A Method of Axion Detection with Mass 10−4–10−3 eV Using a Cylindrical Sample with Low Electrical 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 $I(\sigma =10^{-3}\text{ eV})\simeq 2.8\times 10^{-14}\text{ A }g_{\gamma }\left(\frac{R}{6\text{ cm}}\right)^2 \left(\frac{\sigma }{10^{-3}\text{ eV}}\right)\left(\frac{B_0}{15\text{ T}}\right)\left(\frac{10}{\epsilon }\right) \left(\frac{\rho _a}{0.3\text{ GeVcm}^{-3}}\right)^{1/2}$ 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 a 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 a large sample with $R=80$ cm, we have a large signal-to-noise ratio ($>1$) even at temperature $T=4$ K, $\frac{I(\sigma =10^{-3}\text{ eV})}{I_n({\sigma =10^{-3}\text{ eV})}}\times \sqrt{\frac{\delta \omega \delta t_{ob}}{2\pi }} \simeq 1.1g_{\gamma }\left(\frac{4\text{ K}}{T}\right)^{1/2}\left(\frac{L}{100\text{ cm}}\right)^{1/2}\left(\frac{R}{80\text{ cm}}\right) \left(\frac{B_0}{7\text{ T}}\right)\left(\frac{\rho _a}{0.3\text{ GeVcm}}^{-3}\right)^{1/2} \left(\frac{\delta t_{ob}}{10^3\, \mathrm{s}}\right)^{1/2}$ for $m_a=10^{-4}\text{ eV}$ with $\epsilon =10$ and $\sigma =\epsilon m_a$, where thermal noise is $I_n=\sqrt{\frac{2T\delta \omega }{\pi R_c}}$ with $\delta \omega =10^{-6}m_a$ and resistance $R_c=\frac{L}{\sigma \pi R^2}$ for 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 $m_a =10^{-4}\!-\!10^{-3}\text{ eV}$.