2018MNRAS.473.3500A

We study particle acceleration and magnetic field amplification in the primary hotspot in the north-west jet of radiogalaxy Cygnus A. By using the observed flux density at 43 GHz in a well-resolved region of this hotspot, we determine the minimum value of the jet density and constrain the magnitude of the magnetic field. We find that a jet with density greater than 5 x 10-5 cm-3 and hotspot magnetic field in the range 50-400 µG are required to explain the synchrotron emission at 43 GHz. The upper-energy cut-off in the hotspot synchrotron spectrum is at a frequency ≲5 x 1014 Hz, indicating that the maximum energy of non-thermal electrons accelerated at the jet reverse shock is Ee, max ∼ 0.8 TeV in a magnetic field of 100 µG. Based on the condition that the magnetic-turbulence scalelength has to be larger than the plasma skin depth, and that the energy density in non-thermal particles cannot violate the limit imposed by the jet kinetic luminosity, we show that Ee, max cannot be constrained by synchrotron losses as traditionally assumed. In addition to that, and assuming that the shock is quasi-perpendicular, we show that non-resonant hybrid instabilities generated by the streaming of cosmic rays with energy Ee, max can grow fast enough to amplify the jet magnetic field up to 50-400 µG and accelerate particles up to the maximum energy Ee, max observed in the Cygnus A primary hotspot.