Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measuring the Field Quality in Accelerator Magnets with the
  Oscillating-Wire Method -- a Case Study for Solving Partial Differential
  Equations   The single stretched-wire method is commonly used to measure the magnetic
field strength and magnetic axis in an accelerator magnet. The integrated
voltage at the connection terminals of the wire is a measure for the flux
linked with the surface traced out by the displaced wire. The stretched wire
can also be excited with an alternating current well below the resonance
frequency. It is thus possible to measure multipole field errors by making use
of the linear relationship between the wire-oscillation amplitude, integrated
field, and current amplitude. This technique is a good example for solving
partial differential equations, or more precisely, boundary value problems in
one and two dimensions. In particular, the field in the aperture of accelerator
magnets is governed by the Laplace equation, which leads to a boundary-value
problem that is solved by determining the coefficients in the series of
eigenfunctions from measurements of the field components or wire-oscillation
amplitudes on the domain boundary. The oscillation of the taut string is an
example of a one-dimensional, in-homogenous wave equation. The metrological
characterization of the oscillating-wire system yield the feedback on the
uncertainties (and limitations) of the method, as only the linearized equations
of the wire motion and the integrated field harmonics of the magnet are
considered.

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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: math
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int