Abstract
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.
Highlights
The magnetic measurement section within the magnet group of CERN’s technology department is responsible for the qualification of all superconducting and normal conducting magnets in CERN’s accelerator complex
To supplement the long rotating-coil magnetometers and stretched-wire systems we have recently developed moving induction-coil arrays, axial and transversal rotating-coil scanners [1], and inductioncoil transducers for solenoidal magnets
Its spectrum will have the shape of a/x function, containing zeros at the frequencies fk = k/ls, for k = {0, 1, ..., K }, where ls is the length of the pulse, i.e., the hard-edge model of the induction coil
Summary
To supplement the long rotating-coil magnetometers and stretched-wire systems (the section’s workhorses for magnetic measurements) we have recently developed moving induction-coil arrays, axial and transversal rotating-coil scanners [1], and inductioncoil transducers for solenoidal magnets. Applications of these tools require, a sophisticated post-processing step based on the regularity conditions of electromagnetic fields. The raw measurement data from the field transducers are induced voltages that are integrated using a digital integrator, triggered by an angular encoder Developing these signals into Fourier series results in convoluted
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