TOF and beam energy¶

Top row: TOF, ns
Bottom row: beam energy reconstructed in ToF plane (before F5), MeV
Left coloumn: MWPC measurement data
Right coloumn: experimental data

Left coloumn: MWPC measurement data
Right coloumn: experimental data

The ToF distribution for different data is presented in the TOP row. The raw histograms were smoothed (4 iterations).  In the most right figure (red and blue graphs), one can see the shift of the ToF.
As long as the lower energy beam particles loose more energy in the installed  MWPC and moreover, amount of low-energy 9Li particls (with bigger ToF) prevails, it was decided to compare the low-energy 9Li's. These low energy are located in the right slopes of the ToF distributions.

The problem was how to properly compare the right low-energy slopes of the ToF distributions. The second row illustrates different methods of time-shift calculation.
 

Time of the Red and green  points was obtain by analysing the distribution slopes by the Constant Franction Discriminator method. Its realization is shown in the 2 bottom rows. The raw graph was summed with the negative one, amplified by 0.5 and shifted by 1.5 ns to the right / 0.5 ns to the left. The times with the zero value in the obtained graphs are Times of the Red and green points.The values of the shift (1.5 and 0.5 ns) are the halfs of the slopes range (left and right). 

Purple points - the inflection points of the right slopes. (maximum of the first derivative) 

Red lines in the second row - lines at the 50% of the maximum amplitude value

The time differenct of:
green points 0.535 ns
purple points 0.535 ns 

red points 0.385 ns ( this value is less informative as it was obtained from the high energy 9Li, which has low statistics. for this region ToF graph has much more fluctuations)

Whole low-energy slopes compare¶

Another method allows to compare the whole low-energy slopes with each other.
For this purpose, both graphs was rescaled to the maxumim value of the experimental graph 

As one can see, that on the distribution from experiment, the right slope is more steep. 
In order to make right slopes of both graphs more similar, the experimental graph was amplified by 0.9
Then, the time shift was chosen so, that the low-energy slopes cross in their middle (half length or at points with half-maximum values)

The time-shift was 0.55 ns in this method

The 270 MeV 9Li beam was delayed by 0.55 ns, by placing some passive volume in 4758 to F5 plane. 
That means that, the energy loss was ~4.8 MeV, which means that the thickness of the MWPC in Si equivalent is 150 micron.