On collisions driven negative energy waves and Weibel instability of a   relativistic electron beam in a quasi-neutral plasma
  A new quasi-neutral model describing the Weibel instability of a high-current relativistic beam propagating through a resistive plasma is developed. It treats beam electrons as kinetic particles, and ambient plasma as a non-relativistic fluid. For a finite-temperature beam, a new class of negative energy magneto-sound waves is identified, which can possess negative energy. Their growth due to collisional dissipation in the cold return current destabilizes the beam-plasma system even for high beam temperatures. We perform detailed two- and three-dimensional particle-in-cell (PIC) simulations of the thermal beam and collisional plasma. It is shown that in three dimensions, the Weibel instability persists even for physically collisionless background plasma. The anomalous plasma resistivity is then caused by the two-stream instability. 
Anupam Karmakar, Naveen Kumar, Gennady Shvets, Oleg Polomarov,   Alexander Pukhov