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Two energetic millisecond pulsars (MSPs) within globular clusters (GC),J1823-3021A in NGC 6624 and PSR B1821-24 in M28, have been recently discoveredto emit pulsed GeV gamma-rays. These MSPs are expected to eject energeticleptons. Therefore, GCs have been proposed to produce GeV-TeV gamma-rays as aresult of the comptonization process of the background radiation within a GC.We develop this general scenario by taking into account not only the diffusionprocess of leptons within a GC but also their advection with the wind from theGC. Moreover, we consider distribution of MSP within a GC and the effectsrelated to the non-central location of the dominating, energetic MSP. Such morecomplete scenario is considered for the modelling of the GeV-TeV gamma-rayemission from the core collapsed GC M15 and also for GCs which contain recentlydiscovered energetic MSPs within NGC 6624 and M28. The confrontation of themodelling of the gamma-ray emission with the observations with the presentCherenkov telescopes and the future Cherenkov Telescope Array (CTA) allows toconstrain more reliably the efficiency of lepton production within the innermagnetosphere of the MSPs and re-accelerated in their vicinity. We discuss theexpected limits on this parameter in the context of expectations from thepulsar models. we conclude that deep observations of GCs, even with the presentsensitivity of Cherenkov telescopes (H.E.S.S., MAGIC, VERITAS), should start toconstrain the models for the acceleration and radiation processes of leptonswithin the inner pulsar magnetosphere and its surrounding.

TeV gamma-ray emission initiated by the population or individual millisecond pulsars within globular clusters