  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.
