Simulations and expected performances

In order to determine the performances of GRAND in detecting neutrinos, an End-to-End simulation code is being developed.

The End-to-End simulation code had to take into account the specific features of the GRAND detection concept, and in particular the non-flat topography of the ground and the very large surface of the instrumented area. The latter implies a huge CPU time request, while the former significantly complicates the geometry of the simulation. It implies that particles have to be tracked step-by-step all along their trajectories.

No existing simulation tool fully complies with these very specific requests. Our simulation chain is therefore mostly genuine. It was however successfully tested against other codes.

The simulation chain can be divided into four independent parts: for each simulated neutrino, we first propagate the neutrino and daughter particles from trajectory definition down to the tau decay (Niess and Martineau-Huynh 2018), then compute the electromagnetic radiation induced by the subsequent shower at the GRAND antenna positions using a novel method called radio-morphing (Zilles et al. 2018). Following, we simulate response of the HorizonAntennas to these radio transient signals and finally implement a trigger algorithm to determine if each neutrino-induced shower is detected by the GRAND array. The simulation chain is presented in more details in the GRAND White Paper and in the Github repository GRAND-mother.

The simulation chain was run over a 10,000 km2 area situated at the Southern rim of the TianShan mountain range. The simulated detector is composed of 10,000 HorizonAntennas deployed along a square layout with 1 km step size. The site could constitute one possible hotspot of the final GRAND200k detector. This simulation area is called HotSpot1 (HS1) in the following. 20,000 air showers initiated by tau neutrino interactions with the Earth target were simulated, with the additional condition that the shower trajectories cross HS1.

Sensitivity results

The figure below  shows the 90% C.L. upper limit of HS1 differential sensitivity during 3 years of exposure time. The sensitivity of the full 200,000 km2 array is derived from this result, assuming its effective area will be 20 times larger than HS1’s. This will have to be confirmed through further simulations, where the actual locations and respective sizes of the additional hotspots will be defined. The resulting 90% C.L. differential and integral sensitivity curves of the GRAND200k array are also plotted in the figure below.

Angular resolution reconstruction

The arrival direction of a shower is inferred from the arrival times of the signals and positions of triggered antennas, assuming a specific shape for the radio wavefront. Models and measurements converge on wavefronts being hyperbolic-shaped, but GRAND will map the shape of the wavefront of inclined showers with unprecedented accuracy.

A mean angular resolution of <0.05 degrees is achievable in principle with GRAND, assuming a 5 ns relative timing precision, reachable with state-of-the-art GPS timing. This excellent performance is due to the antennas being deployed over a large range in elevation, which provides a good handle on zenith resolution even for very inclined events, unlike arrays deployed over flat areas.


The measurement of the shower maximum Xmax is the most robust technique to infer the nature of the primary particle in radio-detection experiments. In GRAND, high-precision studies of ultra-high-energy cosmic rays will depend on the ability to resolve Xmax. The ultimate goal is to match the present best accuracy of ~20 g cm-2 in the 108-11 GeV range. This level of performance still has to be demonstrated, but prospects are encouraging. For studies of neutrinos and gamma rays, a lower resolution, of ~40 g cm-2, would be enough to distinguish them from nuclei primaries.