Gradient Hypomagnetic Fields Modeling Based on Square Helmholtz Coils

Helmholtz coils are widely used to generate controlled magnetic fields in magnetometer calibration, electromagnetic system testing, material property research experiments, and biotesting. Existing limitations in the homogeneity region of magnetic fields create difficulties in implementing experimental studies. Using multilevel generators with adjustable currents in coils allows generating gradient fields, which speeds up biotesting and increases its accuracy. This work is devoted to modeling gradient hypomagnetic fields using square Helmholtz coils. In COMSOL Multiphysics 6.1, a finite element model has been developed for analyzing magnetic fields generated by DC coils interacting with the Earth’s external magnetic field. The patterns of field formation for different coil orientations relative to the declination and inclination angles of the magnetic field vector have been studied. The study of the formation patterns of gradient hypomagnetic fields in the space between square Helmholtz coils placed in the external magnetic field of the Earth was carried out using finite element modeling in the COMSOL Multiphysics software environment. The effect of currents in the coils on the distribution of the hypomagnetic field intensity in space and along the axis was investigated. Dependences of the informative parameters of the gradient curve of the hypomagnetic field intensity on the value of currents in the coils were obtained, allowing one to construct control functions for currents in square Helmholtz coils to form multi-level fields with an adjustable attenuation coefficient. The results of numerical modeling performed for cases of uniform and gradient distribution of magnetic fields were experimentally confirmed. The conducted full-scale experiments made it possible to compare the calculated data with actual measurements, which indicates a high reliability of the developed model.