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A gamma-ray burst (GRB) jet running into an external medium is expected togenerate luminous GeV-TeV emission lasting from minutes to several hours. Thehigh-energy emission results from inverse Compton upscattering of prompt andafterglow photons by shock-heated {\it thermal} plasma. At its peak thehigh-energy radiation carries a significant fraction of the power dissipated atthe forward shock. We discuss in detail the expected TeV luminosity, using arobust "minimal" emission model. Then, using the statistical properties of theGRB population (luminosity function, redshift distribution, afterglow energy)we simulate the expected detection rates of GRBs by current and upcomingatmospheric Cherenkov instruments. We find that GRBs exploding into alow-density interstellar medium must produce TeV emission that would havealready been detected by the currently operating Cherenkov telescopes. Theabsence of detections is consistent with explosions into a dense wind of theGRB progenitor. If the typical environment of long GRBs is a Wolf-Rayetprogenitor wind, as suggested by the recent analysis of Fermi LAT data, thenthe upcoming Cherenkov Telescope Array (CTA) should be able to detect afraction of GRBs that trigger the space-borne detectors. Since absorption bythe extragalactic background light limits the detectability above 0.1 TeV forall but the most nearby bursts ($z\lesssim 1$), the reduced energy threshold ofCTA is the key improvement over current instruments, which should boost thedetection rate by at least a factor of 3.

On the prospects of gamma-ray burst detection in the TeV band