Magnetic field uniformity of the practical tri-axial Helmholtz coils systems

Abstract

In this paper, effects of the assembly misalignments and the manufacturing mismatches on the magnetic field uniformity of a practical tri-axial Helmholtz coils system have been modeled mathematically. These undesired effects regularly occur in any practical tri-axial Helmholtz coils system. To confirm the mathematical calculations, a tri-axial Helmholtz coils system has been constructed and the uniformity of its magnetic field has been measured under different conditions. The experimental results are in good agreement with the mathematical analyses.

Parametric design of tri-axial nested Helmholtz coils

“…for c ∈ {2, 3}. The nominal coil width W c can then be computed using (15) and the resulting outer coil width W oc and gap size G c can be calculated with (12) and (13), respectively. This process is used to solve for all of the parameters for the middle Helmholtz coil (c = 2) and then repeated for the outer coil (c = 3).…”

“…Prior work has characterized how manufacturing and assembly errors affect the uniformity of the field in tri-axial coils. 13 There has been a significant recent interest in the use of tri-axial Helmholtz coils for the generation of magnetic fields for the control of "microrobots," both for applications under the guidance of an optical microscope, 11 as well as for applications in the human body. 12 In each of the various projects that have used tri-axial Helmholtz coils, the respective research groups have redesigned the coils, starting from the basic spacing definition, such that their coils are customized to their specific needs in terms of magnitude of the field that can be generated, access to the central workspace (e.g., to place samples), access for imaging the central workspace (e.g., for a microscope lens), the current amplifiers required, and the size and cost of the final system.…”

Optimization of a Coil System for Generating Uniform Magnetic Fields inside a Cubic Magnetic Shield

“…The magnetic flux density that is generated by Merritt coil inside the cubic shield are simulated in COMSOL (COMSOL Multiphysics, Stockholm, Sweden), and compared with the flux density generated by Merritt coil without any shield, as shown in Figure 1. B c is the flux density at the center, B(x, y, z) is the flux density at (x, y, z) point, the practical deviation rate of flux density between (x, y, z) and the center point is defined as Equation (1), which is a conventional index in practice [18]. It can be seen that the magnetic field uniformity generated by Merritt coil inside the cubic shield is very significantly degraded.…”

Magnetic Field of Coaxial Square Coils Enclosed With High-Permeability Material

“…For 3, da the enclosure is not close enough to the coils and its influence is weak. However, for 3, da the presence of the enclosure causes the increase of the height of the volume of the uniform field. This increase can be explained through the contribution of the four images in the first layer that are coaxial with the original loops and having the current in the same direction as in the original loops.…”

“…According to (7),  depends on , da , xa and . za Plots of the contour lines of absolute value of  for Helmholtz coils with enclosure, [2,3]…”