Collective Modes in Neutrino `Beam' Electron-Positron Plasma Interactions

Astronomy and Astrophysics – Astrophysics

Scientific paper

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27 pages; LaTex. Replaced by published version. - Appendix about neutrino Wigner functions added and main text correspondingly

Scientific paper

10.1103/PhysRevD.63.013008

We derive semiclassical neutrino-electron transport equations in the collisionless (Vlasov) limit from the coupled Dirac equations, incorporating the charged and neutral weak current-current as well as electromagnetic interactions. A corresponding linear response theory is derived. In particular, we calculate the response functions for a variety of beam-plasma geometries, which are of interest in a supernova scenario. We apply this to the study of plasmons and to a new class of collective {\it pharon} resonance modes, which are characterized by $\omega < q$. We find that the growth rates of the unstable modes correspond to a strongly temperature ($\propto T_\nu^2T_e^3$) and linearly momentum dependent e-folding length of about $10^{10}$ km under typical conditions for Type II supernovae. This appears to rule out such long-wavelength collective modes as an efficient means of depositing neutrino energy into the plasma sphere.

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