Magnetostatics.jl

A Julia package for computing magnetostatic fields from current sources.

Overview

Magnetostatics.jl provides solvers and analytical models for computing magnetic fields produced by steady-state current distributions.

Methods

Analytical Models

Exact solutions for specific geometries:

HarrisSheet: Harris current sheet model ( $B_{x} (z) = B_{0} \tanh (z / L)$ ).
AsymmetricHarrisSheet: Asymmetric current sheet ( $B_{x} (z) = \frac{B_{1} + B_{2}}{2} + \frac{B_{1} - B_{2}}{2} \tanh (z / L)$ ).
ForceFreeHarrisSheet: Force-free sheet ( $B_{x} (z) = B_{0} \tanh (z / L)$ , $B_{y} (z) = B_{0} sech (z / L)$ ).
BifurcatedHarrisSheet: Double-peaked current sheet ( $B_{x} (z) = \frac{B_{0}}{2} [\tanh ((z - d) / L) + \tanh ((z + d) / L)]$ ).
FadeevIsland: 2D magnetic island equilibrium ( $A_{y} (x, z) = - B_{0} L \ln [\cosh (z / L) + ϵ \cos (x / L_{x})]$ ).
Dipole: Magnetic dipole field.
CurrentLoop: Analytics for circular current loops using elliptic integrals.
getB_mirror: Two-coil magnetic mirror configuration.
getB_bottle: Magnetic bottle configuration (mirror + central coil).
getB_tokamak_coil: Tokamak field from 16 toroidal coils + plasma current.
getB_tokamak_profile: Tokamak field from safety factor $q$ -profile.
getB_zpinch: Z-pinch wire field.

Numerical Solvers

General-purpose solvers for arbitrary geometries:

BiotSavart: Numerical integration of the Biot-Savart law for arbitrary wire geometries.
FFTSolver: Spectral method for computing B from a volumetric current density J on a uniform grid with periodic boundaries.
VectorPotential: Computes the magnetic vector potential A for wires, current loops, and dipoles.
PoissonSolver: Finite-difference Poisson solver (∇²A = −μ₀J) on a Cartesian grid with Dirichlet boundary conditions, supporting anisotropic grid spacing via LinearSolve.jl.

Quick Start

julia

using Magnetostatics
using StaticArrays

# Create a circular current loop and discretize it into wire segments
loop = CurrentLoop(1.0, 1.0, [0, 0, 0], [0, 0, 1])
wire = discretize_loop(loop, 100)

# Compute B at a point using the Biot-Savart solver
B = solve(BiotSavart(), wire, SVector(0.0, 0.0, 0.5))

# Compare with the analytical solution
B_exact = getB_loop(SVector(0.0, 0.0, 0.5), loop)

API Reference

Magnetostatics.jl ​

Overview ​

Methods ​

Analytical Models ​

Numerical Solvers ​

Quick Start ​