# TOF Detector

Time of Flight (ToF) systems measure signal time difference between two detectors, which work as a start and stop counter, with a very good time resolution. In particle and astroparticle physics, they are mainly used to distinguish particle types. Typical detectors consist of scintillator counters and photodetectors with a time resolution of ~50-100 µs (see AMS-02 ToF) or of Resistive Plate Chamber (RPC) with a time resolution of ~30-50 µs. This configuration is a cost effective solution for large detectors (see MRPC of the ALICE experiment).
If the momentum of particles is known because it is selected naturally by the beam-line elements or measured by other detectors as a magnetic spectrometer, a further observable is necessary to identify particles. The difference between the time that two particles with the same momentum take to travel the distance between the two counters of a ToF system is proportional to the difference in the particle square masses. The sensitivity the system can achieve is dependent to the distance between the two counters and to the momentum of particles.

A schematic view of a typical ToF system is shown in FIG. 1 - left. The observable measured by the system is the time taken for a particle to go from the first to the second scintillator, i.e. the difference between start and stop time Δt = t2 – t1 = L/(cβ), where L is the distance between the two scintillator, and β is the particle velocity. To distinguish between two particles, we have to consider the time-of-flight difference.

$\Huge\triangle T =\frac{L}{c}\biggl(\frac{1}{\beta_p1} - \frac{1}{\beta_p2}\biggl) \sim \frac{L}{cp^2}\biggl (m^2_{p1} - m^2_{p2}\biggl)$

where p is the momentum, βp1 and βp2 are the velocity of the two particles, and mp1 and mp2 are their masses.
If our particles are pions and kaons (mk~500 MeV, mπ~140 MeV), for example, assuming p=1GeV and L=1m, ΔT ~ 300 ps. Therefore a system with a time resolution of about 300 ps allows us to separate pions and kaons up to 1 GeV (FIG. 1 - right).

AMS-02 (Alpha Magnetic Spectrometer) is a detector designed to operate on the International Space Station (ISS) with the aim to study the universe and its origin by searching for antimatter and dark matter, and by performing precision measurements of cosmic rays composition and flux. The core of the AMS-02 spectrometer is a large magnet necessary to measure the sign of the charge of each particle traversing the instrument. The combined use of several detectors (FIG. 2) helps to identify particle types and their characteristics.

A TRD (Transition Radiation Detector) identifies electrons and positrons among other cosmic-rays. A Silicon Tracker detects the particle charge sign, separating matter from antimatter.
A Ring-Imaging Cherenkov Detector (RICH) is used to measure with high precision the speed of cosmic-rays, an Electromagnetic Calorimeter (ECAL) allows to know the energy of incoming electrons, positrons and γ-rays; finally an Anti-Coincidence Counter (ACC) rejects cosmic rays traversing the magnet walls.
The AMS-02 ToF system is composed by 4 planes of scintillation counters, 2 above and 2 below the magnet. Its main goal is to inform the other sub-detectors of the incoming of an incident cosmic-ray; a particle able to traverse the Upper and Lower ToF is said to be inside to the AMS acceptance. The particle transit time into AMS is measured with a high level of precision (1.5×10-10 s) by the ToF, which provides the first level trigger for charged particles.

The ToF time resolution is sufficient to distinguish upward from downward moving particles, electrons from anti-protons at E < 1.5 GeV and, finally, also permit to distinguish nuclei up to Z≤20.

Each plane of the TOF system covers roughly a circular area of about 1.2 m2, with 12 cm wide scintillator pads of different length, overlapped by 0.5 cm to avoid geometrical inefficiencies. The scintillators are coupled at both ends via plexiglass light guides to 4/6 Photo-Multipliers (PMTs); a bidimensional readout is provided. The upper and lower ToF planes are shown in FIG. 3.

The high absolute value of the magnetic ﬁeld at the position of the PMTs (1.5 ÷ 2kG) forced the adoption of a special kind of PMT, the ﬁne mesh Hamamatsu R5946.
The PMT has a bialkali photocathode, a borosilicate glass window and 16 fine mesh dynodes. The spectral response ranges from 300 to 600 nm with a maximum response at ∼ 420 nm (corresponding to a quantum efficiency of about 20%).
The fine mesh PMTs can operate inside intense magnetic fields, but their response depends strongly on the angle between the field and their longitudinal axis. Thus, tilted light guides were designed in order to minimize this angle for each PMT.
Since AMS-02 works on the ISS, the ToF detector undergoes variations of temperature from −20° C to +50° C. A group of 10 PMTs were tested in the thermal-vacuum simulator at the INFN laboratories of Bologna at a pressure of 10−7 ÷ 10−6 mbar with temperature varying between −30° C and +55° C. They were re-calibrated after each cycle of temperature and their characteristics remained the same.