It is not very complex:
... the permeability is actually the slope of the BH curve. The
steeper the curve, the higher the permeability as shown below...
But a bit more complex then just multiplying H by permeability to get B:
That BH curve is not a straight line,
it reaches saturation, which depends on the material:
..The typical saturation flux density of Power Ferrite material is
under 4000 gauss (400mT). Whereas the saturation flux density of MPP
material is 7000 gauss. High Flux is 15,000 gauss and Iron Powder is
Cobalt based alloys have been developed which have high saturation :
The important series of alloys from cobalt?s point of view are the
Co/Fe series typified by Permendur ? this alloy being modified by
vanadium additions to improve ductility. The reason for the use of
cobalt is that this alloy benefits from the maximum saturation known,
23,500 gauss (2.35 Tesla) with a square shaped hysteresis loop, and
also from the high Curie Point.
It all depends on Temperature too, of course -
and required frequency response - and
size and uniformity of field in a cavity...
do a search on
SEARCH TERM: curie point, saturation, hysteresis, slew rate
You may want to learn from the people who build
MRI machines and particle accelerators.
MRI equipment ranges from 0.2 to 9.0 Tesla,
accelerators use superconducting coils ..
Here is an example of 'state of the art' MRI:
"..High Power MRI Machine Coming to the Center for Biomedical Imaging
at NYU ... a team of scientists who designed and installed the world's
first 3-Tesla MRI ..."
You did not describe the scope of the effort and resources.
It gets expensive as you reach for higher flux density and size of the cavity.
Here is a technical paper on design of MRI coils which reach 3T
Here is an example of 'your tax money at work' in a national lab:
They call 2.3 T a low field magnet
(built with and limited by saturation of the iron core)
rare earth materials and 'commercially available HTS' for
design of High Density magnets.
It is a actually a field of study to which whole monographs and
courses are dedicated: