GPU-Accelerated Analytic Simulation of Sparse Signals in Pixelated Time Projection Detector

TL;DR

Two generic contributions are introduced: an effective-charge calculation based on Gaussian quadrature rules for numerical integration and a sparse, block-binned tensor representation that enables efficient FFT-based computation of induced signals on readout electrodes for sparsely activated detector volumes.

Abstract

This paper presents a GPU-accelerated simulation package, TRED, for next-generation neutrino detectors with pixelated charge readout, leveraging community-driven software ecosystems to ensure sustainability and extensibility. We introduce two generic contributions: (i) an effective-charge calculation based on Gaussian quadrature rules for numerical integration, and (ii) a sparse, block-binned tensor representation that enables efficient FFT-based computation of induced signals on readout electrodes for sparsely activated detector volumes. The former captures sub-grid structure without requiring dense sampling, while the latter achieves low memory usage and scalable runtime, as demonstrated in benchmark studies. The underlying data representation is applicable to large-scale detectors and to other computational problems involving sparse activity.

Figures (12)

• Figure 1: Flowchart of signal formation and processing from track segments generated in GEANT4 to analysis-ready simulation data. Physics processes are noted in brackets: R: recombination at the initial ionization; A: electron attachment during transport due to finite lifetime; D: drift under the external electric field; Q: rasterization and charge-weighting using Gaussian quadrature rules; I: induced current calculation using the field response function. The side arrows represent the control flow, annotating the outer loop over raster index $i$ and the inner loop over response index $j$.
• Figure 2: Illustration of the field response grid and quadrature nodes. (a) Field-response grid defined in pixel pitches, showing the central pixel of interest together with its neighboring pixel areas used in the response calculation. (b) Enlargement of a single pixel area from (a), subdivided into a $10\times10$ grid of sub-cells, where electrons are released at the center of each sub-cell. (c) Sampling within selected sub-cells, showing the electron release point (dot) and the associated quadrature nodes (crosses) used for the discrete formulation of the detector response in this article.
• Figure 3: Induced current from a single drifting electron on the pixelated anode plane of the DUNE ND-LAr detector. Top: response measured on the central (reference) pixel for an electron located at the pixel center and at the pixel boundary. Bottom: responses measured on the first (+1) and second (+2) neighboring pixels for an electron located at the center of the reference pixel. The field response model is generated using COMSOL and validated with the pochoir package.
• Figure 4: Trigger--reset scheme of the LArPix ASIC Dwyer:2018phu. Two consecutive hits are illustrated. The channel threshold is represented by a horizontal dashed line. The vertical dashed line indicates the time at which the input signal crosses the discriminator threshold. The integrated charge on the preamplifier is sampled after a fixed window, marked by the dash--dotted line. Following a short reset interval, ending at the dotted line, charge accumulation on the preamplifier resumes.
• Figure 5: Distribution of the number of track segments per neutrino beam spill and per TPC drift volume, simulated from edep-sim.