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Theta Pinch

ElectromagneticFields.ThetaPinch — Module

θ-pinch equilibrium in (x,y,z) coordinates with covariant components of the vector potential given by

\[A (x,y,z) = \frac{B_0}{2} \big( - y , \, x , \, 0 \big)^T\]

resulting in the magnetic field with covariant components

\[B (x,y,z) = \big( 0 , \, 0 , \, B_0 \big)^T .\]

Parameters: B₀: B-field at magnetic axis

source

Constructing the Field

using CairoMakie
using ElectromagneticFields

equ = ThetaPinch.init()
θ-Pinch Equilibrium in (x,y,z) Coordinates with
  B₀ = 1.0

Plotting

The magnetic field is homogeneous and points along $z$, so the two components of the vector potential are linear in $y$ and $x$ respectively:

plot_equilibrium(equ)
Example block output

This is the simplest field in the collection and therefore a good starting point when checking that a new integrator or diagnostic behaves as expected.