Divisionally analytical reconstruction of the magnetic field around an electromagnetic velocity probe

Abstract

Determination of the magnetic field around an electromagnetic velocity probe is a key work for the dry calibration of the probe. In the paper, a novel divisionally analytical reconstruction approach to determine the magnetic field is introduced. It is especially suitable to be used in the dry calibration due to following advantages: no numerous measurements needed, unnecessary to know the inner magnetic exciting structure of the probe, high accuracy and convenient for further calculations. It is a measurement and calculation joint approach, in which the magnetic field is calculated from the measured boundary conditions through solving a Laplace’s equation of magnetic scalar potential. To obtain an analytical solution of the Laplace’s equation, the complex calculation geometry around the probe is divided into two simple ones using an auxiliary surface, and then the Laplace’s equation in the each generated geometry is analytically solved through a method of separation of variables. The divisionally analytical solution is pre-requisite since a pure analytical solution can bring convenience for further calculations in the dry calibration and such a solution is still lacked due to the complexity of the calculation geometry. A magnetic scanning device used to measure the distributions of the normal component of magnetic field on the surface of probe and the auxiliary surface is also introduced. The measured data provide the required boundary conditions for the determination of the magnetic field. Finally, the novel approach is validated through reconstructing the magnetic field around an actual electromagnetic velocity probe and comparing the results with the experimentally measured data.