Streaming instabilities driven by mildly relativistic proton beams in plasmas

M. E. Dieckmann, B. Eliasson, P. K. Shukla

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


The interaction between relativistic ion beams,electrostatic waves and particles in plasmas is studied numerically. This beam-particle interaction is important for the acceleration of electrons above the threshold, where they can perform Fermi acceleration across shocks perpendicular to the magnetic field direction. The electrons form Bernstein–Greene–Kruskal (BGK) modes, which are unstable due to a sideband instability. This process heats the electrons to relativistic temperatures and the electrons finally attain a flat-top momentum distribution with exponentially decreasing tails of the momentum distribution function. A scaling law, depending on the ion beam speed, is found for the electrondistribution function. Furthermore, in the fully nonlinear phase, ion phase space vortices, or proton BGK modes are formed in the beam, which continue to interact with the electrons after the electron BGK modes have collapsed.
Original languageEnglish
Pages (from-to)1394-1401
Number of pages8
JournalPhysics of Plasmas
Issue number4
Early online date29 Mar 2004
Publication statusPublished - Apr 2004


  • relativistic ion beams
  • electrostatic waves
  • ion phase space vortices
  • particle distribution function


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