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Re: Forces on a small diamagnetic sphere in an AC/DC field

"nortonsm" <nortonsm@xxxx> wrote:
Dave,

You bring up a question I had when you mentioned that the
boundary conditions would take care of themselves. As a newbie to
FEMM, I'm currently demo'ing Femlab (a finite element analysis
program that works with Matlab). One thing not covered well in the
documentation (and not answered yet in an email to support) is when
certain boundary conditions are applicable such as the "special"
boundary conditions below.

> > 1) Electric insulation/continuity: n(dot)J=0, n(curl)H=0
> > or
> > 2) Magnetic discontinuity: n(curl)H1=n(curl)H2
3) Magnetic Potential: Aphi0=Aphi1
4) Surface current: -n (curl) H = Js

Will eddy currents (and resulting magnetic polarization) set up in
the diamagnetic sphere "automatically" be taken care of in femm once
I switch to AC fields?

Yes.

And off hand, do you know an example for each
of the above boundary conditions? For instance, doesn't magnetic
discontinuity above just mean that there is no surface current? So
far it seems that setting up correct boundary conditions is the more
difficult part of femm modeling. It doesn't seem clear for different
materials and situations where one boundary condition is prefered
over another.

You generally never have to apply any of those boundary conditions--internal boundaries always "take care of themselves." For example, 1) is never an issue, because in the 2-D formulations, all current flows in the into-the-page direction. (You can, however, set up constraints on the total current carried in a set of regions to define how they are hooked together). Number 2) , by which I think that you mean that the part of H that is tangential a boundary should be continuous across the boundary, gets enforced "automatically" because this is a property of the vector potential formulation and the type of elements used. (To be really strict and use the correct terminology, it is automatically "weakly" enforced). 3) Again, this is imposed automatically by the finite element formulation. Since the nodes are always made to line up along boundaries, and the boundary nodes are members of elements on either side of an interface, you get continuity of A automatically. With 4), I haven't implemented surface currents on internal boundaries. You have to either define currents over a finite (but possibly very thin) area, or define point currents. Surface currents on the edges of a domain can be defined the "mixed" type of boundary condition (corresponds to the c1 parameter), but I'd say that people almost never do this.

Typically, you just have to define boundary conditions explicitly on the outer boundaries of the domain. Most often people are interested in objects that are surrounded by free space. In this case, it is generally sufficient to define a solution region that is somewhat bigger than the object that you are interested in and define A=0 all around the edge of the solution region. You can do more elaborate boundary conditions if you want to exploit symmetry, periodicity, or do a slicker approximation of an unbounded domain.

As an example, see the attached problem. This is supposed to be an iron ball sitting in a spatially homogeneous field of amplitude 0.1 T that varies at 1 Hz. The problem domain looks like a cylinder with the ball in the middle. The only boundary condition I had to define was a fixed A boundary condition for the outer edge that sets the flux in the domain--I've seen other people do this sort of problem by explicitly modeling a coil that produced the field and assigning A=0 to a far away boundary, which is an equally valid approach. Anyhow, you can see you the interface between different permeabilies, the induced currents, and their reaction field, all sort themselves out.

Dave.
--
David Meeker <http://femm.berlios.de/dmeeker>

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