In this work the efficiency of particle acceleration at the forward shock right after the SN outburst for the particular case of the well-known SN 1993J is analyzed. Plasma instabilities driven by the energetic particles accelerated at the shock front grow over intraday timescales and drive a fast amplification of the magnetic field at the shock, that can explain the magnetic field strengths deduced from the radio monitoring of the source. The maximum particle energy is found to reach 1-10 PeV depending on the instability dominating the amplification process. We derive the time dependent particle spectra and the associated hadronic signatures of secondary particles arising from proton proton interactions. We find that the Cherenkov Telescope Array (CTA) should easily detect objects like SN 1993J in particular above 1 TeV, while current generation of Cherenkov telescopes such as H.E.S.S. could only marginally detect such events. The gamma-ray signal is found to be heavily absorbed by pair production process during the first week after the outburst. We predict a low neutrino flux above 10 TeV, implying a detectability horizon with a KM3NeT-type telescope of 1 Mpc only. We finally discuss the essential parameters that control the particle acceleration and gamma-ray emission in other type of SNe.
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