4.3 Data Analysis
4.3.1 Timing with the Constant Fraction Method
The softwareExtract−timestamps(previous PhD works of [Hau 99] [Kno 08]
[Sun 08a]) for the TOF data analysis was extended to determine precision ion arrival time from the online experimental data and from the offline data. With a help of the software it is possible to analyze the whole spectra from the the online experimental data as well as single signals from the offline experiments. The software modified to accept data acquired with different oscilloscopes with different sampling rates. Two main event time determination methods are included in to the software: Constant Fraction Discrimination (CFD) method and extrapolation to zero [Kno 08] [Sun 08a].
In this work the CFD method was used.
An arrival time of the signal - event time is of a high interest in the ion revolution time measurements. The main uncertainties of the event time determination are summarized in Figure 3.13.
LeCroy Waverunner 6100A E
E
P C
Data Storage
Control Area Experimental
Area
Remote control
Monitoring of the spectra
Ion
Trigger from an injection
B
e -e
-Figure 4.5: Data acquisition system used in the online experiment. In the experimental area the signal from the anode connected with a cable to the oscilloscope that digitized the signal spectra and saved on the external harddrive. The voltages for TOF detector as well as the scope setting can be set and viewed directly in the control area remotely. As a trigger for the oscilloscope an injection trigger into the ESR is used.
In the TOF detector an electron charge produced from the MCPs is col-lected on the anode and can vary drastically. It means that the amplitude varies significantly from signal to signal also the rise time can vary some-what. In Figure 4.7 two signals with different amplitudes are shown from the online experiment. To minimize walk effects the experimental data have to be treated with an appropriate timing method. The CFD method is one of the most efficient and flexible method of the event time determination.
In this method, the logic signal is generated at a constant fraction f of the peak height to produce essential walk-free timing signal [Leo 87]. The technique by which the CFD method is achieved is shown in the Figure 4.8.
To determine the baseline the amplitudes of all signals are histogrammed to get the noise distribution [Mat 04]. The Constant Fraction Discriminating
100 200 300 400 500 600 700 800 -1,4
-1,2 -1,0 -0,8 -0,6 -0,4 -0,2 0,0
Amplitude/V
Tim e / s 238
U 73+
fission fragments
Figure 4.6: Online spectrum of stored ions with LeCroy oscilloscope in the experiment with 238U fission fragments. An oscilloscope was set to store the spectrum with record length of 800µm what corresponds to about 1600 revolution turns in the ESR.
method depends on two main parameters: the fraction factor f and the delayb. The original signal is split into two components. At first one of the component is attenuated with a certain fraction f and shifted by time b in such way that 0≪ b ≤ trise (blue curve), the other component is inverted (green curve). These two components are summed (red curve) and the zero crossing with a baseline defines the event time (Figure 4.8).
In the analysis of the online data with the CFD method in this work the following parameters were used: f=0.5, b=3. An optimal selection of those parameters is a guarantee for a good timing determination. A more detailed explanation of significance and right choice of the CFD parameters one can find in [Mat 04].
The timing precision of the TOF detector was determined by measuring the jitter in time difference between two coincidence signals from forward and backward MCP detectors. Time-stamps recorded from both MCP detec-tors, corresponding to the same time event were subtracted from each other and plotted as a histogram. The coincidence time-of-flight distribution in the case of 20Ne10+ beam (upper part) and 238U fission fragments (lower part) is shown in the Figure 4.9 and Figure 4.10.
-0,6 -0,4 -0,2 0,0
Amplitude/V
Tim e / ns
0 1 2 4 6
Figure 4.7: Comparison of two signals from one particle with different am-plitudes. The signal indicated with violet color needs a longer time to reach its maximum than the one with orange color. This effect, which will cause the time jitter in the event time termination, is called amplitude walk and can be minimized by the Constant Fraction Discriminating method.
From the coincidence time-of-flight distribution for the data with 20Ne10+
beam one can see an additional artifact on the right tail of the distribution indicated with blue color. The signals corresponding to those coincidences were investigated more detailed. It was observed that those signals belong to the truncated signals. Truncated signals are the signals with the amplitudes larger than the maximum voltage range of the oscilloscope display setting.
In those cases the correct signal maximum and so the correct CFD technique can not be applied. Therefore this artifact was not taken into analysis and the distribution indicated with grey color was fitted with a Gaussian func-tion (red curve). A standard deviafunc-tion of σ(Ne)branch=48 ps is calculated.
For the experiment with uranium fission fragments (Figure 4.10) the sigma of coincidence time-of-flight distribution is obtained asσ(fiss.frag.)branch=45 ps. For both experiments the same number of coincidences were taken; 1272 coincidences were analyzed. These standard deviations obtained from both online experiments are in a good agreement with the results from the offline experiments.
An uncertainty distribution of each event time determination using the CFD
-1,0 -0,5 0,0 0,5 1,0
Amplitude
Tim e
0 1 2 3 4 x
inverted signal
event time
original signal
attenuated &
shifted signal
Figure 4.8: The principle of the constant fraction discriminating technique.
One component of the signal is attenuated with a certain fraction f and shifted by timeb(blue curve), the other component is inverted (green curve).
Finally both components are summed (red curve) and the timing is deter-mined as a zero crossing with baseline.
method is shown in Figure 4.11. The error calculation for the data treated with the CFD method implemented in the software is explained in [Mat 04].
In case of the measurement with 20Ne10+ stable beam (upper part) the un-certainty in the event time determination is equal to about 8 ps. In the experiment with uranium fission fragments it is equal to 11.5 ps. In the calculation of the event time uncertainty the error of the signal amplitudes is assumed to be equal to the standard deviation σ(U0) of the distribution obtained for the baseline determination [Mat 04]. From the Figure 4.11 one notice that the uncertainties for the event times determination for forward detector are larger than for the backward detector in both experiments.
This is explained by the voltage settings of the channel of the oscilloscope.
In both experiments 200 mV/div was set in the channel where the spectra from the forward detector were acquired and 50 mV/div for the backward channel. Therefore the noise level of the spectrum and thus the σ(U0) in case of the forward detector is larger.
-1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 0
20 40 60 80 100 120 140
160 20
Ne 10+
stable beam
Countsperbin
Coincidence tim e-of -f light / ns branch
=48 ps
Figure 4.9: Coincidence time-of-flight determination for the data obtained with 20Ne10+ stable beam. The spectra are stored for both detectors and the event times are calculated with the CFD software method. Then the event times corresponding to the same event subtracted between each other and plotted as a histogram. The standard deviation is calculated with the Gaussian fit function (red curve). An additional artifact on the right part of the distribution indicated with blue color corresponds to the coincidences which belong to the truncated signals. Those signals were not taken into analysis and the sigma σbranch=48 ps is calculated from the distribution shown with grey color.