This document discusses an algorithm to evaluate magnetic field lines using the Biot-Savart law and 4th order Runge-Kutta integration. It applies the algorithm to a simple circular loop example, showing color-coded equipotential surfaces, and notes that field lines in this scenario do not close or stretch to infinity, instead having infinite densities near the loop even though the field intensity is finite. Benefits of this algorithm are listed as reduced computation time and the ability to model more complex conductor shapes.

1. Yannic Gagnon
Department of Physics and Astronomy,
University of Hawaii at Manoa

2.  Magnetic Reconnection
 Tokamak
 Theoretical Considerations

3.  Derive algorithm to enable evaluation of field
lines
 Applications of algorithm in a simple example
 Applications of algorithm in a multiple-
conductor scenario
 Description of resulting field line topology

4.  Biot-Savart law:
 4th Order Runge-Kutta
 Field Line Trajectory:

6. Color-coded equipotential surfaces corresponding to Φ = 1, 2, 3, 4, and 5

9.  Field lines do not close and do not stretch to
infinity (in circular loop).
 Volumes close to the circular loop contain
infinite field-line densities, even though the
field intensity is finite. Thus, the density of
field lines do not necessarily indicate the
magnetic field intensity.

10. 
 Benefits to using :
 Computation time
 Allows more general
conductor shapes