论文标题
用振荡线方法测量加速器磁铁的场质量 - 解决部分微分方程的案例研究
Measuring the Field Quality in Accelerator Magnets with the Oscillating-Wire Method -- a Case Study for Solving Partial Differential Equations
论文作者
论文摘要
单个拉伸线方法通常用于测量加速器磁铁中的磁场强度和磁轴。电线的连接端子处的集成电压是与流离线导线所追踪的表面相关的通量的量度。拉伸线也可以用低于共振频率的交流电流激发。因此，可以通过使用线性振荡幅度，集成场和电流幅度之间的线性关系来测量多极场误差。该技术是解决部分微分方程的一个很好的例子，或更准确地说是一个和二维中的边界价值问题。特别是，加速器磁体孔径中的场受拉普拉斯方程的控制，这导致边界值问题通过确定域中的测量值或域上的线件振荡的测量中的系列特征函数中的系数来解决边界值问题。绷紧弦的振荡是一维内源波方程的一个例子。振荡线系统的计量表征会产生该方法的不确定性（和局限性）的反馈，因为仅考虑了电线运动的线性化方程和磁体的集成场谐波。
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.
