Differential Analysis of Magnetic Field Measurements with Applications

This report describes the use of cubic spline fitting to compute, for the median plane z = 0, the vertical magnetic-field component, B(u, w, o) and its first, second, and third partial derivatives from a set of measurements of B at mesh points (ui, wj). The arguments (u, w) may be either rectilinear (x, y) or polar (??, R). The results of the fitting are used for a third-order approximation of the field components Bu, Bw, and Bz at any point (u, w, z) within the domain of measurement for (u, w) and for small z. These field components are used in the equations of motion for tracking charged particles through the magnetic field. In particular, the application of this process to the magnetic field of the Bevatron (Berkeley) is discussed.