Axion-radiation conversion by super and normal conductors

We have proposed a method for the detection of dark matter axion. It uses superconductor under strong magnetic field. As is well known, the dark matter axion induces oscillating electric field under magnetic field. The electric field is proportional to the magnetic field and makes charged particles oscillate in conductors. Then, radiations of electromagnetic fields are produced. Radiation flux depends on how large the electric field is induced and how large the number of charged particles is present in the conductors. We show that the electric field in superconductor is essentially identical to the one induced in vacuum. It is proportional to the magnetic field. It is only present in the surface because of Meissner effect. On the other hand, although the magnetic field can penetrate the normal conductor, the oscillating electric field is only present in the surface of the conductor because of the skin effect. The strength of the electric field induced in the surface is equal to the one in vacuum. We obtain the electric field in the superconductor by solving equations of electromagnetic fields coupled with axion and Cooper pair described by Ginzburg-Landau model. The electric field in the normal conductor is obtained by solving equations of electromagnetic fields in the conductor coupled with axion. We compare radiation flux from the cylindrical superconductor with that from the normal conductor with same size. We find that the radiation flux from the superconductor is a hundred times larger than the flux from the normal conductor. We also show that when we use superconducting resonant cavity, we obtain radiation energy generated in the cavity two times of the order of the magnitude larger than that in normal conducting resonant cavity.