Projection of purification performance for the RELICS experiment

This paper presents a validated comprehensive purity evolution model that incorporates non-uniform impurity transport mechanisms to project the purification performance for the upcoming RELICS-10 and RELICS-50 dual-phase liquid xenon detectors designed to search for reactor-induced coherent elastic neutrino-nucleus scattering.

The Gist

Imagine you are trying to listen to a whisper in a room filled with a noisy, buzzing crowd. That is essentially what the RELICS experiment is trying to do. They want to detect a very faint signal: neutrinos (ghostly particles from a nuclear power plant) bouncing off the nuclei of xenon atoms.

To hear this "whisper," the room (the detector) must be incredibly quiet and clean. If the xenon gas is dirty with even tiny amounts of impurities (like oxygen or water), those impurities will "eat" the signal before it can be heard.

This paper is the story of how the scientists built a super-cleaning system for their xenon room, tested it, and proved it will work for their big future experiments.

Here is the breakdown in simple terms:

1. The Goal: A Pristine Room

The scientists are building a giant tank of liquid xenon (RELICS-10 and RELICS-50). They need this liquid to be pure enough that an electron can swim through it for a long time without getting stuck. They measure this "swimming time" (called electron lifetime). The longer the swim, the cleaner the room.

2. The Problem: The "Dirty Laundry" Effect

Even if you start with clean xenon, the materials inside the tank (like the plastic walls, metal pipes, and cables) constantly "sweat" tiny amounts of gas. This is called outgassing. It's like a new car smelling of "new car smell" because the plastics are releasing gases. In a super-sensitive detector, this "smell" is actually a poison that ruins the experiment.

3. The Solution: The "Recycling Loop"

To fix this, the team built a circulation system. Think of it like a giant, high-tech vacuum cleaner and air filter for the xenon.

• The Loop: They pump the xenon out of the tank, run it through a super-hot filter (a "getter" made of zirconium) that acts like a magnet for dirt, and then pump the clean gas back in.
• The Challenge: It's not just about pumping. The xenon changes between liquid and gas, and it flows through different pipes. The scientists had to figure out exactly how the "dirt" moves through this complex maze.

4. The Training Wheels: The Prototypes (Run 7 & Run 9)

Before building the big tanks, they built two smaller "training wheels" versions to test their cleaning theory.

• Run 7 (The Diving Bell): Their first prototype used a "diving bell" design to control the liquid level. It worked, but they found a problem: the pipes weren't sealed perfectly. It was like trying to fill a bucket with a hose that had a small hole; a lot of the "clean water" was leaking out before it reached the bucket.
• Run 9 (The Overflow Cup): They fixed the leaks by using better connectors (VCR fittings) and changed the design to an "overflow chamber" (like a bathtub with an overflow drain). This time, the cleaning worked much faster. They also discovered that the "dirt" was moving between the liquid and gas phases faster than they expected, which actually helped clean the tank!

5. The "Math Magic" (The Model)

The scientists didn't just guess; they built a computer simulation (a mathematical model).

• They treated the detector like a city with different neighborhoods (pipes, tanks, the main chamber).
• They tracked how much "dirt" was being produced in each neighborhood and how fast the "cleaning crew" (the pump) could remove it.
• They used data from the two prototypes to "teach" the model. They adjusted the numbers until the computer's prediction matched what they actually measured in the lab.

Key Discovery: They found that in the first prototype, the cleaning was slow because the "clean water" was leaking out of the main tank. In the second prototype, once they fixed the leaks, the cleaning speed skyrocketed.

6. The Future: Predicting the Big Tanks

Now that their "math magic" model is proven to work on the small prototypes, they used it to predict how the big future detectors (RELICS-10 and RELICS-50) will perform.

• The Prediction: They predict that with their improved cleaning system and by baking the materials first (to stop them from "sweating" so much), the big tanks will achieve a purity level that is perfect for detecting neutrinos.
• The Result: They expect the "electron swimming time" to be long enough (around 1.4 to 2.1 milliseconds) to catch those ghostly neutrino signals.

The Big Picture Analogy

Imagine you are trying to make the clearest glass of water in the world.

1. The Problem: The bucket you are using is made of sponge that leaks a little bit of dust into the water.
2. The Fix: You have a machine that sucks the water out, filters the dust, and pours it back in.
3. The Test: You try this with a small cup (Run 7) and realize your hose is leaking. You fix the hose and try again with a better cup (Run 9).
4. The Prediction: Now that you know exactly how much dust the sponge leaks and how fast your filter works, you can confidently say, "If we build a giant swimming pool with this same system, the water will be crystal clear."

Conclusion: This paper is the "proof of concept" that says, "We know how to keep our xenon clean, we have the math to prove it, and we are ready to build the big machine to catch neutrinos."

Technical Summary

1. Problem Statement

The RELICS (REactor neutrino LIquid xenon Coherent elastic Scattering) experiment aims to detect Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS) induced by reactor antineutrinos using a dual-phase liquid xenon (LXe) Time Projection Chamber (TPC).

• The Challenge: CE$\nu$NS signals manifest as sub-keV nuclear recoils. Detecting these requires ultra-high purity in the liquid xenon to minimize signal attenuation caused by electronegative impurities (primarily oxygen and water) capturing drifting electrons.
• The Gap: Maintaining sufficient purity in a large-scale detector is difficult due to continuous material outgassing from internal components (PTFE, PEEK, stainless steel, etc.) and complex transport mechanisms (circulation, phase changes, gas-liquid exchange). Existing models often lack the granularity to predict purity evolution under varying operational conditions and detector geometries.
• Goal: To develop, validate, and utilize a comprehensive purity evolution model to predict the purification performance of future RELICS detectors (RELICS-10 and RELICS-50) based on prototype data.

2. Methodology

A. Experimental Setup and Prototypes

The study utilized two prototype campaigns (Run 7 and Run 9) at the Sanmen nuclear reactor site, employing different TPC architectures to test robustness:

• Run 7 (Diving Bell Design): Used a "diving bell" structure to actively control the liquid-gas interface. It featured a room-temperature outgassing vessel installed upstream of the purifier to intentionally constrain and measure getter efficiency.
• Run 9 (Overflow Chamber Design): Replaced the diving bell with a passive overflow chamber for more stable liquid level control. It utilized reinforced VCR fittings and flexible hoses to improve sealing integrity.
• Purification System: Both runs used a circulation loop with a metal bellows pump, a high-temperature zirconium getter (Simpure 9NG) operating at 300–400°C, and mass flow controllers. Xenon was circulated via Liquid In (LI), Gas In (GI), Liquid Out (LO), and Gas Out (GO) modes.

B. Purity Measurement

• Electron Lifetime ($\tau_e$): Purity was quantified by measuring the electron lifetime using monoenergetic calibration sources ($^{83m}$Kr and $^{37}$Ar). The attenuation of the S2 (ionization) signal relative to the drift time follows an exponential decay: $N(t_z) = N_0 e^{-t_z/\tau_e}$.
• Material Characterization: Outgassing rates for key materials (Stainless Steel, PTFE, PEEK, Kapton) were measured at room temperature using the Rate-of-Rise (ROR) method and extrapolated to cryogenic temperatures using an Arrhenius-type diffusion model.

C. Modeling Approach

A comprehensive Purification Model was developed based on mass conservation and impurity transport dynamics:

• Control Volumes: The detector and circulation loop were divided into distinct, well-mixed control volumes (e.g., TPC liquid, TPC gas, cryocooler, overflow chamber, outgassing vessel).
• Differential Equations: A system of coupled differential equations described the impurity concentration evolution in each volume, accounting for:
  • Circulation flow rates ($a_i$).
  • Material outgassing rates ($f_i$).
  • Gas-liquid exchange fluxes ($T_i$) driven by Henry's Law.
  • Getter purification efficiency ($e$).
  • Liquid delivery line efficiency ($p$).
• Fitting Strategy: The model parameters were constrained using Bayesian Markov Chain Monte Carlo (MCMC) methods (using the emcee package) against the experimental electron lifetime data from Runs 7 and 9.

3. Key Contributions

1. Development of a Multi-Volume Impurity Transport Model: Unlike previous simplified models, this work incorporates non-uniform transport mechanisms, including phase changes (liquefaction/evaporation), gas-liquid exchange, and specific structural features (diving bell vs. overflow chamber).
2. Validation via Dual-Prototype Campaigns: The model was rigorously validated against two distinct detector configurations (Run 7 and Run 9), demonstrating its ability to describe impurity dynamics across different geometries and operational modes.
3. Identification of Critical System Limitations:
   • Run 7: Revealed that the liquid delivery line had poor sealing integrity, causing ~93% of purified liquid to bypass the sensitive volume (M0) and enter the external reservoir (M1). This was identified as the primary bottleneck for rapid purification.
   • Run 9: Confirmed that while sealing improved, electric field non-uniformity became the limiting factor for the measured electron lifetime, creating an artificial upper bound unrelated to impurity concentration.
4. Quantification of Gas-Liquid Exchange: The study successfully isolated and quantified the gas-liquid exchange term, finding it to be a significant purification mechanism in the Run 9 configuration, effectively acting as an additional purification flow.

4. Results

A. Prototype Performance & Parameter Extraction

• Getter Efficiency ($e$): Both runs confirmed the getter operates at high efficiency, removing 98–99% of electronegative impurities.
• Sealing Efficiency ($p$):
  • Run 7: Only ~7% of purified liquid reached the sensitive volume.
  • Run 9: Improved to ~43% due to reinforced VCR fittings.
• Outgassing Rates: The fitted outgassing rates at cryogenic temperatures were significantly lower than room-temperature extrapolations, suggesting the Arrhenius extrapolation coefficients have large uncertainties.
• Cold Head Ice: Run 7 data revealed a transient impurity source ($f_{coldhead}$) attributed to ice formation on the cryocooler cold head, which was resolved after operational adjustments.

B. Projection for RELICS-10 and RELICS-50

Using the validated model and projected operational parameters (circulation rates of 20 SL/min for RELICS-10 and 50 SL/min for RELICS-50), the study forecasts:

• Steady-State Electron Lifetime:
  • RELICS-10: $\approx$ 2.1 ms
  • RELICS-50: $\approx$ 1.4 ms
• Impurity Concentration: These lifetimes correspond to electronegative impurity concentrations in the ppb (parts per billion) range.
• Uncertainty Analysis: The dominant uncertainty in the final purity prediction stems from the material outgassing rates (due to the difficulty of extrapolating from room temperature to cryogenic conditions). The getter efficiency and liquid delivery sealing are the next most influential factors.

5. Significance

• Physics Readiness: The projected purity levels (electron lifetimes > 1 ms) are sufficient to detect sub-keV CE$\nu$NS signals with minimal attenuation, ensuring the scientific viability of the RELICS experiment.
• Design Optimization: The study provided actionable feedback for the final detector design:
  • Adoption of the Overflow Chamber design for passive stability.
  • Implementation of reinforced VCR connections to maximize liquid delivery efficiency.
  • Necessity of vacuum baking detector materials to suppress outgassing by an order of magnitude.
  • Critical need to address electric field uniformity (e.g., via optimized field-shaping rings) to prevent measurement saturation in future large-scale detectors.
• Methodological Advance: The developed model serves as a robust tool for predicting purity evolution in future multi-tonne liquid xenon experiments, moving beyond empirical rules to physics-based simulations of impurity transport.

In conclusion, this work successfully bridges the gap between prototype testing and full-scale deployment, providing a validated framework that guarantees the RELICS experiment can achieve the ultra-high purity required for precision reactor neutrino physics.