Heavy ion collision has been the almost unique method to study properties of dense nuclear matter in the laboratory[1-5]. The Cooler-Storage-Ring(CSR) External-target Experiment(CEE)[6], which is being constructed since 2020, will be the first large-scale experiment in high-energy nuclear physics built in China covering the GeV energy region. In the future, it can also be used at the High Intensity heavy ion Accelerator Facility(HIAF)[7], which is now under construction. Experimental studies utilizing CEE aim at many physical goals including the phase structure of QCD matter in high baryon density region, as well as the equation of states of nuclear matter at super-saturation densities. CEE includes a micro-pixel beam monitor, a large volume Time Projection Chamber(TPC), a Multi-Wire Drift Chamber(MWDC) array, Time-of-Flight detectors(TOF) and a large acceptance super-conducting dipole magnet.
TPC’s[8] are widely used in high energy and nuclear experiments. The CEE TPC has a sensitive volume of about 1 $ {\rm m}^{3} $, which will be the largest TPC ever constructed and used in China. It can provide track information, including 3-dimensional position, momentum, charge and energy loss, for charged particles, which is crucial for almost all physics analyses that will be conducted at CEE in the future. Thus the TPC is the most important detector for CEE. Fig. 1 shows a schematic plot of the CEE TPC. It has a sensitive volume filled with gas, where uniform electrical and magnet fields are applied in the vertical direction. When a charged particle goes through the sensitive volume, the curvature of its trajectory in the magnet field can be used to obtain its charge and momentum. Electrons created via the ionization process along the charged particle trajectory would drift in the electrical field towards 4 layers of large area standard Gas Electron Multiplier(GEM) foil[9] at the top of the TPC, where electron avalanche will happen to amplify the signal by a factor of about one thousand. A plane of read-out pads is positioned above the GEM layers. The read-out pads are directly connected to SAMPA read-out electronics chips[10]. Each SAMPA chip integrates 32 channels of charge sensitive amplifiers, semi-Gaussian shapers and 10-bit Analog-to-Digital Converters(ADC). The state-of-the-art SAMPA chips make CEE TPC capable of reading out data at an event rate of 10 kHz. And the usage of the GEM technology instead of traditional anode wires minimizes space charge caused by positively charged ions from avalanche drifting back to the sensitive volume, which would destroy the uniformity of the electrical field. 3-dimensional information of the ionization position can be reconstructed from the signals recorded by the read-out pads. Ionization position in the drift direction (drift distance) can be calculated by measured drift time and drift velocity, while the ionization position in the rest 2 dimensions can be reconstructed from the position of fired pads. Eventually, three-dimensional trajectories of charged particles can be reconstructed. Heavy ion collisions at CEE can create up to 200 charged particles. It is a great challenge to reconstruct the trajectories of so many charged particles with required efficiency ($>90\%$) and momentum resolution ($<5\%$).
The design and key technologies of the CEE TPC is being developed. For now, a basic version of TPC design is used for this study. The sensitive volume of TPC is a box of 120 cm×80 cm×90 cm along $ x, y $ and $ z $ directions respectively, where $ z $ is the beam line direction and $ y $ is parallel to the drift electrical field and magnetic field, as shown in Fig. 1. The read-out plane is divided along $ z $ direction into 75 pad rows. Each pad row consists of 240 pads with the size of 5 mm ($ x $)×12 mm ($ z $). Working gas of the TPC is Ar 90%+CH$ _{4} $ 10% at the pressure of 1 atm. With drift electrical field strength of 130 V/cm, the electron drift velocity is 5.5 cm/µs. We use SAMPA in a mode with the read-out frequency of 10 MHz. The corresponding drift length per time bin is 0.55 cm. The 80 cm drift length thus corresponds to about 145 time bins.
To reconstruct the trajectory of a charged particle, the first step is to group together signals at neighboring pads and time bins in the same pad row, into a so-called cluster. Usually, one cluster corresponds to the signals that a particle creates when it goes through a $ x $-$ y $ gas layer that projects to a pad row, called a hit. When the particles are very dense in space, hits from different particles may also create signals adjacent to each other. In this case, one cluster may contain more than one hit. It is important to be able separate hits from different particles in the same cluster, in order to have good double-track separation ability and track reconstruction efficiency. In the following sections of this paper, the cluster reconstruction algorithm for the CEE TPC, as well as some results from it will be reported. The CEE TPC cluster construction software has been made taking the cluster reconstruction software for the NICA-MPD experiment[11] as reference. It is a part of the CeeRoot package, which is being developed based on the FairRoot package[12]. The output hits of cluster reconstruction can later be connected to form tracks. The software for track reconstruction is being developed. The current TPC design will be further optimized in the future once the track reconstruction software is available.
The read-out signals used in this study are generated by Monte-Carlo(MC) simulation. The particle transportation and energy loss in the TPC sensitive volume is simulated using the GEANT package[13]. Then ionization is simulated by randomly generating electrons along the particle trajectory. Next, drift and diffusion of these electrons in the sensitive volume, as well as electron avalanche in the GEM layers, are simulated according to parameters extracted from a simulation study using the GarField++[14] software. Signals are then distributed on read-out pads according to avalanche positions, spreads and magnitudes. Finally, the SAMPA chip electronics responses are simulated, using measured Quasi-Gaussian response signal shape and noise level. The output read-out signals are ADC values at different pad rows, pad numbers and time bins. Complicated effects such as nonuniform electrical and magnetic fields, space charge due to positively charged ions in the sensitive volume, and cross-talk between different read-out channels, are not considered in the current simulation.