Challenges in extracting pseudo-multipoles from magnetic measurements

Extracting the coefficients of Fourier–Bessel series, known as pseudo-multipoles or generalized gradients, from magnetic measurements of accelerator magnets involves technical and mathematical challenges. First, a novel design of a short, rotating-coil magnetometer is required that does not intercept any axial field component of the magnet. Moreover, displacing short magnetometers, step-by-step along the magnet axis, yields a convolution of the local multipole field errors and the sensitivity (test function) of the induction coil. The deconvolution must then contend with the limited signal-to-noise ratio of the measured quantities, which are integrated voltages corresponding to spatial flux distributions. Finally, the compensation schemes, as implemented on long coils and based on scaling laws derived for the integrated field harmonics, cannot be applied to short magnetometers intercepting only a local field distribution. All this requires careful design of experiment to derive the optimal length of the induction coil, the step-size of the scan, and the highest order of pseudo-multipoles in the field reconstruction. This paper presents the theory of the measurement method, the data acquisition and deconvolution, and the design and production of a saddle-shaped, rotating-coil magnetometer.