# ToF Results from Run 06C

# 

On 12 September 2006, we took Time of Flight data with 1000 MeV
(nominal) protons.

The MCR recorded the beam energy coming out of the booster as 1007 MeV.

We placed our two detectors (5cm x 5cm x 2mm) at the usual target
location in the NSRL beam line and took events triggered by the
coincidence of the two discriminators. Discriminator thresholds were set
to -25 mV. The two phototubes were set to -1800 Volts for efficient
triggering on protons. Event rates were very high, typically 50-100k
triggers per spill, with \~600 events per spill being recorded. This did
not appear to degrade the performance of the detectors significantly.
Discriminator outputs were 20ns wide for ToF2, and 50ns wide for ToF1.
ToF2 was cable-delayed to start in the middle of ToF1 so that ToF2
determines the TDC Start timing in most cases.

Data was taken at two locations. In Location 1, the two phototube
holders were abutting each other as closely as possible, with the two
scintillators separated by 3.75 inches. The rail locator indicated that
the ToF1 position was 250.0 inches. Location 2 was 125 inches upstream
at 125 inches.

Plots show the pulse height spectra for the two counters, and the timing
distributions. For ToF analysis, we take the difference in time between
the primary counter ToF2, and the secondary counter ToF1.

![](media/image1.png){width="5.440277777777778in"
height="5.302777777777778in"}

Figure 1: Pulse height distribution for ToF1 in ADC counts.

![](media/image2.png){width="5.433333333333334in"
height="5.302777777777778in"}

Figure 2: Pulse height distribution for ToF2 in ADC counts.

Note that there is no evidence for a peak in either of the spectra. This
may be due to high levels of background from photons coming from
activation in the target room. We had been running high intensity
protons all day, and background levels were observed to be very high. It
could be that the peak was obscured due to pile-up at these high trigger
rates. Whatever the cause, we were not able to isolate a clean proton
peak to do the ToF analysis on.

![](media/image3.png){width="5.440277777777778in"
height="5.302777777777778in"}

Figure 3: Pulse height distributions for ToF2 vs ToF1 in ADC counts.

The analysis was performed on 4 separate regions in the ADC scatterplot,
in order to understand how the pulse height might effect the Time of
Flight measurements. Region 1 was low pulse height in ToF1 and large in
ToF2. Region 2 was high in ToF2 and high in ToF1. Region 3 was low in
ToF2 and high in ToF1. Region 4 was low in both. Statistics were poor in
all regions except Region 4, but there was no trend observed in any of
the regions.

TDC distributions are also shown below.

![](media/image4.png){width="5.433333333333334in"
height="5.302777777777778in"}

Figure 4: Timing distribution for ToF2 in TDC counts.

![](media/image5.png){width="5.433333333333334in"
height="5.302777777777778in"}

Figure 5: Timing distribution for ToF1 in TDC counts.

Note that the ToF1 TDC distribution is not symmetric. The cause of this
asymmetry is not understood at this time.

When plotting ToF1 vs ToF2, there is little indication of any
correlation between the two TDC values. This is different from what had
been observed in earlier running where it was necessary to subtract one
from the other in order to get unbiased timing.

![](media/image6.png){width="5.433333333333334in"
height="5.302777777777778in"}

Figure 6: ToF1 TDC vs ToF2 TDC, in TDC counts. Z axis is logarithmic.

In order to obtain Time-of-Flight measurements, we made use of the TDC
calibration performed several times previously. See details in
[NSRL-TN-05-002](http://www.bnl.gov/medical/nasa/CAD/technotes/NSRL-TN-05-002.pdf)
where the SRS Precision Pulser was used to calibrate the TDC at 35.78
ps/bin.

Fits were made to the time difference, ToF2-ToF1 (even though we saw no
correlation), for the four difference regions of interest in the pulse
height, giving the following results.

  ----------------- ------------------ ------------------ ----------------
  **ADC Region**    **∆T at Location   **∆T at Location   **∆T**
                    1**                2**                

  450\<ADC\<550     -8.48 bins         329.99 bins        337.71

  550\<ADC\<750     -6.51              329.92             336.86

  750\<ADC\<1000    -8.20              330.74             335.56

  1000\<ADC\<5000   -6.26              330.28             337.24

  All               -6.52              330.18             336.82
  ----------------- ------------------ ------------------ ----------------

Table 1: TDC Shifts between ToF1 and ToF2 at 2 locations.

  ------------------------ --------------- --------- ---------------------
  **ADC Region**           **∆Time (ns)**  **β**     **Kinetic Energy**

  450\<ADC\<550            12.12           0.874     989

  550\<ADC\<750            12.09           0.876     1005

  750\<ADC\<1000           12.05           0.879     1030

  1000\<ADC\<5000          12.11           0.875     998

  All                      12.09           0.876     1006
  ------------------------ --------------- --------- ---------------------

Table 2 Proton Beam Kinetic Energy from fitting to the time difference
between ToF1 and ToF2 at 2 locations.

The ADC for ToF1 had a pedestal at bin 421, and the regions specified in
the tables 1 and 2 are not pedestal subtracted. The four ADC regions of
interest were selected to have comparable statistical significance.

The result for all the data gives 1006 MeV, to compare with the value of
1007 MeV from the RF. Although the result agrees well, the data show the
extreme sensitivity of the energy to small fluctuations in ∆T and
calibration. The systematic uncertainty in these measurements comes from
three sources; TDC calibration, distance between counters, and peak
fitting.

The TDC calibration, as determined from pulser studies, was set to 35.9
± 0.1 ps/bin. This contributes 18 MeV to the systematic uncertainty on a
kinetic energy of 1000 MeV.

The distance was measured to ±0.032". This contributes 2 MeV to the
error.

The peak of the timing distribution was determined by fitting a Gaussian
function to the top 50% of the peak. Since some of these peaks were not
symmetric, the choice of the fitting region affected the fit results.
There were also small systematic variations with pulse height, as
illustrated in Table 1. I have assigned an uncertainty in peak fitting
of ± 1 bin based on experience fitting under a variety of conditions.
This contributes 19 MeV to the error.

The statistical uncertainty in this measurement is completely
negligible. The total uncertainty obtained by combining these three in
quadrature is 26 MeV. Each of these uncertainties is a very steep
function of beam energy.

# 200 MeV Measurement

We repeated the ToF technique with large beam protons at \~200 MeV,
giving the following results.

  ------------ --------- -------------- --------- ---------- ---------- ---------
  **Bin        **Delta   **Velocity**   **β**     **γ**      **γ-1**    **KE**
  Shift**      t**                                                      

  632.2        22.70     17.12          0.571     1.2182     0.2182     205

  632.5        22.71     17.11          0.571     1.2180     0.2180     205

  632.3        22.70     17.12          0.571     1.2181     0.2181     205
  ------------ --------- -------------- --------- ---------- ---------- ---------

Table 3: Proton Beam Kinetic Energy from fitting to the time difference
between ToF1 and ToF2 at 2 locations for 200 MeV protons.

Contributions to the uncertainty were 1.5 MeV from the TDC calibration,
0.9 MeV from peak fitting,and 0.1 MeV from distance for a total of 1.8
MeV. These results should be compared to the Bragg Peak measurement of
205 MeV.

# 500 MeV Measurement

We repeated the ToF technique with large beam protons at \~500 MeV,
giving the following results.

  ------------- --------- --------- --------- --------- --------- ---------
  474.3         17.03     22.82     0.761     1.5422    0.5422    509

  474.2         17.02     22.83     0.761     1.5427    0.5427    509

  474.2         17.03     22.83     0.761     1.5425    0.5425    509
  ------------- --------- --------- --------- --------- --------- ---------

Table 4: Proton Beam Kinetic Energy from fitting to the time difference
between ToF1 and ToF2 at 2 locations for 500 MeV protons.

Contributions to the uncertainty were 10 MeV from the TDC calibration, 4
MeV from peak fitting,and 0.4 MeV from distance for a total of 10.2 MeV.
No Bragg Peak results could be obtained for the 500 MeV proton beam.

Both the 200 MeV and 500 MeV results were obtained with large beam at a
trigger rate of \~20,000 -- 50,000 coincidences per spill. The data
taking took only a couple of minutes at a rate of \~600 events per spill
for a total sample of \~15,000 events total at each point. It is not yet
clear whether we need to take a "close" point each time, or can obtain
as reproducible results with just a single "far" point. This would make
ToF measurements much simpler.