A Way of Axion Detection with Mass $10^{-4} \text{-}10^{-3}$eV Using Cylindrical Sample with Low Electric Conductivity

Abstract

A dark matter axion with mass $m_a$ induces an oscillating electric field in a cylindrical sample placed under a magnetic field $B_0$ 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. $\sigma = 10^{-3}\text{eV}$, the electric current flows inside the bulk of the cylinder. Within the QCD axion model, the current $I$ is estimated as $I(\sigma=10^{-3}\text{eV})\simeq 2.8\times 10^{-14}\text{A}g_{\gamma}\big(R/6\text{cm}\big)^2 \big(\sigma/10^{-3}\text{eV}\big)\big(B_0/15\text{T}\big)\big(10/\epsilon\big)\big(\rho_a/0.3\rm GeVcm^{-3}\big)^{1/2}$ for $m_a=10^{-4}$eV, with radius $R$, permittivity $\epsilon = 10$ of the cylinder and axion energy density $\rho_a$, where $g_{\gamma}$ is model dependent parameter; $g_{\gamma}(\text{KSVZ}) = -0.96$ and $g_{\gamma}(\text{DFSZ}) = 0.37$. Because the current is proportional to $R^2$, using large sample with $R=80$cm, we have large signal-noise ratio ( $>1$ ) even in temperature $T=4$K, $I(\sigma=10^{-3}\text{eV})/I_n({\sigma=10^{-3}\text{eV})}\times \sqrt{\delta \omega \delta t_{ob}/2\pi} \simeq 1.1g_{\gamma}(4\text{K}/T)^{1/2}(L/100\text{cm})^{1/2}(R/80\text{cm}) (B_0/7\mbox{T})(\rho_a/0.3\rm GeVcm^{-3})^{1/2} (\delta t_{ob}/10^3\,\text{s})^{1/2}$ for $m_a=10^{-4}\text{eV}$ with $\epsilon=10$ and $\sigma=\epsilon m_a$, where thermal noise is $I_n=\sqrt{2T\delta \omega/\pi R_c}$ with $\delta \omega=10^{-6}m_a$ and resistance $R_c=L/(\sigma \pi R^2)$ 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 $m_a =10^{-4}\text{-}10^{-3}\text{eV}$.