Plasma Phys. Control. Fusion 41 (1999) A699–A707. Printed in the UK PII: S0741-3335(99)97514-0 The physics of collective neutrino–plasma interactions P K Shukla†¶, L O Silva‡, H Bethe§, R Bingham, J M Dawson‡, L Stenflo¶, J T Mendon¸ ca + and S Dalhed ∗ † Institut f ¨ ur Theoretische Physik IV, Fakult¨ at f¨ ur Physik und Astronomie, Ruhr-Universit¨ at Bochum, D-44780 Bochum, Germany ‡ Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA § Department of Physics, Cornell University, Ithaca, NY 14853, USA  Rutherford Appleton Laboratory, Chilton, Didcot, OX11 OQX, UK ¶ Department of Plasma Physics, Umeå University, S-90187 Umeå, Sweden + GoLP/Centro de F´ ısica de Plasmas, Instituto Superior T´ ecnico, 1096 Lisboa Codex, Portugal ∗ Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Received 3 July 1998 Abstract. A review of recent work on collective neutrino–plasma interactions is presented. The basic physical concepts of this new field as well as some possible astrophysical problems where the physics of collective neutrino–plasma interactions can have a radical impact, are discussed. 1. Introduction Neutrinos are produced in violent processes following the big bang leading to what we call the relic neutrinos-equivalent to the microwave background. Copious amounts of neutrinos are created during supernova explosions as well as from fusion reactions in the Sun. Even though neutrinos are among the most abundant elementary particles in the universe, they are also the most elusive. Some important questions about their properties (mass and helicity, for instance) remain to be answered in a definite way. Recent results from the superkamiokande experiment in Japan suggest that neutrinos have a mass of 0.1 eV or greater. Yet, neutrinos play a fundamental role in some of the most extraordinary events in the universe; from the big bang to the solar neutrino problem, from supernova explosions to the dark matter problem, the systematic presence of neutrinos has lead the physics community to devote a considerable effort to studies of the neutrino properties (Bahcall 1989, Bahcall and Ostriker 1996). The strongest effort towards the understanding of the neutrino properties has been made by the particle physicists: the interaction of the neutrinos with matter is well understood from a single-particle non-self-consistent point of view (see, for example, Kuo and Pantaleone 1989). However, at several scales of the universe, very intense neutrino fluxes are present. The fluxes can be so intense that the background matter is disturbed, which in turn affects the neutrino propagation. For example the gravitational binding energy of massive stars, of the order of 10 53 ergs s −1 , is released in the form of neutrinos during a supernova explosion. Therefore, we are in the presence of a scenario requiring a self-consistent description of neutrino propagation in matter, eventually leading to several types of instabilities. An electron beam, or a photon beam, propagating through a plasma generates plasma waves, which perturb and eventually 0741-3335/99/SA0699+09$19.50 © 1999 IOP Publishing Ltd A699