a1 RUB International Chair, International Centre for Advanced Studies in Physical Sciences, Institute for Theoretical Physics V, Faculty of Physics & Astronomy, Ruhr University Bochum, 44780 Bochum, Germany; Scottish Universities Physics Alliance (SUPA), Department of Physics, University of Strathclyde, Glasgow, Scotland; School of Physics, University of KwaZulu-Natal, Durban 4000 Durban, South Africa; and Departamento de Física and Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1049-001 Lisboa, Portugal, firstname.lastname@example.org, email@example.com)
It is shown that a pre-existing electron density ripple in a dense plasma can excite electron neutrino oscillations. For our purposes, we use the dispersion relation for neutrino oscillations and derive the Mathieu equation for the propagation of neutrino oscillations in the presence of a spatially oscillating electron density ripple. The Mathieu equation predicts instability of neutrino oscillations. The criterion under which instability occurs is presented. Analytical expressions for the neutrino oscillation frequency and the growth rate are obtained. The possible relevance of our investigation to non-thermal neutrino oscillations in dense plasma environments (e.g. the supernovae, the core of white dwarf stars etc.) is briefly mentioned.
(Received November 19 2010)
(Accepted November 26 2010)
(Online publication January 21 2011)