A population of globular clusters ( GCs ) has been recently established by the Fermi -LAT telescope as a new class of GeV \gamma -ray sources .
Leptons accelerated to TeV energies , in the inner magnetospheres of MSPs or in their wind regions , should produce \gamma -rays through the inverse Compton scattering in the dense radiation field from the huge population of stars .
We have conducted deep observations of the globular cluster M15 with the MAGIC telescopes and used 165 hrs in order to search for \gamma -ray emission .
A strong upper limit on the TeV \gamma -ray flux < 3.2 \times 10 ^ { -13 } \mathrm { cm ^ { -2 } s ^ { -1 } } above 300 GeV ( < 0.26 \% of the Crab nebula flux ) has been obtained .
We interpret this limit as a constraint on the efficiency of the acceleration of leptons in the magnetospheres of the MSPs .
We constrain the injection rate of relativistic leptons , \eta _ { e } , from the MSPs magnetospheres and their surrounding .
We conclude that \eta _ { e } must be lower than expected from the modelling of high energy processes in MSP inner magnetospheres .
For leptons accelerated with the power law spectrum in the MSP wind regions , \eta _ { e } is constrained to be much lower than derived for the wind regions around classical pulsars .
These constraints are valid for the expected range of magnetic field strengths within the GC and for the range of likely energies of leptons injected from the inner magnetospheres , provided that the leptons are not removed from the globular cluster very efficiently due to advection process .
We discuss consequences of these constraints for the models of radiation processes around millisecond pulsars .