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Tangential Magnetic Flux Condition

The tangential magnetic flux condition is a boundary condition which enforces the magnetic flux density \(\tilde{\mathbf{B}}\) to be tangential to the boundary by imposing

\[ \mathbf{n} \cdot \tilde{\mathbf{B}} = 0 \quad \text{on} \quad \Gamma. \]

Equivalently, the tangential component of the magnetic vector potential is pinned, \(\mathbf{n} \times \tilde{\mathbf{A}} = 0\) — a Dirichlet condition. No magnetic flux crosses \(\Gamma\); flux lines run parallel to the surface.

Flux density tangential to the boundary
Figure 1: The flux density runs parallel to the boundary $\Gamma$; no flux line crosses it ($\mathbf{n} \cdot \tilde{\mathbf{B}} = 0$).


Applicability

Applicable on boundary surfaces. It is an essential (Dirichlet) condition: it pins the tangential vector potential, constraining degrees of freedom directly rather than adding a weak-form term. Use it wherever the flux is known to run parallel to the surface. The condition takes no parameters.

When to use this

  • Far-field truncation. On the outer faces of an air box surrounding the device. When the box is large enough that the field has decayed, forcing flux to be tangential is a good approximation of an unbounded domain.
  • Symmetry planes. On planes where the magnetic field is parallel to the cut plane (i.e. \(\mathbf{B} \cdot \mathbf{n} = 0\) by symmetry).
  • Open-coil ports. The inlet and outlet faces of an open Excitation Coil must carry this condition so the prescribed current is well-defined.
  • Idealized superconductors. Surfaces that expel flux (Meissner effect) — useful for first-order screening studies.

Usage

from mufem.electromagnetics.timeharmonicmagnetic import (
    TangentialMagneticFluxBoundaryCondition,
)

tangential_flux_bc = TangentialMagneticFluxBoundaryCondition(
    name="FarField",
    marker="Air::Boundary" @ Bnd,
)

time_harmonic_magnetic_model.add_condition(tangential_flux_bc)