Importance of Multiple Planes in Single-Phase LArTPC
Exploring the necessity of having 4 planes in a single-phase LArTPC for optimal data collection and reduction of ambiguities through detailed analysis using Toy MC simulations. The study showcases how the number of planes significantly impacts the accuracy and efficiency of hit detection in LArTPC detectors.
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Why do we need 4 planes for single-phase LArTPC? Xin Qian, Tingjun Yang, Chao Zhang 1
How many planes do we need? LArTPC provides us three sources of information: Time: When does a hit arrive? Geometry: Which wire does the hit fire? Charge: How big is the hit? The number of planes largely belongs to the geometry information Intuitively, we know three planes are better than two planes, but how to quantitatively evaluate this? 2
Toy MC Assume that we have n planes If we have a real hit at a particular time slice, it would then fire n wires If there are n wires (one from each plane) passing through a point, this point will be a potential hit Now we can study number of potential hits vs. number of the true hits as a function of the number of planes 3
Description of the Toy MC We assume the wire pitch is 3 mm We assume the layout of the plane is symmetric If 2-plane, the angle is 90 degrees apart If 3-plane, the angle is 60 degrees apart If 4-plane, the angle is 45 degrees apart Each hit only fire a single wire 4
Toy MC, with symmetric wire angles 2-plane will immediate have ambiguities Three-plane setting is much better than two-plane setting, the latter has two much ambiguities 5
Linear Scale For busy situations, four planes are better than three planes as expected 6
Consideration of Dead Channels = n p Assume p is the efficiency of a single plane n = + 1 n n (1 ) p n p p 1 n Let s look at the case where there are some dead channels, their percentage is described as (1-p) We can thus estimate the fake hits as ( ( (1 ) ((1 ) n p F = + ) ) + F p F F 1 1 n n n n p F ) 1 1 n n F represents the number of potential hits 7
Lets take three cases: 1%, 5%, 10% 1% (n/n-1) 5% 10% 3-plane 97% / 99.97% 85.7% / 99.2% 73% / 97% 4-plane 96% / 99.94% 81.5% / 98.6% 66% / 95% 5-plane 95% / 99.90% 77.4% / 97.7% 59% / 92% 6-plane 94% / 99.85% 73.5% / 96.7% 53% / 88.6% 1% dead 5% dead 8
10% dead Clearly, 4plane is much more robust against the dead channels in terms of less fake hits 9
Discussion Two-plane setting has too many ambiguities Three-plane setting is much better Four-plane setting is even better, especially when things are busy Four planes are more robust against potential dead channels efficiency is high The increase of ghost hits are limited 10
Simple Cell Number of cells in a single time slice can be very big 100k We can also look at the so-called merged cell 11
Merged Cell 10% dead Number of merged cells for nue_cc events (< 6 GeV) in DUNE within fiducial volume for all time slices Note: merged cell can be quite big, up to 50 fake hits, for some cases, # of potential hitscan be much larger 12
Challenges in Induction Signal Processing 13
TPC Signal Formation Shockley Ramo theorem = i q E v w q vq: velocity Ew: weighting field q: charge All signals (collection/induction plane) are induction signals For collection plane, unity weighting potential can be reached No additional signal is generated, when the electron is collected 14
Field Response Function The induction signal is bipolar, thus, suppression at low frequency 15
Example of Some Typical Signals MIP signal is about 18k electrons for a 3 mm pitch, so we can look at the signal of 1us, 10 us long, 100 us long, 1000 us long As signal becomes longer in the time domain, its frequency content is shifting towards the low frequency Low-frequency (high-pass) filter will remove long signal 16
Measured Signal ( ) = ( ) ( ) M t S t R t t dt 0 0 M = S( ) R( ) ( ) As expected, the induction plane signal has suppression at low- frequency. The longer signal is, the more reduction is 17
Comparison with Expected Noise Clearly, induction plane is more sensitive to the electronic noise, especially when the signal is long Electronic noise should be scaled down by 1/sqrt(T) 18
Why Region Of Interest (ROI) is important for Induction Signal? ROI window Minimum frequency 2 us 0.5 MHz 10 us 0.1 MHz 100 us 0.01 MHz 1000 us 0.001 MHz The longer the signal is, the less signal to noise ratio is 19
Why ROI is important for Induction Plane Signal? If the signal length is T ,and the ROI is 2*T Minimum frequency will be smaller by ~ 1/2 smaller signal to noise ratio Noise will also be larger due to larger window by ~sqrt(2) Even more difficult to identify the signal Finding proper ROI is crucial for processing induction signal No such complication for the collection signal 20
Discussion Cold Electronics significant reduction of the electronics noise by x5 with respect to warm electronics Less electronics noise means lower threshold for induction plane signal at fixed time length Less electronics noise means more acceptance of the induction plane signal (in terms of time length) 21
Discussion about ROI For single-phase TPC, the induction plane needs ROIs to have the best signal to noise ratio For short-hit, one can find ROI based on the raw signal itself (with a low-frequency filter) This becomes difficult when the signal is long in time (separation between signal and noise is small) In this case, one can rely on the other planes, which have good ROIs, to help to find ROI on the long signal Note: some tracks can just have long signal on only one plane In this case, three other planes is much more desired than the two other planes 22
ENC and DNC for Collection Plane ENC: equivalent noise charge, proportional to the RMS of noise in terms of ADC DNC: deconvoluted noise charge, can be directly compared with the ionization electrons DNC is about factor of 4 smaller than ENC for the collection plane For 2D deconvolution, this factor is even higher 24
For DUNE case We can estimate ENC as 410 electrons for 6 meter We can thus deduce DNC as 410/280.*50.~73 for a time tick For perpendicular track, we have signal to noise ratio as 68:1 2.1 MeV/cm 0.7 0.08 cm ~ 5.0 electrons 23.6 eV k For parallel track, we have signal to noise ratio as 43:1 without electron lifetime 25
For 5 mm LAr, we have 4 * 0.307/2. MeV /mol cm^2 * 18/40. * 1.4/0.5 ~ 0.19 MeV as FWHM So the sigma would be 0.08 MeV So the intrinsic fluctuation is about 8% corresponding to 12.5 : 1 signal to noise ratio Much smaller than the ratio due to the electronics noise! Cold electronics in principle allow for a split of collection signal (two collection planes? Possible?) 27
Summary Cold Electronics reduce noises Significantly enlarge the acceptance of induction plane Enable potential split of collection plane signal (intrinsically limited by the energy deposition fluctuation) Induction plane signal processing is still challenging Need robust method to find ROIs (use other planes, need >=3) Also shorter wires for induction plane? Three plane is much better than two plane in terms of reducing fake hits 3 planes in dual phase! Four planes is needed for the single phase Much more robust against the dead channels Enable 3-other-plane ROI finder for any induction plane 28
