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Computation of Electromagnetic Boundary Data from Magnetic Measurements in Accelerator Magnets
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Europe/Zurich
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CERN
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Abstract: Beam-dynamic studies require evaluations of magnetic potentials, or flux densities in the neighbourhood of a reference trajectory of the article beam. Consequently, a suitable representation for the magnetic field has to be found. Most established approaches are based on a two-dimensional expansion of the Laplace equation in polar coordinates, by so-called field harmonics. However, field harmonics are limited to integrated field quantities in circular apertures of straight magnets. More generally, the three dimensional magnetic field can be expressed by boundary data, enclosing an arbitrarily shaped domain of interest [1]. While it is common practice and straight forward to derive such boundary representations from numerical simulations, their extraction from magnetic measurement is still an open topic of research and will be discussed in this presentation. For cylindrical domains, we make use of short rotating coil measurements in order to extract the coefficients of a Bessel-Fourier-Fourier series. Apart from the sensors small longitudinal extension no specific measurement equipment is needed and benefits of classical bucking schemes can be exploited. To treat more general magnet geometries, such as dipoles with a large aspect ratio, or curved magnets, we make use of Kirchhoff’s integral equation and represent the magnetic field by sheets of single and double layer potentials, enclosing the domain of interest. Extracting the boundary potentials from measured voltages yields an inverse problem, which can be solved by Bayesian inversion. In this context we present results obtained from two different sensor systems, recently developed at CERN: A translating induction coil magnetometer and a three axis Hall probe mapper system.
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Jerome Fleiter
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