Wire Field Response Hanyu WEI Brookhaven National Lab Workshop on Calibration and Reconstruction for LArTPC detectors Dec 10-11, 2018 Fermilab
Single-phase LArTPC detector C. Rubbia 1977 Fully active (space & time) detector with excellent tracking and calorimetry Charged capabilities particles ü Ionized electron drift along E-field ü Sense wire planes at anode as readout Cathode ü Photon sensor to record prompt light Plane signals Incoming Neutrino Wire readout Ionization ü Cost & Power consumption in LAr electrons ✗ Lose information: where the charge along the wire (pixel ! " → 3 ⋅ ! wire) Sense Wire Planes E drfit 12/10/18 2
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What is this “transform”? 12/10/18 17
Field Response Induced current on a wire from a drifting ionized electron Ramo’s theorem " = −& 3 ) ⋅ ⃗ 6 7 2D drift + 2D profile of wire planes *+, − ( ./01/ ) ! "#$ = &(( ) ) Electron drift path (E field) Transparency condition: + a set of bias voltages on three Weighting wire planes with which the ionized electrons are collected potential U plane wires by the last wire plane. given a ü No amplification of target wire V plane wires ionization electrons in single-phase LArTPC Y plane wires ü More wire plane views, less ambiguity 12/10/18 18
Induction & Collection plane • Collection plane Field response ⊗ electronics • Electron collected by the wire response (2 us shaping) • Big unipolar signal • Induction plane Normalization: collection plane integral=1e • Electron drift towards and past • Small bipolar signal LArTPC detector response ruled by field response!! MicroBooNE ü Shape ü Scale Kernel in signal processing ü Smear (charge extraction)! 12/10/18 19
Waveforms for various track topologies JINST 13 P07006 MicroBooNE Wire-Cell TPC full simulation for ideal tracks U Plane V Plane Y Plane 10 35 ADC (Baseline Subtracted) ADC (Baseline Subtracted) ADC (Baseline Subtracted) 5 10 30 0 25 5 ° 0 − 5 ° 10 20 0 ° 20 − 10 ° 30 15 − 5 ° 40 − 15 ° 50 10 − ° 10 60 − 20 ° 70 5 ° − − 15 80 25 0 − 30 − − − − − − − − − − − 150 100 50 0 50 100 150 60 40 20 0 20 40 60 100 80 60 40 20 0 20 40 60 80 100 µ µ µ Sample Time [ s] Sample Time [ s] Sample Time [ s] Vary the angle relative to drift direction for tracks 0 degree: parallel to wire plane, isochronous track Field response makes 90 degree: perpendicular to wire plane, the most extreme prolonged track quite a difference for different tracks and Induction plane has significantly smaller signal for prolonged tracks even different wire planes! though more charge per wire pitch ß bipolar signal cancellation 12/10/18 20
2D Field response (MicroBooNE) • 2D: Time (longitudinal) + Wire (transverse) • The residual 1D: Same along wire orientation (Plot in log scale, arbitrary unit) JINST 13 P07006 Collection Shielding from U plane Long-range induction especially Y-axis projection: Induced current on Target wire target wire given a drifting ionization for induction planes! electron at this transverse distance Difficulty in signal processing (charge extraction)! 12/10/18 21
Long-range induction inter-wire effect • Summation of responses over adjacent wires = Signal on a single wire from an isochronous track (parallel to wire plane) 12/10/18 22
Long-range induction intra-wire effect When an electron drifts at the wire “boundary” (center between two wires) Timing: ü Sizable delay (e.g. 4 us) for collection plane Amplitude: ü Considerable difference for induction plane 2D vs 3D model? [e.g. saddle point in the 2D model is not real …] JINST 13 P07006 12/10/18 23
Importance of field response • Rule the detector response (signal shape for various track topologies) • Long-range induction (inter- & intra-wire effect) • Induction vs collection planes • Kernel of the signal processing (charge extraction: conversion of raw waveforms to number of electrons) which is the first step to all downstream event reconstructions • Specifically, the bipolar signal leads to difficulties for induction planes and to well address this issue is extremely important to fully exploit LArTPC capabilities (all wire planes equally used to mitigate the wire readout ambiguity) See my talk “Signal Processing & 2D deconvolution” tomorrow! 12/10/18 24
How we get the field response? ✗ So far we don’t have a good method to extract the field response in real data due to the complexity of the real signal (lose information …) • bipolar shape & long-range induction of field response, diffusion, track topology dependency, sizable noise ✓ Ab-initio analytic calculation of the field response ✓ Garfield: a drift-chamber simulation program ✓ Geometry ✓ Electrostatic field ✓ Material in drift-chamber ✓ External table of the drift velocity vs E-field ✓ Drift-lines of electrons, current on sense wires ✓ Not support three-dimension structures 12/10/18 25
Garfield calculation setup (MicroBooNE) • Well-aligned 2D profile of the wires for three wire planes (not a “real” but an “average” cross section along the wire orientation) • The 2D setup is an approximation of the 3D wire structures 12/10/18 26
Garfield calculation setup (MicroBooNE) ü Fine-grained: 10 drift paths (per 0.3 mm) per wire pitch ü Long-range: 0 (central wire) ± 10 wires ü 126 (21 wires × 6) field responses are calculated (considering symmetry) 12/10/18 27
Wire-Cell drift simulation ( integrated in larsoft ) • Kernel: 2D field response (long-range & fine-grained & interpolation) !"# $%&'()* = ,-./ ⊛ ,1234-1 ⊛ ,564/1 + 8/29- × ,2;242<-1 (x, y, z, t0, # of electrons) Data-driven input + 2 MHz sampling, analytic method max 2000 mV, 12- bit ADC 1. Fine-grained: Gaussian diffusion + field response (1/10 wire pitch) 2. Long-range: 21 wires 3. Two-dimensional ü Field response (pre-calculated 2D Garfield calculation) à Time & memory optimization ü Pre-amplifier electronic response (gain, shaping time) Kernel: ü Additional response (RCRC filter, intermediate gain) =>?@ A ⋅ =>?@ C ⨂EFGHI C, A ü Ionized electron absorption (electron lifetime in LAr) ⨂KLG>MN (A)⨂QR(A)⨂QR(A) ü Gaussian diffusion (longitudinal / transverse ) ü Fluctuation (for each gird of the discretized 2D Gaussian cloud) 12/10/18 28
Simulation vs Data • The elegant Wire-Cell simulation enables a direct comparison with the raw waveforms in data • Validate the ab-initio calculation of field response • Comparison should be made for a certain track topology • Any inconsistency helps to re-tune the Garfield calculation by changing the setup (generally not needed) JINST 13 P07007 Tracks: angle between x-z plane projection and x axis, 5° < $ %& < 15° 12/10/18 29
Comparison across planes • Since the 2D field response is the kernel in signal processing, the good matching of deconvolved charges from all three wire planes indicate the correctness of the field response. JINST 13 P07007 MicroBooNE Data JINST 13 P07007 MicroBooNE Data ü ~10% smear originating from electronics noise ü Deviation due to the imperfection of detector Agreement in amplitude! Agreement in shape! 12/10/18 30
Summary • The field response is the kernel in both simulation and signal processing, of great importance to make “low-level” reconstruction right. • Obtained by analytic calculation, e.g. Garfield • Long-range induction (2D), fine-grained, proper interpolation • Several ways to validate the calculated field respones • Raw waveform comparison data vs simulation • Charge matching among all planes after signal processing 12/10/18 31
Discussions – long range • Wire range in the 2D field response (e.g. MicroBoonE U plane w/o shielding in front of it) Wire geometry and track topology dependent Isochronous track data vs. simulation 12/10/18 32
Discussions – 3D calculation • Finite Element Method (FEM) • Garfield: not support three dimensional structures • Detector edge effect • CPU/RAM requirements scale with “volume” of the problem • “Impossible”? to do 3D at LArTPC wire readout (mm) scale • Leon Rochester @ slac is braving this challenge with custom FEM • Boundary Element Method (BEM) solves some problems • CPU/RAM requirements scale with “surface” • Fewer software implementations (compared to FEM) • Brett Viren @ BNL is exploring on this • A dedicated test-stand facility would greatly aid in validating the residual 3D effect to a 2D field response calculation ( LArFCS initiated by Chao Zhang @ BNL ). 12/10/18 33
3D Field response ( from B. Viren ) Qualitative agreement (preliminary). Subtle features will be smeared out by electronics. 12/10/18 34
Back up 12/10/18 35
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