Upscaling ARDM for Ton-Scale LAr TPCs

• Upscaling ARDM is the process of extending small-scale argon dark matter prototypes into ton- and multi-ton liquid argon TPCs while preserving sensitivity and background rejection.
• It involves scaling detector subsystems such as drift field uniformity, charge amplification, scintillation light collection, and cryogenics to maintain performance as volume increases.
• Key engineering solutions include optimized high-voltage delivery, advanced argon purification to improve electron lifetime, and optical segmentation to ensure consistent light yield.

Upscaling ARDM refers to the set of principles, subsystem adaptations, and engineering methodologies required to extend the Argon Dark Matter (ArDM) experiment from small laboratory prototypes (few-liter LEM-TPCs) to ton-scale, and ultimately multi-ton, liquid argon time projection chambers (LAr TPCs) for rare-event searches. The process addresses scaling laws for drift fields, charge amplification, scintillation light readout, cryogenics, argon purification, backgrounds, mechanical containment, and data acquisition, ensuring that sensitivity, stability, and background rejection are preserved or improved as mass, drift length, and detector volume increase by orders of magnitude (Collaboration et al., 2016, Collaboration et al., 2015, Collaboration et al., 2010, Amsler et al., 2010, Collaboration et al., 2016, Collaboration et al., 2010).

1. Fundamental Detector Subsystems and Scaling Laws

Each major ArDM subsystem—electric drift field, charge readout, light collection, cryogenics, purification, and background shielding—exhibits distinct geometric and physical scaling requirements. Typical upscaling factors from R&D devices (3–10 L) to the 1-ton prototype are ~10² in target mass and ~10× in linear dimensions.

Drift Field and High Voltage:

The electric field $E=V/d$ must remain uniform over drift lengths $d$ that grow from centimeters to meters. Required cathode voltage increases linearly with drift length; e.g., for $E=1$ kV/cm over $d=2$ m, $V=200$ kV. Field uniformity is preserved by proportionally increasing both the number and diameter of field-shaping rings, with their axial pitch scaling as $\Delta\propto R$ to maintain $\Delta E/E \lesssim 1\%$ (Collaboration et al., 2010, Collaboration et al., 2016, Collaboration et al., 2010).

Charge Amplification (LEM or Dual-Phase):

Effective charge amplification via Large Electron Multipliers (LEM) or THGEM is required to compensate increasing electronic noise due to larger anode capacitance ($C\propto$ strip length $\propto R$). Single-stage LEMs provide $G\sim30$, while staged/tiled gains of $d$0 are needed at the multi-ton scale to preserve S/N for low-energy recoils (Collaboration et al., 2010, Collaboration et al., 2010). The area of LEM tiles must scale with the detector cross-section ($d$1), and charge readout channels scale similarly.

Scintillation Light Collection:

Maintaining a fixed photon detection efficiency as fiducial volume increases requires scaling the total photocathode area (PMTs and/or SiPM arrays) and optimizing wavelength shifter (WLS) and reflector coverage. Key geometric scaling: total inner surface area $d$2, so to keep a constant light yield per keV, $d$3. The overall photoelectron yield per unit energy is $d$4, necessitating upgrades to $d$5 (coverage fraction), $d$6 (reflectivity), and $d$7 as volume increases (Amsler et al., 2010, Collaboration et al., 2015).

Cryogenics and Heat Load:

The LAr volume and associated surface area increase $d$8, and $d$9 (for fixed aspect ratio). Heat ingress scales with surface area; to maintain boil-off and temperature stability, total refrigeration power must scale accordingly. Multi-layer insulation and vacuum dewars are necessary for $E=1$0 m³ targets (Collaboration et al., 2016, Collaboration et al., 2015, Collaboration et al., 2010).

Argon Purification and Electron Lifetime:

Longer drift lengths demand improved electron lifetime $E=1$1 (typically $E=1$2–3 ms for $E=1$3–2 m), requiring sub-ppb levels of O$E=1$4, H$E=1$5O, and other electronegative or VUV-absorbing impurities. LAr recirculation and purification flows must scale with volume ($E=1$6), and char-coal cold traps or advanced getters are necessary to suppress VUV absorbers that limit light attenuation length $E=1$7 (Collaboration et al., 2016, Collaboration et al., 2016, Collaboration et al., 2010).

2. Technical Challenges and Derived Design Solutions

High Voltage Delivery:

Ton- and multi-ton scale detectors require cathode feedthroughs rated for $E=1$8–$E=1$9 kV, field shaper alignment over meter lengths, and stable submerged Cockcroft-Walton (CW) multipliers. Empirically, multipliers deliver $d=2$070% of the ideal voltage due to nonlinearity and shunt capacitance; $d=2$130% voltage overhead is provisioned (Collaboration et al., 2010, Collaboration et al., 2016, Collaboration et al., 2010).

Charge Readout and Noise Control:

Anode strip capacitance increases with module size, raising Johnson noise. To retain $d=2$2 for few-keVr events, multi-stage or larger-area LEMs are deployed, and readout segmentation must be balanced against feasible channel counts and electronics noise. Multiplexed or grouped readout is often required in the multi-ton regime (Collaboration et al., 2010, Collaboration et al., 2016, Collaboration et al., 2015).

Light Attenuation and VUV Purity:

Measured VUV attenuation lengths in ArDM are $d=2$3m in the presence of $d=2$410–100 ppb impurities (notably NO$d=2$5, CH$d=2$6, NH$d=2$7, SO$d=2$8, with $d=2$9–$V=200$0 Mbarn) (Collaboration et al., 2016). In larger detectors, average photon path scales as linear size $V=200$1, so with $V=200$2 m, millimeter-scale detectors would lose $V=200$3 of primary light. To enable $V=200$4 m, sub-ppb impurity levels or optical segmentation and in situ calibration are employed.

Background Mitigation:

The lower surface-to-volume ratio at scale reduces relative surface backgrounds, enabling larger fiducials. Self-shielding and increased neutron/gamma attenuation within LAr allow for deeper fiducial regions and active/passive external shields (e.g. HDPE, water veto) (Collaboration et al., 2010, Collaboration et al., 2016, Collaboration et al., 2015).

3. Performance Benchmarks Across Scales

A comparison of prototype, ton-scale, and upscaled-multi-ton ArDM system parameters shows:

Parameter	3 L Prototype (Collaboration et al., 2010)	1 ton ArDM (Collaboration et al., 2015, Collaboration et al., 2016)	Multi-ton Design Target
Drift length (m)	0.05–0.10	1.2	2–5
Cathode voltage (kV)	5–10	120	200–600
Light yield (pe/keV$V=200$5)	0.5	1.17 (PMTs), 4 (SiPM future)	2–4
Electron lifetime ($V=200$6s)	500	$V=200$71,500	$V=200$82,000
Heat load (W)	10	470	1,000+
Fiducial mass (kg)	2	1,200	5,000

This scaling preserves $V=200$9keV thresholds, $\Delta\propto R$0 energy resolution at sub-MeV, and background levels dominated by internal $\Delta\propto R$1Ar decay ($\Delta\propto R$21 Bq/kg) (Collaboration et al., 2015, Amsler et al., 2010).

4. Impurity Control and Optical Transport

A limiting factor for upscaling is the VUV attenuation length. In ton-scale ArDM, with $\Delta\propto R$3 m, only aggressive impurity removal enables substantial increases in linear dimension; achieving $\Delta\propto R$4–4 m requires sub-ppb levels of major absorbers (NO$\Delta\propto R$5, CH$\Delta\propto R$6, NH$\Delta\propto R$7, H$\Delta\propto R$8O, O$\Delta\propto R$9) (Collaboration et al., 2016). Strategies include:

• Charcoal cold-traps in LAr recirculation to freeze out heavy molecules.
• Advanced multi-component getters for hydrocarbons and NO$\Delta E/E \lesssim 1\%$0.
• Fractional distillation for Kr/Xe removal.
• Continuous in-line mass spectrometry for purity monitoring.
• Optical segmentation to limit mean photon path.
• Ray-tracing Monte Carlo for optimizing WLS, PMT/SiPM placement, and reflector coverage; results indicate that with $\Delta E/E \lesssim 1\%$1 m and $\Delta E/E \lesssim 1\%$2 side-wall coverage, 3 m radius detectors can retain $\Delta E/E \lesssim 1\%$370% of prompt light (Collaboration et al., 2016).

5. Engineering Lessons and Prospects for Large-Scale LAr TPCs

Key empirical lessons from ArDM upscaling include:

• Performance is preserved by modular subsystem engineering: tiling LEMs, distributing PMTs/SiPMs, pumping parallel recirculation, and distributed high-voltage braking (Collaboration et al., 2010, Collaboration et al., 2016).
• Drift time increases $\Delta E/E \lesssim 1\%$4 from bench-top to ton-scale devices, requiring deeper DAQ buffers and zero-suppression to constrain data rates ($\Delta E/E \lesssim 1\%$510 MB/s after sparsification).
• Thermal load grows with $\Delta E/E \lesssim 1\%$6, necessitating larger cryostats and insulation, but not scaling as $\Delta E/E \lesssim 1\%$7; cryogenic efficiency and insulation become central (Collaboration et al., 2016).
• The transition from laboratory R&D modules ($\Delta E/E \lesssim 1\%$8keV threshold, few p.e./keV, G$\Delta E/E \lesssim 1\%$910–100, $C\propto$0 ms) to ton-scale ArDM validated the upscaling approach and informs designs for O(10 t) detectors in future dark matter, neutrino, and rare-event physics (Collaboration et al., 2015).

6. Future Directions and Remaining Barriers

Realizing multi-ton, meter-scale LAr TPCs for dark matter and neutrino physics requires:

• Further advances in liquid/gas purification, including technology for sub-ppb-level multispecies removal.
• Optimization of photodetector architecture (hybrid SiPM/large-PMT, full 3D surround, segmented reflective charge readout).
• Mechanical solutions for supporting and insulating large, tall structures with low thermal loss and minimal vibrational coupling.
• Automated, continuous monitoring and calibration of VUV attenuation and detector response via in situ injected sources (e.g., $C\propto$1Kr) (Collaboration et al., 2016).
• Refined data acquisition architectures that manage $C\propto$21,000–10,000 channels, provide ms-scale drift buffering, and sustain low-energy thresholds with high discrimination power (Collaboration et al., 2016, Collaboration et al., 2010).

A plausible implication is that upscaling beyond current (ton-scale) ArDM designs to $C\propto$310-tonne fiducial masses while retaining sub-keV energy thresholds, $C\propto$4 photon survival over 2–3 m, and ms-scale drift times will require order-of-magnitude improvements in both impurity control and optical segmentation; these requirements are not volumetric, but scale with linear dimension (for optics) and with S/V ratio (for backgrounds and thermal loads).

(Collaboration et al., 2016, Collaboration et al., 2015, Collaboration et al., 2010, Amsler et al., 2010, Collaboration et al., 2016, Collaboration et al., 2010)