Abstract
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 × 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 × 10^14 Hz, indicating that the maximum energy of non-thermal electrons accelerated at the jet reverse shock is E_e, 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 E_e, 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 E_e, max can grow fast enough to amplify the jet magnetic field up to 50–400 μG and accelerate particles up to the maximum energy E_e, max observed in the Cygnus A primary hotspot.