Presets
Playback
Drive
Material
Jiles-Atherton parameters.
Tools
Layers
Model checks
The science
What hysteresis is
A ferromagnet's magnetisation M depends on its history, not only on the applied field H. Sweeping H up and down traces a closed loop in the B-H plane, B = μ0(H + M). The loop is described by the remanence Br (B left when H returns to 0), the coercivity Hc (reverse field needed to bring B to 0) and the saturation Bs.
Energy lost in one cycle
w = ∮ H dB (J per m3 per cycle) P = f · w / ρ (W/kg)The area of the loop (red shading) is converted to heat. A transformer core wants a thin loop (soft steel), a permanent magnet wants a wide loop (large Hc and Br).
The Jiles-Atherton model used here
The page integrates the Jiles-Atherton (1986) model. The anhysteretic curve is the Langevin function of the effective field He = H + αM:
Man = Ms [coth(He/a) − a/He]Domain-wall pinning makes the irreversible part Mirr lag behind Man:
dMirr/dH = (Man − Mirr) / (kδ − α(Man − Mirr)), M = Mirr + c (Man − Mirr)with δ = sign(dH/dt) and the update applied only if it moves Mirr toward Man. Parameters: Ms saturation, a domain-wall shape, k pinning (roughly the coercivity), c reversibility, α domain coupling. The domain picture shows the fraction of aligned moments, 50 % + 50 % M/Ms.
Honest simplifications
- The model is quasi-static: no eddy currents or frequency dependence, so the "drive frequency" only sets how fast the picture moves.
- The material constants in the presets are typical orders of magnitude, not data for a specific grade.
- The domain picture is a cartoon (random sites flip as M changes), not a micromagnetic simulation.
- Minor loops inside the main loop are approximated; the model can show small unphysical dips in M(H) at extreme parameter choices.
- Loss in W/kg assumes a density of 7650 kg/m3.
What to try
- Run Soft iron then Hard magnet and compare the loop width (coercivity) and loss.
- Raise the field amplitude with the slider: the loop grows until the ends reach saturation, then only the upper corners move.
- Press Demagnetise: a slowly decaying field spirals the trace into the origin, leaving M = 0.
- Set c close to 1 (Nearly lossless): the loop collapses toward the anhysteretic curve and the loss falls to zero.
- Look at the red loss-versus-amplitude graph: the loss grows faster than the amplitude squared in the middle.