On proportional scintillation in very large liquid xenon detectors

On proportional scintillation in very large liquid xenon detectors 1 corresp first-author Corresponding author, pratibhajuyal@sjtu.edu.cn Corresponding author, pratibhajuyal@sjtu.edu.cn pratibhajuyal@sjtu.edu.cn https://orcid.org/0000-0001-6577-4419 1 1 1 School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai Key Laboratory for Particle Physics and Cosmology(INPAC), 800 Dongchuan Road, Shanghai 200240, China School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai Key Laboratory for Particle Physics and Cosmology(INPAC), 800 Dongchuan Road, Shanghai 200240, China The charge read out of a liquid xenon (LXe) detector via proportional scintillation in the liquid phase was first realized by the Waseda group 40 years ago, but the technical challenges involved were overwhelming. Although the tests were successful, this method was finally discarded, and eventually nearly forgotten. Currently, this approach is not considered for large LXe dark matter detectors. Instead, the dual phase technology was selected despite many limitations and challenges. In two independent studies, two groups from Columbia University and Shanghai Jiao Tong University reevaluated proportional scintillation in the liquid phase. Both studies established the merits for very large LXe detectors, but the Columbia group also encountered apparent limitations, namely, the shadowing of the light by the anode wires, and a dependence of the pulse shape on the drift path of the electrons in the anode region. The differences between the two studies, however, are not intrinsic to the technique, but a direct consequence of the chosen geometry. Taking the geometrical differences into account, the results match without ambiguity. They also agree with the original results from the Waseda group. Liquid detectors Time projection chambers (TPC) Multiplication and electroluminescence in rare gases and liquids 1 Introduction 1 Liquid xenon (LXe) detectors have undergone rapid development in recent years, which is reflected most obviously in their target masses. New detectors are being used deep underground for direct detection of dark matter (DM), where they look for the rare nuclear recoils of weakly interacting massive particles (WIMP). With an expected rate of less than one interaction/kg/day, sufficiently large and efficient detectors are required for DM detection. The target mass for such detectors has increased from the initial 5 - 10 kg about 15 years ago to the current range of 5 - 10 tons. These DM searches take advantage of the intrinsic properties of LXe, such as high density and atomic mass, self-shielding due to the absence of long-lived radioactive isotopes, and the scalability of the liquid medium. The nuclear recoil of WIMPs can be detected by scintillation light or from liberated charges when an electric field is applied. For comprehensive reviews of LXe detectors, see e.g. [ 1 1 - 3 3 1-3 ]. The simplest design principle for LXe DM detectors uses large, single volume scintillators like the XMASS experiment [ 4 4 ]. However, the deposited energy is rather low (1 - 50 keV ee ), and the measured energy and location do not provide much information about background rejection from X-rays and γ - rays. More information becomes available when the interactions are also registered by additional observables, e.g., by their liberated charge. WIMPs interact with the Xe nucleus producing recoil. This class of events is referred to as Nuclear Recoil (NR). Nearly all the background events are caused by X-rays, β -rays, and γ - rays via Electron Recoil (ER). The two event types can be distinguished by the ratio S2/S1 of the charge signal (S2) and the light (S1). A cut at an appropriate value can suppress the ER background by a factor of nearly 100 [ 5 5 ]. The amount of energy is so small that a charge read out with a charge sensitive amplifier is impossible [ 6 6 ]. The charges to be measured are much smaller than 0.1 fC, and the capacitance of large anodes is very high. The noise level of even the best amplifiers is far above the signal level. For detection of such low charge signals in liquid detectors, Dolgoshein [ 7 7 ] developed the "Dual Phase" (DP) method. The ionization electrons are extracted from the liquid, which generate proportional scintillation in a strong homogeneous electric field in the gas above the liquid. The weak light signal can be detected via noiseless amplification in a photomultiplier tube (PMT). Except for the XMASS experiment, all large LXe DM detectors currently use this principle. However, the DP principle introduces severe restrictions on the geometry and the operating point of detectors. Limitations arise due to obvious conditions such as the liquid level being within the sensitive volume, and the anode being parallel to the liquid level. These conditions become challenging when the diameter of the anode grows beyond 1 m, and the mass is in the order of several tons. However, proportional scintillation for charge measurement in LXe is also possible, and it was first investigated by the Waseda group [ 8 8 , 9 9 ] in 1979. They used the comparatively high energy electrons (1 MeV) from 207 Bi. The high electric field strengths required for electroluminescence (EL) occur in the 1/r field around thin wires. Although the Waseda tests were a success, the group encountered many technological difficulties. The published results were soon largely forgotten. The benefits of EL in single phase (SP) detectors were never exploited. Most of these benefits are associated with the absence of a liquid level in the sensitive volume. Recently, proportional scintillation in the liquid was investigated in view of future large mass DM detectors. The results of two studies, one each from the Columbia Astrophysics Lab (CAL) [ 10 10 ] and Shanghai Jiao Tong University (SJTU) [ 11 11 ], confirmed the original Waseda results. The next step in the development would be a full scale test in a large underground detector, where the performance at low energies under realistic background conditions can be verified. This would be crucial for future large DM detectors [ 12 12 ]. However, any such discussion is short-circuited by remarks that the CAL results imply severe drawbacks, incompatible with high-resolution measurements, namely the shadowing of the light by the anode wires and a dependence of the pulse shape on the drift path of the electrons in the anode region. In this study, we argue that this erroneous interpretation of the results stems from an unfavorable geometry of the anode region in the CAL test detector. We do not present any new measurements, but we fully explain the assumed drawbacks with a critical discussion. The effects will not interfere with the performance of DM detectors. In the future, a single phase design might be able measure the proportional light in liquids. We hope that a detailed understanding of the presumed drawbacks of single phase (SP) detectors might replace DP designs in the future with fewer compromises, easier operation, and reasonably good performance. 2 Dual and Single Phase Detectors 1 All LXe DM detectors currently in operation are DP, with the exception of XMASS, which is only a scintillation detector. In the nomenclature in the literature, the SP often refers to scintillation only detectors. However, in the following discussion, we use SP for any LXe detector not using the gaseous form of xenon. We are mostly interested in TPC detectors that measure both charge and light. Thus, we deal with SP detectors that measure the charge with proportional scintillation in the liquid. 2.1 Dual Phase Method 2 The DP principle is often explained with a drawing similar to Fig. 1 Fig. 1 . The left part of the figure shows the active LXe volume with a sample interaction producing scintillation photons and free drifting electrons. The direct light is then detected by the two PMT arrays below the cathode and above the anode in the gas phase. The charges drift in the applied electric field, and are extracted from the liquid. They produce proportional scintillation in the strong homogeneous field above the liquid level, which in turn is also seen by the two PMT arrays. The right hand side depicts the equivalent SP detector to be discussed later. The main differences are in the anode wire diameter (20 μ m instead of 100 μ m), and the liquid level which is above the top PMT array in this case. The DP method is an elegant way to address the lack of adequate charge sensitive amplifiers. This technique is so sensitive that even a single drifting electron can be detected [ 13 13 ]. Practically, however, this simple principle also imposes stringent limitations on detector design. For example, the anode potential controls two different processes, the extraction from the liquid, and the proportional scintillation in the gas gap. The potential has to be sufficient to assure a good extraction efficiency, but high fields result in a very large gain and the potential formation of electron avalanches or saturation of the read out electronics. The best choice for the anode potential involves a compromise. For these operating conditions, the PMTs have to detect everything from the weak direct scintillation light at low energies to the intense proportional light at high energies. The dynamic range of the read out will eventually define the effective energy range of the measurements. Fortunately, there is a combination of design parameters that yields adequate performance. The gas gap between the liquid and the anode is typically kept at 3-5 mm, and the anode potential around 5 kV. Naturally, the anode must be transparent to the scintillation light, and stretched wires or meshes are used to achieve this. The wires must not sag under the influence of gravity or the electric field within the required precision. Meshes are considered simpler, but the manufacturing by etching or electro-forming does not produce round cross sections. At the sharp corners of the conductors, the 1/r field is much higher than that in the parallel gap. This might lead to local avalanche formation, or worse breakdowns. Localized avalanche formation in a fraction of the events may reduce the energy resolution, especially at high energies where statistical fluctuations in the number of S1 photons are small. Evidence can be observed in the pulse shapes of the charge signals. The observed initial signals from the PMTs are very fast pulses of the direct light at t = t 0 . The subsequent pulses are from the proportional light. With the known drift velocity, the arrival time relative to t 0 is a measure of the z-coordinate of the interaction. There is one S1 in an event, but there can be more than one S2 pulses, e.g., when a γ -ray interacts via Compton scattering. As mentioned earlier, we observe the event types, NR for WIMP candidates and ER for γ -ray backgrounds. The light from both types has the same wavelength, but the decay time and the fraction of charge to light (S2/S1) production is different. The details of the signal formation have been discussed in a recent study [ 14 14 ]. Practically, the discriminator against ER events is the ratio S2/S1. The S1 pulse shape is determined by the original light pulse, and pulse shaping by the cable connections. It is a very fast and prompt signal. The S2 pulses are produced every time the electrons cross the gap between the liquid level and the anode. Therefore, the S2 pulse shape should be a 1 μ s wide flat top pulse. With the usual 10 ns binning, the statistical fluctuation in each bin is large, and it is difficult to detect any structure within the recorded pulse. This very short description already points to the main drawbacks of DP. The active volume must include the liquid level, i.e., S2 depends on the path length between the liquid level and the anode. Therefore, the anode must be completely parallel to the liquid level. Any deviation will make the S2 position dependent. The gap between the anode and the liquid level must be controllable, i.e, we must be able to adjust the liquid level. This becomes a challenge when the diameter of the anode goes beyond 1 m, and the mass of the detector is more than a few hundred kilograms. We also have to remember that the anode and its HV connection are in the gas phase. The anode wires or meshes must be entirely planar, despite the presence of gravity and the forces from the electrical fields of order 10 kV/cm. Any disturbance in the field can lead to spurious discharges. For long run periods, the anode HV is kept below the optimal value to avoid breakdowns, but this implies a reduced extraction efficiency. Detecting the location of the S2 pulses with a large PMT array determines the position of the interaction with good precision, even with the granularity of 3" PMTs. Thus, we get a good spatial resolution in the order of a few mm. However, this only applies for single site events. At high energies, γ -rays prefer to Compton scatter with a small scattering angle, i.e., with low energy deposition. After scattering, they have nearly the same energies, and can Compton scatter again. We can reject such an event as ER, if we can separate the two interaction sites. The position resolution in the anode plane (x-y) is very good with the PMT array, but the 'Double Hit’ resolution is not. We can still separate the two locations in the z-coordinate, i.e., in case they are separate in this projection. This separation is easy to apply, except for small distances due to the square shape of the S2 pulses of 1 μ s duration with statistical fluctuations. Despite these and other drawbacks, DP detectors have still provided good results even in very large detectors such as XENON100 [ 15 15 ], PandaX [ 16 16 ], LUX [ 17 17 ], and XENON1T [ 18 18 ]. 2.2 Single Phase Method 2 The construction of SP detectors is quite similar to DP detectors, but with the liquid level outside the active volume. The anode structure is again an array of three electrodes, two shielding grids with the anode in the center, but all are immersed in the liquid. The anode is made of stretched wires, normally 20 μ m gold-plated tungsten. The arrangement of the electrodes resembles a Multi Wire Drift Chamber, with two shielding grids sandwiching the anode. The event generation, charge drift, and S1 detection are identical to the DP operation. When the electrons approach the shielding grid, they encounter the stronger field [ 19 19 , 20 20 ] of the anode, and are guided by the field lines around the wires of the shielding grid. The anode potential causes a strong 1/r field around the thin wires. Close to the wire when the field strength exceeds 412 <math id="M1"><mrow><msubsup><mrow/><mrow><mo>−</mo><mn>133</mn></mrow><mrow><mo>+</mo><mn>10</mn></mrow></msubsup></mrow></math> kV/cm, the electrons produce proportional scintillation. Above 725 <math id="M2"><mrow><msubsup><mrow/><mrow><mo>−</mo><mn>139</mn></mrow><mrow><mo>+</mo><mn>48</mn></mrow></msubsup></mrow></math> kV/cm, electron multiplication would set in. The given threshold values were measured by the CAL group [ 10 10 ], and are in agreement with the findings of the Waseda and SJTU groups. Since avalanches introduce additional statistical fluctuations, the anode potential should be chosen such that this value cannot be reached before the electrons hit the wire surface. Practically, proportional scintillation only occurs very close to the wire, normally less than the radius value above the surface. There are no space charge effects, since no positive ions are produced. In addition, there are no avalanches since the S2 photons cannot liberate the electrons. The S2 gain is different, since the photons are no longer produced over the long distance between the liquid level and the anode, and the S2 pulse will be less than 100 ns. 2.3 Major Differences of Dual Phase and Single Phase 2 The most obvious difference of SP and DP detectors is the absence of the liquid level in the active volume. There are many more differences when considering the details. The advantages of a SP detector over a DP detector are not the subject of this publication. Their impact on the operation and performance depends on the size and specific design. For a more detailed discussion, see [ 10 10 , 11 11 ]. Keeping a large LXe DM detector in mind, some of the differences in detector design are compiled in Table 1 Table 1 . 1 1 S.N. 1 1 Factors 1 1 Dual Phase 1 1 Single Phase 1 1 Benefits 1 1 1 1 1 Liquid level 1 1 Anode has to be parallel to the liquid level. Precision of wire position is important 1 1 Liquid level not in active volume 1 1 No level control mechanism 1 1 1 1 1 1 1 1 1 1 No leveling of the detector required 1 1 1 1 1 1 1 1 1 1 Electrons can drift in any direction 1 1 1 1 1 1 1 1 1 1 Multiple drift regions are possible 1 1 1 1 1 1 1 1 1 1 No total internal reflection in the liquid level 1 1 1 1 1 1 1 1 1 1 Active shield (LXe) in front of top PMTs 1 1 1 1 1 1 1 1 1 1 Waves or ripples have no effect 1 1 2 1 1 Position of anode 1 1 Anode is about 3 mm above the liquid level in gas 1 1 Anode and HV connections within liquid 1 1 No more ‘spurious anode HV trips’ 1 1 1 1 1 1 1 1 1 1 No extraction efficiency 1 1 3 1 1 Multiple drift regions 1 1 Only one drift region is possible 1 1 Multiple drift regions are possible 1 1 Significantly shorter max drift distance 1 1 1 1 1 1 1 1 1 1 Reduced cathode HV 1 1 1 1 1 1 1 1 1 1 Cathode HV far from PMTs 1 1 1 1 1 1 1 1 1 1 Less electron attachment to impurities 1 1 4 1 1 S2 pulse 1 1 1 ls long flat top S2 pulse 1 1 Short S2 pulses (lt; 100 ns) 1 1 Better double pulse　recognition 3 Assumed Disadvantages for DM detectors 1 There were three independent evaluations of proportional scintillation in LXe. The experiment by the Waseda group proved the feasibility of a charge read out in SP. Two recent studies have aimed at evaluating the method for use in future large DM experiments, one from CAL [ 10 10 ], and the other from SJTU [ 11 11 ]. The technological challenges were eliminated in these studies. The CAL study used a simple geometry of a single 10 μ m wire centered between two planes of stretched wires viewed by two large PMTs, one above and one below the active volume. The wire arrangement was staggered, i.e., the anode wire was between the locations of two adjacent grid wires in the x-y plane. In the SJTU approach, three stretched wire grid planes formed the anode structure. The gold-plated tungsten wires were thicker with 20 μ m diameters, similar to the standard wires in Multi-wire proportional chambers (MWPCs). The grids were aligned such that the wires were located one behind the other in the three planes. Two arrays of four PMTs each were used to detect the light above the anode and below the cathode. The results from all three studies overlap, and would be in favor of the SP approach. However, the CAL study also observed in their experiment that the drifting electrons followed three different paths in the detector. This of course produces different pulse shapes on their anode wire. This would imply a reduction in the energy resolution in large detectors. Since the S2 light is produced only in the last few μ m before the electron hits the wire surface, they also observed a severe shadowing effect in their top PMT array. This reduces the observable S2 signal when only the top array is used for S2 determination like in a DP detector. 3.1 Triple Pulse Component 2 The CAL experiment observed the drifting electrons from a 241 Am alpha source on the cathode. The range of the alphas is of order 20 μ m, i.e., the events are point-like. The ionization electrons drift towards the anode assembly, following the field lines. Close to the shielding grid, the field lines are focused to pass through the spaces in the grid towards the anode. Depending on the exact location of the alpha, the drift path either goes straight up to the wire, or passes through the adjacent spaces in the grid. The path is different in the three cases, producing different pulses. The different paths are shown on the left side of Fig. 2 Fig. 2 . This is the original plot from the CAL publication. However, the implemented geometry is not a good approximation of DM detectors. There will never be only a single anode wire, but an array of wires like in an MWPC. Adding the next adjacent wires will change the field lines for the paths on the two sides. These drifting electrons will be guided to the adjacent anode wires. To evaluate the effect, we do not have to recalculate the field lines, but can deduce the changes by symmetry considerations. This is illustrated on the right hand side in Fig. 2.b Fig. 2.b , showing also the field lines if the adjacent anode wires would have been present. The drift path, and thus, the pulse shape, are then indistinguishable from the central channel. This discrepancy in the results is therefore caused by the use of a single anode wire. 3.2 Shadowing 2 With an anode wire diameter of 10 μ m as in the CAL study, the drifting electrons will produce proportional scintillation once the 1/r field is above the threshold (412 kV/cm). Increasing the field strength would push the start of the region farther away from the wire, but as explained earlier, the field strength at the surface must remain below the threshold for electron multiplication. Staying within these limits practically means that the maximum path length over which proportional scintillation is produced is very short. For easy estimations, it is typically less than the wire radius. Naturally, such a short light source at the surface of a wire will always cast a shadow. Fig. 2 Fig. 2 shows that the electrons in the CAL geometry hit the wire from below. Obviously, most of the light for the top PMT array is blocked by the wire. The CAL group calculated the relative light on the top and bottom PMT in dependence of its distance from wire surface. This calculation is shown in Fig. 3 Fig. 3 , reproduced from the CAL publication. The bottom PMT sees a constant amount of light, but the top PMT not only has a much lower Light Collection Efficiency (LCE), but also varies dramatically with distance. If correct, this plot is misleading. The scale of the plot reaches out to 1 mm away from the wire. With their 10 μ m wire, however, proportional light will only be produced in the first 5 μ m. Since the electrons are focused on the center of the wire, one might expect that the LCE would be 0 at very small distances from simple ray tracing. Fig. 4 Fig. 4 shows the field distribution for the SJTU geometry with aligned wires. The electrons are deviated around the bottom grid wire, and continue until they are bent towards the anode wire by the field lines from the top grid. There are no electrons hitting the anode from the bottom, i.e., in the region of maximum shadow for the top PMT. Many of the electrons approach the wire from the side, and a large fraction of the proportional light will be observed with the top PMT. This is complemented with more photons being seen by the bottom PMT. Thus, both PMTs see an S2 pulse. The S2 light is used for two different tasks, position reconstruction in the X - Y plane, and total charge measurement. With the aligned arrangement of wires, a sizable amount of photons go to the top array. Thus, the first task can be accomplished with just the top PMTs. Additionally, earlier tests with PandaX I data showed that the S2 signal on the bottom array alone is also sufficient to determine the event position. However, PandaX I [ 21 21 ] was a very shallow detector, and the position information might be washed out on the bottom PMTs due to reflections on the Polytetrafluoroethylene (PTFE) walls. This might require instrumentation of the side walls with additional PMTs. For the second task, the total energy measurement, we can add the top and bottom PMT signals. Thus, shadowing will not be a concern in an SP detector for the position determination and the total charge measurement. 3.3 Expected Signal Size and S2 Gain 2 Determining the operating conditions in a DP detector is not an easy task. The number of proportional scintillation photons depends on several parameters, which cannot be chosen freely. Other considerations, like stability of operation and mechanical tolerances also enter the optimization process. For example, the anode potential has to be of order 5 kV to efficiently extract the electrons into the gas phase, but such high voltages enhance the probability of spurious breakdowns at any imperfection of the structure, including the connection in the gas. Thus, the voltage is a compromise between the extraction efficiency and stability of operation. The distance between the anode and the grid wires, typically 5 mm, is another example. This gap is cut in half by the liquid level, and the field above the liquid level is supposedly homogeneous. The gap cannot be made significantly smaller, because of the mechanical tolerances in a large detector with diameter more than 1 m. And any deviation due to sagging wires or imperfections in leveling will have a large local effect on the S2 signal. Any gap width significantly larger would require an excessive anode voltage. The situation in an SP detector is very different. There is no extraction efficiency, and the S2 production only depends on the first 5 - 10 μ m around the anode wire. Field calculations show that displacing the anode wire by a full 1 mm does not significantly change the field in this region. Although it is convenient to have a strong S2 signal, all the light has to be observed by the same PMTs. The read out must be sensitive to the weak S1 light at the lowest energies, as well as the strong S2 light of the highest energies of interest. In a DP detector, the S2 gain is of order 200 - 300 Photon/electron(Ph/e - ). Such a high gain can easily cause the read out to saturate. The S1 light is produced deep inside the active volume, and any given PMT will normally only see a few photons. This is not so for the strong S2 light, as it is produced at the edge of the active volume, and many photons will hit the same PMT. Practically, it means that the read out must have a very large dynamic range to accommodate these signal levels. Traditionally, a digitizer with 14 bit resolution was chosen. This is adequate to record data, and for γ -ray calibration with sources such as 137 Cs at 662 keV, the S2 signal might be out of range. Reducing the overall sensitivity of the read out is not an option, since low energy S1 from DM candidates would no longer be detectable. The CAL group measured the S2 gain in their test as 287 <math id="M3"><mrow><msubsup><mrow/><mrow><mo>−</mo><mn>75</mn></mrow><mrow><mo>+</mo><mn>97</mn></mrow></msubsup></mrow></math> Ph/e - . At this gain, S2 pulses are equivalent in amplitude to their DP detector. To reach this gain, they had to increase the anode potential beyond the avalanche threshold. Thus, their gain includes a factor 14 from electron multiplication. If we remove this factor to avoid electron multiplication, we expect an S2 gain of about 20 Ph/e - . The number of photo electrons in the top PMTs might be too low for an accurate position reconstruction at very low energies. At the lowest energies, a limited amount of multiplication might be a better optimization for detectors. A lower gain does not mean a lower resolution, since the statistics of the measurement is controlled by the number of drifting electrons, which remains unaltered. In the data analysis, most calculations involve both the S2 and S1 signals. In all these cases, the weaker S1 signal dominates the error. Recently, there is a heightened interest in high energy events, e.g. from neutrinoless double beta decay of 136 Xe with a Q-value of 2458 keV. Since the natural abundance of 136 Xe is 8.9 %, similar to present LXe DM detectors, the future LXe DM detectors will also contain a large amount of this isotope. Even at such high energies, the two electrons will form a single-site event, and the length of the track will be much smaller than the spatial resolution of the TPC read out. Due to the reduced S2 gain, the signals can now all be within the limits of the electronics with no saturation. Remaining effects from PMT saturation can easily be corrected. 4 Conclusion and Outlook 1 'DP LXe TPCs’ are powerful tools, and in recent years, they have tremendously contributed to the search for DM. The DP approach is an ingenious way to achieve sensitivity in low energy charge measurements, where even the best Charge Sensitive Amplifiers fail. In future, with ever larger detectors, the DP technique might be too difficult to implement, and might limit performance. Moreover, effects neglected until now might become a limiting factor, e.g., ripples and waves on the liquid Level caused by liquid returning from purification. Proportional scintillation around thin wires in LXe was first studied 40 years ago. It can now be used in SP detectors observing both charge and light. The method offers several unique features that might be beneficial. The evaluation of EL in LXe for DM applications was renewed by two teams, one from CAL, and the other from SJTU. They both explicitly conclude that the method can be used for future DM detectors. Despite the general consent, some results of the CAL study are interpreted as incompatible, specifically, the splitting of the S2 pulse shapes and the shadowing of the S2 light. We showed that the pulse splitting is entirely due to an inaccurate choice of geometry of staggered versus aligned anode wires. Moreover, the shadowing will diminish with a different anode wire arrangement. The remaining effect can be eliminated by observing the S2 light by both the top and bottom PMT arrays. The negative impact can be avoided in very large LXe TPCs. For the next generation of LXe WIMP detectors, we would expect a substantially easier design and a better overall performance. There still remains the concern that the S2 gain might be too low at the low end of the energy range. However, the S2 gain can be increased in an SP detector by simply raising the anode potential, allowing a controlled amount of electron multiplication. This was done in the CAL results, and they reached a gain comparable to that in DP detectors. Unlike the SP mode, it is not easy to control the gain in the DP mode, since the anode potential also determines the extraction efficiency and the probability of spurious breakdowns. We intentionally limited the anode potential to restrict any electron multiplication, since it introduces additional fluctuations. However, at very low energies, the statistics might be poor. This might call for a better optimization of detectors, by allowing a controlled amount of electron multiplication. References M. I. Lopes and V. Chepel , Rare gas liquid detectors. In Electronic Excitations in Liquefied Rare Gases , Ed. W. F. Schmidt ans E. Illenberger , American Scientific Publishers , ( 2005 ) 331 - 388 . Rare gas liquid detectors. In Electronic Excitations in Liquefied Rare Gases E. Aprile , A.E. Bolotnikov , A.I. Bolozdynya et al ., Noble Gas Detectors , WILEY-VCH , ( 2006 ) https://doi.org/10.1002/9783527610020 https://doi.org/10.1002/9783527610020 Noble Gas Detectors E. Aprile , T. Doke , Liquid Xenon detectors for particle physics and astrophysics, Rev . Mod. Phys . 82 ( 2010 ) 2053 . https://doi.org/10.1103/revmodphys.82.2053 https://doi.org/10.1103/revmodphys.82.2053 Liquid Xenon detectors for particle physics and astrophysics, Rev K. Abe , K. Hieda , K. Hiraide et al ., XMASS Detector , Nucl. Instr. Meth. A 716 ( 2013 ) 78 . https://arxiv.org/abs/1301.2815v1 https://arxiv.org/abs/1301.2815v1 XMASS Detector E. Aprile , J. Angle , F. Arneodo et al ., (XENON10 collaboration), Design and Performance of the XENON10 Dark Matter Experiment, Astropart . Phys . 34 ( 2011 ) 679 , https://doi.org/10.1016/j.astropartphys.2011.01.006 https://doi.org/10.1016/j.astropartphys.2011.01.006 (XENON10 collaboration), Design and Performance of the XENON10 Dark Matter Experiment, Astropart V. Chepel , H. Arajo , Liquid noble gas detectors for low energy particle physics , JINST 8 ( 2013 ) R04001 . https://doi.org/10.1088/1748-0221/8/04/r04001 https://doi.org/10.1088/1748-0221/8/04/r04001 Liquid noble gas detectors for low energy particle physics B.A. Dolgoshein et al ., New Method of Registration of Ionizing Particle Tracks in Condensed Matter , JETP Lett . 11 ( 1970 ) 351 https://ui.adsabs.harvard.edu/abs/1970JETPL..11..351D https://ui.adsabs.harvard.edu/abs/1970JETPL..11..351D New Method of Registration of Ionizing Particle Tracks in Condensed Matter M. Miyajima , Y. Hoshi , T. Doke et al ., A Self-Triggered Liquid Xenon Drift Chamber by the Use of Proportional Ionization or Proportional Scintillation, Nucl Instr and Meth . 160 ( 1979 ) 239 . https://doi.org/10.1016/0029-554x(79)90599-8 https://doi.org/10.1016/0029-554x(79)90599-8 A Self-Triggered Liquid Xenon Drift Chamber by the Use of Proportional Ionization or Proportional Scintillation, Nucl Instr and Meth K. Masuda , S. Takasu , T. Doke et al ., A Liquid Xenon Proportional Scintillation Counter , Nucl. Instrum. Meth . 160 ( 1979 ) 247 . https://doi.org/10.1016/0029-554x(79)90600-1 https://doi.org/10.1016/0029-554x(79)90600-1 A Liquid Xenon Proportional Scintillation Counter E. Aprile , H. Contreras , L.W. Goetzke et al ., Measurements of Proportional Scintillation and Electron Multiplication in Liquid Xenon using Thin Wires , JINST 9 ( 2014 ) P 11012 . https://doi.org/10.1088/1748-0221/9/11/p11012 https://doi.org/10.1088/1748-0221/9/11/p11012 Measurements of Proportional Scintillation and Electron Multiplication in Liquid Xenon using Thin Wires T. Ye , K.L. Giboni , X. Ji , Initial Evaluation of Proportional Scintillation in Liquid Xenon for Direct Dark Matter Detection , JINST 9 ( 2014 ) P 12007 . https://doi.org/10.1088/1748-0221/9/12/p12007 https://doi.org/10.1088/1748-0221/9/12/p12007 Initial Evaluation of Proportional Scintillation in Liquid Xenon for Direct Dark Matter Detection J. Aalbers , F. Agostini , M. Alfonsi et al ., Darwin: Towards the ultimate Dark Matter Detector, JCAP 1611 (2016) 017 . https://doi.org/10.1088/1475-7516/2016/11/017 https://doi.org/10.1088/1475-7516/2016/11/017 Darwin: Towards the ultimate Dark Matter Detector, JCAP 1611 (2016) 017 E. Aprile , M. Alfonsi , K. Arisaka et al ., Observation and applications of single-electron charge signals in the XENON100 experiment , J. Phys. G 41 ( 2014 ) 035201 , https://doi.org/10.1088/0954-3899/41/3/035201 https://doi.org/10.1088/0954-3899/41/3/035201 Observation and applications of single-electron charge signals in the XENON100 experiment Hogenbirk , J. Aalbers , P. A. Breur et al ., Precision Measurements of the Scintillation Pulse Shape for Low-Energy Recoils in Liquid Xenon , JINST 13 ( 2018 ) P 05016 . https://doi.org/10.1088/1748-0221/13/05/p05016 https://doi.org/10.1088/1748-0221/13/05/p05016 Precision Measurements of the Scintillation Pulse Shape for Low-Energy Recoils in Liquid Xenon E. Aprile , M. Alfonsi , K. Arisaka et al ., (XENON100 Collaboration), Dark Matter Results from 225 Live Days of XENON100 Data , Phys. Rev. Lett . 109 ,( 2012 ) 181301 . https://doi.org/10.1103/physrevlett.109.181301 https://doi.org/10.1103/physrevlett.109.181301 (XENON100 Collaboration), Dark Matter Results from 225 Live Days of XENON100 Data Andi Tan M. Xiao , X. Cui et al ., (PandaX collaboration), Dark Matter Results from First 98.7 Days of Data from the PandaX-II Experiment , Phys. Rev. Lett. , 117 ( 2016 ) 121303 . https://doi.org/10.1103/physrevlett.117.121303 https://doi.org/10.1103/physrevlett.117.121303 (PandaX collaboration), Dark Matter Results from First 98.7 Days of Data from the PandaX-II Experiment D. S. Akerib , H. M. Arajo , X. Bai , et al ., (LUX collaboration), Results on the Spin-Dependent Scattering of Weakly Interacting Massive Particles on Nucleons from the Run 3 Data of the LUX Experiment , Phys. Rev. Lett . 116 , ( 2016 ), 161302 . https://doi.org/10.1103/physrevlett.116.161302 https://doi.org/10.1103/physrevlett.116.161302 (LUX collaboration), Results on the Spin-Dependent Scattering of Weakly Interacting Massive Particles on Nucleons from the Run 3 Data of the LUX Experiment E. Aprile , J. Aalbers , F. Agostini et al ., (XENON1T collaboration), XENON1T dark matter data analysis: Signal and background models and statistical inference , Phys.Rev. Lett . 99 , ( 2019 ), 112009 . https://doi.org/10.1103/physrevd.99.112009 https://doi.org/10.1103/physrevd.99.112009 (XENON1T collaboration), XENON1T dark matter data analysis: Signal and background models and statistical inference O. Bunemann , T. E. Cranshaw , J. A. Harvey , Design of Grid Ionization Chambers , Can. J. Res . 27 ( 1949 ) 191 . https://doi.org/10.1139/cjr49a-019 https://doi.org/10.1139/cjr49a-019 Design of Grid Ionization Chambers E. Gatti , G. Padovini , L. Quartapelle et al ., Considerations for the Design of a Time Projection Liquid Argon Ionization Chamber , IEEE NS 26 ( 2 ) ( 1979 ) 2910 . https://doi.org/10.1109/tns.1979.4330558 https://doi.org/10.1109/tns.1979.4330558 Considerations for the Design of a Time Projection Liquid Argon Ionization Chamber X. Cao , X. Chen , Y. Chen et al ., PandaX: a liquid xenon dark matter experiment at CJPL , Sci China-Phys Mech Astron , ( 2014 ), 57 . https://doi.org/10.1007/s11433-014-5521-2 https://doi.org/10.1007/s11433-014-5521-2 PandaX: a liquid xenon dark matter experiment at CJPL 10.1007/s41365-020-00797-4 This work has been supported by a grant from the Ministry of Science and Technology of China (NO. 2016YFA0400301). 2020-03-28 2020-06-17 2020-07-13 2020-09-01 2020-09-01 2021-04-10 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2020 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-020-00797-4 http://dx.doi.org/10.1007/s41365-020-00797-4 . 2020 Nuclear Science and Techniques 9 31