Coil Type: Solid Coil¶
A solid coil is a coil made from a single continuous conducting body with no internal insulation or strand structure.
Solid coils typically have only one or a few windings and a large cross-section in order to carry high electric currents. They are commonly used in induction-heating coils, bus-bars, high-current bars in electrolysis, generator end-windings, and any single-turn / few-turn high-current applications where skin and proximity effects matter.
The conductor is modeled as a fully conductive volume in which eddy
currents are explicitly resolved.
Unlike a stranded coil, a solid coil does not homogenize the current
over its cross-section. The current distribution is an unknown field
that is solved as part of the electromagnetic problem.
Eddy-current effects can be disabled by assigning a material with
has_eddy_currents=False.
Details¶
An important phenomenon for solid coils driven at high frequencies is the skin-depth effect: the electric currents in the conductor induce eddy currents that force the net current to concentrate near the surface of the conductor.
Assume a copper solid conductor with diameter \(d_c = 1\,\mathrm{cm}\) and electrical conductivity \(\sigma = 5.8 \times 10^7\,\mathrm{S/m}\). At a frequency \(f = 1000\,\mathrm{Hz}\), the skin depth is $$ \delta_s = \sqrt{\frac{2}{\omega \mu \sigma}} = \sqrt{\frac{2}{ \left(2\pi \cdot 1000\,\mathrm{Hz}\right) \left(4\pi \cdot 10^{-7}\,\mathrm{H/m}\right) \left(5.8 \times 10^7\,\mathrm{S/m}\right) }} \approx 2.1\,\mathrm{mm}. $$
Since \(\delta_s \lesssim d_c\), a strong current redistribution occurs, with most of the current flowing near the surface.
This effectively reduces the conducting cross-section of the coil, increasing its effective electrical resistance and reducing its internal inductance.
Nearby conductors can further distort the current distribution via the proximity effect.
Example¶
A solid coil is created as follows:
Drive method¶
The solid-coil weak form supports two drive methods (see Sterz 2003):
DriveMethod.Circuit(default) — couples the coil to a circuit equation; the appropriate choice for voltage or current excitation.DriveMethod.Source— treats the coil as a pure current source, skipping the circuit coupling. Useful for prescribed-current benchmarks.