LoopFieldCalc

Compute the magnetic field due to current-carrying loops at arbitrary locations.

Installation

Install via Julia package manager

] add https://github.com/archermarx/LoopFieldCalc.jl.git

Example 1: Field due to a single loop

We define a current loop as follows

using LoopFieldCalc

# Define current loop with radius of 50 cm, current of 1 A, centered at the origin
loop = LoopFieldCalc.CurrentLoop(
  LoopFieldCalc.CartesianPoint(0.0, 0.0, 0.0);    # cartesian coordinates of the loop center
  radius = 0.5,         # radius in meters
  current = 1.0,        # current in Amperes
)

Loop center coordinates can be specified using either cartesian coordinates or cylindrical coordinates.

# Define current loop with radius of 50 cm, current of 1 A, centered at the origin
loop = LoopFieldCalc.CurrentLoop(
  center = LoopFieldCalc.CylindricalPoint(0.0, 0.0, 0.0);    # cartesian coordinates of the loop center
  radius = 0.5,         # radius in meters
  current = 1.0,        # current in Amperes
)

To compute the magnetic field components at a given point, use the field_at_point function. The loop normal vector is assumed to be parallel to the z axis.

# Define the point at which the magnetic field is computed in Cartesian space
point_to_compute = LoopFieldCalc.CartesianPoint(1.0, 1.0, 1.0)

# Compute the field strength, stream function, and scalar potential
Bx, By, Bz, stream_func, scalar_potential = LoopFieldCalc.field_at_point(loop, point_to_compute)

If you want to compute the magnetic field at many points, you can broadcast field_at_point over a Vector of CartesianPoints

# Define equally-spaced points along the z-axis
points = [LoopFieldCalc.CartesianPoint(0.0, 0.0, z) for z in 0.0:0.1:2.0]

# Compute the field at these points
fields = LoopFieldCalc.field_at_point.(loop, points)

If your points form a regularly-spaced grid, you can use the field_on_grid function to compute the magnetic field due to multiple loops at the grid points

# Define grid points along x, y, and z axes. We have a 2D grid of points in the y-z plane.
xs = 0.0:0.0
ys = -1.0:0.01:1.0
zs = -2.0:0.01:2.0

# Define current loops. Here, we only have the single loop, defined above
loops = [loop]

# Compute the magnetic field components, along with magnetic stream function and scalar potential
Bx, By, Bz, streamfunc, potential = LoopFieldCalc.field_on_grid(loops, xs, ys, zs)

You can write output of this function to a Tecplot-compatible ASCII data format

LoopFieldCalc.write_field("examples/example_1.dat", ys, zs, By[1, :, :], Bz[1, :, :])

We can visualize this in Tecplot:

Example 2: 2D magnetic field due to offset concentric coils

This example computes the field generated by the magnetic coil configuration below

using LoopFieldCalc

# Define grid on which we compute magnetic field strength.
# This is a 2D grid in the y-z plane
xs = 0.0:0.0
ys = -0.4:0.005:0.4
zs = -0.3:0.005:0.3

# Define number of wire turns per coil
nturns = 10

# Define geometry of inner coil
inner_coil_radius = 0.1
inner_coil_width = 0.15
inner_coil_offset = -0.1
inner_coil_current = 1.0

# Generate loops for inner coil
inner_coil = [
    LoopFieldCalc.CurrentLoop(
        LoopFieldCalc.CylindricalPoint(inner_coil_offset + z, 0.0, 0.0)
        radius = inner_coil_radius,
        current = inner_coil_current / nturns,
    )
    for z in LinRange(0.0, inner_coil_width, nturns)
]

# Define geometry for outer coil
outer_coil_radius = 0.25
outer_coil_width = 0.15
outer_coil_offset = -0.15
outer_coil_current = 0.3 * inner_coil_current

# Generate loops for outer coil
outer_coil = [
    LoopFieldCalc.CurrentLoop(
        LoopFieldCalc.CylindricalPoint(outer_coil_offset + z, 0.0, 0.0)
        radius = outer_coil_radius,
        current = outer_coil_current / nturns,
    )
    for z in LinRange(0.0, outer_coil_width, nturns)
]

# Combine inner and outer coil loops into a single vector and compute field
loops = [outer_coil; inner_coil]
Bx, By, Bz, streamfunc, potential = LoopFieldCalc.field_on_grid(loops, xs, ys, zs)

# Write output. By reversing z and y and transposing the magnetic field matrices, we
# can rotate the output so that the loop axis is aligned with the x axis
LoopFieldCalc.write_field("examples/example_2.dat", zs, ys, Bz[1, :, :]', By[1, :, :]')

The result (visualized in Tecplot) is below