bluemira.magnetostatics.semianalytic_2d
Semi-analytic methods for Bx, Bz, and psi for circular coils of rectangular cross-section.
Functions
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Calculate the Bx and Bz fields from a rectangular cross-section circular |
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Calculate the Bx and Bz fields from a rectangular cross-section circular |
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Calculate the poloidal magnetic flux from a rectangular cross-section circular |
Module Contents
- bluemira.magnetostatics.semianalytic_2d.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.
- Parameters:
xc (float) – Coil x coordinate [m]
zc (float) – Coil z coordinate [m]
x (float | numpy.ndarray) – Calculation x location
z (float | numpy.ndarray) – Calculation z location
d_xc (float) – The half-width of the coil
d_zc (float) – The half-height of the coil
- Returns:
Radial magnetic field response (x, z)
- Return type:
float | numpy.ndarray
Notes
\(B_{x}=\dfrac{\mu_{0}Jx}{2\pi}\sum^{2}_{i=1}(-1)^{i+j}\) \(P_x(R_{i},Z_{j})\)
References
- bluemira.magnetostatics.semianalytic_2d.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.
- Parameters:
xc (float) – Coil x coordinate [m]
zc (float) – Coil z coordinate [m]
x (float | numpy.ndarray) – Calculation x location
z (float | numpy.ndarray) – Calculation z location
d_xc (float) – The half-width of the coil
d_zc (float) – The half-height of the coil
- Returns:
Vertical magnetic field response at (x, z)
- Return type:
float | numpy.ndarray
Notes
\(B_{z}=\dfrac{\mu_{0}Jx}{2\pi}\sum^{2}_{i=1}(-1)^{i+j}\) \(P_z(R_{i},Z_{j})\)
References
- bluemira.magnetostatics.semianalytic_2d.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.
- Parameters:
xc (float) – Coil x coordinate [m]
zc (float) – Coil z coordinate [m]
x (float | numpy.ndarray) – Calculation x location
z (float | numpy.ndarray) – Calculation z location
d_xc (float) – The half-width of the coil
d_zc (float) – The half-height of the coil
- Returns:
Poloidal magnetic flux response at (x, z)
- Return type:
float | numpy.ndarray
Notes
The function returns
\[2 \times 10^{-7} {\frac{1}{4 d_{xc} d_{zc}}} \psi\]The function integrates \(x B_z\) to resolve psi. More analytical approaches are possible and will no doubt be faster.