magnetic field calculation program for air-core solenoids which can control the precision of a magnetic field

Abstract

A numerical method of magnetic field calculation for the air-core solenoid is presented in this paper. In application of the Biot- Savart law, the magnetic field induced from the source current can be obtained by a double integration ormula. The numerical method named composite Simpson’s rule for the integration is applied to the program and the adaptive quadrature method is used to adjust the step size in the calculation according to the precision we need. When the target point is in the solenoid and the tegrand’s denominator may be zero in the process of calculation, the method still can provide an appropriate result. We have developed a program which calculates the magnetic field with at least 1ppm precision and named it as rzBI() to implement this method. The method has been used in the design of an MRI magnet, and the result show it is very flexible and convenient.