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.

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.

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)

SphereMagnet#

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

Uniformly magnetized spherical magnet.

Parameters:

position (ArrayLike3, optional) – Center of the sphere [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) – Sphere diameter 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 SphereMagnet
from scipy.spatial.transform import Rotation

magnet = SphereMagnet(
    position=[0.0, 0.0, 0.0],
    orientation=Rotation.from_euler('x', 90, degrees=True),
    diameter=0.01,
    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

TriangleMagnet#

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

Uniformly magnetized triangular magnet.

Parameters:

position (ArrayLike3, optional) – Base position of the triangle [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.
polarization (ArrayLike3, optional) – Remanence polarization vector [Bx, By, Bz] in Tesla. Defaults to [0.0, 0.0, 1.0].
vertices (list, optional) – List of 3 vertices, each a list of 3 floats, in meters. Defaults to [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 0.0]].

Examples

from pymagba.magnets import TriangleMagnet

magnet = TriangleMagnet(
    position=[0.0, 0.0, 0.0],
    polarization=[0.0, 0.0, 1.0],
    vertices=[[0.01, 0.0, 0.0], [0.0, 0.01, 0.0], [0.0, 0.0, 0.0]],
)

TetrahedronMagnet#

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

Uniformly magnetized tetrahedral magnet.

Parameters:

position (ArrayLike3, optional) – Base position of the tetrahedron [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.
polarization (ArrayLike3, optional) – Remanence polarization vector [Bx, By, Bz] in Tesla. Defaults to [0.0, 0.0, 1.0].
vertices (list, optional) – List of 4 vertices, each a list of 3 floats, in meters. Defaults to [[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]].

Examples

from pymagba.magnets import TetrahedronMagnet

magnet = TetrahedronMagnet(
    position=[0.0, 0.0, 0.0],
    polarization=[0.0, 0.0, 1.0],
    vertices=[[0.0, 0.0, 0.0], [0.01, 0.0, 0.0], [0.0, 0.01, 0.0], [0.0, 0.0, 0.01]],
)

MeshMagnet#

class pymagba.magnets.MeshMagnet(position=None, orientation=None, polarization=None, vertices=None, faces=None)[source]#

Uniformly magnetized mesh magnet.

Parameters:

position (ArrayLike3, optional) – Base position of the mesh [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.
polarization (ArrayLike3, optional) – Remanence polarization vector [Bx, By, Bz] in Tesla. Defaults to [0.0, 0.0, 1.0].
vertices (ArrayLike3, optional) – The vertices of the mesh as an Nx3 array. Defaults to empty.
faces (ArrayLike3, optional) – The faces of the mesh as an Mx3 array of indices. Defaults to empty.

Magnets#

Common Interface#

Available Magnets#

CylinderMagnet#

CuboidMagnet#

Dipole#

SourceCollection#

SphereMagnet#

TriangleMagnet#

TetrahedronMagnet#

MeshMagnet#

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