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Bridging the gap between two stream and filamentation instabilities



We investigate intermediate unstable modes between two stream and filamentation instabilities. We detail the problem of the angle between the wave vector and its electric field and use an electromagnetic formalism allowing for any value for this angle. We display analytical results for 3 different models: cold beam-cold plasma, cold beam-hot plasma and cold relativistic beam-hot plasma. We demonstrate that plasma temperature prompts a critical angle for which waves are unstable at any k and show that for a relativistic beam, the most unstable waves are obtained for wave vectors which are neither normal nor perpendicular to the beam.


Corresponding author

Address correspondence and reprint requests to: Antoine Bret, Laboratoire de Physique des Gaz et des Plasmas, (UMR-CNR 8578), Université Paris XI, Bâtiment 210, Orsay 91405, France. E-mail:


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Laser and Particle Beams
  • ISSN: 0263-0346
  • EISSN: 1469-803X
  • URL: /core/journals/laser-and-particle-beams
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