Generation of uniform magnetic field using a single-layer solenoid with multi-current method

The magnetic field of a single-layer solenoid (length L=1020 mm, average radius R=114.67 mm, pitch p=1.0001 mm and wire diameter d=0.799 mm) with a multi-current method was calculated to improve the uniformity and optimized by using Legendre polynomials. The optimum conditions obtained by the calculations for the uniform magnetic field lead to insensitive magnetic field with respect to the radius variations. Therefore, the uncertainty of the generated magnetic field within ±2 cm from the center of the solenoid amounts to about 1 × 10⁻⁷ normalized by the central magnetic field. The solenoid coil constant was measured to be 1.2548214 mT/A obtained under compensation of the Earth’s magnetic field in 25 °C air.