Kinetic theory on the current-filamentation instability in collisional plasmas

The current filamentation instability (CFI) or Weibel-type instability is studied for a nonrelativistic electron beam penetrating an infinite uniform plasma, taking into account both the collisional effects and the space-charge effect (SCE). We consider three configurations for the beam and plasma: the kinetic domain, the hydrodynamic domain, and the hybrid domain with one in kinetic and the other in hydrodynamic domain. It is shown that the CFI is determined by the current-driven drift-anisotropy rather than the classical anisotropy of the beam and the background plasma. Therefore, collisional effects can either attenuate or enhance the CFI depending on the drift-anisotropy of the beam and the background plasma. It is found that the collisional effects usually attenuate the CFI for nearly symmetric counterstreaming in the whole unstable range but enhance it for asymmetric counterstreaming in the long wavelength region both in the kinetic and the hydrodynamic domains, although the mechanisms are different. As for the case of the hybrid domain the collisional effects enhance the CFI growth rate in the long wavelength region but reduce it in the short wavelength region. The SCE can be ignored for the hydrodynamic domain while for the kinetic and the hybrid domains it is still significant though damped by the collisional effects. The combination of the SCE and the collisional effects usually reduce the CFI growth rate and suppress the unstable range further, especially in the short wavelength region.