Analytical Description of Two-Dimensional Magnetic Arrays Suitable for Biomedical Applications

Two-dimensional magnetic arrays are used to generate a magnetic field that pervades a layer of volume above the array's surface, often creating regions of high magnetic flux density gradients. We have recently employed an array with equally oriented magnetic moments of individual elements in several biomedical experiments. We have chosen this type of array because of the slowly decreasing magnetic field it produces, which extends far from the array's surface and permeates the experimental volume. In order to fully define experimental conditions related to the applied magnetic field, we derive exact closed-form expressions for the magnetic flux density. Based on these analytical expressions and exploiting the array periodicity, a method is proposed for the approximate assessment of the main magnetic field parameters of interest-mean magnetic flux density and mean gradient of its component perpendicular to the array's surface. The obtained approximate assessment can further serve as a tool for the design of arrays with the desired mean field parameters. All the results are verified and validated by comparison with the finite element modeling as well as measurements.