3D modeling of electromagnetic levitation coils

Electromagnetic levitation (EML) enables the handling of samples in a containerless manner, facilitating more precise measurements or manipulation of materials. Currently, EML coil design is based on two-dimensional (2D) mathematical models combined with empirical data and experience. We propose that employing a truly 3D model enables a more accurate and rational coil design. This approach shows significant differences in magnetic field, and the resulting lift and heating properties, when comparing a 2D and a 3D coil. A 3D coil, resembling the geometry of a 2D coil, requires more current to generate the same lift. Reversing the situation, a 3D coil producing the exact same magnetic field as a 2D coil has a vastly different design. Furthermore, we show that the assumption that the magnetic field is homogeneous in the axial plane within the sample volume is invalid, even for small samples, in the upper and lower regions of the coil. Using a 3D model, we design a coil capable of levitating and melting an iridium sphere with a diameter of 6 mm.