Axion Dark Matter Detection with a Biconical Nested Plasma Haloscope and Differential Readout

Abstract

We propose an experimental scheme for axion dark matter detection utilizing a topological plasma toroidal cavity within a bipolar nested cone structure. This structure consists of two reversely nested conical solenoids with a waist radius of 2.55 cm and a total height of 13.7 cm. By alternately applying magnetic flux drive and pulsed electron beam drive, we excite the E-toroidal mode (electric-field dominant) and M-toroidal mode (magnetic-field dominant) within the same physical structure. Starting from Maxwell's equations, we prove that under the condition of (p,q) helical degeneracy, the pseudoscalar invariant E·B of the two modes must differ in time phase by π. This anti-phase relationship is a necessary consequence of electromagnetic duality breaking, determined by the negative sign in Lenz's law within Faraday's law, and its strict validity relies on the degeneracy locking of the spatial distribution functions by the bipolar cone structure. COMSOL numerical simulations further confirm the complete spatial anti-phase, with a Pearson correlation coefficient of r = -1.0000 ± 0.0001.Based on this anti-phase relationship, we design a differential readout scheme: the difference channel (S₋ = S_M - S_E) extracts the axion signal, while the sum channel (S₊ = S_M + S_E) suppresses the axion signal and preserves common-mode noise. The response frequency of the plasma filling the waist is determined by the plasma density nₑ and the external magnetic field B, independent of the cavity's geometric eigenfrequency. By tuning nₑ = 5×10¹⁷ - 2×10¹⁹ m⁻³ and B = 0.25 - 1.5 T, the frequency can be continuously tuned from 6 to 44 GHz, fully covering the QCD axion mass window of 28 ± 2 μeV predicted by lattice QCD. Under a conservative estimate of Q ~ 100, the expected signal power is approximately 10⁻²¹ W. With about 100 hours of integration, a 5σ detection sensitivity of gₐᵧ ~ 2×10⁻¹⁵ GeV⁻¹ can be achieved. The main limitation of this scheme is that the differential measurement suppresses the dilaton signal, requiring a single-mode absolute measurement for its detection. Key technical challenges include the spectral control of the pulsed electron beam and plasma stability. 中文摘要 (Chinese Abstract)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2.55cm,总高度为13.7cm。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,证明在(p,q)螺旋简并条件下,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,其严格成立依赖于双锥体结构对空间分布函数的简并锁定。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 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nₑ和外部磁场B决定,与腔体几何本征频率无关。通过调节 nₑ = 5×10¹⁷ - 2×10¹⁹ m⁻³ 和 B = 0.25 - 1.5 T,可在6-44GHz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gₐᵧ ~ 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。