Axion Dark Matter Detection with a Biconical Nested Plasma Haloscope and Differential Readout (基于双锥体对向嵌套结构的等离子体耦合轴子haloscope与双模差分读出方案)

Abstract

Abstract We propose an experimental scheme for axion dark matter detection using a topological toroidal plasma cavity embedded in a biconical nested structure. The structure consists of two back-to-back nested conical solenoids with a waist radius of 2.5 cm and a total height of 13.7 cm. By alternately applying magnetic flux drive and pulsed electron beam drive, the E-toroidal mode (electric-field dominated) and the M-toroidal mode (magnetic-field dominated) are excited within the same physical structure. Starting from Maxwell's equations, we rigorously prove that the pseudoscalar invariant E·B of the two modes must differ by a phase of π in time — an anti-correlation dictated by the Lenz's law sign in Faraday's law, arising as an inevitable consequence of electromagnetic duality breaking, independent of the specific geometry. COMSOL numerical simulations further confirm the complete spatial anti-correlation, yielding a Pearson correlation coefficient of r = −1.0000 ± 0.0001. Exploiting this anti-correlation, we design a differential readout scheme: the difference channel S₋ = S_M − S_E = 2g_{aγ} a(t) G₀ extracts the axion signal, while the sum channel S₊ = S_M + S_E suppresses the axion signal and retains common-mode noise. The response frequency of the plasma filling the waist region is determined by the plasma density n_e and the external magnetic field B, and is independent of the cavity's geometric eigenfrequency. By tuning n_e = 5×10¹⁷–2×10¹⁹ m⁻³ and B = 0.25–1.5 T, continuous tuning over the 6–44 GHz range is achievable, fully covering the QCD axion mass window of 28 ± 2 μeV predicted by lattice QCD. Under a conservative quality factor Q ~ 100, the expected signal power is approximately 10⁻²¹ W, and a 5σ detection sensitivity of g_{aγ} ~ 2×10⁻¹⁵ GeV⁻¹ can be reached with approximately 100 hours of integration. The main limitation of this scheme is that the differential measurement suppresses the dilaton signal, whose detection would require single-mode absolute measurement. Spectral control of the pulsed electron beam and plasma stability are the key technical challenges for the realization of this scheme. 摘要 我们提出一种利用双锥体对向嵌套结构中的拓扑等离子体环面腔来探测轴子暗物质的实验方案。该结构由两个反向嵌套的锥形螺线管组成,腰部半径为2.5 cm,总高度为13.7 cm。通过交替施加磁通驱动和脉冲电子束驱动,在同一物理结构中分别激发E-环面模式(电场主导)和M-环面模式(磁场主导)。本文首先从麦克斯韦方程组出发,严格证明两种模式的赝标量不变量E·B在时间相位上必然相差π,这一反相关系由法拉第定律中的楞次定律负号决定,是电磁对偶性破缺的必然结果,不依赖于具体几何结构。COMSOL数值仿真进一步证实了空间分布上的完全反相,Pearson相关系数r = −1.0000 ± 0.0001。基于这一反相关系,我们设计了差分读出方案:求差通道S₋ = S_M − S_E = 2g_aγ a(t) G₀提取轴子信号,求和通道S₊ = S_M + S_E抑制轴子信号并保留共模噪声。腰部填充的等离子体响应频率由等离子体密度n_e和外部磁场B决定,与腔体几何本征频率无关。通过调节n_e = 5×10¹⁷–2×10¹⁹ m⁻³和B = 0.25–1.5 T,可在6–44 GHz范围内连续调谐,完整覆盖格点QCD预言的QCD轴子质量窗口28 ± 2 μeV。在保守估计Q~100的条件下,预期信号功率约为10⁻²¹ W,通过约100小时的积分,可达到5σ探测灵敏度g_aγ ~ 2×10⁻¹⁵ GeV⁻¹。本方案的主要局限在于,差分测量会抑制伸缩子信号,其探测需采用单模绝对测量。脉冲电子束的频谱控制与等离子体稳定性是实现本方案的关键技术挑战。