Flux Linkage Report

The MagneticFluxLinkageReport computes the magnetic flux linkage for a coil The flux linkage quantifies the total magnetic flux linked with a coil due to its own current and the currents in other coils.

What Is Flux Linkage?

The magnetic flux linkage is defined as

\[\Psi = \int_S \mathbf{B} \, \mathrm{d}S \quad.\]

Here \(\Psi [{\rm Wb}]\) is the flux linkage, \(B [{\rm T}]\) is the magnetic flux density, and \(S\) is the surface enclosed by the coil winding.

The flux linkage plays a central role in computing induced voltage in the coil via Faraday’s law:

\[V = \frac{\mathrm{d} \Psi}{\mathrm{d}t} \quad.\]

The total magnetic energy stored in the system can also be expressed using flux linkage:

\[W = \frac{1}{2} \sum_i \Psi_i I_i\]

Usage Example

from mufem.electromagnetics.coil import MagneticFluxLinkageReport

help(MagneticFluxLinkageReport)

Help on class MagneticFluxLinkageReport in module mufem.electromagnetics.coil:

class MagneticFluxLinkageReport(mufem.ReportTrait)
 |  Method resolution order:
 |      MagneticFluxLinkageReport
 |      mufem.ReportTrait
 |      pybind11_builtins.pybind11_object
 |      builtins.object
 |
 |  Methods defined here:
 |
 |  __init__(...)
 |      __init__(self: mufem.electromagnetics.coil.MagneticFluxLinkageReport, name: str, coil_index: int) -> None
 |
 |  evaluate(...)
 |      evaluate(self: mufem.electromagnetics.coil.MagneticFluxLinkageReport) -> Value
 |
 |  get_name(...)
 |      get_name(self: mufem.electromagnetics.coil.MagneticFluxLinkageReport) -> str
 |
 |  ----------------------------------------------------------------------
 |  Static methods inherited from pybind11_builtins.pybind11_object:
 |
 |  __new__(*args, **kwargs) class method of pybind11_builtins.pybind11_object
 |      Create and return a new object.  See help(type) for accurate signature.