2x2 Demonstrator: Modular Testbed Design

• 2x2 Demonstrator is a modular prototype comprised of four interconnected modules arranged in a 2x2 formation, enabling scalable testing in particle physics, neutron detection, and cellular automata.
• Its design integrates advanced techniques such as pixelated charge readout, dielectric light collection, and synchronized data acquisition to achieve high event rates and precise 3D imaging.
• The demonstrator validates critical technologies for robust argon purity, event deconvolution, and scalable neutron detection, providing actionable insights for full-scale deployments.

A 2x2 Demonstrator denotes a technical prototype or critical testbed composed of four interconnected modules arranged in a two-by-two formation. Such demonstrators appear in diverse domains, notably in modular high-rate particle detection technology and cellular automaton emulation. This article details the principal 2x2 demonstrators in experimental particle physics, neutron detection, and theoretical computer science, emphasizing their structure, functionality, and the scientific rationale behind their implementation.

1. Definition and Domains of the 2x2 Demonstrator

A 2x2 Demonstrator is an engineered system or model comprised of a quartet (two-by-two) of building blocks—be they detection modules or functional partitions—serving as a scalable prototype for larger systems. In the context of hardware detectors, the 2x2 configuration validates integration and readout architectures before full-scale deployment. In cellular automata, "2x2" refers to a specific local block-update rule, yielding emergent phenomena distinctive from canonical automata like Conway's Game of Life.

Domains of implementation include:

• Modular liquid argon time-projection chambers (LArTPCs) in neutrino physics (Collaboration et al., 6 Sep 2025).
• Pixelated neutron detection modules for high-flux experiments and industrial radiography (Jaksch et al., 2017).
• Theoretical models in 2D cellular automata, particularly the B36/S125 "2x2" rule (Johnston, 2012).

2. Modular Design in Particle and Nuclear Detection

2x2 LArTPC Demonstrator (DUNE ND-LAr)

The 2x2 Demonstrator developed for the DUNE Near Detector consists of four individual LArTPC modules, each with two optically isolated volumes for a total of eight independent drift regions. Each module, measuring 60% of the planned full transverse dimension and 40% of the full height, is suspended in a liquid argon bath within a 6.1 m³ vacuum-jacketed cryostat. The modules are physically joined with millimeter-scale separations maintained by steel cross bars and sealed with indium to preserve cryogenic integrity. Upstream and downstream, solid-scintillator tracking planes (repurposed from the MINERvA experiment) enable charged particle tracking before and after interaction within the argon volume (Collaboration et al., 6 Sep 2025).

Key features of the 2x2 design here include:

• Modular segmentation to improve scalability, reduce pileup, and inform systematics relevant to high-rate beam operation.
• Mechanical and electrical interfaces designed for future expansion into arrays covering substantially larger fiducial masses.

2x2 SoNDe Neutron Detector Demonstrator

The SoNDe 2x2 Demonstrator integrates four identical neutron detector modules in a 2×2 frame. Each module incorporates a pixelated scintillator/carrier glass sandwich, a Hamamatsu H8500 multi-anode photomultiplier tube (MaPMT), and a two-stage readout system with separate front-end analog processing and a digital controller (S-DAM). The full 2x2 array validates small-module integration, aiming for footprints less than 5×5 cm² per module, and supports high event rates (up to 100 kHz/channel), with sub-100 ns timing accuracy and Ethernet-based data acquisition (Jaksch et al., 2017).

3. Enabling Technologies and Architectural Innovations

Charge and Light Readout (LArTPC)

The LArTPC 2x2 Demonstrator implements several novel technologies:

• A "low-profile resistive field shell" composed of a carbon-loaded Kapton film laminated onto G10. This replaces traditional resistor-chain cages, ensuring a uniform drift field with minimized material and sheet resistances on the order of 10⁹ Ω/sq for field shells and 10⁶ Ω/sq for cathode panels.
• Native 3D ionization pixelated imaging via LArPix ASICs, each monitoring 64 channels. The charge readout system captures two spatial coordinates from the pixel array, with drift time encoding the third dimension, yielding full 3D event reconstruction from on-chip self-triggered pixels. Signal windows of ~200 µs overlap the 9.6 µs beam spill for efficient event capture.
• Complementary dielectric light readout systems: TPB-coated fiber Light Collection Modules (LCMs) with SiPMs and ArCLight (ACL) tiles with dichroic mirror foils, providing approximately 29% geometrical coverage for scintillation photon detection with sub-nanosecond resolution.
• Continuous argon recirculation through O₂/H₂O getters maintains electron lifetime ~1.25 ms, ensuring extraction of ionization charges with minimal loss.

High-Rate Modular Dataflow (SoNDe)

Critical performance parameters validated by the SoNDe 2x2 include:

• A linear ADC response to input charge (demonstrated to ~80 pC).
• Reliable event identification per channel, each with a timestamp and per-event energy estimate during calibration.
• Clock synchronization among modules with mean trigger delays ~110 ns, ensuring inter-module data alignment for seamless image reconstruction (Jaksch et al., 2017).

4. Calibration, Testing, and Operational Performance

LArTPC 2x2 (DUNE)

Commissioning involved detector assembly at the University of Bern, validation with cosmic ray data, underground transport and installation at Fermilab (102 m below grade), and phased cryogenic filling via 160 L dewars. During the physics-quality run (4.5 days), more than 30,000 neutrino interactions were recorded in the liquid argon active volume, verified via both on-beam triggers and off-beam self-triggering. Visualized event displays confirm the successful separation of overlapping neutrino interactions, cosmic muons, and rock muons within a single beam window (Collaboration et al., 6 Sep 2025).

Operational challenges addressed include:

• A leak at the module-to-cryostat indium seal, initially compromising LAr purity, overcome by continuous gaseous argon addition and replacement of a defective condenser component.
• Calibration of SiPM bias voltages (mean 46.8 V), ASIC pedestal/threshold configuration, and optimization of integration windows matched to beam structure.

SoNDe 2x2

Electronic performance was validated using synthetic test pulses (9.4–94 pC) to confirm linearity, and timing variation was characterized as a function of trigger threshold. Irradiation in a neutron beam (for example, with 4.7 Å neutrons) demonstrated discrimination of neutron versus gamma events and confirmed uniform detector response across all submodules. Synchronous, Ethernet-based data collection supported coherent image formation with submodule identification, satisfying specifications for event rate and timing precision (Jaksch et al., 2017).

5. Scientific, Industrial, and Computational Applications

LArTPC (DUNE ND-LAr)

The 2x2 Demonstrator validates, at experimental scale, the modular LArTPC concept intended for the DUNE Near Detector. Its successful operation in a high-flux neutrino beam with robust argon purity and three-dimensional imaging capability directly informs:

• Strategies for pileup mitigation and event deconvolution in high-rate environments.
• Design specifications for scaling up to square-meter-scale detectors with hundreds of modules.
• Improvement of systematic controls crucial to DUNE's oscillation and CP violation physics reach.

SoNDe 2x2

The modular, high-rate neutron detector paradigm enabled by the SoNDe 2x2 design opens applications in:

• Neutron scattering at spallation sources, through modular expansion to large-area detectors.
• PET imaging, industrial non-destructive evaluation, process control in food/extrusion industries, and radiation portal security systems.
• Scenarios demanding robust event discrimination (neutron/gamma), compact form factor, and scalable synchronous data aggregation.

Cellular Automaton "2x2"

In theoretical computational science, the "2x2" label refers to the life-like B36/S125 rule, which exactly emulates Margolus block dynamics on 2x2 blocks. The system serves as a venue for analytic investigation of pattern evolution, oscillator periodicities (with formula $p=2(2^k-1)$ for $2\times (4n)$ rectangles), and upper limits on propagation velocities for "spaceships":

• Diagonal limit $c/3$ (maximum one-third speed of light equivalent per time step).
• Orthogonal limit $c/2$. These results provide a touchstone for complexity and emergence in discrete dynamics (Johnston, 2012).

6. Scalability, Limitations, and Future Pathways

Both hardware and computational variants of the 2x2 Demonstrator offer pathways for systematic scaling:

• For LArTPCs, lessons from the 2x2 configuration guide full-scale demonstrators and the assembly of rows or planes of active modules, directly impacting future ND-LAr implementations.
• For neutron detectors, transition from 2x2 modules to meter-scale coverage relies on validated electrical, mechanical, and DAQ interconnects proven in the demonstrator phase.
• In cellular automata, analysis of block oscillator families and Margolus block emulation in 2x2 establishes that periods and dynamics can be systematically extended by algebraic construction, with demonstrator patterns serving as archetypes for these generalizations.

A plausible implication is that integration density, mechanical serviceability, and time synchronization remain the core design constraints as 2x2 demonstrator architectures transition to large-scale, deployment-grade configurations.

7. Summary Table: Representative Specifications for 2x2 Demonstrator Systems

Domain/theme	2x2 Demonstrator Structure	Notable Performance Metrics
LArTPC (DUNE ND-LAr)	Four modules, pixelated CRS, light traps	>30,000 events, 500 V/cm, 1.25 ms electron lifetime
SoNDe Neutron Detector	Four modules, scintillator+MaPMT+S-DAM	100 kHz/channel, <100 ns timing, linear to ∼80 pC
Cellular Automaton (CA)	2×2 blocks, Margolus emulation	Oscillator period $2^\ell(2^k-1)$, speed $c/3$, $c/2$

Each implementation of a 2x2 Demonstrator is defined by its strict modularity, its role in bridging unit-scale design with system-scale deployment, and its function as a controlled environment for elucidating the scaling, integration, and emergent properties fundamental to its field.