### Physical background

In inductive heating an alternating current is passed through the coils. The current you specify in the heater dialog is only equal to the actual current in the coil, if you set the electrical conductivity in the coil to 0, thus eliminating self-induction in the coil. This is what one usually should do. You can however specify a non-0 electrical conductivity in the coil, thus enabling self-induction in the coil, and calculation of energy dissipation in the coil itself. Please take into account that you are actually specifying a voltage, which you can calculate from cross section of your coil, electrical conductivity, and the specified current. Also, generally the effective currents in different windings of a coil will NOT be the same - you can try to manually adjust using the power fractions. Since version 4.3.18, there is also an experimental feature allowing to automatically adjust the current in every winding of an induction heater such that the effective current matches the prescribed current. This adjustment is performed by adjusting the power fraction factors for the individual regions (windings) of the heater. This feature can be enabled in the heater dialog by clicking the "adjust eff." in the current field. As mentioned, please consider this for the moment experimental, and it will probably only work for fixed prescribed currents. The azimuthal current produces an approximately orthogonal time-varying magnetic field outside the coils (Ampère's law) which in turn generates (induces) an oscillating azimuthal electric field (Faraday's law). Both fields penetrate electrical conductive regions to an extent that depends in part on the electrical conductivity itself. The electric field within the conductive region causes a parallel current flow (Ohm's law). The product of the electric field strength with the current describes the rate of energy dissipation in the conductive region - the familiar I² R heating - in the form of temporal and spatial volumetric heating.

In CrysMAS the effects of an alternating magnetic field are described by a vector potential defined as:

• C (r, z) = In-phase component

• S (r, z) = Out-of-phase component

Once C(r,z) and S(r,z) are known, the induced heat sources can be computed by the following formula:

• σ = electrical conductivity

• ω = frequency of the current ( ω = 2 π f)

The interaction of matter and the electro-magnetic field is described by the skin depth δ :

• σ = electrical conductivity

• ω = frequency of the current ( ω = 2 π f)

• μ = magnetic permeability

The skin depth δ is an important parameter for the treatment of alternating magnetic fields. It reflects the length at which the amplitude of the magnetic field is reduced to 1/c of its initial value.