Algorithms for Computing the Magnetic Field, Vector Potential, and Field Derivatives for a Thin Solenoid with Uniform Current Density
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
A numerical algorithm for computing the field components Br and Bz and their r and z derivatives with open boundaries in cylindrical coordinates for radially thin solenoids with uniform current density is described in this note. An algorithm for computing the vector potential Aθ is also described. For the convenience of the reader, derivations of the final expressions from their defining integrals are given in detail, since their derivations are not all easily found in textbooks. Numerical calculations are based on evaluation of complete elliptic integrals using the Bulirsch algorithm cel. The (apparently) new feature of the algorithms described in this note applies to cases where the field point is outside of the bore of the solenoid and the field-point radius approaches the solenoid radius. Since the elliptic integrals of the third kind normally used in computing Bz and Aθ become infinite in this region of parameter space, fields for points with the axial coordinate z outside of the ends of the solenoid and near the solenoid radius are treated by use of elliptic integrals of the third kind of modified argument, derived by use of an addition theorem. Also, the algorithms also avoid the numerical difficulties the textbook solutions have for points near the axis arising from explicit factors of 1/r or 1/r2 in the some of the expressions.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1374295
- Report Number(s):
- LA-UR-17-27024
- Country of Publication:
- United States
- Language:
- English
Similar Records
Algorithm to calculate off-plane magnetic field from an on-plane field map
ZONAL TOROIDAL HARMONIC EXPANSIONS OF EXTERNAL GRAVITATIONAL FIELDS FOR RING-LIKE OBJECTS