Size of a Diamagnetic for Levitation

[moejoe]

Hello,

I have been interested in the problem of diamagnetic levitation where you have typically 2 slabs of some pyrolitic graphite (which is diamagnetic) and between it you have some rare Earth magnet that's levitating thanks to those graphites (and 1 more magnet somewhere above).
I have been looking into a research paper that states that the vertical stability of the floating magnet is achieved when:
$$K_v = C_z - \frac{1}{2} M B'' > 0$$
where $$C_z = \frac{6 M^2 |\chi| \mu_o}{\pi D^5}$$
M: Magnetic Dipole Moment
B'': double derivative of the magnetic field B
X: Magnetic Susceptibility
mu: Permeability of free space
D: gap between the 2 diamagnetic slabs

It's interesting to note that it does not depend on the dimensions of the diamagnetic slabs at all, rather only on the susceptibility of them and the spacing between them.
So I get the impressions that a single particle of this stuff will suffice... which it obviously doesn't. When there's no slab the Cz term is 0, when there's only one of them its divided by 2. Anyone have any knowledge about this?

 

[moejoe]

I got those equations from this paper:
"Diamagnetically stabilized magnet levitation" by LO Heflinger
Link: http://netti.nic.fi/~054028/images/LeviTheory.pdf

I was thinking it may have to do with some kind of potential energy of the diamagnetic with relation to the levitating magnet, so for example a big magnet vs. small diamagnetic might not work out too well.. i don't know.. does anyone know??