Excitation Coil Model¶

Introduction¶

Excitation coils are widely used in electromagnetic devices such as motors, transformers, inductors, induction heaters, electromagnets, and MRI gradient coils. They generate magnetic fields by driving electric current through conductors.

The Excitation Coil is a support model for the Time-Domain Magnetic and Time-Harmonic Magnetic models: it supplies the divergence-free current density those models need on the right-hand side. The current density can be derived from a prescribed current, an applied voltage, or a circuit-coupled excitation.

Transformer with primary and secondary coils (CC BY-SA 4.0).	Solenoid coil of a linear actuator.

To add an excitation coil model to a simulation:

from mufem.electromagnetics.coil import ExcitationCoilModel

coil_model = ExcitationCoilModel()
sim.get_model_manager().add_model(coil_model)

Coil Specification¶

Each coil is described using a CoilSpecification, which defines:

• Name — identifier of the coil
• Marker — the geometric region or boundary to which the coil applies
• Topology — whether terminals are open or closed
• Type — physical realization of the winding
• Excitation — how the coil is electrically driven
• Reverse Direction (optional) — part of the coil where current flows the opposite way

All but reverse_direction are required.

from mufem.electromagnetics.coil import CoilSpecification

coil = CoilSpecification(
    name="Coil",
    marker=my_coil_marker,
    topology=my_coil_topology,
    type=my_coil_type,
    excitation=my_coil_excitation,
)

coil_model.add_coil_specification(coil)

Topology¶

The topology specifies how the electrical circuit connects to the coil.

Name	Description	Illustration
Open coil	The coil has electrical terminals. Current enters and leaves through designated boundary faces.
Closed coil	The coil is electrically closed. Current circulates internally without terminals.

Type¶

The type defines how the conductor is physically represented.

Name	Description	Illustration
Stranded coil	Individual wires are not resolved. The winding is modeled as a homogenized conducting region. Valid when strand diameter is much smaller than the skin depth. Common in motors, transformers, and actuators.
Solid coil	The entire conductor is explicitly meshed. Eddy currents are fully resolved. Required when skin depth is comparable to conductor size.
Litz wire coil (not yet supported)	Individual strands twisted and insulated from each other to reduce eddy-current losses. Used at high frequencies to suppress skin and proximity effects.
Foil coil (not yet supported)	Layered conducting foils separated by insulation. Current flows within each foil but not between layers. Common in high-current transformer windings.

Excitation¶

A coil is driven by an electrical source — either a prescribed terminal current or an applied voltage with a series resistance. Voltage excitation adds a circuit equation that couples the coil current to the back-EMF induced by a time-varying field, capturing realistic inductive loading.

Name	Description	Illustration
Current excitation	The coil current is prescribed directly.
Voltage excitation	A voltage is applied. Coil resistance and inductance determine the resulting current.

Reverse Direction¶

In a real winding the go side and the return side carry the same current but in opposite physical directions along the wire. The optional reverse_direction argument of CoilSpecification selects the cells where the local conductor direction \(\boldsymbol{\hat{\tau}}\) should be flipped.

Everything that depends on direction — the driving current term, the flux linkage, and the current arrows shown in post-processing — picks up the sign automatically. You do not need to split the winding into two opposite specs or keep track of signs by hand.

Coil Groups¶

A real winding often consists of many separate conductor bodies that all carry the same current — for example the eight coil sides of one phase in a three-phase motor. Instead of writing one CoilSpecification per body, you can describe the whole winding with a single specification whose marker covers every body at once (typically via a regex).

Each separate piece of conductor covered by such a marker is called a coil group. All groups in the same specification

• carry the same current (they are wired in series),
• share the same number of turns, topology, type, and excitation.

This collapses many near-identical specs into one and is the recommended way to describe distributed windings.

Constraint. The reverse_direction marker must be uniform inside each coil group: one conductor cannot carry current in two directions at the same time. If reverse_direction covers only part of a group, the model raises an error.

Coefficients¶

The excitation coil model registers the following coefficients on the CoefficientFunctionManager. They can be exported with the field exporter or referenced in user expressions to build custom integrands.

Reports¶

The following reports are available. Some apply only to specific magnetic models, as noted.

Example¶

Stator Phase Windings¶

A three-phase distributed winding with 4 slots per phase per side has 24 coil bodies marked Coil::+{U,V,W}::n and Coil::-{U,V,W}::n. With coil groups and reverse_direction the three phases are described by three specs:

from mufem import Bnd, CffSinusoidal, Vol
from mufem.electromagnetics.coil import (
    CoilSpecification,
    CoilExcitationCurrent,
    CoilTopologyOpen,
    CoilTypeStranded,
)

I_peak = 10.0      # A
frequency = 50.0   # Hz
phase_current = {
    phase: CffSinusoidal(amplitude=I_peak, frequency=frequency, phase=offset)
    for phase, offset in (("U", 0.0), ("V", -120.0), ("W", -240.0))
}

for phase in ("U", "V", "W"):
    coil = CoilSpecification(
        name=f"Coil::{phase}",
        marker=Vol(rf"Coil::[+-]{phase}::.*"),
        topology=CoilTopologyOpen(
            Bnd(rf"Coil::[+-]{phase}::.*::In"),
            Bnd(rf"Coil::[+-]{phase}::.*::Out"),
        ),
        type=CoilTypeStranded(number_of_turns=35),
        excitation=CoilExcitationCurrent(current=phase_current[phase]),
        reverse_direction=Vol(rf"Coil::\-{phase}::.*"),
    )
    coil_model.add_coil_specification(coil)

Each spec covers 8 disjoint sub-coils; current flows the opposite way in the 4 Coil::-{phase}::.* slots, so a single MagneticFluxLinkageReport over the spec yields the signed phase flux linkage \(\psi_\text{phase}\) directly.