bluemira.equilibria.coils._tools

Tools for Coilgroups

Functions

make_mutual_inductance_matrix(→ numpy.ndarray)

Calculate the mutual inductance matrix of a coilset.

_get_symmetric_coils(...)

Coilset symmetry utility

check_coilset_symmetric(→ bool)

Check whether or not a CoilSet is purely symmetric about z=0.

get_max_current(→ numpy.float64 | numpy.ndarray)

Get the maximum current in a rectangular coil cross-sectional area

rename_coilset(coilset)

Rename the coils.

Module Contents

bluemira.equilibria.coils._tools.make_mutual_inductance_matrix(coilset: bluemira.equilibria.coils.CoilSet, *, square_coil: bool = False) → numpy.ndarray

Calculate the mutual inductance matrix of a coilset.

Parameters:

  • coilset (bluemira.equilibria.coils.CoilSet) – Coilset for which to calculate the mutual inductance matrix

  • square_coil (bool) – Whether or not to use a square coil approximation for the self-inductance diagonal terms. Defaults to a elliptical integral of a circular cross-section coil.

Returns:

The symmetric mutual inductance matrix [H]

Return type:

numpy.ndarray

Notes

Multi-filament coil formulation. The mutual inductance between two coils is calculated based on the number of filaments in each coil (numerical discretisation, which is then normalised). The number of turns in each coil determine the actual multiplier of the mutual inductance.

  • Off-diagonal terms (\(i \neq j\)):

    \[M_{ij} = n_i n_j \sum_{k=0, m=0}^{n_k, n_m} G(x_{i,n}, z_{i,n}, x_{j,m}, z_{j,m})\]

    where \(G\) is the Green’s function for mutual inductance.

  • Diagonal terms (\(i = j\)):

    \[M_{ii} = n_i^2 L_i\]

    with \(L_i\) as the self-inductance using elliptic integrals.

bluemira.equilibria.coils._tools._get_symmetric_coils(coilset: bluemira.equilibria.coils.CoilSet, rtol: float = 1e-05) → tuple[list[numpy.typing.NDArray], numpy.typing.NDArray, list[list[int]]]

Coilset symmetry utility

Parameters:

  • coilset (bluemira.equilibria.coils.CoilSet) – CoilSet to get symmetric coils from

  • rtol (float) – Relative tolerance used when comparing coil values, rtol = 1.e-5 is the default value for np.allclose. The values for the secondary coil in the pair will be set to be equal to the primary coil values if they are within rtol.

Returns:

  • Symmetric coilset data

  • Counts of number of coils in group

  • indexes from original coilset

Return type:

tuple[list[numpy.typing.NDArray], numpy.typing.NDArray, list[list[int]]]

bluemira.equilibria.coils._tools.check_coilset_symmetric(coilset: bluemira.equilibria.coils.CoilSet, rtol: float | None = None) → bool

Check whether or not a CoilSet is purely symmetric about z=0.

Parameters:

  • coilset (bluemira.equilibria.coils.CoilSet) – CoilSet to check for symmetry

  • rtol (float | None)

Return type:

Whether or not the CoilSet is symmetric about z=0

bluemira.equilibria.coils._tools.get_max_current(dx: float | numpy.ndarray, dz: float | numpy.ndarray, j_max: float | numpy.ndarray) → numpy.float64 | numpy.ndarray

Get the maximum current in a rectangular coil cross-sectional area

Parameters:

  • dx (float | numpy.ndarray) – Coil half-width [m]

  • dz (float | numpy.ndarray) – Coil half-height [m]

  • j_max (float | numpy.ndarray) – Coil current density [A/m^2]

Return type:

Maximum current [A]

Notes

\[I_{\text{max}} = j_{\text{max}} \cdot (4 \cdot dx \cdot dz)\]
bluemira.equilibria.coils._tools.rename_coilset(coilset: bluemira.equilibria.coils.CoilSet)

Rename the coils.

Returns:

The coilset containing the renamed coils

Return type:

Coilset

Parameters:

coilset (bluemira.equilibria.coils.CoilSet)