bluemira.magnetostatics.circular_arc

Analytical expressions for the field due to a circular current arc of rectangular cross-section, following equations as described in:

DOI: 10.1109/TMAG.1985.1064259

Classes

CircularArcCurrentSource

3-D circular arc prism current source with a rectangular cross-section and

Module Contents

class bluemira.magnetostatics.circular_arc.CircularArcCurrentSource(origin: numpy.typing.NDArray[numpy.float64], ds: numpy.typing.NDArray[numpy.float64], normal: numpy.typing.NDArray[numpy.float64], t_vec: numpy.typing.NDArray[numpy.float64], breadth: float, depth: float, radius: float, dtheta: float, current: float)

Bases: bluemira.magnetostatics.baseclass.CrossSectionCurrentSource

Inheritance diagram of bluemira.magnetostatics.circular_arc.CircularArcCurrentSource

3-D circular arc prism current source with a rectangular cross-section and uniform current distribution.

Parameters:

  • origin (numpy.typing.NDArray[numpy.float64]) – The origin of the current source in global coordinates [m]

  • ds (numpy.typing.NDArray[numpy.float64]) – The direction vector of the current source in global coordinates [m]

  • normal (numpy.typing.NDArray[numpy.float64]) – The normalised normal vector of the current source in global coordinates [m]

  • t_vec (numpy.typing.NDArray[numpy.float64]) – The normalised tangent vector of the current source in global coordinates [m]

  • breadth (float) – The breadth of the current source (half-width) [m]

  • depth (float) – The depth of the current source (half-height) [m]

  • radius (float) – The radius of the circular arc from the origin [m]

  • dtheta (float) – The azimuthal width of the arc [°]

  • current (float) – The current flowing through the source [A]

Notes

The origin is at the centre of the circular arc, with the ds vector pointing towards the start of the circular arc.

Cylindrical coordinates are used for calculations under the hood.

_origin
_breadth
_depth
_length
_radius
_dtheta
_rho
_dcm
_points
property radius: float

Get the radius of the CircularArcCurrentSource

Returns:

Radius of the CircularArcCurrentSource

Return type:

float

property breadth: float

Get the breadth of the CircularArcCurrentSource.

Returns:

Breadth of the CircularArcCurrentSource

Return type:

float

_update_r1r2()

Update

static _local_to_cylindrical(point: numpy.typing.NDArray[numpy.float64]) → numpy.typing.NDArray[numpy.float64]

Convert from local to cylindrical coordinates.

Returns:

Cylindrical coordinates of point.

Parameters:

point (numpy.typing.NDArray[numpy.float64])

Return type:

numpy.typing.NDArray[numpy.float64]

_cylindrical_to_working(zp: float) → tuple[float, float, float, float]

Convert from local cylindrical coordinates to working coordinates.

Returns:

r +- breadth and z +- depth.

Parameters:

zp (float)

Return type:

tuple[float, float, float, float]

_BxByBz(rp: float, tp: float, zp: float) → numpy.typing.NDArray[numpy.float64]

Calculate the field at a point in local coordinates.

Returns:

(Bx, By, Bz) at a point

Parameters:

  • rp (float)

  • tp (float)

  • zp (float)

Return type:

numpy.typing.NDArray[numpy.float64]

Note

By set to 0.

field(x: float | numpy.typing.NDArray[numpy.float64], y: float | numpy.typing.NDArray[numpy.float64], z: float | numpy.typing.NDArray[numpy.float64]) → numpy.typing.NDArray[numpy.float64]

Calculate the magnetic field at a point due to the current source.

Parameters:

  • x (float | numpy.typing.NDArray[numpy.float64]) – The x coordinate(s) of the points at which to calculate the field

  • y (float | numpy.typing.NDArray[numpy.float64]) – The y coordinate(s) of the points at which to calculate the field

  • z (float | numpy.typing.NDArray[numpy.float64]) – The z coordinate(s) of the points at which to calculate the field

Returns:

The magnetic field vector {Bx, By, Bz} in [T]

Return type:

numpy.typing.NDArray[numpy.float64]

_calculate_points() → numpy.typing.NDArray[numpy.float64]

Calculate extrema points of the current source for plotting and debugging.

Returns:

extrema points

Return type:

numpy.typing.NDArray[numpy.float64]

plot(ax: matplotlib.pyplot.Axes | None = None, *, show_coord_sys: bool = False)

Plot the CircularArcCurrentSource.

Parameters:

  • ax (Union[None, Axes]) – The matplotlib axes to plot on

  • show_coord_sys (bool) – Whether or not to plot the coordinate systems