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

• Published in: Journal of plasma physics 2022-04, Vol.88 (2), Article 905880206
• Main Authors: Davidson, Conor, Sheng, Zheng-Ming, Wilson, Thomas, McKenna, Paul
• Format: Article
• Language: English
• Subjects: Astronomical models; Cold; Cosmic rays; Electron beams; Laboratories; Magnetic fields; Particle beams; Particle in cell technique; Plasma; Plasma interactions; Plasma physics; Positron beams; Proton beams; Radiation; Simulation; Weibel instability
• ISSN: 0022-3778; 1469-7807
• DOI: 10.1017/S0022377822000253

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 $\sqrt {2}$ 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.