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Considering the balance of acceleration and energy losses/escape within the astrophysical accelerators, the wealth of information encoded into the shape of the energy spectrum cut-off (maximum energy region) is highlighted. Following this, some of the brightest GeV gamma-ray sources observed by the Fermi-LAT are analysed, with focus placed on the energy spectrum cut-off shape. The sources chosen for this investigation were the brightest gamma-ray sources observed in the last 10 years, namely 3C 454.3, 3C 279, the Vela pulsar, and a solar flare event. For these sources a constraint on the cut-off shape parameters is investigated. Some of the significant potential improvements on such constraints by future observations with next generation ground based Cherenkov telescopes, represented in our study by the Cherenkov Telescope Array (CTA), are also highlighted.


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