Dipole

ElectromagneticFields.Dipole — Module

Dipole magnetic field in (x,y,z) coordinates Based on Xinjie Li, Ruili Zhang, and Jian Liu, Symplectic Runge-Kutta methods for the guiding center dynamics.

The covariant components of the vector potential are given by

\[A (x,y,z) = \frac{B₀}{r^3} \big( y , \, -x , \, 0 \big)^T ,\]

resulting in the magnetic field with covariant components

\[B (x,y,z) = - \frac{B₀}{r^5} \big( 3xz, \, 3yz, \, 2z^2 - x^2 - y^2 \big)^T .\]

source

Constructing the Field

The only parameter is the field strength $B_0$, which defaults to 1000.0:

using CairoMakie
using ElectromagneticFields

equ = Dipole.init()

Dipole Field in (x,y,z) Coordinates

The vector potential circles the $z$ axis with a magnitude $B_0 \, \rho / r^3$, where $\rho$ is the distance from the axis and $r$ the distance from the origin. The plot shows its two non-vanishing components in the plane $z = 1$:

plot_equilibrium(equ)

Dipole

Constructing the Field

Plotting