Y. Karadzhov MICE Video Conference Thu April 9 Slide 1 Absolute Time Calibration Method General description of the TOF DAQ setup For the TOF Data Acquisition three TDC boards are used. The transit time of the signal through the PMT and the delays introduced by the cable bringing it to the control room and the discriminating electronics for a given channel is not known and it has to be measured. The digital values recorded by the TDCs correspond to the absolute time since the last reset of each TDC board. The board clocks are not synchronized, but the first channel (Ch0) of each board receives a copy of the Particle Trigger signal and this signal is used as a reference for all the PMTs of the TOF stations.

Y. Karadzhov MICE Video Conference Thu April 9 Slide 2 Absolute Time Calibration Method General description of the TOF DAQ setup (con’t) The Particle Trigger signal is generated by hardware logic units in the DAQ racks. It is given by the first twofold coincidence of the PMTs connected to the same slab. The recorded TDC value can only make sense if referred to the Particle Trigger time. The PMT (channel) which is delivering the trigger depends on the position on the hit, therefore the delay of the Particle Trigger signal depends on the position of the hit to.

Y. Karadzhov MICE Video Conference Thu April 9 Slide 3 Absolute Time Calibration Method Calibration constants : –40 t0 i ij constants (one per PMT/channel) for TOF0 : the difference between the delay in channel i (delays in the slab material, PMT, cables, …) and the delay of the channel which delivers the trigger when pixel ij is hit. –100 Relative trigger delays Δ T tr ij (one per pixel) for TOF0 : the difference between trigger delay (the delay in the channel which is delivering the trigger) from pixel ij and the trigger delay for a pixel used as a reference. –28 t0 m constants (one per PMT/channel) for TOF1 : the delay in channel m of TOF1. –40 additional t0 k constants (one per PMT/channel) will be needed for TOF2. More detailed explanation of the method is available in the MICE Note :

Y. Karadzhov MICE Video Conference Thu April 9 Slide 4 Time walk correction The adoption of leading edge discriminators introduces a dependence of the discrimination crossing time on the collected charge (time walk). To calculate the time walk correction the difference of the time measured by the PMT and a reference time is measured. The dependence of this time difference on the maximum of the signal of the PMT measured by the FADC is fitted with some function (see the formula). The precision in the calculation of the time walk correction is limited by the very poor statistics of events with maximum of the signal of the PMT under 1000 or above 3000 ADC counts. The reference time is given by a PMT in the other plane of the station and the time walk effect in the measurement of the reference time is suppressed by an offline constraint on the variation of the ADC pulse height in the PMT used as a reference.

Y. Karadzhov MICE Video Conference Thu April 9 Slide 5 Time walk correction The effect of the time walk correction for a typical pixel. The difference between the time measured by slab 5 in plane 0 and slab 4 in plane 1 of TOF0, before and after the time walk correction

Y. Karadzhov MICE Video Conference Thu April 9 Slide 6 Obtained results The calculation was done by the method described above, using the data from runs 849, 886, 890 and 891 (300 MeV/c pions). This amount of data is sufficient for calibration of only 9 pixels in TOF0 and 2 pixels in TOF1. TOF0 TOF1

Y. Karadzhov MICE Video Conference Thu April 9 Slide 7 The effect of the time calibration and time- walk correction The plots show overall distribution of the time difference between the vertical and horizontal slabs for all the counters in TOF0 without (top) and with (bottom) the time corrections. The measurements from the calibrated pixels (the peak at zero) and from the still uncalibrated pixels are clearly distinguishable.

Y. Karadzhov MICE Video Conference Thu April 9 Slide 8 TOF0 time resolution The time difference between the vertical and horizontal slabs in the same station can be used also to measure the time resolution obtained after the calibration. The resolution on the difference in the calibrated pixels in TOF0 is ~ 102 ps. This translates into ~ 51 ps resolution for the full detector with crossed horizontal and vertical planes.

Y. Karadzhov MICE Video Conference Thu April 9 Slide 9 TOF1 time resolution The resolution on the difference in the calibrated pixels in TOF1 is ~ 124ps. This translates into ~ 62ps resolution for the full detector with crossed horizontal and vertical planes.

Y. Karadzhov MICE Video Conference Thu April 9 Slide 10 Time of flight spectrum Time of flight between TOF0 and TOF1 for the so called positron (red) and pion (blue) beams in normal (left) and logarithmic (right) scale. The first peak which is present in both distributions is considered as the time of flight of the positrons and is used to determine the absolute value of the time in TOF1.

Y. Karadzhov MICE Video Conference Thu April 9 Slide 11 Time of flight spectrum A natural interpretation of the other two peaks in the time of flight spectrum from the so called pion beam is that they are due to forward flying muons from pion decay and pions themselves, but the calculated time of flight of nominal 300 MeV/c pions is ~ 29.4 ns instead of ~ 30.0 ns, where the third peak maximum is positioned. This difference may be partly explained by the energy loss inside the TOF0 and the two upstream Cerenkovs, that amounts to ~ 17 MeV.

Y. Karadzhov MICE Video Conference Thu April 9 Slide 12 Conclusions Even with the small collected amount of data, we’ve been able to obtain resolutions in the time measurement in TOF0 and TOF1 that are in agreement with (TOF0), or very close to (TOF1) the desired values. There is an area for improvement in the time walk correction but we need significantly larger amount of data for this. A detailed and well understood simulation of the MICE beam channel in order to understand fully the obtained TOF spectrum for the so called 300 MeV/c pion beam is urgently needed.