bluemira.magnetostatics.semianalytic_2d
=======================================

.. py:module:: bluemira.magnetostatics.semianalytic_2d

.. autoapi-nested-parse::

   Semi-analytic methods for Bx, Bz, and psi for circular coils of rectangular
   cross-section.



Functions
---------

.. autoapisummary::

   bluemira.magnetostatics.semianalytic_2d.semianalytic_Bx
   bluemira.magnetostatics.semianalytic_2d.semianalytic_Bz
   bluemira.magnetostatics.semianalytic_2d.semianalytic_psi


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

.. py:function:: semianalytic_Bx(xc: float, zc: float, x: float | numpy.ndarray, z: float | numpy.ndarray, d_xc: float, d_zc: float) -> float | numpy.ndarray

   Calculate the Bx and Bz fields from a rectangular cross-section circular
   coil with a unit current using a semi-analytic reduction of the Biot-Savart
   law.

   :param xc: Coil x coordinate [m]
   :param zc: Coil z coordinate [m]
   :param x: Calculation x location
   :param z: Calculation z location
   :param d_xc: The half-width of the coil
   :param d_zc: The half-height of the coil

   :returns: Radial magnetic field response (x, z)

   .. rubric:: Notes

   :math:`B_{x}=\dfrac{\mu_{0}Jx}{2\pi}\sum^{2}_{i=1}(-1)^{i+j}`
   :math:`P_x(R_{i},Z_{j})`

   .. rubric:: References

   .. doi:: 10.1109/TMAG.2011.2167981


.. py:function:: semianalytic_Bz(xc: float, zc: float, x: float | numpy.ndarray, z: float | numpy.ndarray, d_xc: float, d_zc: float) -> float | numpy.ndarray

   Calculate the Bx and Bz fields from a rectangular cross-section circular
   coil with a unit current using a semi-analytic reduction of the Biot-Savart
   law.

   :param xc: Coil x coordinate [m]
   :param zc: Coil z coordinate [m]
   :param x: Calculation x location
   :param z: Calculation z location
   :param d_xc: The half-width of the coil
   :param d_zc: The half-height of the coil

   :returns: Vertical magnetic field response at (x, z)

   .. rubric:: Notes

   :math:`B_{z}=\dfrac{\mu_{0}Jx}{2\pi}\sum^{2}_{i=1}(-1)^{i+j}`
   :math:`P_z(R_{i},Z_{j})`

   .. rubric:: References

   .. doi:: 10.1109/TMAG.2011.2167981


.. py:function:: semianalytic_psi(xc: float, zc: float, x: float | numpy.ndarray, z: float | numpy.ndarray, d_xc: float, d_zc: float) -> float | numpy.ndarray

   Calculate the poloidal magnetic flux from a rectangular cross-section circular
   coil with a unit current using a semi-analytic reduction of the Biot-Savart
   law.

   :param xc: Coil x coordinate [m]
   :param zc: Coil z coordinate [m]
   :param x: Calculation x location
   :param z: Calculation z location
   :param d_xc: The half-width of the coil
   :param d_zc: The half-height of the coil

   :returns: Poloidal magnetic flux response at (x, z)

   .. rubric:: Notes

   The function returns

   .. math::
       2 \times 10^{-7} {\frac{1}{4 d_{xc} d_{zc}}} \psi

   The function integrates :math:`x B_z` to resolve psi. More analytical
   approaches are possible and will no doubt be faster.