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A new quasi-neutral model describing the Weibel instability of a high-currentrelativistic beam propagating through a resistive plasma is developed. Ittreats beam electrons as kinetic particles, and ambient plasma as anon-relativistic fluid. For a finite-temperature beam, a new class of negativeenergy magneto-sound waves is identified, which can possess negative energy.Their growth due to collisional dissipation in the cold return currentdestabilizes the beam-plasma system even for high beam temperatures. We performdetailed two- and three-dimensional particle-in-cell (PIC) simulations of thethermal beam and collisional plasma. It is shown that in three dimensions, theWeibel instability persists even for physically collisionless backgroundplasma. The anomalous plasma resistivity is then caused by the two-streaminstability.

On collisions driven negative energy waves and Weibel instability of a relativistic electron beam in a quasi-neutral plasma