Prospecting for Lunar ³He with a Radio-Frequency Atomic Magnetometer

1. Introduction

The Moon is not only a stepping stone for space exploration [1], but also the home of valuable extraterrestrial resources [2]. Mining lunar ³He has attracted considerable interest, on the one hand because of its limited availability on Earth, and on the other because of its potential use in nuclear fusion [3]. Unlike conventional D-T fusion, D-³He reactions produce minimal neutron radiation, enhancing power production efficiency while minimizing long-term radioactive waste [4]. Its nuclear fuel potential aside, ³He is already used for low temperature physics and cryogenics [5,6,7,8,9], increasingly applied to emerging quantum technologies [10,11], for magnetic resonance imaging [12], and nuclear physics [13,14].

Lunar regolith blankets moon’s surface and contains measurable quantities of ³He, at the level of 1-30 ppb [15,16,17], implanted by the solar wind [18,19], and measured by analyzing samples returned by the Apollo [20] and later missions [21,22]. Over time, exposure to solar wind has led to the gradual accumulation of ³He, particularly in titanium-rich minerals such as ilmenite [23], with an estimated quantity around ${10}^6$ tons [24].

Extraction of ³He proceeds by heating regolith to temperatures around $1000\mathrm{K}$ [25,26], and separating, e.g. cryogenically, the released gases [27]. The low abundance of ³He requires processing of large regolith mass, hence the extraction process would have to be performed on moon’s surface. Given the extraction’s non-trivial technical demands [28], it is crucial to precisely prospect for ³He and identify areas with the highest abundance.

Here we propose a direct measurement to detect regolith-implanted ³He by use of an atomic magnetometer, in particular a radio-frequency magnetometer. The proposed method is able to detect lunar ³He from a $200\mathrm{g}$ regolith sample at the level of 5 ppb within a measurement time of 5 min, while consuming minimal power, and being light-weight. Thus, the proposed detection technique is readily deployable in the lunar environment. The cost of the relevant apparatus is negligible compared to mission costs, and significantly less than alternative prospecting methodologies. Hence, from the economic perspective, the proposed technique enables swift prospecting campaigns with a compact device, potentially saving on mission duration, complexity and cost.

For completeness, we note that several authors [29,30,31,32] have questioned the combined technical/economic viability of proposals for mining lunar ³He, further claiming that other earth-based sources could come online, like ³He-breeding reactors. While such arguments are indeed sound, we note that there are intricate, and many times surprising links between economy and technology. For example, the outlook of economic viability could change abruptly if the same infrastructure could be used for mining additional resources. In any case, we here opt to remain agnostic regarding the business case for mining lunar ³He, and merely delve into the technical exercise of prospecting for this gas.

The structure of the paper is the following. In Sec. II we briefly discuss existing methodologies for detecting lunar ³He. In Sec. III we present the possibility of using a radio-frequency (rf) atomic magnetometer. We conclude in Sec. IV.

2. Existing Techniques for Quantifying Lunar ³He

Indirect measurements are primarily based on remote sensing [33,34,35,36,37,38] from lunar orbiters, most of which probe for titanium, which shows strong correlation with ³He abundance. While remote sensing methods provide valuable first-order estimates for identifying promising regions containing ³He, they are inherently limited in precision and reliability as they rely on correlations rather than direct measurements. Factors like regolith depth, surface exposure history, and the efficiency of solar wind implantation introduce significant variability difficult to resolve. Thus, direct in-situ measurements remain critical for any mission aiming to mine ³He at economically viable scales.

So far, such measurements rely mostly on mass spectrometers [39,40,41,42,43,44,45,46], with several variants like Quadrupole Mass Spectrometry, Resonance Ionization Mass Spectrometry, or Time-of-Flight Mass Spectrometry. Such techniques ionize atoms or molecules with different ionization schemes, and then use electromagnetic fields to separate the resulting ions based on their mass-to-charge ratios. While they require very small sample mass and provide for highly sensitive ³He detection, at the level of 1 ppb, the necessary equipment is rather bulky, massive, and costly.

3. Measurement with an Atomic Magnetometer

Atomic magnetometers [47,48,49,50,51,52,53,54,55] detect magnetic fields by optical probing a spin-polarized alkali-metal vapor. The quantum state of the atoms in the vapor is influenced by the optical pumping and probing light, atomic collisions, internal atomic hyperfine interactions, and last but not least, by the magnetic field to be measured.

Spin-exchange-relaxation-free-magnetometers [56,57] have demonstrated sub-fT magnetic sensitivity at a zero background magnetic field. On the other hand, rf-magnetometers [58,59,60,61,62,63,64,65,66] are tuned to work at a specific non-zero bias magnetic field, and detect a weak ac magnetic field at the respective Larmor frequency. Such magnetometers utilize the fact that large spin polarization also suppresses spin-exchange relaxation, and additionally, working at high frequencies alleviates technical noise, such as magnetic noise produced by the material used to magnetically shield the former devices.

The general idea of the proposed measurement is the following. Lunar ³He shall be extracted from regolith, spin-polarized, and captured in a small measurement cell. A free-induction decay will then be induced [67]. The precessing spins of the magnetized ³He vapor will produce a dipolar magnetic field oscillating at the precession frequency. The rf magnetometer will detect this ac field, as in atomic-magnetometer-detected nuclear magnetic resonance [68,69,70,71]. The envisioned measurement setup is shown in Figure 1.

3.1. Number of ³He Atoms Captured in the Measurement Cell

In more detail, lunar ³He shall be extracted by heating a small regolith sample at $T_h=1000\mathrm{K}$ [72]. Some of the released gases, like ${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{SO}}_2$ or ${\mathrm{H}}_2\mathrm{S}$, will be captured by a cold trap at a temperature, e.g., $T_p=100\mathrm{K}$. The rest of the gases not liquifying will diffuse towards the measurement volume. Such gases include ⁴He, ${\mathrm{H}}_2$, $\mathrm{CO}$, ${\mathrm{CO}}_2$, ${\mathrm{N}}_2$. For this prospecting measurement, there is no need to separate them from ³He, as they are nonmagnetic and their effect on ³He spin relaxation time is negligible at the low pressure of this measurement.

Now, we consider the measurement cell of volume $V_{\mathrm{He}}=1{\mathrm{cm}}^3$, also being at temperature $T_p$. Within the temperature gradient defined by the heating temperature $T_h$ and the measurement cell temperature $T_p$, the capture efficiency $\mathcal{C}$ of ³He atoms by the measurement cell should approach [79]$\mathcal{C}=(V_{\mathrm{He}}/V_p)\sqrt{T_h/T_p}/(V_h/V_p+\sqrt{T_h/T_p})$, where $V_h$ and $V_p$ is the gas volume at temperature $T_h$ and $T_p$, respectively. Noting that $V_p=V_{\mathrm{gh}}+V_{\mathrm{He}}$, where $V_{\mathrm{gh}}$ is the volume of the gas handling system (also at temperature $T_p$) other than the measurement cell, and assuming $V_{\mathrm{gh}}=V_{\mathrm{He}}$ and $V_p=V_h$, it follows that $\mathcal{C}\approx 38\%$.

Given a regolith sample of mass $m_{\mathrm{s}}=200\mathrm{g}$ and density $1.5\mathrm{g}/{\mathrm{cm}}^3$, and denoting by $\tilde{m}$ (with unit ppb) the ³He mass abundance, the resulting ³He atom number in the measurement cell will be

$$N_{\mathrm{He}}\approx 2\times {10}^{16}\left[{\displaystyle \frac{\mathcal{C}}{38\%}}\right]\left[{\displaystyle \frac{\tilde{m}}{1\mathrm{ppb}}}\right]\left[{\displaystyle \frac{m_{\mathrm{s}}}{200\mathrm{g}}}\right]$$

(1)

3.2. Thermal Spin-Polarization of ³He

Before entering the measurement cell, ³He shall be pre-polarized inside a polarizing magnetic field $B_p=1\mathrm{T}$ and at temperature $T_p$. Such magnetic field can be readily established with small permanent magnets in a Halbach design [74,75]. In this step, ³He spins will be thermally polarized, attaining polarization $P_{\mathrm{He}}\approx \mu B_p/k_B{T}_p$, where $\mu =1.07\times {10}^{-26}\mathrm{J}/\mathrm{T}$ is the nuclear magnetic moment of ³He and $k_B=1.38\times {10}^{-23}\mathrm{J}/\mathrm{K}$ Boltzmann’s constant. It follows that

$$P_{\mathrm{He}}\approx 8\times {10}^{-6}{\displaystyle \frac{\left[B_p/1\mathrm{T}\right]}{\left[T_p/100\mathrm{K}\right]}}$$

(2)

During this pre-polarization step, ³He will be diffusing through a porous material [73], which serves to slow down the diffusion of ³He atoms and thus increase the time they spend in the polarizing magnetic field. The transit time through this material should be larger than the longitudinal relaxation time $T_1$. This can be accommodated by materials like aerogels [76]. For example, consider the sol-gel used to coat spin-polarized ³He glass cells [77]. In one example, for a 2 atm cell having 2.5 cm diameter, the longitudinal relaxation time was $T_1\approx 300\mathrm{h}$. The ³He self-diffusion coefficient at this pressure and at room temperature is about [78] $1{\mathrm{cm}}^2/\mathrm{s}$, thus ³He atoms collide with the cell walls about ${10}^6$ times within the time $T_1$. For a porous cylinder made of the same material, having 100 nm pores, length 1 mm and diameter 1mm, ³He atoms will collide with the material about ${10}^8$ times before exiting, thus there is enough time for the ³He spin polarization to equilibrate at the value $P_{\mathrm{He}}$.

The measurement cell resides in a holding magnetic field $B_h<B_p$, e.g., $B_h=10\mathrm{G}$. This is because it is less straightforward to create a strong magnetic field for volumes large enough to accommodate the measurement cell. Thus we opt to pre-polarize the ³He in the “large” polarizing field $B_p$. Then the measurement can proceed in a lower, albeit homogeneous holding magnetic field $B_h$. The rf magnetometer resides in a smaller magnetic field, chose so that the Larmor resonance of the employed alkali-metal atom coincides with the precession frequency of the ³He spins.

3.3. Measurement of the ³He Dipolar Magnetic Field with an rf-Magnetometer

With a $\pi /2$-pulse the ³He spins can be tipped to a direction orthogonal to the holding magnetic field, and will precess about it with frequency $\omega =\gamma B_h$, where $\gamma =2\pi \times 3.24\mathrm{kHz}/\mathrm{G}$. Let $\mathbf{z}$ be the unit vector along the common direction of the polarizing magnetic field, the holding magnetic field, and the initial magnetization of ³He. After the $\pi /2$-pulse, ³He spins will precess in the x-y plane (see Figure 1), and their total magnetic moment will be $\mathbf{m}=M(\mathbf{x}cos\omega t+\mathbf{y}sin\omega t)e^{-t/T_2}$, where $M=\mu N_{\mathrm{He}}{P}_{\mathrm{He}}$, with $N_{\mathrm{He}}$ and $P_{\mathrm{He}}$ given by Eq. (1) and Eq. (2), respectively, and $T_2$ being the transverse spin relaxation time.

Assuming a spherical measurement cell, the dipolar magnetic field produced by magnetized ³He gas at a distance R away from the measurement cell’s center along the x-axis will be $B_{\mathrm{He}}{e}^{-t/T_2}cos\omega t$, where the magnitude $B_{\mathrm{He}}={\mu }_{0}M/2\pi R^3$, with ${\mu }_0=4\pi \times {10}^{-7}\mathrm{Tm}/\mathrm{A}$ being vacuum’s magnetic permeability. This magnetic field is to be sensed by the rf magnetometer. Given that the magnetometer sensor cell is not point-like, we assume an average distance between center of the sensor cell and center of the measurement cell $R\approx 3\mathrm{cm}$. Then,

$$B_{\mathrm{He}}=\left(12\mathrm{aT}\right){\displaystyle \frac{\left[B_p/1\mathrm{T}\right]}{\left[T_p/100\mathrm{K}\right]}}\left[{\displaystyle \frac{\mathcal{C}}{38\%}}\right]\left[{\displaystyle \frac{\tilde{m}}{1\mathrm{ppb}}}\right]\left[{\displaystyle \frac{m_{\mathrm{s}}}{200\mathrm{g}}}\right]$$

(3)

The ³He partial pressure in the measurement cell is about 0.2 torr. We assume the rest of the gases being released from heating the regolith sample have a mass abundance similar to ³He, thus we consider a total pressure of 1 torr in the measurement cell. At such low pressures and for a realistic homogeneity of the holding magnetic field, with gradient at the level of $|\nabla B_h|\approx 1\mathrm{mG}/\mathrm{cm}$, the transverse spin relaxation time of ³He is on the order of 1 h [80]. Indeed, at such temperature (100 K) and pressure (1 torr), the ³He self-diffusion coefficient is [78]$D\approx 300{\mathrm{cm}}^2/\mathrm{s}$. The transverse spin relaxation time is [81]$T_2\approx 175D/16{\gamma }^2{R}^4{|\nabla B_h|}^2$, where $R\approx 0.6\mathrm{cm}$ is the measurement cell radius for a measurement cell volume $V_{\mathrm{He}}=1{\mathrm{cm}}^3$. Thus $T_2\approx 2400\mathrm{s}$.

Currently, rf magnetometers have sensitivities around $\delta B=1.0\mathrm{fT}/\sqrt{\mathrm{Hz}}$ [61,63,63]. Thus, for a measurement time $\tau =300\mathrm{s}$ one can detect a magnetic field $B_{\mathrm{He}}$ at the level of $\delta B/\sqrt{\tau }=0.06\mathrm{fT}$, which translates to measuring the abundance of regolith-implanted ³He with sensitivity 5 ppb. In other words, the sensitivity, $\delta \tilde{m}$, of the proposed measurement can be expressed as a function of all parameters as

$${\displaystyle \frac{\delta \tilde{m}}{5\mathrm{ppb}}}={\displaystyle \frac{[\delta B/1.0\frac{\mathrm{fT}}{\sqrt{\mathrm{Hz}}}]}{\left(12\mathrm{aT}\right)\sqrt{\left[\tau /300\mathrm{s}\right]}}}{\displaystyle \frac{\left[T_p/100\mathrm{K}\right]}{\left[B_p/1\mathrm{T}\right]}}{\displaystyle \frac{1}{\left[m_{\mathrm{s}}/200\mathrm{g}\right]\left[\mathcal{C}/38\%\right]}}$$

(4)

As a consistency check, the parameter dependence of $\delta \tilde{m}$ makes intuitive sense: $\delta \tilde{m}$ is reduced by reducing $\delta B$ (increasing the magnetometer sensitivity), increasing measurement time $\tau$, increasing the sample mass $m_s$ (more ³He atoms extracted), reducing the temperature or increasing the polarizing magnetic field (larger ³He spin polarization), increasing the capture efficiency (more ³He atoms).

We note that the numerical values of the relevant parameters entering Eq. (4) are what we think reasonable and indicative for the workings of this measurement. In an actual realization, several technical design limitations might require different choices for those parameter values. The way the final result is expressed in Eq. (4) can readily accommodate other choices of the parameters and easily lead to the corresponding value for $\delta \tilde{m}$ by inspection.

4. Discussion

Here we wish to discuss the deployability of the proposed measurement in the lunar environment. Regarding apparatus volume, we note that there is steady progress towards developing compact atomic magnetometers [82,83,84,85], thus the magnetic sensor, including the associated electronics, should not contribute significantly to the volume of the apparatus of Figure 1. The most voluminous component should be the Helmholtz coil producing the holding magnetic field. For a 5 cm radius coil, this volume is about $400{\mathrm{cm}}^3$. Aside the regolith sample of volume somewhat larger than $100{\mathrm{cm}}^3$, the rest of the apparatus consists of small tubing for gas handling, and thus a total volume less than 1 lt seems feasible.

Regarding mass, the Helmholtz coil is again expected to dominate as a single component, since e.g. a 10 G field can be produced with 200 turns in total of AWG 12 wire, with a mass around 1 kg. Electronics, heating, and gas-handling systems could add another 1-2 kg, thus we expect a total mass of the apparatus smaller than 5 kg.

Regarding power requirements, there are three major loads. The heating of the atomic magnetometer requires on the order of 100 W, and the electronics associated with the sensor around 100 W (both numbers are exaggerated on the high side). More substantial is the power requirement for the heating of the regolith material. To heat $m_{\mathrm{s}}=200\mathrm{g}$ of lunar regolith to $1000\mathrm{K}$, given the specific heat capacity $c\approx 1\mathrm{kJ}/\mathrm{kg}/\mathrm{K}$, and the temperature change from 100 K of the lunar night to 1000 K, i.e. $\Delta T=900\mathrm{K}$, the thermal energy required is $Q=mc\Delta T\approx 180\mathrm{kJ}$. Over 300 s this translates to 600 W. We neglect the power needed to cool the parts of the apparatus required to be at low temperature, since the ambient temperature during the lunar night is as low. In total, given an available power on the order of 1 kW, a single prospecting measurement, including the heating phase and the magnetometry phase, takes about 10 min and consumes energy on the order of 100 Wh. The duration could be reduced if more power is available. Equivalently, one could increase the measurement time, thus reducing further the required sample volume according to Eq. (4). This point reiterates our previous comment that the specific parameter values entering Eq. (4) will eventually relate to other mission design parameters, e.g. the available power.

Regarding cost, it is not straightforward to estimate the cost incurred by designing and implementing space-grade hardware realizing the scheme of Figure 1, but the required equipment altogether should cost significantly less than $0.5 M if it were to be used in a laboratory.

In Table 1 we summarize the aforementioned performance metrics, again, not within the precision of a technical design report for a space mission, but within reasonable estimates based on current laboratory-grade technology.

In summary, the proposed methodology can fit a compact and low-cost design taking advantage of the robust and simple-to-operate modern atomic magnetometers. Thus, such prospecting equipment could be readily mounted on a small lunar rover. One could imagine several exploratory prospecting campaigns performed by such a rover, which in short time could survey an area for the highest abundance of ³He, before the actual mining equipment takes over.