3.2 Calibration of the STK on-ground and on-orbit
3.2.6 Charge-loss correction on-orbit
This part was adopted from [83] and the data used is relative to more than one year of on-orbit acquisition. The charge corresponding to that of the protons and of the helium nuclei was obtained from the combined information of the two layers of PSD.
The variable used is:
PSDglobal =
rPSDx+ PSDy
2·EMIP (3.7)
CHAPTER 3. SILICON-TUNGSTEN TRACKER (STK)
Cluster Charge [ADC]
0 20 40 60 80 100 120 140 160 180 200
0 500 1000 1500 2000 2500 3000
Energy ladder 112 VA 0 Z = 1
= 51.20 ADC Smax
Cluster Charge [ADC]
0 20 40 60 80 100 120 140 160 180 200
0 500 1000 1500 2000 2500 3000
Energy ladder 112 VA 1 Z = 1
= 51.98 ADC Smax
Cluster Charge [ADC]
0 20 40 60 80 100 120 140 160 180 200
0 500 1000 1500 2000 2500 3000 3500
Energy ladder 112 VA 2 Z = 1
= 52.42 ADC Smax
Cluster Charge [ADC]
0 20 40 60 80 100 120 140 160 180 200
0 500 1000 1500 2000 2500 3000
3500 Energy ladder 112 VA 3 Z = 1
= 53.00 ADC Smax
Cluster Charge [ADC]
0 20 40 60 80 100 120 140 160 180 200
0 500 1000 1500 2000 2500 3000 3500
Energy ladder 112 VA 4 Z = 1
= 51.64 ADC Smax
Cluster Charge [ADC]
0 20 40 60 80 100 120 140 160 180 200
0 500 1000 1500 2000 2500 3000
Energy ladder 112 VA 5 Z = 1
= 50.30 ADC Smax
Figure 3.32: Cluster charge distribution in each of the 6 VAs for a ladder that reads the x coordinate of the track inηregion 0 (read-out strip) in the period 01.01.2016- 29.02.2016, before the gain equalization. The distributions are fitted with a Landau convoluted with a Gaussian noise function. Smax corresponds to the most probable value of the fit function.
80
Cluster Charge [ADC]
Cluster Charge [ADC]
0 20 40 60 80 100 120 140 160 180 200
Cluster Charge [ADC]
0 20 40 60 80 100 120 140 160 180 200
Cluster Charge [ADC]
0 20 40 60 80 100 120 140 160 180 200
Cluster Charge [ADC]
0 20 40 60 80 100 120 140 160 180 200
Cluster Charge [ADC]
0 20 40 60 80 100 120 140 160 180 200
Figure 3.33: Cluster charge distribution in each of the 6 VAs for a ladder that reads the x coordinate of the track inηregion 0 (read-out strip) in the period 01.11.2017- 30.12.2017, after the gain equalization. The distributions are fitted with a Landau convoluted with a Gaussian noise function. Smaxcorresponds to the most probable value of the fit function.
CHAPTER 3. SILICON-TUNGSTEN TRACKER (STK)
before VA eq. (01-02/2016) Smax
before VA eq. (01-02/2016) Smax
after VA eq. (11-12/2017) Smax
Figure 3.34: Smax distributions for the STK VA before (empty black distribution) and after (filled black distribution) the VA equalization. The distribution of Smaxbefore the gain correction is the same in both pictures. This is compared on the left with the correction applied to a proton sample in January and February 2016 and on the right with a sample of the period November-December 2017.
where PSDx,yare the x and the y measurements of the PSD corrected for the path length of the particle inside the PSD bar. EMIP is the energy that a minimum ionizing particle loses in 10 mm of PSD (for an accurate parametrization and more details see [70]). The distribution of PSDglobalis shown in Fig. 3.35. Proton and helium candidates are selected requiring PSDglobal(p) ∈ [0.94,1.24] and PSDglobal(He) ∈ [2.04,2.26], as depicted with the red distribution in Fig. 3.35. The impact angle on the XZ (θx) and YZ (θy) views are obtained from the reconstructed track in STK. In order to select particles crossing
[a.u.]
Figure 3.35: PSDglobal distribution for proton and helium. The red distribution represents the selected proton and helium nuclei.
the STK detector, a sample of events containing tracks with 5 or 6 reconstructed points is selected. The cluster charge distribution of ladders belonging to the first two STK layers as a function of η is shown in Fig. 3.36, for Z = 1 and for Z = 2 and for two different impact angles, after the path length correction and the VA gain correction. In the 3-dimensional plots of Fig. 3.36, like in section 3.2.4, the black points correspond
82
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 η1
dE/dx [ADC]
0 20 40 60 80 100 120
1 10 102 103
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 η1
dE/dx [ADC]
150 200 250 300 350 400 450 500
1 10 102 103
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 η1
dE/dx [ADC]
0 20 40 60 80 100 120
1 10 102 103
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 η1
dE/dx [ADC]
150 200 250 300 350 400 450 500
1 10 102 103
Figure 3.36: Cluster charge as a function of η for a selected sample of protons (figures on the top) and helium nuclei (figures on the bottom) for 5◦ < |θx,y| < 10◦ (figures left) and 25◦ <|θx,y| <30◦ (figures right). The dashed lines correspond to the cluster charge value at which we want to correct.
to the most probable value of the cluster charge (examples for proton and helium are reported in Fig. 3.37). We can notice the variation of the signal values depending onη for different particles. A smooth spline function connects the points to show the overall behavior. The dashed lines correspond to the value of the energy loss at which we want to correct and that is the same for all the inclinations of each particle (the energy loss for particles that impinge vertically on the read-out strips). The correction factors for proton and helium in the first point of STK were computed for various inclinations within the range 0◦ <|θx,y|<35◦, with 5◦ step as:
corrparam= MPV(Zi)/fun(ηZ i,θx,y) (3.8) where MPV(Zi) is the most probable value of the cluster charge for η ∈ [0, 0.12] and for |θx,y| < 5◦ for proton or helium (Zi) particles; fun(ηZ i,θx,y) is the spline function for the particles Zi evaluated atη for the inclination θx,y. These correction parameters were applied to the cluster charge in ADC (∝ energy loss dE/dx of the particle) of all the 192 STK ladders as:
ADCcorr = ADC·corrparam. (3.9)
A cut on the cluster charge was also applied in order to reduce particles interacting inside the STK and the presence of misidentified protons in PSD. Fig. 3.38 shows the energy loss distributions for protons and helium nuclei in all the ladders before and after the energy loss correction. The improvement in the cluster charge shape is evident.
CHAPTER 3. SILICON-TUNGSTEN TRACKER (STK)
100 150 200 250 300 350 400
0
100 150 200 250 300 350 400
0
Figure 3.37: Top figures: cluster charge for protons forη∈[0.12,0.14] (left) andη∈[0.38,0.40]
(right) both for 5◦ < |θx,y| < 10◦. Bottom figures: cluster charge for helium nuclei for η ∈ [0.52,0.54] and|θx,y|<5◦ (left), 5◦<|θx,y|<10◦(right). A fit with a Landau convoluted with a Gaussian noise function is also shown for each case. Note the different collection efficiency as a function ofη.
To obtain the average charge value that combines all the measurements of the clusters
dE/dx [ADC]
p before charge loss correction p after charge loss correction
dE/dx [ADC]
He before charge loss correction He after charge loss correction
Figure 3.38: Cluster charge distributions for protons (left) and helium nuclei (right) in the STK ladders before (blue) and after (red) the charge-loss correction. A fit with a Landau convoluted with a Gaussian noise function for the corrected distributions is also shown in black.
belonging to the track, we used the truncated mean ST defined as:
ST= P#clu
i=1 Si−SMax
#clu−1 (3.10)
84
where Si is the signal of cluster i and SMax is the maximum signal among the clusters associated to the track. The square root of the truncated mean is used since it is directly proportional to the particle charge (√
ST ∝Z). We divided √
ST by the square root of the signal for protons, and its distribution before and after the charge-loss correction is shown in Fig. 3.39. By fitting the charge distribution in Fig. 3.39 with a Gaussian function for each charge after the charge-loss correction, we obtained the preliminary measurement of the charge resolution for protons and helium nuclei in STK in charge units (c.u.): σp = 0.04 c.u. andσHe = 0.07 c.u. The statistical uncertainties of the fits are very small and considered negligible. The charge resolutions have improved after the charge-loss correction by≈13% for protons and ≈21% for helium nuclei.
Tracker Z
0.5 1 1.5 2 2.5 3
0 20 40 60 80 100 120 140 160 180
103
×
before charge loss correction after charge loss correction
Figure 3.39: Tracker charge distribution before (blue) and after (red) applying the charge-loss correction.
CHAPTER 3. SILICON-TUNGSTEN TRACKER (STK)
86
Chapter 4
Measurement of the Proton Flux
4.1 Introduction to the flux measurement
The measurement of the differential flux Φ of cosmic-ray protons is defined adapting Eq. 1.25 to the DAMPE measurement in an energy interval [E, E+dE], as follows:
Φ(E,E + dE) = Np(E,E + dE)
∆T×AGeom×dE. (4.1)
• Np(E,E + dE) is the number of candidate protons selected minus the background events between E and E + dE, unfolded with the selection efficiencyεin the same energy interval:
Np(E,E + dE) = 1 ε(E,E + dE)
X
i
P(E|Emeas,i)·Np,meas,i (4.2) where P(E|Emeas,i) is the probability to reconstruct a proton candidate that has an energy E in the energy bin i.
• ∆T is the effective data collection time (called live time) of DAMPE for the ana-lyzed data set;
• AGeomis the geometrical acceptance of DAMPE;
• dE is the energy bin.