1 Introduction

The time projection chamber (TPC) is a type of gas detector possessing excellent imaging capabilities [1]. It yields good space-time resolution, high detection efficiency, and almost 4\(\pi\) solid-angle coverage. Owing to these advantages, it has been widely used in high-energy physics experiments for several decades [2,3,4,5,6,7,8]. In recent years, with the development of research in nuclear physics involving the usage of radioactive ion beams (RIB), the TPC has also gradually been applied in low-energy nuclear physics experiments, with some relevant modifications [9,10,11,12,13,14].

Because the beam intensity of RIBs is typically low, a thick target is often used to mitigate this constraint. However, a thick target limits the momentum resolution and acceptance of the detector; therefore, a difficult compromise must be made between the target thickness and resolution. Active target TPCs (AT-TPCs), in which the reaction target also serves as the detection material, serve as a good solution here. These can determine the location of the reaction vertex and the tracks of the ions emitted from the reaction, along with the associated energy loss inside the gas volume. This enables the use of a thick target to increase the reaction yield while retaining good resolution and acceptance at each reaction location [15, 16]. For instance, a prototype AT-TPC, designed by NSCL and applying micromegas amplification technology, involves a large active volume and detects the \(\alpha\) cluster structure in \(^{14}\)C through resonant scattering [17]. Recently, the MAIKo detector, designed by Kyoto University and applied \(\mu\)-PIC for electron amplification and two-dimensional readout, was successfully applied to observe the 3\(\alpha\) breakup events from the Hoyle state in \(^{12}\)C [18]. The latest progress has also been covered in a review article [19].

Clustering in the light mass region is of special importance for understanding the exotic nuclear structure as well as nucleosynthesis in cosmos. For nearly five decades, clear experimental evidence on nuclear clustering has been accumulated, but several unknowns remain, particularly in the case of unstable nuclei [20]. For studies on unstable nuclei using RIBs, the AT-TPC has the advantage of recording the complete kinematic information under a relatively low beam intensity, which is particularly useful for cluster-structure studies by using resonant scattering on the helium target [21, 22]. The requirement for the resolution of the reconstructed energy spectrum is approximately 50–100 keV [19]. Our research group is also interested in investigating cluster structures in unstable nuclei [23, 24], for which new detection technologies such as the AT-TPC are required. In the present study, a compact AT-TPC was developed to measure the resonant scattering of clustering systems.

Previously, the first version of the AT-TPC prototype was reported, and it was equipped with one-dimensional readout strips and provided two-dimensional track images [25]. Currently, however, specially designed two-dimensional readout strips allowing for the recording of three-dimensional images have been implemented. The structure details and detection performance of this second-version prototype are reported in this article.

2 Design of the CAT-TPC

2.1 Overall description

A schematic view of the compact active target time projection chamber (CAT-TPC) is shown in Fig. 1. The CAT-TPC in this study consisted of a gas vessel, field cage, and an end-cap readout board collected in the electronic circuit. The volume of the field cage was 140 \(\times\) 140 \(\times\) 140 mm\(^3\). The drift field was provided by a number of 100 \({\upmu }\)m-diameter gold-plated tungsten wires, doubly wound with 10-mm spacing around the cage frame composed of a printed circuit board (PCB). The cage was installed between the cathode plate at the top and the readout board at the bottom. When a charged particle passed through the cage volume filled by the sensitive gas, the deposited energy caused gas ionization along the particle track. The electric field in the cage drove the electrons (ions) to drift toward the electrodes. The electron signals were then multiplied by a thick gas-electron-multiplier (thick GEM) foil [26]. The sensitive area of the GEM foil was only 100 \(\times\) 100 mm\(^2\), which limited the sensitive volume of the TPC to approximately 100 \(\times\) 100 \(\times\) 140 mm\(^3\). Details of the GEM foils are described in Sect. 2.2. The signals from the GEM foil were collected using two-dimensional copper strips printed on a PCB, as shown in Fig. 2a. Among them, 48 parallel strips were placed in the X direction, perpendicular to the other 40 parallel strips in the Y direction. The latter set of 40 strips were divided into 80 half-strips by isolating the cut at the middle (refer to Sect. 3.3 for an elaboration). To distinguish the strips, the 40 half-strips on the left side of the Y-axis were numbered using even numbers, while those on the right side were numbered using odd numbers. This two-dimensional strip-readout configuration effectively reduces the number of readout electronics while maintaining the necessary spatial resolution in the X–Y dimensions.

Fig. 1
figure 1

(Color online) Schematic view of the CAT-TPC

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To describe the TPC performance, it is convenient to define a coordinate system with the Z-axis along the average electron drift direction in the cage, and the X–Y axes lying in the readout plane. A total of 48 parallel X-strips 700-\({\upmu }\)m in width and 48 rows of pads were positioned alternatively, as shown in Fig. 2b. Each pad was extended to the rear side of the board via a hole and collected to one of the Y-strips. In order to enhance the position resolution, each Y-strip was divided into two sections using an isolating cut near the strip-middle, as can be seen in Fig. 2a.

Fig. 2
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(Color online) a Schematic view of readout PCB and b amplified details of X–Y readout structure

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2.2 Thick GEM foils

Thick GEM readout is a new technique enabling signal amplification with high spatial resolution, whereby higher voltages can be withstood, and a high tolerance of PM 2.5 to air dust can be obtained [27,28,29]. The thick GEM adopted in this study was 200 \({\upmu }\)m in thickness, consisting of a dielectric clad on both sides of a thin copper layer, which is characterized by a high-density array of holes. When a voltage of 300–400 V was applied to the copper layer, the electron signal collected from the field cage could be amplified by two to three orders of magnitude. Two thick GEM layers, separated by 3 mm, were employed in the present design. A bias voltage of approximately 300 V was applied to each thick GEM through a custom-made circuit (Fig. 3). Notably, a gain of \(10^3\) can be achieved for electron multiplication via this double-thick GEM arrangement [30, 31]. In addition to thick GEM, home-made charge-sensitive preamplifiers were also used, the sensitivity of which was approximately 20 mV/MeV.

Fig. 3
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(Color online) HV circuit for the field cage and the GEM foils

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2.3 Field cage

The method to supply high voltage (HV) to the field cage is depicted in Fig. 3. The field cage provides a vertical static electric field inside its sensitive volume, with some field distortion near the edge owing to the finite range of the electrode and the wires. Based on the Garfield code simulation [32], a guard ring was applied to improve the uniformity of the drift field. The ring was located 3.0 mm above the first GEM foil (Fig. 3). The high voltage applied to the guard ring was supplied independently and could be tuned to yield the best performance. According to the test, the field intensity at the edge was sensitive to the guard ring voltage. The best field uniformity was obtained at approximately 900 V [25].

2.4 Signal processing and acquisition

As part of the experiments in this study, a \(^{241}\)Am \(\alpha\)-particle source was applied to generate particle tracks in the field cage (Fig. 4). The signals from the anode readout strips were sent to the PKU preamplifiers, which were connected to the data acquisition (DAQ) system. In addition to the CAT-TPC, a silicon detector with a 48 \(\times\) 48 mm\(^2\) active area was employed to provide the trigger signal.

A general-purpose digital DAQ system (GDDAQ) was used [33], which is based on the Pixie-16 module of XIA LLC [34]. The Pixie-16 processor was designed as an industry standard compact PCI/PXI module. When compared to the traditional CAMAC or VME DAQ systems, it has the advantages of a relatively high data transfer rate (up to 109 MByte/s) and enables online digital spectrometry and waveform acquisition for 16 input signals per module. Several modules can be hosted in a single crate.

Fig. 4
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(Color online) Readout electronics and DAQ

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2.5 Working gas mixture

The CAT-TPC was installed in a sealed gas chamber filled with a gas mixture that functioned as the target material as well as the active detection medium. The main gas composition was of \(^4\)He, with 4% of CO\(_2\), which helped to stabilize the gain [18]. The gas pressure was set to 400 mbar and controlled via a floating gas pneumatic system.

3 Test measurements

3.1 Experimental setup

Fig. 5
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(Color online) Top view of the experimental setup. The reference system is indicated in the upper right corner

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A schematic top view of the experimental setup is presented in Fig. 5. The entire detection system was installed in a gas chamber filled with the working gas. A calibration board was inserted between the \(\alpha\)-particle source and CAT-TPC. A two-dimensional array of holes, each with a diameter of 2 mm and distanced by 5 mm from one another, were made on the board. Located on the other side of the CAT-TPC was an auxiliary Si detector providing the start timing signal.

Fig. 6
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(Color online) Track profile of particles passing through the holes on the calibration board and recorded by the CAT-TPC

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Limited by the size of the Si detector, only the particles passing through an array of 3 \(\times\) 3 holes can be recorded appropriately. Figure 6 demonstrates an example of the track profile in Y–Z plane (Fig. 5).

3.2 Track position determination

When a particle passes through the sensitive gas volume, the deposited energy generates ions and electrons around the track. Electrons drift towards the GEM foil along the electric field lines in the Z-direction. The recorded drift times correspond to the Z-positions of the track, while the crossing points of the fired X- and Y-strips yield the corresponding X- and Y-positions. This is the principal of CAT-TPC, which provides a three-dimensional image of a particle track.

First, the timing signals from various strips are matched to one another by using the correct time offset for each readout channel. This was realized herein using a pulse generator, which allows for the matched signals to be sent to all strips. After calibration of the time offset, a \(3\times 3\) matrix of holes may be selected on the calibration board in front of a small \(\alpha\)-particle source (refer to Fig. 5 for the arrangement). The recorded drift-time track profiles may produce corresponding \(3\times 3\) centroids on the plane on the left side of the field cage. The corresponding absolute Z-positions of these centroids can be obtained by projecting straight lines between the source and calibration holes onto the left-side plane of the cage. By using these drift-time centroids and the corresponding absolute positions, the drift velocity along the Z-direction can be deduced. Using this calibration method, all drift times from each individual track can be converted into the corresponding Z-positions, as shown in Fig. 6 as an example.

Fig. 7
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Drift velocity as a function of Y-position

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During the experiment, HVs of \(-2150\), \(-820\) and \(-890\) V were applied to the cage, GEM foil, and guard ring, respectively. Under this condition, drift velocities between 9.91 and 10.08 mm/\({\upmu }\)s were obtained for different readout strips, as shown in Fig. 7, which is in good agreement with the simulation results using Garfield code. This variation may be attributed to the uniformity of the electric field, determination of the centroid of the track profile, and transmission of the electric signals.

The time resolution of the CAT-TPC along the Z-axis can be deduced using the residual method [25, 35]. For each measured track, a straight line was applied to fit the drift-time data. The residual time for the i-th readout strip is defined as:

$$\begin{aligned} t_i=T_i^{\text {F}}-T_i^{\text {D}}, \end{aligned}$$
(1)

where \(T_i^{\text {F}}\) and \(T_i^{\text {D}}\) are the fitted and detected times, respectively. Repeated for many tracks, \(t_i\) normally forms an approximate Gaussian distribution, from which the standard deviation \(\sigma _{ti}\) can be extracted as the time resolution. This resolution for all Y-strips varies from 6.6 to 15.5 ns, corresponding to Z-position resolutions from 0.07 to 0.15 mm by considering the average drift velocity of approximately 10 mm/\({\upmu }\)s. The time resolution due to electronics is approximately 1.9–4.6 ns, depending on the readout strip, which is relatively small.

The spatial resolution in the X or Y directions for the readout board is modulated by the period of the readout strips and can be estimated as \(\sigma _X\) = 2 (mm)/\(\sqrt{12}\) = 0.58 (mm), \(\sigma _Y\) = 2.5 (mm)/\(\sqrt{12}\) = 0.72 (mm) [36], where 2 mm and 2.5 mm are the strip pitches along the X and Y directions, respectively. A more realistic X-Y plane resolution is analyzed in Sect. 3.3.

Based on the performance of spatial resolution, the track angular resolution along the Z direction can be estimated. Each measured particle track can be divided into two sections: the upstream and downstream ones. Each section contains data from 20 readout strips that can be fitted by a straight line. The trajectory angles for the two sections are denoted as \(\theta _\text {up}\) and \(\theta _\text {down}\) [18], respectively, as indicated in Fig. 8. The difference between these two angles, \(\theta _\text {up}\) – \(\theta _\text {down}\), can be accumulated for many tracks. The distribution thereof became a Gaussian-type spectrum, from which a standard deviation of \(\sigma _\text {up-down}=0.39\pm 0.01\) degree was extracted for the present measurement. The track angular resolution was approximately \(\sigma _\text {track}=\sigma _\text {up-down}/\sqrt{2}=0.28\) degree [18].

Fig. 8
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(Color online) Example of a \(^4\)He beam track of the anode strips

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3.3 3-D tracking reconstruction

Using the recorded X–Z and Y–Z information for each track, we could reconstruct its 3-dimensional pattern. We adopted the following algorithm:

  1. (1)

    Fit all data points in X–Z plane by a two-dimensional straight-line to obtain the function \(Z=f(X)\) and its inverse function \(X=g(Z)\);

  2. (2)

    For each (\(Y_i\),\(Z_i\)) point, find an associated \(X_i = g(Z_i)\).

  3. (3)

    Collect all (\(X_i\),\(Y_i\),\(Z_i\)) to form a 3-dimensional track.

Fig. 9
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(Color online) The reconstructed three-dimensional tracks for an \(\alpha\)-He scattering event and its projection onto X–Z, Y–Z and X–Y planes

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Obviously, the above process may be started from the \(Y-Z\) plane as well. In the case of scattering or reaction, two trajectories may appear following the interaction point (vertex). This point is related to a sudden change in signal amplitude. An example of the detected \(\alpha\)-He scattering event is shown in Fig. 9 as an example. In Sect. 2.1, we provide a description of the readout Y-strips, which are divided into two sections of half-strips (Fig. 2a). The reason for adopting this complexity is mainly to obtain better two-track discrimination. As shown in Fig. 9, when two tracks appear after a scattering or reaction, each associated Y-strip should record two signals. If these two signals are too close to each other in comparison with the signal discrimination, the information for the two tracks would be lost or biased. By using the divided Y-strips, at least for an incident track near the center of the X-coordinate (middle of the Y-strip), signals for the two tracks after scattering or reaction will be separately recorded by the two strip-sections; hence, the overlap of close-by signals will not occur and the scattering (reaction) image, including that around the vertex, can be clearly reconstructed, as demonstrated in Fig. 9.

It should be noted that when a track is almost parallel to the X-Y plane and all acquired \(Z_i\)-positions have similar values, \(X_i = g(Z_i)\) conversion has no unique result, and the above method is no longer valid. In this case, we may simply allocate the two-end values of the X-strips to the track-start and -stop positions, with the former being related to the particle incident (or scattering vertex) X-position. The other X-positions can then be deduced according to linear interpolations.

The position of each track on the X–Y plane can be reconstructed using the algorithm described above. Similar to the aforementioned residual analysis method [25, 35] for the Z-dimension, a straight line can also be applied to fit the projected track in the X–Y plane. The distance between the measured positions and fitting line was recorded to form the residual distribution. The value of the root-mean-square of this distribution is approximately 0.70 mm, which may represent the spatial resolution in the X–Y plane. The angular resolution for a three-dimensional track can also be evaluated by applying the two-section method described above. The result from the present test measurement was approximately 0.45 degree. A similar method may also be applied to determine the closest distance between the incident and scattered tracks. The present mean value is 0.49 mm, which is consistent with the overall position resolution.

4 Summary

In this study, a newly developed two-dimensional strip readout structure was successfully applied to the CAT-TPC, along with the thick GEM foil amplification and GDDAQ. This readout structure was deployed for the three-dimensional image reconstruction of a particle track or scattering event. The Y-strips were divided into two sections such that scattering or reaction events could be reasonably recorded. The detector performance was tested using a \(^{241}\)Am \(\alpha\) source. A time resolution (standard deviation) of less than 16 ns and a spatial resolution of less than 0.15 mm along the Z-dimension were obtained. The uncertainty in the X- or Y-dimension was approximately 0.7 mm, according to the residual analysis. Based on the readout-strip design and the reconstruction algorithm, the scattering or reaction event can be clearly imaged under an angular resolution of approximately 0.45 degree. These performances are sufficient for this CAT-TPC to be used in low-energy nuclear physics experiments, such as in the resonant scattering experiment for cluster-structure studies.