A Hybrid 3D/2D Field Response Calculation for Liquid Argon Detectors with PCB Based Anode Plane

Liquid Argon Time Projection Chamber (LArTPC) technology is commonly utilized in neutrinodetector designs. It enables detailed reconstruction of neutrino events with high spatialprecision and low energy threshold. Its field response (FR) model describes the time-dependentelectric currents induced in the anode-plane electrodes when ionization electrons drift nearby. Anaccurate and precise FR is a crucial input to LArTPC detector simulations and chargereconstruction. Established LArTPC designs have been based on parallel wire planes. It allowsaccurate and computationally economic two-dimensional (2D) FR models utilizing the translationalsymmetry along the direction of the wires. Recently, novel LArTPC designs utilize electrodesformed on printed circuit board (PCB) in the shape of strips with through holes. The translationalsymmetry is no longer a good approximation near the electrodes and a new FR calculation thatemploys regions with three dimensions (3D) has been developed. Extending the 2D models to 3D wouldbe computationally expensive. Fortuitously, the nature of strips with through holes allows for acomputationally economic approach based on the finite-difference method (FDM). In this paper, wepresent a new software package pochoir that calculates LArTPC field response for these newstrip-based anode designs. This package combines 3D calculations in the volume near the electrodeswith 2D far-field solutions to achieve fast and precise field response computation. We apply theresulting FR to simulate and reconstruct samples of cosmic-ray muons and $^{39}$Ar decays from aVertical Drift (VD) detector prototype operated at CERN. We find the difference between real andsimulated data within 5%. Current state-of-the-art LArTPC software requires a 2D FR which weprovide by averaging over one dimension and estimate that variations lost in this average aresmaller than 7%.