Classical Casimir pressure in the presence of axion dark matter

We study the effects of an oscillating axion field on the pressure between two metallic plates. We consider the situation where a magnetic field parallel to the plates is present and show that the electric field induced by the coupling of the axion to photons leads to resonances. When the boundary plates are perfect conductors, the resonances are infinitely thin whilst they are broadened when the conductivity of the boundary plates is taken into account. The resonances take place at the tower of distances close to dn = (2n+1){\pi}/m where m is the axion mass and have a finite width and height depending on the conductivity. The resulting resonant pressure on the plate depends on the induced polarisation at the surface of the plates. We investigate the reach of future Casimir experiments in terms of the axion mass and the conductivity of the boundary plates. We find that for large enough conductivities, the axion-induced pressure could be larger than the quantum Casimir effect between the plates.