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

Abstract 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 $I(\sigma =10^{-3}\mathrm{eV})\simeq 2.8\times 10^{-14}\rm {A}g_{\gamma }\left(\frac{R}{6\mathrm{cm}}\right)^2 \left(\frac{\sigma }{10^{-3}\mathrm{eV}}\right)\left(\frac{B_0}{15\mathrm{T}}\right)\left(\frac{10}{\epsilon }\right) \left(\frac{\rho _a}{0.3\mathrm{GeVcm}^{-3}}\right)^{1/2}$ 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, $\frac{I(\sigma =10^{-3}\mathrm{eV})}{I_n({\sigma =10^{-3}\mathrm{eV})}}\times \sqrt{\frac{\delta \omega \delta t_{ob}}{2\pi }} \simeq 1.1g_{\gamma }\left(\frac{4\mathrm{K}}{T}\right)^{1/2}\left(\frac{L}{100\mathrm{cm}}\right)^{1/2}\left(\frac{R}{80\mathrm{cm}}\right) \left(\frac{B_0}{7\mathrm{T}}\right)\left(\frac{\rho _a}{0.3\mathrm{GeVcm}}^{-3}\right)^{1/2} \left(\frac{\delta t_{ob}}{10^3\, \mathrm{s}}\right)^{1/2}$ for ma = 10−4eV with ε = 10 and σ = εma, where thermal noise is $I_n=\sqrt{\frac{2T\delta \omega }{\pi R_c}}$ with δω = 10−6ma and resistance $R_c=\frac{L}{\sigma \pi R^2}$ 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.