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The single stretched-wire method is commonly used to measure the magneticfield strength and magnetic axis in an accelerator magnet. The integratedvoltage at the connection terminals of the wire is a measure for the fluxlinked with the surface traced out by the displaced wire. The stretched wirecan also be excited with an alternating current well below the resonancefrequency. It is thus possible to measure multipole field errors by making useof the linear relationship between the wire-oscillation amplitude, integratedfield, and current amplitude. This technique is a good example for solvingpartial differential equations, or more precisely, boundary value problems inone and two dimensions. In particular, the field in the aperture of acceleratormagnets is governed by the Laplace equation, which leads to a boundary-valueproblem that is solved by determining the coefficients in the series ofeigenfunctions from measurements of the field components or wire-oscillationamplitudes on the domain boundary. The oscillation of the taut string is anexample of a one-dimensional, in-homogenous wave equation. The metrologicalcharacterization of the oscillating-wire system yield the feedback on theuncertainties (and limitations) of the method, as only the linearized equationsof the wire motion and the integrated field harmonics of the magnet areconsidered.

Measuring the Field Quality in Accelerator Magnets with the Oscillating-Wire Method -- a Case Study for Solving Partial Differential Equations