Feasibility study of TPC detector at high luminosity $Z$ pole on the circular collider

With the development of the circular collider, it is necessary to make accurate physics experimental measurements of particle properties at higher luminosity $Z$ pole. Micro-pattern gaseous detectors (MPGDs), which contain Gaseous Electron Multiplier (GEM) and Micro-mesh gaseous structures (Micromegas), have excellent potential for development as the readout devices of the time projection chamber (TPC) tracker detector. To meet the updated physics requirements of the high luminosity $Z$ from the preliminary concept design report (preCDR) to concept design report (CDR) at the circular electron positron collider (CEPC), In this paper, the space charge distortion of the TPC detector is simulated with the CEPC beam structure. Using the multi-physics simulation software package, the distribution of ion estimated by Geant4 is used as the input for the differential equation, and the relationship between the ion density distribution and electric field in the detector chamber is simulated. These simulation results show that the maximum deviation for Higgs $mathcal{O}$(25 $mu$m) meets the performance requirements in CEPC TPC detector at the high luminosity $Z$ pole, while it is still a considerable challenge for $Z$ pole, with the maximum deviation $mathcal{O}$($>100~mu$m). According to the previous developments, the cascaded structure of GEM and Micromegas detector has been measured. The new considerations of the detectors requirements were given, the gain needs to be reached to about 2000 with IBF$times$Gain under 0.1, and IBF means the ions back flow ratio of the detector. The pixel TPC is a potential option to replace the traditional MPGDs with the low gain, low occupancy, and outstanding pattern recognition. Finally, some update parameters and experiments results were compared.