In 2008, the blazar Mrk421 entered in a very active phase and was one of the brightest sources in the sky at TeV energies, showing strong and frequent flaring. We searched for gamma-ray emission at energies E>0.8 TeV during the whole 2008 with the ARGO-YBJ experiment, a full coverage air shower detector located at Yangbajing (4300 m a.s.l., Tibet, P.R. China). The observed signal is not constant and in correlation with X-ray measurements. The average emission, during the active period of the source, was about twice the Crab Nebula level. This paper concentrates on 2008 June when the Mrk421 flaring activity has been studied from optical to 100 MeV gamma rays, and only partially up to TeV energies, since the moonlight hampered the Cherenkov telescope observations after 8 June. Our data complete these observations, with the detection of a second flare of intensity of about 7 Crab units on June 11-13, with a statistical significance of 4.2 standard deviations. The observed flux is consistent with a prediction made in the framework of the Synchrotron Self-Compton model, in which the flare is caused by a rapid acceleration of leptons in the jet.
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