IceCube
IceCube Neutrino Observatory

PDD - Dynamic Range and Linearity

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6 Experimental Requirements

6.3 Dynamic Range and Linearity

The basic requirement is a dynamic range of 200 PEs per 15 ns. The interval 15 ns represents the typical time duration of a single PE pulse. This requirement is mostly driven by the reconstruction of energy and direction of very high-energy showers, typically 1 PeV. These produce measurable light over times of several hundreds of nsec. The amplitude and the waveform of the light pulses at the OM carry information on the position, the directionality and the energy of the shower. Figure 58 shows AMANDA-II PMT pulses from an in situ N2 laser pulse with a light output equivalent to a 1 PeV shower. The oscilloscope pulses shown are from OMs at three distances between 45 and 167 m.

Because of scattering of the photons in the ice, the shape of the photon pulse broadens with increasing distance from the point of emission. For example, at a distance of 60 m (about half the string spacing in IceCube) a 1 PeV shower will generate a PMT pulse of 1000 (200) PEs with a FWHM of 100 ns (150 ns) in forward (backward) direction of the shower. The example illustrates the directionality information contained in these data. Such an event will be observed by hundreds of OMs up to distances of more than 250 m from the interaction. The maximum current in this event reaches 12 PE/ns, or 180 PE/15 ns. Because of the greatly enhanced cross-section at 6.4 PeV (Glashow resonance), events at this energy may be preferentially observed, despite a falling spectrum. For these events, the peak input signal is more than 1000 PE/15 ns (at a distance of 60 m).

The non-spherical shape of the initial light pattern can be exploited for good directional and energy reconstruction. While the number of PMTs that saturate increases with higher energies (10 PeV and higher), the total number of PMT that observe a signal grows by an even larger number. Based on evaluations of simulated waveforms, we conclude that a dynamic range of about 15 PE/ns would be sufficient for an accurate reconstruction of the relevant event parameters (energy, direction), even though OMs nearest the shower will saturate.

Figure 58: PMT signals from a 335 nm nitrogen laser signal simulating a 1 PeV shower (about 1010 photons). The light is detected by AMANDA-II optical modules with fiber-optic readout at distances of approximately 45 m (black trace), 115 m (red trace), and 167 m (cyan trace).

PMTs that are very close to the shower core will saturate at the maximum anode current that a PMT is able to sustain. In the case of the Hamamatsu 10 in PMT, which is a prime candidate for IceCube, the anode current is limited to 80 mA, which sets an upper limit on the dynamic range in PE that depends on the gain. The operating conditions of IceCube suggest a gain of ∼ 107, corresponding to a theoretical peak of 500 PE/15 ns. It seems reasonable to expect that the PMT can sustain anode currents of 200 PE per 15 ns for intervals of about 100–200 ns. Recognizing the limitations on the dynamic range set by the PMT, and accepting a saturation of the 10% of the OMs near the shower core, we set the physics requirement for the dynamic range to 200 PE/15 nsec.