bluemira.magnetostatics.biot_savart
===================================

.. py:module:: bluemira.magnetostatics.biot_savart

.. autoapi-nested-parse::

   Biot-Savart filament object



Classes
-------

.. autoapisummary::

   bluemira.magnetostatics.biot_savart.BiotSavartFilament


Module Contents
---------------

.. py:class:: BiotSavartFilament(arrays: bluemira.geometry.coordinates.Coordinates | numpy.typing.NDArray[numpy.float64] | list[bluemira.geometry.coordinates.Coordinates] | list[numpy.typing.NDArray[numpy.float64]], radius: float, current: float = 1.0)

   Bases: :py:obj:`bluemira.magnetostatics.baseclass.CurrentSource`

   .. autoapi-inheritance-diagram:: bluemira.magnetostatics.biot_savart.BiotSavartFilament
      :parts: 1
      :private-bases:


   Class to calculate field and vector potential from an arbitrary filament.

   :param arrays: The arbitrarily shaped closed current Coordinates. Alternatively provide the
                  list of Coordinates objects.
   :param radius: The nominal radius of the coil [m].
   :param current: The current flowing through the filament [A]. Defaults to 1 A to enable
                   current to be optimised separately from the field response.


   .. py:attribute:: _d_l


   .. py:attribute:: _d_l_hat


   .. py:attribute:: _mid_points


   .. py:attribute:: _points


   .. py:attribute:: _arrays


   .. py:attribute:: _radius


   .. py:attribute:: current
      :value: 1.0



   .. py:method:: _check_discretisation(d_l: numpy.typing.NDArray[numpy.float64])
      :staticmethod:


      Check the discretisation of the array.



   .. py:method:: potential(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 vector potential of an arbitrarily shaped Coordinates.

      :param x: The x coordinate(s) of the points at which to calculate the potential
      :param y: The y coordinate(s) of the points at which to calculate the potential
      :param z: The z coordinate(s) of the points at which to calculate the potential

      :returns: The vector potential at the point due to the arbitrarily shaped Coordinates



   .. py:method:: 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 field due to the arbitrarily shaped Coordinates.

      :param x: The x coordinate(s) of the points at which to calculate the field
      :param y: The y coordinate(s) of the points at which to calculate the field
      :param z: The z coordinate(s) of the points at which to calculate the field

      :returns: The field at the point(s) due to the arbitrarily shaped Coordinates

      .. rubric:: Notes

      :math:`\dfrac{\mu_{0}}{4\pi}\oint \dfrac{Idl \times\mathbf{r^{'}}}{|\mathbf{r^{'}}|^{3}}`

      This is the original Biot-Savart equation, without centre-averaged
      smoothing. Do not use for values near the coil current centreline.



   .. py:method:: inductance() -> float

      Calculate the total inductance of the BiotSavartFilament.

      :returns: The total inductance (including self-inductance of reference Coordinates) [H]

      .. rubric:: Notes

      :math:`\dfrac{\mu_{0}}{4\pi}\oint \dfrac{d\mathbf{x_{1}} \cdot d\mathbf{r_{x}}}{|\mathbf{x_{1}}-\mathbf{x_{2}}|}`

      https://arxiv.org/pdf/1204.1486.pdf

      You probably shouldn't use this if you are actually interested in the
      inductance of an arbitrarily shaped Coordinates...



   .. py:method:: rotate(angle: float, axis: str | numpy.ndarray)

      Rotate the CurrentSource about an axis.

      :param angle: The rotation degree [degree]
      :param axis: The axis of rotation



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

      Plot the CurrentSource.

      :param ax: The matplotlib axes to plot on
      :param show_coord_sys: Whether or not to plot the coordinate systems