A Way of Axion Detection with Mass 10−4-10−3eV Using Cylindrical Sample with Low Electric Conductivity

A dark matter axion with mass ma induces an oscillating electric field in a cylindrical sample placed under a magnetic field B0 parallel to the cylinder axis. When the cylinder is made of a highly electrically conductive material, the induced oscillating current flows only at the surface. In contrast, if the cylinder is composed of a material with small conductivity, e.g. σ = 10−3eV, the electriccurrent flows inside the bulk of the cylinder. Within the QCD axion model, the current I is estimated as $I(σ =10⁻³eV) 2.8× 10⁻¹⁴Agγ(R/6cm)^2 ({σ }{10⁻³eV})(B_0/15T)(10/ε ) ({ρ _a}{0.3GeVcm⁻³})1/2$ for ma = 10−4eV, with radius R, permittivity ε = 10 of the cylinder and axion energy density ρa, where gγ is model dependent parameter; gγ(KSVZ) = −0.96 and gγ(DFSZ) = 0.37. Because the current is proportional to R2, using large sample with R = 80cm, we have large signal-noise ratio ( >1 ) even in temperature T = 4K, ${I(σ =10⁻³eV)}{I_n({σ =10⁻³eV)}}× √{{δ ω δ tob}{2π }} 1.1gγ(4K/T)1/2(L/100cm)1/2(R/80cm) (B_0/7T)(ρ _a/0.3GeVcm⁻³)1/2 ({δ tob}{10^3\, s})1/2$ for ma = 10−4eV with ε = 10 and σ = εma, where thermal noise is $I_n=√2Tδ ω /π R_c$ with δω = 10−6ma and resistance $R_c=L/σ π R^2$ of the cylinder with length L. Although a superconducting solenoid sufficiently large to accommodate such a sample is required, the detection of dark matter axions in our proposal may be feasible in the mass range ma = 10−4-10−3eV.