# Multigap Resistive Plate Chambers for Time of Flight Applications
## 1 Introduction  
To reveal many aspects of the physics program, techniques of particle identification (PID) [1] are the key requirements in particle and high energy physics experiments. Different particles can be identified through one or several combined detector systems to measure their mass or how they interact with matter. More details can be found in [1]. Among them, the time of flight (ToF) system is an essential part, especially for identifying hadrons. The ToF system can provide the velocity information \(\beta\) of the charged particle by measuring the traveling time \(t\) of a given distance \(L\). Combined with the momentum \(p\) obtained from the magnetic spectrometer, the mass \(m\) of the particle, as a basis for identification, can be calculated:  
\[\beta=\frac{p}{c}=\frac{L}{tc}=\frac{1}{\sqrt{\left(\frac{mc}{p}\right)^{2}+1}} \tag{1}\]  
\[m=\frac{p}{c}\sqrt{\frac{c^{2}t^{2}}{L^{2}}-1} \tag{2}\]  
If we want to identify particles with the same momentum, their flight time difference can be obtained according to Equation (2):  
\[|t_{1}-t_{2}|=\frac{L}{c}\bigg{|}\sqrt{\left(\frac{m_{1}c}{p}\right)^{2}+1}- \sqrt{\left(\frac{m_{2}c}{p}\right)^{2}+1}\bigg{|} \tag{3}\]  
The separation power (\(n_{\sigma_{\text{TJF}}}\)), used to evaluate the reliability of separation, is defined as the ratio of the flight time difference and standard deviations. Usually \(n_{\sigma_{\text{TJF}}}>3\) is required in many experiments. Assuming \(p\gg mc\), it can be derived and given by:  
\[n_{\sigma_{\text{TJF}}}=\frac{|t_{1}-t_{2}|}{\sigma_{\text{TJF}}}=\frac{Lc}{2 p^{2}\sigma_{\text{TJF}}}\Big{|}m_{1}^{2}-m_{2}^{2}\Big{|} \tag{4}\]where \(\sigma_{\text{ToF}}\) is the time resolution of the _ToF_. There are many candidate detectors that can be considered for the construction of the ToF system. In the early 1990 s, the parallel plate chambers (PPC) [2; 3], a gaseous detector with only one gas gap between two metallic electrodes, were investigated for possible use at the LHC. However, because its gas gain must be kept low to maintain its avalanche mode, which leads to difficulty with both a high-efficiency (<90%) and a good timing resolution (>250 ps), it wouldn't be considered nowadays. For advances in ToF techniques, the fast photon detectors have been considered and had major improvements. Scintillators with photomultipliers are frequently used because of their excellent time resolution. For example, the LIDAL system [4] use fast plastic scintillators coupled with photomultiplier tubes (PMTs) to perform ToF measurements. The beam test results have demonstrated that a time resolution below 100 ps can be achieved. A systematic test of several medium-sized plastic scintillators [5] has shown a time resolution below 10 ps. However, the light yield of scintillators [6] will change under different magnetic fields; the magnetic field tolerance of PMTs demands careful consideration due to the effect of both electric and magnetic field on the trajectories of electrons; the scintillators are challenging to be highly segmented in order to determine the hit multiplicity; the particle experiments are usually large in size, and the PMTs are high-priced. Over the years, Si-based technologies have gained much attention. For example, silicon photomultipliers (SiPMs) [7; 8; 9] are indeed replacing the standard PMTs and are playing a vital role in future collider experiments [10] like the high luminosity large hadron collider (HL-LHC) [11] or medical applications like TOF-PET [12; 13] thanks to the many advantages: a higher efficiency, lower bias voltage, higher segmentation and insensitivity to magnetic fields. Moreover, low gain avalanche diodes (LGAD) [14], which are n-on-p silicon sensors with internal charge multiplication, have shown a time resolution of better than 20 ps. The ATLAS and CMS experiments [15; 16] are designing LGAD detectors to address the good timing measurements and pile-up challenge at the HL-LHC.