  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 penetrates 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.
