bgpulse.cpp File Reference

#include <belfem_user_api>
#include <cmath>

Include dependency graph for bgpulse.cpp:

Functions
real	background_pulse (const real t)
	applied background flux density
void	BgPulse_init (SourceFunction *source)

Function Documentation

background_pulse()

real background_pulse

(

const real

t

)

applied background flux density

Parameters

t

time (s)

Returns

flux density (T)

Two logistic steps: up at gTUp, down at gTDown. The difference gives a plateau between them and returns to zero afterwards.

WHY NOT A STEP. The first version of this file cut the field to zero in one instant, and the run answered with J/Jc > 20. That is not stiffness, it is the power law being handed an unphysical excitation: with n = 25, J/Jc = 20 means E/Ec = 20^25, about 3e32. The critical-state model caps |J| at Jc exactly because the textbook field sweep is quasi-static – Iwasa 2009 Sec. 5.2 sweeps 0 -> Hm -> 0 as a continuous sweep, and Russenschuck 2010 Sec. 16.1 says a time-transient field drives the current density only "slightly above Jc", relaxing back to Jc once the sweep stops.

A finite transition is therefore not a numerical convenience but the physical statement. A logistic is steepest at its centre, where the slope is B0/( 4*gTau ) = 25 T/s, and its 10-90% transition takes 4.4*gTau = 44 ms. By E ~ ( dB/dt )*r/2 and J/Jc = ( E/Ec )^( 1/n ) that lands near J/Jc ~ 1.4 – "slightly above", and still a fast cut against the 100 ms plateau.

The two steps sit 10*gTau apart, so they overlap by exp( -5 ): the plateau reaches 0.9866*B0 rather than B0 exactly. Widen the separation or shrink gTau if a flat top matters more than a sharp cut.

The physics under test is unchanged: after the field returns to zero the screening currents have nowhere to go, and the disk keeps a remanent magnetization ( Iwasa Eqs. 5.6-5.7, -M = Hp/2 for a Bean slab ) which no external field can remove – only warming past Tc does that.

BgPulse_init()

void BgPulse_init

(

SourceFunction *

source

)