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Flux Linkage Report

The MagneticFluxLinkageReport computes the magnetic flux linkage \(\Psi\) of a coil — the total magnetic flux threading the winding due to its own current and the currents of other coils.

What Is Flux Linkage?

The flux linkage is defined as

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

Here \(\Psi\) [Wb] is the flux linkage, \(\mathbf{B}\) [T] the magnetic flux density, and \(S\) a surface bounded by the coil winding. For a homogenised stranded coil this is equivalent to the volume form \(\Psi = \int_\Omega \mathbf{A} \cdot \boldsymbol{\tau} \, d\Omega\), which is what the implementation evaluates.

Flux linkage enters Faraday's law for the induced voltage,

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

and the magnetic energy of a multi-coil system,

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

Usage

from mufem.electromagnetics.coil import MagneticFluxLinkageReport

flux_linkage_report = MagneticFluxLinkageReport(
    name="Coil Flux Linkage",
    coil_index=0,
)

flux_linkage = flux_linkage_report.evaluate()
print(f"Flux linkage: {flux_linkage}")

When to use this

  • Transformer design — primary / secondary flux linkages give the turns ratio and leakage flux.
  • Saturation studies of soft-magnetic cores — flux linkage vs. current is the integral form of the BH characteristic at the device level.
  • Inductance extraction by sweeping current and reading \(L = \Psi / I\).