Study on Magnetic Field Mapping Method in the Center Volume of the Air-Core Solenoid

Mapping is a useful tool in the magnetic field analysis and design. In some specific research area, such as the nuclear magnetic resonance or the magnetic resonance imaging (MRI), it is important to map the magnetic field in the interesting space with high accuracy and low time consumption. In this paper, a numerical way for mapping the magnetic field in the center volume of an air-core solenoid is presented, based on the solution of the Laplace's equation for the field. Through the mathematical analysis on the mapping calculation, the error of the mapping can be estimated using the condition number of the matrix, which is related by the measurement points and the highest order of the solution of the Laplace's equation. Considering the simplicity and the accuracy, the helical cylindrical line (HCL) method is described to measure the magnetic flux density using one probe. As an example, a practical MRI magnet was mapped by the HCL method. The measurement values of the magnetic flux density are simulated according to the parameters of the MRI magnet. Based on these values, the magnetic flux density in the estimated volume can be obtained through the HCL method. Comparing the measurement value with the mapping result, the method is feasible and convenient to produce satisfactory results in the field mapping. This method will give some convenience and accuracy for mapping the magnetic field in the center volume of the air-core solenoid.