How to compute magnetic plasma frequency of a metamaterials

I found a lot of papers extract permeability of a metamaterial slab based on the Lorentz models. However, I cannot find a paper introduce how to decide plasma frequency in magnetic field. The only thing I get is an equation used in Split ring resonators which relate it with a filling factor as wp^2=Fw^2. But I don't use SPP in my design. Does anyone know how I calculate the plasma frequency with a given geometric models and Inductance? Or any other method to complete it?

See papers such as "Volumetric layered transmission-line metamaterial exhibiting a negative refractive index".

If you have a transmission line model, you can compute it knowing the host TL properties and the loading component values -- what kind of unit cell structure are you using?

I am using a structure as shown in picture,

. It is a 3D unit cell with multilayers of coils in series.

Dr. Grbic's research group works with similar 3D structures, maybe start there?

The structure in "A Broadband Three-Dimensionally Isotropic Negative-Refractive-Index Medium" looks similar, perhaps start your search there? There aren't equations in that paper, but you should be able to find them elsewhere.

Good Luck