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

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