We firstly report an axion haloscope search with toroidal geometry. In this pioneering search, we exclude the axion-photon coupling gaγγ down to about 5 × 10 −8 GeV −1 over the axion mass range from 24.7 to 29.1 µeV at a 95% confidence level. The prospects for axion dark matter searches with larger scale toroidal geometry are also considered. PACS numbers: 95.35.+d, 14.80.Va According to precision cosmological measurements [1], more than 80% of the matter content in the Universe is now believed to be cold dark matter (CDM). However, the CDM composition is beyond the standard model of particle physics, and thus is still unknown to date. One of the most compelling candidates for CDM is the axion [2], provided its mass is above 1 µeV [3] and below 3 meV [4]. The axion is the result of the breakdown of a new symmetry proposed by Peccei and Quinn [5] to solve the strong CP (Charge-conjugation and P arity) problem in Quantum Chromodynamics [6]. As a result of the axion production mechanism, the axion mass range is very large with the above range being optimum for CDM.The axion search method proposed by Sikivie [7], also known as the axion haloscope search, involves a microwave resonant cavity with a static magnetic field that induces axion conversions into microwave photons. The conversion power corresponding to the axion signal should be enhanced when the axion mass m a matches the resonant frequency of the cavity mode ν, m a = hν/c 2 . The power would be detected as the axion signal iswhere g aγγ is the axion-photon coupling strength, whose two popular benchmark models are KSVZ [8] for hadronic axions and DFSZ [9], which also includes axion coupling to leptons, ρ a ≈ 0.45 GeV/cm 3 is the local dark matter density, ω = 2πν, andB 2 dV is energy stored in a magnetic field in the cavity volume V , where B is a static magnetic field provided by magnets in the axion haloscopes. The cavitymode-dependent form factor C whose general definition can be found in Ref.[10] and quality factor Q are also shown in Eq. (1) and Q/(1+β) corresponds to the loaded quality factor Q L , where β denotes the mode coupling to the load. Assuming the axions have an isothermal distribution, the signal power given in Eq. (1) would then distribute over a Maxwellian shape with an axion rms speed of about 270 km/s in our galaxy [11], which is the basic model considered in this paper.Most of the axion haloscope searches to date [12][13][14][15][16] have employed a cylindrical resonator without an open resonator [17]. In this paper, we report the first axion haloscope search with toroidal geometry. As reported in our previous publication [10], as long as ∇ × B ∼ 0 is valid, Eq.(1) and the definition of the cavity-modedependent form factor C therein are valid as they are in axion haloscopes in spite of the lack of an axion to a photon magnetic field coupling in the form factor C, which is also true for toroidal geometry. We refer to this axion dark matter search as ACTION for "Axion haloscopes at CAPP with ToroIdal resONators". The prospects for la...