Shim coil design by Fourier synthesis

Area of Science:

• Physics
• Electromagnetism
• Applied Physics

Background:

• Generating precise spherically harmonic fields is crucial for various scientific and technological applications.
• Existing methods for creating these fields can be complex and difficult to fabricate accurately, especially for higher orders and degrees.

Purpose of the Study:

• To propose a new, simplified method for generating spherically harmonic fields.
• To establish a direct relationship between azimuthal current spatial frequency and the resulting magnetic field's spherical harmonic degree.
• To demonstrate a design that facilitates easier fabrication and potentially more accurate field generation.

Main Methods:

• The method involves applying sampled sinusoidal azimuthal currents to conducting arcs on an axially aligned cylinder.
• The spatial frequency of the current waveform directly corresponds to the desired degree of the generated spherically harmonic axial magnetic field.
• Repeating this structure at different axial positions with varied current amplitudes allows for a combination of harmonics.

Main Results:

• Analytical calculations demonstrate the feasibility of the proposed method.
• The design allows for the generation of mixed harmonics up to a maximum degree determined by the number of axial positions.
• The complexity is shifted from construction to external electronics, with potential for easy fabrication using foil or ribbon cable.

Conclusions:

• The proposed technique offers a promising approach for more accurate generation of higher-order spherically harmonic fields.
• The design simplifies fabrication by transferring complexity to exterior electronics.
• A conceptual high-efficiency current driver is also mentioned, further enhancing the method's potential.