Machine-learning correction for the calorimeter saturation of cosmic-ray ions with the Dark Matter Particle Explorer: towards the PeV scale

TL;DR

DAMPE's calorimeter saturates for high-energy cosmic-ray ions, biasing energy reconstruction up to the PeV scale. The authors implement a CNN-based regression that ingests a $14\times22$ BGO image to predict a correction via $\lambda = \ln\left(\frac{E_{dep}^{(simu)}}{E_{dep}^{(reco)}}\right)$, trained across multiple ion species to form an ion-agnostic correction. Results show the correction is robust to incident energy and the number of saturated bars, with significant improvement over previous methods, except in the most severely saturated cases, and validated on pseudo-saturated on-orbit data. This approach extends the DAMPE calorimeter’s effective energy reach to the PeV regime, supporting spectral measurements and knee-region studies of cosmic-ray ions.

Abstract

The Dark MAtter Particle Explorer (DAMPE) instrument is a space-borne cosmic-ray detector, capable of measuring ion fluxes up to $\sim$500 TeV/n. This energy scale is made accessible through its calorimeter, which is the deepest currently operating in orbit. Saturation of the calorimeter readout channels starts occurring above $\sim$100 TeV of incident energy, and can significantly affect the primary energy reconstruction. Different techniques -- analytical and machine-learning based -- were developed to tackle this issue, focusing on the recovery of single-bar deposits, up to several hundreds of TeV. In this work, a new machine-learning technique is presented, which benefits from a unique model to correct the total deposited energy in DAMPE calorimeter. The described method is able to generalise its corrections for different ions and extend the maximum detectable incident energy to the PeV scale. This work is a continuation of the results presented in [1].

Figures (13)

• Figure 1: schematic view of the DAMPE calorimeter DAMPE_mission.
• Figure 2: simulated event of an iron nucleus crossing the DAMPE calorimeter, with an incident energy of $\sim$1.3 PeV. The figure shows the simulated (on the left) and the reconstructed energy deposits (on the right) on the single BGO bars. Each subplot merges the information from both the layers with x- (odd layers) and y-oriented (even layers) bars. In the reconstructed event, null deposits resulting from saturation are present in the middle of the shower axis, where the release of energy is at its maximum. In both plots, the saturated bars are highlighted with red boxes. In the shown event, $\sim$80% of the true deposited energy is lost because of saturation; after correction, more than 90% of the true deposit is recovered.
• Figure 3: design of a convolutional neural network (CNN) to correct the total energy deposited in the DAMPE calorimeter for saturation. The specific model takes as input a $14 \times 22 \times 1$ image---where each pixel corresponds to a bar in the BGO calorimeter---, and returns a correction factor for the total energy.
• Figure 4: loss of the model during training. The loss function is evaluated at the end of each epoch on both the training and the validation samples. The decreasing trend found in both cases excludes the presence of overtraining.
• Figure 5: ratio of the corrected and simulated total deposited energy, as a function of the particle incident energy. Three plots are shown for the protons (top left), carbon (top right) and iron events (bottom); each plot is split into two subplots: the main one shows the 2D distribution of the events with saturation, and the secondary one the average value and the standard deviation of the y-projection of the corresponding x-bin, from the main plot. The values in the secondary subplot are fitted using a linear function to the 10-logarithm of the incident energy.