Magnets#

Common Interface#

All magnet types in PyMagba share a common interface for computing magnetic fields and geometric properties.

property position: ArrayLike3

Position of the object [x, y, z] in meters.

property orientation: scipy.spatial.transform.Rotation

Orientation as a scipy.spatial.transform.Rotation object.

translate(translation)

Translate the object by a displacement vector.

Parameters:

translation (ArrayLike3) – Displacement [dx, dy, dz] in meters.

rotate(rot)

Rotate the object about its own origin.

Parameters:

rot (Rotation | ArrayLike4) – Rotation to apply. Can be a scipy.spatial.transform.Rotation object or a unit quaternion as a list.

rotate_anchor(rot, anchor)

Rotate the object about an arbitrary anchor point.

Parameters:

  • rot (Rotation | ArrayLike4) – Rotation to apply.

  • anchor (ArrayLike3) – Anchor point [x, y, z] in meters about which to rotate.

compute_B(points)

Compute the magnetic flux density B at a batch of observer points.

Parameters:

points (numpy.ndarray) – Array of shape (N, 3) containing the observer positions [x, y, z] in meters.

Returns:

Array of shape (N, 3) with the [Bx, By, Bz] field vectors in Tesla at each observer point.

Return type:

numpy.ndarray

Available Magnets#

CylinderMagnet#

class pymagba.magnets.CylinderMagnet(position=None, orientation=None, diameter=1.0, height=1.0, polarization=None)[source]#

Uniformly magnetized cylindrical magnet.

All dimensions are in SI units (meters, Tesla).

Parameters:

  • position (ArrayLike3, optional) – Center of the cylinder [x, y, z] in meters. Defaults to [0.0, 0.0, 0.0].

  • orientation (PyRotation, optional) – Orientation as a unit quaternion [x, y, z, w] or a scipy.spatial.transform.Rotation object. Defaults to identity.

  • diameter (float, optional) – Cylinder diameter in meters. Must be positive. Defaults to 1.0.

  • height (float, optional) – Cylinder height in meters. Must be positive. Defaults to 1.0.

  • polarization (ArrayLike3, optional) – Remanence polarization vector [Bx, By, Bz] in Tesla. Defaults to [0.0, 0.0, 0.0].

Examples

from pymagba.magnets import CylinderMagnet
from scipy.spatial.transform import Rotation

magnet = CylinderMagnet(
    position=[0.0, 0.0, 0.0],
    orientation=Rotation.from_euler('x', 90, degrees=True),
    diameter=0.01,
    height=0.02,
    polarization=[0.0, 0.0, 1.0],
)

References

Caciagli, Alessio, et al. “Exact Expression for the Magnetic Field of a Finite Cylinder with Arbitrary Uniform Magnetization.” Journal of Magnetism and Magnetic Materials 456 (2018): 423-432. https://doi.org/10.1016/j.jmmm.2018.02.003

Derby, Norman, and Stanislaw Olbert. “Cylindrical Magnets and Ideal Solenoids.” American Journal of Physics 78, no. 3 (2010): 229-235. https://doi.org/10.1119/1.3256157

CuboidMagnet#

class pymagba.magnets.CuboidMagnet(position=None, orientation=None, dimensions=None, polarization=None)[source]#

Uniformly magnetized cuboid magnet.

All dimensions are in SI units (meters, Tesla).

Parameters:

  • position (ArrayLike3, optional) – Center of the cuboid [x, y, z] in meters. Defaults to [0.0, 0.0, 0.0].

  • orientation (PyRotation, optional) – Orientation as a unit quaternion [x, y, z, w] or a scipy.spatial.transform.Rotation object. Defaults to identity.

  • dimensions (ArrayLike3, optional) – Side lengths [dx, dy, dz] in meters. Defaults to [1.0, 1.0, 1.0].

  • polarization (ArrayLike3, optional) – Remanence polarization vector [Bx, By, Bz] in Tesla. Defaults to [0.0, 0.0, 0.0].

Examples

from pymagba.magnets import CuboidMagnet
from scipy.spatial.transform import Rotation

magnet = CuboidMagnet(
    position=[0.0, 0.0, 0.0],
    orientation=Rotation.from_euler('z', 45, degrees=True),
    dimensions=[0.01, 0.01, 0.02],
    polarization=[0.0, 0.0, 1.0],
)

References

Ortner, Michael, and Lucas Gabriel Coliado Bandeira. “Magpylib: A Free Python Package for Magnetic Field Computation.” SoftwareX 11 (2020): 100466. https://doi.org/10.1016/j.softx.2020.100466

Dipole#

class pymagba.magnets.Dipole(position=None, orientation=None, moment=None)[source]#

Magnetic dipole source.

Models a point magnetic dipole - a useful approximation for small magnets at distances much greater than their physical size.

Parameters:

  • position (ArrayLike3, optional) – Position of the dipole [x, y, z] in meters. Defaults to [0.0, 0.0, 0.0].

  • orientation (PyRotation, optional) – Orientation as a unit quaternion [x, y, z, w] or a scipy.spatial.transform.Rotation object. Defaults to identity.

  • moment (ArrayLike3, optional) – Magnetic dipole moment vector [mx, my, mz] in A·m². Defaults to [0.0, 0.0, 0.0].

Examples

from pymagba.magnets import Dipole

dipole = Dipole(
    position=[0.0, 0.0, 0.0],
    moment=[0.0, 0.0, 1.0],
)

References

Ortner, Michael, and Lucas Gabriel Coliado Bandeira. “Magpylib: A Free Python Package for Magnetic Field Computation.” SoftwareX 11 (2020): 100466. https://doi.org/10.1016/j.softx.2020.100466

SourceCollection#

class pymagba.magnets.SourceCollection(sources=None, position=None, orientation=None)[source]#

A group of magnetic sources that can be transformed and queried as a unit.

SourceCollection wraps a SourceAssembly from Magba, combining multiple magnetic sources (CylinderMagnet, CuboidMagnet, or Dipole) into a single object with its own pose. Transformations applied to the collection move all child sources relative to the collection’s reference frame.

Parameters:

sources (list[Source], optional) – Iterable of magnetic sources to include. Each element must be a CylinderMagnet, CuboidMagnet, or Dipole. Defaults to None.

Examples

from pymagba.magnets import CylinderMagnet, CuboidMagnet, Dipole, SourceCollection
import numpy as np

m1 = CylinderMagnet(
    position=[0.005, 0.0, 0.0],
    diameter=0.01,
    height=0.02,
    polarization=[0.0, 0.0, 1.0],
)
m2 = CuboidMagnet(
    position=[-0.005, 0.0, 0.0],
    dimensions=[0.01, 0.01, 0.01],
    polarization=[0.0, 0.0, -1.0],
)
collection = SourceCollection([m1, m2])
points = np.array([[0.0, 0.0, 0.05]])
B = collection.compute_B(points)  # shape (1, 3)
B = collection.compute_B(points)  # shape (1, 3)