(Beta) Frequency Domain (Eddy Current) A-F Solver
The 3D Eddy Current A-F formulation is based on the electric scalar potential, F, and the magnetic vector potential, A. The relations between those potentials and the fields B and E are given by
With these equations and the material constitutive relations,
Ampere's law and the current continuity equation, Ñ× J = 0, can be rewritten as
where
- H is the magnetic field.
- Jimp is an imposed current density.
- D is the electric induction field.
- E is the electric field.
- B is the magnetic induction field.
- n is the magnetic reluctivity.
- m is the magnetic permeability.
- s is the electric conductivity.
- e is the electric permittivity.
The weak form of the above-presented equations is
Understanding the terms of this equation can clarify its capabilities:
- jwsA is the induced current.
- w2eA is the wave propagation.
- sÑF is the conduction current.
- jweÑF is the displacement current.
In the case of low-frequency applications, the wave propagation and displacement effect terms can be neglected, leading to the low-frequency version of this formulation:
in which only the eddy current and the conduction terms are considered.
One important aspect of the low-frequency version is that F is defined only in the conductive domains, Wc, which reduces the number of unknowns and, consequently, the memory and simulation time. The user can choose between these versions of the A-F by turning on or off the displacement current effect.
Related Topics
3D Eddy Current A-F Solver: Nonlinear Solution
3D Eddy Current A-F Solver: Skin Effects
3D Eddy Current A-F: Solver Field Definitions
3D Eddy Current A-F: Solver Parametric Extraction
Setting Eddy Effects and Displacement Current for 3D