Waveform Fit

The AGET output waveform has an asymmetric shape, as shown in Fig. 5. A fitting function is used to fit the waveform to extract information from the signal waveform, mainly temporal (e.g., peak position) and amplitude information. The waveform is fitted using the following function [31]: $f(t)=B+A{\left(\frac{t-t_0}{\tau }\right)}^3\text{exp}\left(\frac{t-t_0}{\tau }\right)\text{Θ}\left(t-t_0\right)\mathrm{,}$ (1) where B represents the baseline of the waveform, A is a quantity related to the amplitude of the waveform, t₀ is the starting time, τ is the electronics shaping time, and Θ is the Heaviside step function, which has the functional form: $\text{Θ}\left(t-t_0\right)=\{\begin{array}{cc}\mathrm{0,}& t-t_0<0\\ \frac{1}{2}\mathrm{,}& t-t_0=0.\\ \mathrm{1,}& t-t_0>0\end{array}$ (2) To calculate the amplitude, we first determine the maximum value of the fitting function within the region where the waveform is located and subtract the baseline. The resulting value is referred to as the Amplitude. The position at which the Amplitude occurs is the peak position (peakPos). Additionally, the time information of the charged particle is extracted using constant fraction discrimination (CFD), specifically at 20% of the Amplitude, which is denoted as CFDRisingTime. The initial values of the fitting function parameters vary depending on the sampling frequency and shaping time of the AGET. The signals of X-rays and charged particles (such as α particles) were fitted as shown in Fig. 5. For X-rays, which are point sources, the raw pulse signal induced on the readout pad can be approximated as a δ-like function. In contrast, for charged particles such as α particles, the raw pulse has a certain width because the signal collected by the pad corresponds to a short section of the track. The adopted fitting function effectively describes the waveforms of both types of signals.

Fig. 5Full-screen View

Waveforms of the X-ray signal (a) and α particle signal (b), along with the fits of the electronics shaping function. The blue triangles represent the raw sampling points, and the red curves show the fitting function curves. The signal is digitized at a sampling rate of 25 MHz, with 512 12-bit samples, a peaking time of 1 μs and a trigger delay of 15 μs. The term “3-3-18” denotes the specific electronic channel: the 18^th channel of the 3^rd AGET chip on the 3^rd front-end electronics board

X-ray test

The field cage was temporarily removed for the ⁵⁵Fe source test. The voltage divider circuit for the THGEM power supply remained consistent with those used in other tests, as shown in Fig. 3. The cathode consisted of a 25 μm thick double aluminized Mylar film, and the ⁵⁵Fe source was placed outside the drift region, directly in front of the cathode film. The length of the drift region was 4 mm.

X-rays deposit their entire energy at a single point in the operating gas, resulting in a small electron cloud produced by single X-ray photon ionization. This typically generates a signal on one or two pads. Different positions on the THGEM were irradiated using the X-ray source. By selecting events in which only one pad was triggered, we reconstructed the energy deposition spectrum generated by the X-rays on each pad, as shown in Fig. 6. In the spectrum, the full-energy peak and the Ar escape peak of the X-ray are clearly visible. The escape peak is located at half the energy of the full-energy peak. Due to the small drift region, annihilation photons were more likely to escape from the sensitive region of the TPC, resulting in a higher count in the escape peak. The voltage of the cathode was set to 2400 V. With a THGEM operating voltage of -2500 V (-663 V for THGEM 1 and -612 V for THGEM 2), a sampling frequency of 25 MHz, and a shaping time of 1 μs, the scTPC achieved an energy resolution (FWHM) of approximately 22% for the 5.9 keV X-ray.

Fig. 6Full-screen View

Energy spectrum of the 5.9 keV X-ray on one pad

Due to factors such as the manufacturing process of the THGEM, detector assembly, readout electrode collection efficiency, transmission of the electronics, and data acquisition system, gain nonuniformity may occur across different channels. To characterize this nonuniformity, the full-energy peak position in the X-ray energy spectrum for each pad can be extracted. By normalizing the peak positions of all channels, the fluctuations between the channels can be calibrated, as shown in Fig. 7(a). The gain fluctuations across the readout plane reveal that the gain was relatively low for the central electrodes and high for the peripheral electrodes. This discrepancy may be due to differences in the tension experienced by the peripheral and central electrodes during the THGEM manufacturing process and detector assembly. When processing charged particle events, the normalized gain correction factors derived from the X-ray test, as shown in Fig. 7(b), can be applied in the data analysis to partially correct for the degradation in energy measurement caused by channel fluctuations.

Fig. 7Full-screen View

(Color online) Maps of normalized gain (a) and gain correction factor (b) tested with the X-ray for the Ar (95%) + iC₄H₁₀ (5%) gas mixture at local atmospheric pressure (850 mbar). The operating voltages for THGEM 1 and THGEM 2 were -650 V and -600 V, respectively

Drift velocity

The drift velocity of electrons in the scTPC drift region is crucial for the reconstruction of three-dimensional tracks of charged particles. Two methods were adopted to measure the drift velocity: The first method used a 266 nm UV laser. The laser beam was split into two beams through a half-lens (50% transmissive and 50% reflective). These two laser beams entered the drift region of the scTPC through two collimating holes (approximately 1 mm in diameter) on the inner wall of the field cage, and the drift velocity was calculated from the time difference between the two laser beams. Although attempts were made to keep both laser beams parallel to the readout plane, this was still difficult to achieve. There is still an angle between the two laser beams. Therefore, we extrapolated the two laser tracks back to their respective vertices (i.e., the positions of the two collimating holes). The distance between collimating holes was 16 cm. At each of the two collimating hole locations, there was a distinct and pronounced peak in the drift time, as shown in Fig. 8(a). The drift velocity was calculated based on the time difference between collimating holes. The measured drift velocity was 3.95 cm/μs under an electric field of 200 V/(cm atm) in an Ar(95%)+iC₄H₁₀(5%) gas mixture.

Fig. 8Full-screen View

Two methods of measuring the electron's drift velocity. Panel (a) shows the drift time distribution for two laser tracks at the vertex, with the left peak corresponding to the collimating hole with a drift length of 2 cm, and the right peak corresponding to another collimating hole with a drift length of 18 cm. Panel (b) depicts the drift time distribution for cosmic ray tracks, with the red curves representing the fitted curves for the rising and falling edges. The sampling frequency is 25 MHz. The operating gas is the Ar(95%) + iC₄H₁₀(5%) gas mixture at local atmospheric pressure (850 mbar). The reduced electric field in the drift region is 200 V/(cm atm)

The second method utilizes cosmic-ray muons to calculate drift velocity. There were no strict restrictions on the direction of the cosmic rays, which could pass through the scTPC from any position within the drift region. A 20 cm × 20 cm plastic scintillator was placed on the top side of the scTPC to serve as a trigger and provide a common zero time for all cosmic-ray events. This setup allowed for the extraction of the time distribution in the drift direction for all cosmic-ray tracks, as shown in Fig. 8(b). The drift time exhibited a platform-like distribution, with steep leading and trailing edges indicating the closest point (infinitely close to the upper surface of THGEM 1) and the farthest point (infinitely close to the cathode surface) from the upper surface of THGEM 1, respectively. The leading and trailing edges were fitted using the following edge functions [43]: $f(t)=B+A\frac{e^{-t/{\tau }_1}}{1+e^{\left(t-T_0\right)/{\tau }_2}}\mathrm{,}$ (3) where T₀ is the time point of the leading edge (or the trailing edge), which corresponds to the point with the maximum slope. The time difference between the leading and trailing edges reflects the total length (20 cm) of the drift region. The measured drift velocity was 3.91 cm/μs under an electric field of 200 V/(cm atm) in an Ar(95%) + iC₄H₁₀(5%) gas mixture. The drift velocities obtained by both methods are in close agreement, and the drift velocity calculated using Garfield++ [44] is 4.12 cm/μs. The deviation between the calculated and measured results may be attributed to the presence of gas impurities.

The equipment for measuring drift velocity using a laser is complex and only provides the drift velocity at a specific position. In contrast, the method using cosmic rays offers a simpler setup for characterizing the average drift velocity. Since a flow-type gaseous chamber is used, the gas pressure in the chamber fluctuates with the external air pressure, and the purity of the operating gas may vary. Consequently, calibration of the electron drift velocity is essential for each test and experiment. Using cosmic rays, real-time measurement of the drift velocity can be performed easily and quickly.

Track reconstruction

The particle track is three-dimensional and can be projected onto the xy-plane and zy-plane. The x-axis is aligned with the pad row, and the y-axis is aligned with the pad column, as shown in Figs. 2(c) and 7(a). The z-axis represents the direction of the drift electric field, opposite to the drift direction of the electron and perpendicular to the readout plane. The xy-plane is parallel to the readout plane, while the zy-plane is perpendicular to it. A pad with a detected signal is classified as a hit, with the x- and y-coordinates of the hit corresponding to the geometric center of the pad in the horizontal and vertical directions, respectively. All hits in the same row are grouped into a cluster. The y-coordinates of the cluster are defined as the y-coordinates of the row, while the x-coordinates are the average of the x-coordinates of all hits, weighted by the deposited charge (i.e., Amplitude). The z-coordinates of the hits are calculated by multiplying the drift time by the drift velocity, which is 3.91 cm/μs as determined in Sect. 3.3. The drift time is calculated from the leading edge of the signal waveform relative to the zero-th time bucket, i.e., CFDRisingTime as shown in Fig. 5(b). Since the drift time is not an absolute value, it must be referenced to a common zero point. The z-coordinate of the cluster is the average of the z-coordinates of all hits, weighted by the Amplitude. The reconstructed track is a straight line that fits through a series of clusters.

The track resolution consists of the spatial resolution on the xy-plane (referred to as x-resolution) and the spatial resolution on the zy-plane (referred to as z-resolution). The spatial resolution was evaluated using the residuals, which represent the distance from the charge center of the cluster to the fitted track line. For example, in the xy-plane, ${\text{residual}}_x=\frac{k{y}_i+b-x_i}{\sqrt{\left(k^2+1\right)}}\mathrm{,}$ (4) where (xi,yi) represents the charge center of the cluster, and k and b are the parameters of the fitted track line. The standard deviation σ (referred to as the standard deviation throughout the text) of the residual distribution is defined as the x-resolution [23, 45]. The same approach is applied to the zy-plane. Track reconstruction and position resolution measurements of long tracks for the scTPC were performed using cosmic-ray muons and heavy-ion beams.

Cosmic ray test

Cosmic ray muons traverse the scTPC in stochastic directions and positions, enabling a comprehensive assessment of the overall performance of the scTPC. The energy deposition from cosmic rays within the scTPC is low, leading to a suboptimal signal-to-noise ratio. As a result, higher amplification is necessary to clearly detect the cosmic ray track. This amplification may cause unrelated hits to accompany the muon track, resulting in positional inaccuracies (Fig. 9(a)). Additionally, due to the large size of the plastic scintillators, there are instances when multiple tracks are detected within the same sampling time window, though such occurrences are rare. Therefore, track recognition must be performed prior to track reconstruction [46-51]. To address this challenge, we employ the Hough transform for track recognition and derive a flag value ddd in the Hough space to distinguish between effective and ineffective hits [52, 53]. A hit with a d value within a specific range is considered effective, and the judgment condition is determined by analyzing the ddd-distribution of multiple tracks. The Hough transform has been widely applied and extended to particle track recognition due to its simple and intuitive transformation method. The particle under investigation in our future experiments exhibits characteristics similar to cosmic rays, specifically long tracks that penetrate the TPC, with typically only one track present per event. In such cases, the classical Hough transform is effective for recognizing and reconstructing secondary particle tracks. The original coordinate system (x,y,z) (in Euclidean space) is consistent with the coordinate system defined in Sect. 3.4 and Fig. 2 (c).

Fig. 9Full-screen View

(Color online) Hough transform and track recognition on the xy-plane are shown in the following figures. The hit distribution in Euclidean space is presented in panel (a), where the stray hit is highlighted in the yellow circle. Panel (b) shows the hit distribution in Hough space, with the common point indicated by a black circle. Panel (c) depicts the dxy distribution of one track. The hit distribution after track recognition in Euclidean space is shown in panel (d), and panel (e) displays the corresponding hit distribution after recognition in Hough space

The (x,y) coordinates of hits in Euclidean space are first transformed into Hough space, where a point in Euclidean space corresponds to a curve in the Hough space. When multiple hits lie along the same linear track, their corresponding curves in Hough space intersect at a common point. In contrast, the Hough curves of ineffective hits located away from the track do not converge at this common point, as shown in Fig. 9(a) and (b). The coordinates of the common point in Hough space, (θ_xy,com, r_xy,com), were determined, and the minimum distance dxy from each Hough curve to the common point was calculated. For a point on the track, its dxy value should be nearly equal to or slightly greater than zero, while the dxy value of a stray point will be larger, as illustrated in Fig. 9(c). After comparing across multiple tracks, points with dxy≤4.0 are considered effective hits, while those with dxy > 4.0 are deemed ineffective. After applying this dxy discrimination, stray hits can be rejected, and track recognition can be successfully achieved on the xy-plane, as shown in Fig. 9(d) and (e). Note that this threshold may require adjustment depending on the detector design and the complexity of events involving multiple tracks.

Track recognition on the zy-plane using the Hough transform follows a similar approach. The (z,y) coordinates of the hits in Euclidean space are transformed into Hough space, as shown in Fig. 10. The coordinates of the common point in Hough space, (θ_zy,com, r_zy,com), are determined, and the minimum distance dzy from each Hough curve to the common point is calculated. On the zy-plane, points with $d_{zy}\le 2.0$ are considered effective hits, while points with dzy > 2.0 are deemed ineffective.

Fig. 10Full-screen View

(Color online) Hough transform and track recognition on the zy-plane are illustrated in the following figures. Panel (a) shows the hit distribution in Euclidean space, while panel (b) presents the hit distribution in Hough space, with the common point circled by a black circle. Panel (c) depicts the dzy distribution of one track. The hit distribution after track recognition in Euclidean space is shown in panel (d), and panel (e) displays the hit distribution after recognition in Hough space

With the discrimination by dxy and dzy based on the Hough transform, stray hits are discarded. The residual distributions on the xy-plane and zy-plane were then extracted to observe the x and z-resolutions of the cosmic ray track, as shown in Fig. 11. The residual distribution did not follow a standard Gaussian function. Therefore, we fit the residual distribution with the sum of two Gaussian functions, both with means close to zero. The fitting function [54] is expressed as: $\begin{array}{ll}f(x)\hfill & =\frac{A_1}{\sqrt{2\pi }{\sigma }_1}\text{exp}\left(-\frac{{\left(x-{\mu }_1\right)}^2}{2{\sigma }_1^2}\right)\hfill \\ \hfill & +\frac{A_2}{\sqrt{2\pi }{\sigma }_2}\text{exp}\left(-\frac{{\left(x-{\mu }_2\right)}^2}{2{\sigma }_2^2}\right)\mathrm{,}\hfill \end{array}$ (5) where A₁ and A₂ are the integrals of the two Gaussian functions, μ₁ and μ₂ are their means, and σ₁ and σ₂ are the standard deviations of the two Gaussian functions. The track resolution is determined as the weighted root mean square (RMS) of σ₁ and σ₂, given by: ${\sigma }_x=\sqrt{\frac{A_1{\sigma }_1^2+A_2{\sigma }_2^2}{A_1+A_2}}\mathrm{.}$ (6) If the residual distribution can be accurately fitted by a single Gaussian function, the track resolution is considered to be simply given by the standard deviation σ of that Gaussian. However, if the distribution exhibits more complexity and cannot be described by a single Gaussian, two Gaussian functions are employed to fit the residual distribution, as explained previously. For the cosmic ray tracks, efficient tracks were identified and reconstructed. This resulted in a track resolution of 0.86 mm in the x-direction and 0.79 mm in the z-direction. Additionally, in the z-direction, an angular resolution of approximately 0.2° for θ was achieved, considering a typical track length of about 20 cm. This level of precision is critical for several applications, such as calibrating the energy-θ relationship of triton generated from (³He,t) nuclear reactions and reconstructing the angular distribution of the cross section.

Fig. 11Full-screen View

Residual distributions of the muon track on the xy-plane (a) and zy-plane (b). For the cosmic ray track, the x-resolution is 0.86 mm, and the z-resolution is 0.79 mm. The red curves represent the double-Gaussian fitting functions

Beam test

To validate the functionality of the scTPC in the presence of a heavy-ion beam background, a beam test was conducted at the HIRFL. The detector was fully assembled, as shown in Fig. 12. A nonpolarized ³He gas target, encapsulated in a sealed stainless-steel container with three atmospheres of ³He gas (providing an effective target thickness of approximately 2.2 × 10²¹ atoms/cm²), was positioned at the center of the scTPC. The cylindrical stainless-steel container measured 20 cm in length and 3.8 cm in diameter, with a sidewall thickness of 200 μm (i.e., the exit window for secondary particles was 200 μm thick). The two end faces of the container, each 2 mm thick, served as the incoming and outgoing windows for the beam. Given that the beam energy is high but the intensity is low, the energy loss in the beam windows is minimal compared to the total energy of the beam, rendering the heating power negligible. The target was placed on a 3D-printed holder to ensure that its center axis was aligned with the center of the beam. The heavy-ion beam did not pass through the TPC but instead passed through the ³He target. Large-angle scattering of secondary particles penetrated the sidewall of the stainless-steel container and entered the scTPC. The detector was housed in a stainless-steel chamber. The beam used was a 350 MeV/u Kr beam with an intensity of approximately 10⁶ particles per second. The beam entered the chamber through a 25 μm thick window made of aluminized Mylar film with a 40 mm diameter. It then passed through a second 25 μm thick window of aluminized Mylar film, this time with a 55 mm diameter, before exiting the chamber. Eight CsI(Tl) crystals, each with a thickness of 2 cm and a length of 20 cm, were positioned in a curved array around the scTPC outside. The signals from the CsI(Tl) crystals were sequentially extracted, amplified, and discriminated using a preamplifier (Mesytec MPR-16) and a shaping/timing filter amplifier (Mesytec MSCF-16). After an OR operation, the signals from the eight crystals were converted into TTL signals to trigger the AGET. Consequently, the scTPC signal recorded by the AGET corresponds to the long track traversing the scTPC and the energy deposited in the CsI(Tl) crystals.

Fig. 12Full-screen View

(Color online) Complete setup for the detector assembly of the beam test. The red line is the direction of the beam

As shown in Fig. 13, the track is often accompanied by a number of background particles, primarily distributed in the upper part of the readout electrode (near the target). Therefore, track recognition is crucial for the data analysis of beam tests. Track recognition based on the Hough transform is used to reconstruct the particle track, as shown in Fig. 14, with dxy≤4.0 and dzy≤2.0, consistent with the cosmic ray track. The residual distribution of secondary particle tracks was fitted using a double-Gaussian function, as shown in Fig. 15, resulting in x- and z-resolutions of 0.71 mm and 0.73 mm, respectively, for the beam test. These results are consistent with the cosmic ray test outcomes. The angular resolution of the scattering angle, θ, can reach 0.2°. Good angular resolution is essential for establishing a precise relationship between the scattering angle and the differential cross section in the center-of-mass system, particularly for specific points in the cross section, such as local maxima or minima. The detailed shape of the angular distribution aids in better extrapolation of measurements to small-angle scattering regions and reduces extrapolation errors. Due to limitations such as the duration of the beam test, the triton could not be identified. However, the test successfully verified the operation of the detector. First, the scTPC operated normally without discharging under the high background environment caused by the heavy-ion beam and maintained sufficient performance. Second, the CsI(Tl) signal was used to trigger the AGET and effectively detect secondary particle tracks.

Fig. 13Full-screen View

(Color online) Distribution of raw hits on the xy-plane of a long track produced by the secondary particle under the heavy-ion beam test

Fig. 14Full-screen View

(Color online) Projections on the xy-plane (a) and zy-plane (b) after the track recognition of a long track produced by the secondary particle under the heavy-ion beam test

Fig. 15Full-screen View

Residual distributions of secondary particle tracks under the heavy-ion beam test are shown for the xy-plane (a) and zy-plane (b). The x-resolution is 0.71 mm, and the z-resolution is 0.73 mm. The red curves represent the double-Gaussian fitting functions

A Kr-beam experiment was performed to validate the performance of the detector. We were interested in C and O isotopes instead of Kr. Although small-angle scattering near 0° in the center-of-mass frame provides more detailed information on the transition dynamics and nuclear structure, detecting tritons is technically challenging because the kinetic energy of a triton approaches zero in the laboratory frame at this angle range. Consequently, nuclear reaction experiments were designed to measure the recoiled triton with a relatively large kinetic energy in inverse kinematics. Then, combined with the angular distribution of the reaction cross section calculated theoretically, the data for the small-angle range were extrapolated from the measured result to the greatest extent possible. According to the Geant4 simulation [21], the current detector system can measure triton with E_t,lab > 20 MeV and ${\theta }_{\text{t,lab}}{<85}^{\circ }$, considering the energy loss of triton in the insensitive zone of the detector (including the target window and the field cage structure). The maximum energy deposition of triton in CsI(Tl) was approximately 140 MeV, as determined by the thickness of CsI(Tl).

The background from δ electrons must be considered for control and veto in beam experiments. The maximum kinetic energy that can be transferred in a single collision is limited and depends on the kinetic energy of the incident particle. For an incident nucleus with a kinetic energy of 500 MeV/u, the calculated maximum kinetic energy of the δ electron is approximately 1.4 MeV. The results from Geant4 simulations (Fig. 16 and kinematic calculations are in good agreement. As the kinetic energy of the δ electron increases, its generation probability decreases. The vast majority of δ electrons will not enter the TPC, as they are blocked by the ³He target sidewall and the scTPC field cage structure. Those δ electrons that do enter the sensitive region of the detector can be rejected by the CsI(Tl) because they cannot trigger the CsI(Tl). In addition, δ electrons either do not enter the scintillators, or the energy they deposit in the scintillators is generally below the trigger threshold.

Fig. 16Full-screen View

Energy spectrum of the δ electron simulated by Geant4

According to theoretical calculations (see the preprint [55]), for a ²⁰O beam with an intensity of 10⁶ particles per second, the yield rate of our charge exchange reaction (transition between isobaric analog states) is approximately 10 particles per hour in three atmospheres of ³He gas. To achieve the statistical precision required for the experiment (over 1000 counts), approximately 100 hours of beam time were needed to accumulate the data.