Proposal of a Geiger-type Single-Phase Liquid Xenon Time Projection Chamber as Potential Detector Technique for Dark Matter Direct Search
PPrepared for submission to JINST
Proposal of a Geiger-type Single-Phase Liquid XenonTime Projection Chamber as Future Large Detector forDark Matter Direct Search
Qing Lin š,š, š State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China,Hefei 230026, China š Department of Modern Physics, University of Science and Technology of China, Hefei 230036, China
E-mail: [email protected]
Abstract: Dual phase time projection chamber using liquid xenon as target material is one of mostsuccessful detectors for dark matter direct search, and has improved the sensitivities of searchingfor weakly interacting massive particles by almost ļ¬ve orders of magnitudes in past several decades.However, it still remains a great challenge for dual phase liquid xenon time projection chamber tobe used as the detector in next-generation dark matter search experiments (about 50 tonne sensitivemass), in terms of reaching suļ¬ciently high ļ¬eld strength for drifting electrons, and suļ¬cientlylow background rate. Here we propose a single phase liquid xenon time projection chamber withdetector geometry similar to a Geiger counter, as detector technique for future dark matter search.Preliminary ļ¬eld simulation and signal reconstruction study have shown that such single phasetime projection chamber is technically feasible and can have suļ¬ciently good signal reconstructionperformance for dark matter direct search.Keywords: Single phase time projection chamber, dark matter detection, liquid xenon detector Corresponding author. a r X i v : . [ phy s i c s . i n s - d e t ] F e b ontents Dual phase liquid xenon (LXe) Time Projection Chamber (TPC) has been gaining popularityin the ļ¬eld of dark matter direct search during past several decades, thanks to its capability ofsimultaneously reconstructing scintillation and ionization signals of one event and event vertex.Experiments using such detector technique, like PandaX-I/-II [1, 2], XENON100/1T [3, 4], andLUX [5], have been able to keep refreshing the world record of sensitivities for high-mass ( > ā¼
50 tonne sensitive mass) [9],to search for dark matter particles that have weaker interaction rate with baryonic matter than currentexperimental precision. Especially in the sense of reaching high cathode voltage to provide enoughdrift ļ¬eld strength and of mitigating high isolated ionization background rate, R&D eļ¬orts areneeded.On the contrary to the extensive attentions that dual-phase TPCs have received, single phaseTPCs have not raised much interest in the ļ¬eld of dark matter direct search. Although single-phaseTPC using liquid argon as material has been widely deployed nowadays in large-scale neutrinoexperiments, such as MicroBooNE [10], ICARUS [11], and DUNE [12], there is no existingdark matter search experiment utilizing such technique. Unlike dual phase TPC which utilizeelectroluminescence in gas to convert charge signals into proportional lights and collect them,traditional single phase TPC collects charge signals through wire planes [11], thus has a higherā 1 āharge collection threshold that is not suļ¬cient for sensitive dark matter direct search. Recentmeasurements of electroluminescence in LXe [13, 14] have raised new possibilities for single phaseLXe TPC that can reach low charge collection threshold. The results in [14] have shown that theproportional lights in LXe start to become visible when the ļ¬eld strength reaches 412 kV/cm. Theestimated electron ampliļ¬cation is comparable to the one obtained through electroluminescence ingaseous xenon in a dual phase LXe TPC.In this manuscript, we propose a single phase LXe TPC which collects charge signals throughelectroluminescence in LXe and has diļ¬erent geometry than traditional single phase TPC as usedin neutrino experiments. In Section 2, a review of dual phase TPC and a description of proposedGeiger-type single phase TPC will be given. In Section 3 and 4, we show the results of ļ¬eldsimulation and study of signal reconstruction for such proposed single-phase TPC.
Dual phase TPC is currently used in second-generation dark matter search experiments, suchas PandaX-4T [6], XENONnT [7], and LZ [8], which are under commissioning. It is also thedefault detector technique that is going to be used in future next-generation dark matter searchexperiments, like DarkSide-20k [15], DARWIN [9], and PandaX-30T [16]. Although dual phaseTPC has shown excellent signal responses (low threshold and high background rejection power)in past experiments, next-generation dual phase TPCs will face non-trivial challenges since theywill reach unprecedented size (sensitive mass of about several ten tonne) in the ļ¬eld of dark matterdirect search, especially in terms of reaching suļ¬ciently high voltage for drifting electrons andmitigating isolated ionization backgrounds. On the other hand, single phase TPC which collectscharge through electroluminescence in LXe is another possible technique that can be used in next-generation detector. The electroluminescence in LXe has been observed and the ampliļ¬cation factoris comparable with the one obtained through electroluminescence in gaseous xenon.
Dual phase TPC consists of mainly three parallel plane electrodes, light reļ¬ectors and light sensors.PTFEs are traditionally used as light reļ¬ectors, and photo-multipliers (PMTs) as light sensorsplaced at top and bottom of cylindrical TPC sensitive volume. Fig. 1 shows a typical dual phaseTPC diagram. Three parallel plane electrodes are (from bottom to top) cathode, gate, and anode.Usually gate electrode is grounded, negative and positive voltages are applied to cathode andanode, respectively. Cathode voltage is typically in the order of several ten kV to provide a driftļ¬eld strength of several hundred to thousand kV/cm in the sensitive volume. Distance betweenanode and gate is typically ā¼ ā¼ ā¼ ā¼
10 kV/cm in gas for xenon [19]). Because of the high voltages applied to cathode andanode and their proximity to the top and bottom PMTs, additional electrode planes (named screenelectrodes) are needed in front of top and bottom PMTs for their protection.ā 2 ā asLiquid
AnodeGateCathodeBottom screenTop screen
Top PMTsBottom PMTs E drift electrons S1S2 S2S1Time
Figure 1 : Diagram of a typical dual phase TPC.The sensitive volume in a dual phase TPC is a cylinder between cathode and gate planes. Depositenergy in sensitive volume is converted into prompt scintillation lights and ionization electrons.Prompt lights are detected by PMTs, and called S1 conventionally. Ionization electrons are driftedtowards the proportional ampliļ¬cation region which is between gate and anode planes. Understronger ļ¬eld in ampliļ¬cation region, electrons are extracted into gas and produce proportionallights which are detected by PMTs and named S2. S1 signal has fast time response in the scaleof several ten to hundred nanoseconds, determined by the singlet and triplet decay constant ofexcimer of target element. On contrary, S2 signal has relatively slow time response in scale ofseveral microseconds, which is dominated by the electron diļ¬usion during drifting and the electrontraveling in gas gap after liquid surface extraction. Therefore, S1 and S2 signals are distinguishableon recorded event waveform. The ability to reconstruct the scintillation and ionization signalsof an energy deposition is the key of dual phase TPCās success in dark matter direct search.Amplitudes of S1 and S2 signals, as well as the pulse shape information of S1 signal in certainmaterial like argon, can provide discrimination power between electronic recoils (ERs) and nuclearrecoils (NRs), and can further reduce the eļ¬ective backgrounds induced by gamma and betas. Inaddition, time information of S1 and S2 signals and S2 signalās pattern on PMTs can be used toreconstruct the longitude and transverse positions, respectively, giving 3-D position reconstructionof interaction vertex. This also provides extra rejection power against background from external ormaterial radiations through ļ¬ducialization, and against neutron backgrounds through discriminationbetween single and multiple scatters.The excellent reconstructions of S1, S2 and event vertex requires high level of ļ¬eld uniformityin both the drift and ampliļ¬cation regions. On the other hand, high transparency of electrode planeis critical in order to maintain a suļ¬ciently high light collection eļ¬ciency to search for dark mattersignals. This demands the electrode plane to be made of ļ¬ne wires and maintain good tension onā 3 āhem under cryogenic temperature, which by itself is a great challenge to multi-ten-tonne dual phaseTPC. On top of this, the ļ¬eld strength near cathode wires may be large enough so that the probabilityof electrons from electrode metal being extracted out through Fowler-Nordheim eļ¬ect [20] is non-trivial. Extracted electrons can produce proportional scintillation through electroluminescence inliquid material under very strong ļ¬eld near cathode wire, limiting the voltage applied to cathode.Besides, existence of large amount of metal electrodes and liquid surface in dual phase TPC isvery likely one of the major causes for large amount of isolated ionization signals (events withouta detected over-threshold scintillation signal) in past experiments (such as in XENON100 [19]).Photoionization on metal electrodes produces single- or multi-electron emission, and liquid surfacemay trap part of the drifted electrons and release them with a time delay [21, 22]. The issues ofcathode voltage and isolated ionization signals can become even more critical in next-generationdetector as the detector scales up.
We propose a new single phase TPC with detector geometry similar to a Geiger counter. Itampliļ¬es charge signals through electroluminescence in LXe. The simplest conceptual diagram ofthe proposed Geiger-type single phase TPC can be seen in Fig. 2. Geiger-type Single phase TimeProjection Chamber (GS-TPC) has also a cylindrical sensitive volume. Unlike the parallel electrodeplanes in a dual phase TPC, GS-TPC has parallel wires serving as electrodes. A single wire at thecentral axis of GS-TPCās cylinder serves as anode, surrounded by several wires with ļ¬xed spacingas gate wires to regulate the ampliļ¬cation ļ¬elds. Wires at the cylindrical side of GS-TPCās sensitivevolume, parallel to the central axis and equally spaced between adjacent wires, serve as cathode.Light sensors, such as PMTs, can be instrumented to cover the surface of GS-TPCās cylindrical side.
Anode GateCathode PMTs
Liquid E drift E drift E drift E drift XY Z R
AnodeGateCathode CathodePMTs PMTs E drift E drift LiquidS1 S2
Figure 2 : Conceptual diagram of the proposed Geiger-type single phase TPC. Left is the top view,and right plot is the side view. ā 4 āhe signal detection mechanism of GS-TPC is similar to that of a dual phase TPC, but theionized electrons are drifted to the central axis of sensitive volume, and go through proportionalampliļ¬cation near anode wire. Such a GS-TPC geometry can achieve a ļ¬eld above that is needed forelectroluminescence in LXe near anode wire of reasonable macroscopic size, and in the meantimecan also maintain moderate ļ¬eld strengths in the active volume between cathode and gate. The mostimportant information is the radial and zenith positions of an event which is required to performļ¬ducialization of GS-TPC. The radial position in GS-TPC can be reconstructed using the drift time,and the zenith position may be reconstructed using the hit pattern of S2 on light sensors. Theangular position is not critical since detector geometry is axial symmetrical. The S2 hit pattern mayhave ādark zonesā because the proportional lights are produced very near anode wire, aiding thereconstruction of angular position to some extent. Compared to the dual phase TPC, the cathodevoltage can be much small and still maintain moderate ļ¬eld strength in most part of sensitivevolume. The region close to cathode may have low drift ļ¬eld strength and even ļ¬eld distortion,as well as high background rate, and will be removed in analysis. Also, mechanically it is mucheasier to maintain tension on wires in GS-TPC than wires on electrode planes in dual phase TPC. Inaddition, absence of liquid surface and less electrode material used can bring less isolated ionizationsignal in GS-TPC. However, ļ¬eld strength in GS-TPC along radial axis is changing which may bringchallenges for reconstructions of energy and radial position. Dedicate calibrations using injectedsources, such as š Kr [23], with uniform event distribution expected are required to correct theeļ¬ect brought by non-uniform drift ļ¬eld. Ī¼ m wire200- Ī¼ m wire X [meter]X [meter] Y [ m e t er ] V o l t ag e [ V o l t] Figure 3 : Simulated ļ¬eld lines and voltages in gate-anode region for the prototype GS-TPC. Leftplot is for wire with diameter of 200 š m and right plot for wire with diameter of 100 š m. The coloraxes show the voltage at diļ¬erent position.We have performed ļ¬eld simulations using COMSOL [24], to estimate the ļ¬eld conļ¬gurationof a prototype GS-TPC and to conduct a feasibility check of such TPC. The prototype GS-TPC isassumed to have a cylindrical sensitive volume with radius of 10 cm, with 36 cathode wires and 12PMTs instrumented. Twelve gate wires, equally spaced between adjacent wires, are placed 5 mmā 5 āway from the central anode wire. Two simulations are performed with diļ¬erent wire diameters,100 š m and 200 š m, both of which are commercially available wire sizes. Wires made by stainlesssteel or tungsten with such diameters are anticipated to be strong enough, to tolerate the tensioncaused by cryogenic shrinking of large-scale GS-TPC. In most commonly used operation mode, cagesurface of PMT is set at negative voltage (e.g., about -800 V for R8520 1ā Hamamatsu PMT [25]).In order to have minimal amount of electrode wires, there is no screen electrode wires to be placedin front of PMTs in GS-TPC. Therefore, the cathode voltage can not be too high for the protectionof the PMTs. In simulations of the prototype GS-TPCs, the cathode voltage is ļ¬xed at -1 kV andthe gate is grounded. Radius[cm] F i e l d s t r e n g t h [ k V / c m ] Āµ m wire cathode, gate, anodeMean field strengthLXe electroluminescence 10 -3 -2 -1 R e l a t i v e f i e l d s t a n d a r d d e v i a t i o n [ Ć % ] Radius[cm] F i e l d s t r e n g t h [ k V / c m ] Āµ m wire cathode, gate, anodeMean field strengthLXe electroluminescence 10 -3 -2 -1 R e l a t i v e f i e l d s t a n d a r d d e v i a t i o n [ Ć % ] Figure 4 : Distribution of TPC volume on ļ¬eld strength vs. radial position. The red and magentasolid lines give the mean and standard deviation of ļ¬eld strength, respectively, at diļ¬erent radialposition. The vertical dashed lines indicate the position of gate and cathode wires, respectively.The radius of the prototype GS-TPC is 10 cm. The left and right plots are for prototype GS-TPCswith 200- š m and 100- š m wires, respectively. The shaded regions indicate the allowed ļ¬eld rangefor electroluminescence in LXe [14]. In the results, gate wires are grounded and cathode wires areset to -1 kV. +30 kV and +18 kV are applied to anode wires for GS-TPCs with 200- š m and 100- š mwires, respectively.
100 120 140 160 180 200
Radius[um] S c i n t ill a t i o n g a i n [ p h / e / u m ] Āµ m wire
60 80 100 120 140
Radius[um] S c i n t ill a t i o n g a i n [ p h / e / u m ] Āµ m wire Figure 5 : S2 gain as a function of radius for 100- š m (left) and 200- š m (right) anode wires.ā 6 āig. 3 shows the simulated ļ¬eld lines and voltages in gate-anode region for the prototype GS-TPCs with wire diameters of 100 š m and 200 š m, respectively. Fig. 4 shows more quantiļ¬cationof ļ¬eld simulation results at diļ¬erent radial positions for forementioned GS-TPCs. With anodevoltage at +30 kV (+18 kV), prototype GS-TPC with 200- š m (100- š m) wires can surpass thethreshold ļ¬eld strength of about 412 kV/cm [14] near anode wire for electroluminescence in LXe.Using the estimated S2 gain factor of (2.09 + . ā . ) Ć ā ph/e ā /(kV/cm)/ š m obtained by [14], theampliļ¬cation factors are calculated to be 792 + ā and 409 + ā ph/e ā (summarized in Table 1 aswell), respectively, for GS-TPC with 200- š m and 100- š m anode wire. The proportional scintillationstarts at approximately 80 š m (41 š m) away from the anode wire surface for 200- š m (100- š m)wire, which corresponds to an S2 duration of 31 ns (16 ns) assuming a saturated drift velocity of ā¼ š s [26]. This indicates that the time proļ¬le of the proportional lights in such GS-TPCis dominated by electron diļ¬usion during drift. The relation between proportional scintillation gainand distance to anode wire surface for 100- š m and 200- š m anode wires can be found in Fig. 5. Radius[cm] F i e l d s t r e n g t h [ k V / c m ] cathode, gate, anodeMean field strengthLXe electroluminescence -3 -2 -1 R e l a t i v e f i e l d s t a n d a r d d e v i a t i o n [ Ć % ] Figure 6 : Distribution of TPC volume on ļ¬eld strength vs. radial position for a prototype GS-TPCwith radius of 1.5 m. The ļ¬gure description is the same as in Fig. 4.Except for the regions that are roughly 1 cm apart from the gate and cathode wires in prototypeGS-TPC, the standard deviation of ļ¬eld strength in active volume is at approximately 1% level.In analysis, the regions near gate and cathode are to be removed because of the high expectedbackground rate due to radioactivity in wires and from outside. In active volume with moderateļ¬eld variance, the ļ¬eld strength ranges from about 80 V/cm near the cathode to about 700 V/cmnear the gate. Also the number of gate and cathode wires can be increased in large-scale GS-TPCto provide even lower standard deviation of ļ¬elds. An additional simulation for large GS-TPC withsensitive volume radius of 1.5 m, 450 cathode wires, 200- š m wires, and 100 PMTs, is performed,which is shown in Fig. 6. The anode and gate voltages are increased to +40 kV and +10 kV,respectively. Results show that the standard deviation of ļ¬eld strength can reach ā¼
1% in most partof active volume. ā 7 āire diameter [ š m] Anode voltage [kV] S2 ampliļ¬cation factor [ph/e ā ] Singe e ā S2 duration [ns]100 18 409 + ā + ā Table 1 : S2 ampliļ¬cation factors and SE S2 durations for diļ¬erent gate-anode conļ¬gurations inGS-TPC.
Unlike dual phase TPC which has time duration of about several hundred nanoseconds for S2scaused by single electron (SE), GS-TPC has only couple of tens of nanoseconds for SE signals.Although the large S2 signals still can be distinguished through the signal duration in GS-TPC sinceelectron diļ¬usion dominates the time proļ¬le, it has less discrimination power between S1s andSE S2s compared to dual phase TPC. This may cause the increase of isolated S1 signal rate, thusincrease of accidental pileup background. We would like to argue that discrimination power can becompensated by classiļ¬cation using pulse shape discrimination (PSD).
Time [ns] -4 -3 -2 -1 A m p li t u d e [ A . U . ] S1 in 10-cm GS-TPCS2 in 10-cm GS-TPCS1 in 150-cm GS-TPCS2 in 150-cm GS-TPC
Hit Number P S D p o w e r [ x % ] Figure 7 : Left plot shows the time proļ¬le of S1 and SE S2 in GS-TPCs with radius of 10 cm and150 cm, respectively. Right plot shows the classiļ¬cation accuracy between S1s and SE S2s, usinga simple 2-hidden-layer multi-layer perceptron neural network, as a function of hit number, forGS-TPCs with radius of 10 cm and 150 cm, respectively.In LXe, the scintillation lights are generated through excimer decay [27] which has two decaycomponents: fast and slow decay components with lifetime of ā¼ ā¼
24 ns [27] correspondingto singlet and triplet state decays, respectively. The ratio between the singlet and triplet componentsdepends on the recoil type [28], and is about 0.8 for ERs and 7.8 for NRs [28]. Therefore, theS1 pulse shape can be modeled as two exponential functions. On the other hand, SE lights aregenerated, more or less, uniformly along the accelerated electron trajectory near the anode wire (SeeFig. 5). Left plot of Fig. 7 shows the expected pulse shape between S1 and SE S2 in GS-TPCs withradius of 10 cm and 150 cm, respectively. The diļ¬erence in the pulse shapes between 10-cm andā 8 ā50-cm GS-TPCs is caused by the optical light propagation in detector. The time proļ¬le calculationis based on the singlet-to-triplet ratio of 0.8 for ER, which is more conservative in our analysiscompared with 7.8 for NR. Also, ERs are the major background in dark matter direct searches. Thelight propagation in GS-TPC is considered and obtained through optical simulation using GEANT4toolkit [29]. The pulse shape of single photon hit on light sensors is not taken into account, sincethe shaping depends greatly on the type of sensor. A classiļ¬cation using multi-layer perceptron(MLP) with 2-hidden-layer is conducted to estimate the PSD power for GS-TPCs with diļ¬erentdetector size (radius of 10 cm and 150 cm) and diļ¬erent sampling size (typically 1 ns, 4 ns, and10 ns per sample). Training and testing samples are sampled using left plot of Fig. 7, giving auniform hit number distribution between 1 and 40. In the right plot of Fig. 7 shows the PSD power(deļ¬ned as the accuracy of classiļ¬cation) as a function of hit number. GS-TPC with radius of150 cm basically has less PSD power over a smaller one with 10-cm radius, because of the smearingof pulse shape due to optical light propagation in detector. PSD power can reach as high as ā¼ ā¼
80% for 10-cm and 150-cm GS-TPCs, respectively, at hit number of 20. However, both PSDpowers reduce to about 60% when hit number gets as low as 2. This indicates that reaching highcharge ampliļ¬cation factor and high light collection eļ¬ciency for proportional scintillation will beimportant in terms of minimizing the accidental pileup background in such GS-TPC. In addition,the sample size also plays a role in the PSD power for small GS-TPC (improved by approximately5% when reducing sample size from 10 ns to 4 ns or 1 ns), but makes little diļ¬erence for largeGS-TPC. Ļ /2 Ļ Ļ /2 2 ĻĻ [rad] ā ā ā Z [ mm ] R = 98.5 mm; Total hit = 31971 Ļ /2 Ļ Ļ /2 2 ĻĻ [rad] ā ā ā Z [ mm ] R = 0.6 mm; Total hit = 30443 Ļ /2 Ļ Ļ /2 2 ĻĻ [rad] ā ā ā Z [ mm ] R = 1442.6 mm; Total hit = 17973 Ļ /2 Ļ Ļ /2 2 ĻĻ [rad] ā ā ā Z [ mm ] R = 0.7 mm; Total hit = 26137
Figure 8 : Hit pattern of four sample simulated events. The top and bottom rows are events fromGS-TPCs with radius of 10 cm and 150 cm, respectively. The left and right columns are events thatare close to side wall and central anode, respectively. The radial position and total hit number ofeach event are given in the title above each plot.and Rayleigh scattering length of 50 cm in LXe. The reļ¬ectivity of teļ¬on used is assumed to be99%. Teļ¬on planes are placed at top and bottom of GS-TPCs to increase light collection. ThePMT window size is 1-inch square. Two GS-TPCs are simulated: one with radius of 10 cm andheight of 30 cm, and the other with radius of 150 cm and height of 300 cm. Numbers of PMT ringsare instrumented on the side of GS-TPC. PMT rings are spaced with a ļ¬xed distance on š axisto have a light coverage of 50% on the side wall. There are totally 150 and 21948 PMTs for theGS-TPCs with radius of 10 cm and 150 cm, respectively. The PMT arrangements and hit patternsof four sample signals are shown in Fig. 8. The four sample hit patterns are with events all occuron š axis and with š =0 mm. Two of them are very close to TPC side, and two of them are near thecenter axis. Visually, the pattern is more spread as the vertex is further away from the cylindricalside wall, especially for large GS-TPC. Fig. 9 gives the reconstructed š resolution as a function of š position of events. For 10-cm radius GS-TPC, the š resolution can reach approximately 2 cm atthe top and bottom, and minimally about 3 mm in the center of TPC. However, the š resolution of150-cm radius GS-TPC is much worse because Rayleigh scatter smears out š information of theoriginal event. The š resolution is ā¼
20 cm at top and bottom, and ā¼ š resolution near top and bottom edges is critical and 20 cm is not an acceptable resolutionfor future 3rd generation detector. One possible way to improve this is to have light sensors alsoplaced at the top and bottom. Top-bottom asymmetry (TBA) of S2 can provide reconstruction powerof š position. We perform an additional simulation of 150-cm radius GS-TPC with 41 Ć
41 PMTsā 10 ā Z truth /H det āŗ ( Z r e c - Z t r u t h ) ļ¬ [ mm ] R=10cm, H det =30cmR=150cm, H det =300cm
Figure 9 : PMT pattern reconstructed š resolution as a function of š normalized by detector height.The blue circles and red triangles represent the results from GS-TPCs with radius of 10 cm and150 cm, respectively. Z[mm] ( N t o p - N b o tt o m ) / ( N t o p + N b o tt o m ) A . U . Z[mm] ( N t o p - N b o tt o m ) / ( N t o p + N b o tt o m ) Ć Ć Ć Ć Ć Figure 10 : Left plot shows TBA distribution of simulated events in a GS-TPC with radius of 150 cmand height of 300 cm. 1681 PMTs (41 Ć
41) are placed at both top and bottom. Right plot shows theexpected TBA as a function of Z for diļ¬erent scenarios of number of kept top/bottom PMTs.matrix at both top and bottom surfaces. Each matrix covers roughly a 1 m Ć š positionsof simulated events are sampled uniformly from -150 cm to 150 cm (with 0 as the center of GS-TPC).In Fig. 10, the left plot shows the TBA distribution of 1 million simulated events and mean TBA asa function of š position, which can be used to reconstructed š . It is worth noting that placing lightsensors at top and bottom of GS-TPC may bring challenges in maintaining good ļ¬eld uniformity intop and bottom regions, and may increase radioactive background (gamma-rays and neutrons) fromPMT material. It is preferrable to minimize the number of PMTs at top and bottom. In this work,we check the reconstruction results with diļ¬erent number of 1-inch PMTs placed in the central areaof the top and bottom basis plane: 3 Ć
3, 5 Ć
5, 11 Ć
11, 21 Ć
21, and 41 Ć
41 PMTs, corresponding toā 11 ārea coverage of 7.6 Ć Ć Ć Ć Ć . Right plot ofFig. 10 gives the expected TBA (with suļ¬ciently large number of hits on top and bottom PMTs) asa function of š position, for diļ¬erent scenarios of number of top/bottom PMTs as mentioned above.Using simple toy MC, we can derive the resolution of TBA-based position reconstruction. Fig. 11shows the bias and resolution of TBA-based reconstruction as a function of š with number of hitson top/bottom PMTs of 10, 100 and 1000, respectively. The reconstruction resolution āļø š· ( š ššš ) is deļ¬ned as the standard deviation of reconstructed š . The left column of Fig. 11 shows thatthe TBA-based reconstruction has large bias due to very low statistics of number of hits, as wellas >
10 cm resolution. Most importantly due to the low light collection eļ¬ciency of the oppositePMTs, the TBAs of events near top/bottom basis surface are most likely to be 1, leading to largebias and reduced reconstruction power near top/bottom surface, the region of which is of the mostinterest in terms of background rejection through ļ¬ducialization. Despite the regions near top andbottom edges, the reconstruction performances between diļ¬erent scenarios of number of kept PMTshave minor diļ¬erence.
Z[mm] p D ( Z r e c ) [ mm ] Ć Ć Ć Ć Ć Z[mm] Z[mm] Z r e c - Z t r u t h [ mm ] Number of Hit =10 Ć Ć Ć Ć Ć Number of Hit =100
Number of Hit =1000
Figure 11 : Top and bottom rows show the bias and resolution of TBA-based reconstruction,respectively, for diļ¬erent scenarios of number of kept PMTs. The left, middle, and right columnsgive the bias and resolution with number of hits of 10, 100, and 1000, respectively.Besides TBA, the hit pattern on top/bottom PMTs can be used to conduct š reconstruction,especially in near top/bottom regions because of the proximity of top/bottom PMTs to proportionallights. Fig. 12 shows the normalized hit pattern on top PMTs (41 Ć
41) of four sample eventswith diļ¬erent distances to top plane. Number of hits for these events and later samples in CNNreconstruction are roughly between 700 to 3000, depending on number of kept PMTs. It is visiblethat the hit pattern gets more spread as the event happens closer to top. We perform CNN-basedreconstruction for diļ¬erent scenarios of kept number of PMTs. There is minor diļ¬erence in theperformance of the reconstruction for diļ¬erent scenarios. The slight diļ¬erence between diļ¬erentscenarios can be due to the diļ¬erent CNN architecture (depth and complexity), which is out ofscope of this work and can be further optimised with realistic detector. The results are shown inFig. 13. In the region that is within 10 cm away from top/bottom plane, the resolution of š thatā 12 ās reconstructed using hit pattern on top/bottom PMTs can reach sub-cm level when hit number isat about one thousand. In addition, it does not need a large number of PMTs covering top/bottomplane to reach a high š resolution. Fig. 13 shows that the nine PMTs in the very center of top/bottomplane have the most pattern information for reconstruction.
40 20 0 20 40
X[mm] Y [ mm ] Z=1400 mm
40 20 0 20 40
X[mm] Y [ mm ] Z=1450 mm
40 20 0 20 40
X[mm] Y [ mm ] Z=1490 mm
40 20 0 20 40
X[mm] Y [ mm ] Z=1499 mm
Figure 12 : Hit patterns on top 41 Ć
41 PMTs of simulated events. Four events happen 100, 50, 10,and 1 mm away from top plane, respectively.
We propose a new type of single phase TPC (GS-TPC), which has detector geometry similar toa Geiger counter and has the potential to be used as dark matter direct search detector in futureexperiment. With a single wire as anode at central axis of cylindrical sensitive volume, the ļ¬eldstrength near the anode wire can reach the threshold ļ¬eld strength for electroluminescence in LXe(420 kV/cm) with moderate voltages applied. Such GS-TPC conceptually can reduce the rate ofisolated small ionization signals which can aļ¬ect the signal reconstruction and form accidentalbackgrounds, reducing dark matter search sensitivity. GS-TPC has no liquid-gas surface so that ithas no small ionization signals coming from delayed extraction of electrons [21, 22]. Besides, GS-ā 13 ā
00 80 60 40 20 0
Distance to top sensor[mm] āŗ ( Z r e c - Z t r u t h ) ļ¬ [ mm ] Ć Ć Ć
11 PMTs21 Ć
21 PMTs41 Ć
41 PMTs
Figure 13 : Reconstruction resolution as a function of distance to top plane for diļ¬erent scenariosof kept number of PMTs.TPC can have minimal ļ¬eld strength around cathode wires, mitigating the electron emission frommetal wire through Fowler-Nordheim eļ¬ect [20]. In addition, GS-TPC has less mechanic demandson electrode compared to a dual-phase TPC which can help to maintain the stable operation in largedetector.On the other hand, the challenges are that GS-TPC has non-uniform ļ¬eld in sensitive volumealong radial position, proportional lights for a single electron has time proļ¬le close to promptscintillation lights, and position reconstruction. Field simulation shows that in most part of GS-TPCās active volume, the standard deviation of ļ¬eld strength can reach approximately 1% level. It isable to reach good signal quality with correction for GS-TPCās radial dependence of ļ¬eld. The timeduration of SE S2s in GS-TPC is similar to that of prompt S1, but do have diļ¬erent pulse shape. Wehave performed simple MLP-based classiļ¬cation between S1s and SE S2s in GS-TPC using toy MCdata. Results show that PSD classiļ¬cation power can reach about 90% when the light collection ofS2 is suļ¬ciently large to have SE S2 at >
40 hits. The digitizer sampling rate plays a minor rolein the classiļ¬cation performance. Radial positions of events in GS-TPC are reconstructed usingdrift time, thus having high resolution. Angular positions are with low resolution due to Rayleighscattering and ļ¬nite number of gate wires in large GS-TPC. However angular information of eventsis not critical in an axial symmetrical detector. š positions of events in GS-TPC are of greatimportance in terms of rejecting external gamma-rays and surface backgrounds. Using hit patternon detector side, the š reconstruction quality is not good ( ā¼
20 cm near top/bottom) due to the factthat PMTs are far away from detector central axis where S2s are produced. Instrumenting lightsensors on top and bottom surfaces can greatly improve the resolution of š position reconstructionin GS-TPC, both through the top-bottom asymmetry and reconstruction using hit pattern. In regionsnear top/bottom planes, the best š resolution estimated can reach sub-cm level for hit number of ā¼ References [1] X. Xiao et al. (PandaX-I), Phys. Rev. D , 052004 (2015).[2] A. Tan et al. (PandaX-II), Phys. Rev. Lett. , 121303 (2016).[3] E. Aprile et al. (XENON100), Phys. Rev. Lett. , 181301 (2012).[4] E. Aprile et al. (XENON1T), Phys. Rev. Lett. , 111302 (2018).[5] D. Akerib et al. (LUX), Phys. Rev. Lett. , 021303 (2017).[6] H. Zhang et al. (PandaX-4T), Science China Physics, Mechanics & Astronomy , 31011 (2019).[7] E. Aprile et al. (XENONnT), Journal of Cosmology and Astroparticle Physics , 031 (2020).[8] D. Akerib, C. Akerlof, S. Alsum, H. AraĆŗjo, M. Arthurs, X. Bai, A. Bailey, J. Balajthy, S. Balashov,D. Bauer, et al., Physical Review D , 052002 (2020).[9] J. Aalbers et al., Journal of Cosmology and Astroparticle Physics , 017 (2016).[10] R. o. Acciarri (MicroBooNE), Journal of Instrumentation , P02017 (2017).[11] R. Acciarri, C. Adams, R. An, C. Andreopoulos, A. Ankowski, M. Antonello, J. Asaadi, W. Badgett,L. Bagby, B. Baibussinov, et al., arXiv preprint arXiv:1503.01520 (2015).[12] B. Abi, R. Acciarri, M. Acero, M. Adamowski, C. Adams, D. Adams, P. Adamson, M. Adinolļ¬,Z. Ahmad, C. Albright, et al., arXiv preprint arXiv:1807.10334 (2018).[13] L. Arazi, A. Coimbra, R. Itay, H. Landsman, L. Levinson, B. Pasmantirer, M. Rappaport, D. Vartsky,and A. Breskin, Journal of Instrumentation , C12004 (2013).[14] E. Aprile, H. Contreras, L. Goetzke, A. M. Fernandez, M. Messina, J. Naganoma, G. Plante,A. Rizzo, P. Shagin, and R. Wall, Journal of Instrumentation , P11012 (2014).[15] C. E. Aalseth, F. Acerbi, P. Agnes, I. Albuquerque, T. Alexander, A. Alici, A. Alton, P. Antonioli,S. Arcelli, R. Ardito, et al., The European Physical Journal Plus , 131 (2018).[16] J. Liu, X. Chen, and X. Ji, Nature Physics , 212 (2017).[17] E. Aprile, K. L. Giboni, P. Majewski, K. Ni, and M. Yamashita, IEEE Transactions on nuclear science , 1986 (2004).[18] C. M. B. Monteiro, Ph.D. thesis (2011).[19] E. Aprile et al. (XENON100), Journal of Physics G: Nuclear and Particle Physics , 035201 (2014).[20] E. Bodnia, E. Bernard, A. Biekert, E. Boulton, S. Cahn, N. Destefano, B. Edwards, M. Gai, M. Horn,N. Larsen, et al., arXiv preprint arXiv:2101.03686 (2021).[21] P. Sorensen, arXiv preprint arXiv:1702.04805 (2017). ā 15 ā
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