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The local Cosmic Ray (CR) energy spectrum exhibits a spectral softening at energies around 3~PeV. Sources which are capable of accelerating hadrons to such energies are called hadronic PeVatrons. However, hadronic PeVatrons have not yet been firmly identified within the Galaxy. Several source classes, including Galactic Supernova Remnants (SNRs), have been proposed as PeVatron candidates. The potential to search for hadronic PeVatrons with the Cherenkov Telescope Array (CTA) is assessed. The focus is on the usage of very high energy $γ$-ray spectral signatures for the identification of PeVatrons. Assuming that SNRs can accelerate CRs up to knee energies, the number of Galactic SNRs which can be identified as PeVatrons with CTA is estimated within a model for the evolution of SNRs. Additionally, the potential of a follow-up observation strategy under moonlight conditions for PeVatron searches is investigated. Statistical methods for the identification of PeVatrons are introduced, and realistic Monte--Carlo simulations of the response of the CTA observatory to the emission spectra from hadronic PeVatrons are performed. Based on simulations of a simplified model for the evolution for SNRs, the detection of a $γ$-ray signal from in average 9 Galactic PeVatron SNRs is expected to result from the scan of the Galactic plane with CTA after 10 hours of exposure. CTA is also shown to have excellent potential to confirm these sources as PeVatrons in deep observations with $\mathcal{O}(100)$ hours of exposure per source. 34 pages, 16 figures, Accepted for publication in Astroparticle Physics

Supernova remnants exhibit shock fronts (shells) that can accelerate charged particles up to very high energies. In the past decade, measurements of a handful of shell-type supernova remnants in very high-energy gamma rays have provided unique insights into the acceleration process. Among those objects, RX J1713.7−3946 (also known as G347.3−0.5) has the largest surface brightness, allowing us in the past to perform the most comprehensive study of morphology and spatially resolved spectra of any such very high-energy gamma-ray source. Here we present extensive new H.E.S.S. measurements of RX J1713.7−3946, almost doubling the observation time compared to our previous publication. Combined with new improved analysis tools, the previous sensitivity is more than doubled. The H.E.S.S. angular resolution of 0.048° (0.036° above 2 TeV) is unprecedented in gamma-ray astronomy and probes physical scales of 0.8 (0.6) parsec at the remnant’s location. The new H.E.S.S. image of RX J1713.7−3946 allows us to reveal clear morphological differences between X-rays and gamma rays. In particular, for the outer edge of the brightest shell region, we find the first ever indication for particles in the process of leaving the acceleration shock region. By studying the broadband energy spectrum, we furthermore extract properties of the parent particle populations, providing new input to the discussion of the leptonic or hadronic nature of the gamma-ray emission mechanism.