PowerPoint Presentation

Magnetic Field Topology about Variously-Shaped ConductorsYannic GagnonDepartment of Physics and Astronomy,University of Hawaii at Manoa

Importance of Magnetic Field TopologyMagnetic Reconnection

Tokamak

Theoretical Considerations

Project Overview

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

AlgorithmBiot-Savart law:

4th Order Runge-Kutta

Field Line Trajectory:

Circular Loop, Field Lines

Circular Loop, Equipotential Surfaces

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

Circular Loop + Long Straight Wire

Trajectory After 300 Seconds

ConclusionsField 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.

Using the Solid Angle to Find

Benefits to using :Computation timeAllows more general conductor shapes

Lambert Equal-Area Projection