Theoretical and computational studies of the Weibel instability in several beam-plasma interaction configurations

The Weibel instability is investigated theoretically and numerically under three scenarios: counterstreaming electron beams in background plasma, an electron-positron beam and an electron-proton beam in background plasma. These models occur widely in laboratory and astrophysical environments. The Weibel instability growth rates are determined numerically from the corresponding cold-fluid dispersion relations, which are confirmed with two-dimensional particle-in-cell simulations. The maximum growth rates for the counterstreaming beams in background plasma are an order of magnitude smaller than the maximum growth rates for the beams cases in the same range of density ratios and beam energies. The maximum growth rate for the electron-positron beam case is shown to be at most a factor root 2 greater than the electron-proton beam case with similar dispersion behaviours. A non-monotonic relation is found between the maximum Weibel instability growth rates and the electron-positron beam energy, suggesting that increasing beam energies does not entail an increase in the Weibel instability growth rate.

Automated summary

The Weibel instability is investigated in three different scenarios and the growth rates are determined numerically. It is found that the maximum growth rates for counterstreaming beams are smaller than those for the beams in the same range of density ratios and beam energies. The maximum growth rate for the electron-positron beam case is slightly greater than that for the electron-proton beam case. A non-monotonic relation is observed between the maximum Weibel instability growth rates and the electron-positron beam energy.