# Multigap Resistive Plate Chambers for Time of Flight Applications
## 3 Applications in Large Experiments
### Developments for Future ToF Systems
#### 3.3.1 High Rate and Ultrahigh Time Resolution MRPC
The ionized electrons drifting in the gas gap will start the avalanche following the Townsend effect [33] under the applied electric field as soon as they are created and generate an induced signal on the pick-up electrodes according to Ramo theory [39]. The frontend electronics (FEE) response and noise can be included to study the detector performance under different experimental setups. By analyzing the simulation data and full signal information, the performance of detectors with different structures at various working conditions can be easily studied. Figure 11 [89] shows the relations of intrinsic time resolution and MRPC structural  
Figure 10: Particle separation power of different time resolutions for a flight distance of 8 m.  
parameters. It is evident that reducing gap thickness and adding more gaps can achieve a better time resolution. Moreover, to reach the goal of 20 ps time resolution, the possible choices for future MRPCs are mainly the designs with thickness below 160 \(\upmu\)m and at least 20 gas gaps, which ensures the detector resolution better than 10 ps. In general, gaps in this kind of MRPCs are arranged into several stacks so that the applied working voltage can be limited to a reasonable level. Figure 12[89] shows the time resolution changes associated with the number of stacks in a detector. We can see that when fixing the total number of gaps and dividing them into more stacks, the time resolution becomes larger. It is because more stacks mean a much thicker chamber and a longer distance between the very first and last gaps, which will lead to a larger shift of the avalanche time. Based on the Monte Carlo simulation and the above study, a 32-gap MRPC detector [90] was developed. As depicted in Figure 13a, the MRPC is arranged into four stacks, each stack with eight gaps. The thickness of each gap is only 104 \(\upmu\)m. 6 readout strips with 1 cm pitch are configured on the PCB sheets. Five PCBs are required in this design. The cathode and anode signals are transmitted through differential cables. During the preliminary cosmic ray test, the high-performance analog frontend electronics (AFE) [91] from USTC and the Lecroy oscilloscope were used. The crossing time of a signal is determined when setting a fixed threshold, and it is related to the amplitude of the signal. Thus, the time-slewing correction should be carried out, and a general formula is given below  
\[t=a_{0}+\frac{a_{1}}{\sqrt{q}}+\frac{a_{2}}{q}+a_{3}q \tag{9}\]  
where \(t\) is the crossing time of a signal and \(q\) represents the signal amplitude or charge, to are the undetermined coefficients that can be obtained by fitting the relations, as depicted in Figure 13c,d. Figure 11: The simulated time resolution as a function of gap thickness for MRPC detectors with different numbers of gaps. Reproduced with permission from [PERSON] et al., Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment; published by Elsevier B.V., 2020 [89]. Figure 12: The time resolution of MRPCs with different numbers of stacks in a detector. The total number of gaps are fixed to be 10 in (**a**) and 32 in (**b**). Reproduced with permission from [PERSON] et al., Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment; published by Elsevier B.V., 2020 [89]. Figure 13: (**a**) Schematic picture of the 32-gap MRPC. (**b**) The time distribution and resolution results of the cosmic test. The blue line shows the distribution of the time difference and the red line is obtained from the gaussian fitting. The relationship between the crossing time of the signal and the amplitude before (**c**) and after (**d**) the slewing correction. The red line is fitted by Equation (6). The mean values and error bars of each x-axis bin are shown. Reproduced with permission from [PERSON] et al., Journal of Instrumentation; published by IOP Publishing for Sissa Medialab, 2020 [90].