Simulation Method
4.3 Optimization of ARA
To optimize the ARA, 16 dierent antenna spacings and 10 dierent station spacings are selected for the study on the resolution of the neutrino moving direction and the detection e ciency along with studies of noise eect.The optimum would be
Figure 4.10: Illustration of the reconstructed neutrino moving direction (in red) and the generated one (in green).
Figure 4.11: Resolution of neutrino moving direction in zenith angle.
Figure 4.12: Resolution of neutrino moving direction in azimuthal angle.
Figure 4.13: Distribution of the separation angle between the generated ν direction and the reconstructed one. The average of this angle is taken for the comparison of the neutrino angular resolution in this analysis.
achieved when the resolution of the neutrino moving direction, i.e. h∆Θνi, is as good as possible, and the detection e ciency is as high as possible. The detection e ciency is de ned as the number of triggered events that pass the trigger threshold divided by the total number of generated events in the cylinder volume, where the threshold applied to the pulse voltage is 7 σnoise.
Figure 4.14: Resolutions of neutrino direction, h∆Θνi, versus antenna spacings and station spacings.
The antenna spacing varies from 100.7 m to 102.2 m in steps of 0.1 in the power index of 10. The station spacing changes from 1.33km/5 to 1.33km × 2 in steps of 1.33km/5. Note that the antenna spacing means the distance from the top antenna
to the bottom one. The vertical spacings between any two antennas are the same, and the center of the four antennas in a borehole is located at the depth of 200 m.
In addition, the side of the equilateral triangle in a station is set the same as the antenna spacing.
The mean value of the separation angles h∆Θνiversus the antenna spacings are shown in Figs. 4.14 and 4.15 in dierent displays, whereas the detection e ciencies versus the antenna spacings are given in Fig. 4.16.
Figs. 4.14, 4.15, and 4.16 suggest that h∆Θνi can be less than 5◦ if the station
Figure 4.15: 3D display of resolutions of neutrino direction, h∆Θνi (in unit of de-gree), versus antenna spacings and station spacings.
Figure 4.16: Detection e ciencies versus antenna spacings and station spacings.
spacing is set in the range of 1.33 km to 1.9 km and the antenna spacing is set in the range of 40 m to 100 m. One may notice that the detection e ciency reach a saturated value, ∼ 70%, when the station spacing is grater than ∼ 1.5km.
To nalize the optimal choice for the ARA geometry, the eects of dierent noise levels added to the original waveform and dierent trigger thresholds are studied, too. The value of σnoise is set at 0.035 mV for all analysis presented so far with V0gen varying in the range of 0 to 5 V. In the following studies of how the noise levels would aect the resolution of the neutrino moving direction, in each case a dierent level of noise added to the waveform is assumed, i.e. σnoise0 = ασnoise, with α greater than one, whereas V0gen is xed at 5 V. Dierent trigger thresholds are
applied: Viobs > 3.5σnoise, Viobs > 5σnoise, Viobs > 7σnoise. For these studies, only 100 events are generated in each case. The results of h∆Θνiand the detection e ciency versus the noise level under dierent trigger thresholds are presented in Figs. 4.17 to 4.34 for dierent antenna spacings and dierent station spacings. It was found that the larger σnoise0 added to the waveforms, the worse the resolution of the neutrino moving direction, which is as expected. In addition, the higher the trigger threshold, the lower the detection e ciency.
In summary, with the noise eect taken into account, in order to make the reso-lution of the neutrino moving direction as good as possible and detection e ciency as high as possible, the optimal choice for ARA geometry would be 1.6 km for the station spacing and 40 m for the antenna spacing.
Figure 4.17: Resolutions of neutrino direction, h∆Θνi, versus dierent noise levels and antenna spacings, where the station spacing is set at 1.33 km and the trigger threshold is 3.5σnoise.
Figure 4.18: Resolutions of neutrino direction, h∆Θνi, versus dierent noise levels and antenna spacings, where the station spacing is set at 1.60 km and the trigger threshold is 3.5σnoise.
Figure 4.19: Resolutions of neutrino direction, h∆Θνi, versus dierent noise levels and antenna spacings, where the station spacing is set at 1.86 km and the trigger threshold is 3.5σnoise.
Figure 4.20: Resolutions of neutrino direction, h∆Θνi, versus dierent noise levels and antenna spacings, where the station spacing is set at 1.33 km and the trigger threshold is 5σnoise.
Figure 4.21: Resolutions of neutrino direction, h∆Θνi, versus dierent noise levels and antenna spacings, where the station spacing is set at 1.60 km and the trigger threshold is 5σnoise.
Figure 4.22: Resolutions of neutrino direction, h∆Θνi, versus dierent noise levels and antenna spacings, where the station spacing is set at 1.86 km and the trigger threshold is 5σnoise.
Figure 4.23: Resolutions of neutrino direction, h∆Θνi, versus dierent noise levels and antenna spacings, where the station spacing is set at 1.33 km and the trigger threshold is 7σnoise.
Figure 4.24: Resolutions of neutrino direction, h∆Θνi, versus dierent noise levels and antenna spacings, where the station spacing is set at 1.60 km and the trigger threshold is 7σnoise.
Figure 4.25: Resolutions of neutrino direction, h∆Θνi, versus dierent noise levels and antenna spacings, where the station spacing is set at 1.86 km and the trigger threshold is 7σnoise.
Figure 4.26: Detection E ciencies versus dierent noise levels and antenna spac-ings, with the station spacing of 1.33 km and the trigger threshold is 3.5σnoise.
Figure 4.27: Detection E ciencies versus dierent noise levels and antenna spac-ings, with station spacing as 1.60 km and the trigger threshold is 3.5σnoise.
Figure 4.28: Detection E ciencies versus dierent noise levels and antenna spac-ings, with station spacing as 1.86 km and the trigger threshold is 3.5σnoise.
Figure 4.29: Detection E ciencies versus dierent noise levels and antenna spac-ings, with the station spacing of 1.33 km and the trigger threshold is 5σnoise.
Figure 4.30: Detection E ciencies versus dierent noise levels and antenna spac-ings, with station spacing as 1.60 km and the trigger threshold is 5σnoise.
Figure 4.31: Detection E ciencies versus dierent noise levels and antenna spac-ings, with station spacing as 1.86 km and the trigger threshold is 5σnoise.
Figure 4.32: Detection E ciencies versus dierent noise levels and antenna spac-ings, with the station spacing of 1.33 km and the trigger threshold is 7σnoise.
Figure 4.33: Detection E ciencies versus dierent noise levels and antenna spac-ings, with station spacing as 1.60 km and the trigger threshold is 7σnoise.
Figure 4.34: Detection E ciencies versus dierent noise levels and antenna spac-ings, with station spacing as 1.86 km and the trigger threshold is 7σnoise.
Chapter 5
Summary
Angular Resolution of Neutrino Moving Direction: One of the main goals of ARA is to point back to cosmic accelerators through the determination of the UHE neutrino moving directions, so the resolution of it is particularly important.
To optimize the ARA, both the resolution of the neutrino moving direction and the detection e ciency should be considered. Basically, the detection e ciency increases as the station spacing gets larger. From Fig. 4.16, however, it reaches a plateau of ∼ 70% detection e ciency when the station spacing is grater than ∼1.5 km where the regions which each station can cover no longer overlap. With the noise eect taken into account, in order to make the resolution of the neutrino moving direction as good as possible and detection e ciency as high as possible, the optimal choice for ARA geometry would be 1.6 km for the station spacing and 40 m for the antenna spacing.
In the simulation of angular resolution of neutrino direction for Antarctic Ross Ice Shelf ANtenna Neutrino Array (ARIANNA) experiment, the resolution in θ
Figure 5.1: Resolution of neutrino moving direction in θ direction in the simulation for ARIANNA.
direction is 1.1◦, as shown in Fig. 5.1 [34]. However, to reach such a good resolution, ARIANNA has to build its array up to 11 stations per km2, which means that its antenna density has to be 13 times greater than ARA if we set the station spacing as 1.33 km. Based on this comparing, the design of ARA is in a better balance point between the resolution and the cost.
In the future, if ARA can get more funding to increase the density of the antenna number, a much better resolution of neutrino moving direction can be achieved.
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