# Development of a Clock Generation and Time Distribution System for Hyper-Kamiokande +
## 2 Materials and Methods  
### Proposed Solution  
The proposed solution that we describe here is structured around one single time reference point and implements known standard metrology techniques [6; 7; 8]. This reference point distributes a high-frequency clock signal built from an atomic clock. This ensures short-term stability of the time signal as it will be shown later. The system will integrate a GNSS (GPS + other satellite constellations) antenna (B3E6 choke ring [9]) and receiver (Septentrio PolaRx5 [10]) to provide the link to the GNSS time base and to UTC. The system will also include calibration and monitoring components and will distribute timing information to the PMTs and data acquisition system via a two-stage distribution. Finally, full redundancy of signal generation is foreseen in case of a faulty item. The detailed scheme of the proposed solution can be seen in Figure 1.  
Figure 1: Detailed scheme of the proposed timing system for HK (redundancy not included).  
The reason for this choice is that atomic clocks are the best solution for stability at short term (typically hours to days) because their level of white noise is very low. However, they suffer from a long-term drift because of an inherent frequency random walk noise. They may also suffer from a deterministic quadratic drift that can be removed as a first step of analysis. The atomic clock used here is the most common frequency standard: the Rubidium clock (FS725 from Stanford Research [11]). Its performances already meet HK's requirement. However, other more expensive and more stable clocks can be used such as Masers. On the other hand, signals from GNSS poorly behave at short term but do not possess the random walk component to their noise; hence, they become more reliable at long term. The idea is to combine both in HK's system. The way the frequency stability can be measured is always against a reference known to be more stable and through a frequency counter. To represent this stability, the relevant statistical tool to use is the Allan standard deviation [12] which is given by  
\[\sigma_{y}^{2}(\tau)=\frac{1}{2}\langle\ (\overline{y}_{n+1}-\overline{y}_{n})^{2}\ \rangle \tag{1}\]  
It is the variance of the frequency ratio to nominal (\(y\)) as a function of the averaging, or sampling time (\(\tau\)). This can be performed in the time domain as well. It allows us to show stability of the same signal on different time scales. In Figure 2, it can be seen that the Rubidium clock is indeed more stable than the signal from the receiver (lower white noise level) until a certain point (\(\sim\)2 \(\times\) 10\({}^{4}\) s) where the long term drift becomes dominant. While averaging a white noise over a longer time decreases the deviation, it is not the case for a random walk noise. If we correct the clock signal with the GNSS information every 5.5 h only, we are able to combine both stability performances. Two types of references are available at the lab for the R&D process: a signal coming through the optical link from the official time-keeping lab in France: SYRTE laboratory, and a passive hydrogen maser, known to be more stable than the elements to characterize.  
Figure 2: Overlapping Allan standard deviation (ADEV) for the free Rb clock and the GNSS receiver.