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 $I(\sigma =10^{-3}\text{eV})\simeq 2.8\times 10^{-14}\text{A}{g}_{\gamma }(R/6\text{cm}{)}^2(\sigma /10^{-3}\text{eV}\left)\right(B_0/15\text{T}\left)\right(10/ϵ\left)\right({\rho }_a/0.3\mathrm{GeVc}{\mathrm{m}}^{-3}{)}^{1/2}$ for $m_a=10^{-4}$eV, with radius $R$, permittivity $ϵ=10$ 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, $I(\sigma =10^{-3}\text{eV})/I_n(\sigma =10^{-3}\text{eV})\times \sqrt{\delta \omega \delta t_{ob}/2\pi }\simeq 1.1g_{\gamma }(4\text{K}/T{)}^{1/2}(L/100\text{cm}{)}^{1/2}(R/80\text{cm})(B_0/7\text{mbox}T)({\rho }_a/0.3\mathrm{GeVc}{\mathrm{m}}^{-3}{)}^{1/2}(\delta {\mathrm{t}}_{\mathrm{ob}}/10^3\text{s}{)}^{1/2}$ for $m_a=10^{-4}\text{eV}$ with $ϵ=10$ and $\sigma =ϵm_a$, 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 $m_a=10^{-4}\text{-}10^{-3}\text{eV}$.

Comments: 10 pages, 3 figure