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

["nortonsm" <nortonsm@xxxxxxxxx>]

Dave,

Thanks again for the help... This program is really fun! I had a 
question about calculating forces in axisymmetric problems. By 
looking over the past archives I found a couple references to this 
(how one should start and end the contour on the r=0 axis). With 
respect to your "ball" example. Let us say there is an 
axisymmetric "r" component to the magnetic force (rather than being 
uniform). I'm interested in calculating the forces in both z- and r- 
on the ball. i.e. in the case where the ball is diamagnetic there 
should be an "r-" restoring force and a positive "z-" suspension 
force on the ball. However, in the axisymmetric problem the r- force 
would (and should (I havent checked)) turn out to be zero. Is there 
a way to determine the "r- component" restoring force? (even though 
its zero right at the r=0 position). I guess I want the second 
derivative of the radial force (d2F/d2r). How do I calculate that in 
femm and are there "things to watch out for" in terms of the 
calculation?

Thanks!!!
-Scott




--- In femm@xxxx, David Meeker <dmeeker@xxxx> wrote:
> "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>