Algorithm to calculate off-plane magnetic field from an on-plane field map
- Brookhaven National Lab. (BNL), Upton, NY (United States)
An algorithm is presented to calculate the field components [Bx(x,y,z), By(x,y,z), Bz(x,y,z)] of the magnetic field at a point (x,y,z) in space, from the knowledge of the components [Bx(x,y = 0,z), By(x,y = 0,z), Bz(x,y = 0,z)] on a ”reference plane”, which is normal to the y-axis at y=0. The algorithm, which is a general one and is not restricted to fields with mid-plane symmetry is based on the Taylor series expansion of the magnetic field components at any point in space in terms of the distance (y) of the point from the reference plane. The coefficients of the Taylor series expansion are expressed in terms of the on-plane field components and their partial derivatives with respect to spatial coordinates (x,z). The field components are usually generated from magnetic field measurements on a rectangular grid on the plane. The required partial derivatives of the field components on the plane can be computed with two methods; numerically, or by fitting a polynomial function to the experimentally measured values of the field components and subsequently take the required partial derivatives of the polynomial function. Each of these two method which calculates the partial derivatives of the field components on the plane, is applied to calculate the off-plane field components of the magnetic field generated by a modified Halbach magnet [1] of inner radius of 4.4 cm and it is found that each method provides accurate results with a relative error <1% deviation from the ”ideal” fields if the y distance of the point from the reference plane is smaller than 2 cm. This algorithm is part of the RAYTRACE computer code [2] and has been applied [3] on a dipole magnet with median plane symmetry.
- Research Organization:
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- DOE Contract Number:
- SC0012704
- OSTI ID:
- 1440354
- Report Number(s):
- C-A/AP/605; BNL-205737-2018-TECH
- Country of Publication:
- United States
- Language:
- English
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