Amplification of neutrino oscillations by a density ripple in dense plasmas

Abstract

Abstract. 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.Neutrinos, which are the least massive subatomic ghostly elementary particles in the set of building blocks of nature, were produced in the Big-Bang, which began the universe, and are emitted by the Sun and all other stars (e.g. neutron stars, white dwarf stars, magnetars etc.) These are also produced in violent astrophysical events in cosmos, e.g. explosions of supernovae, which occur when an old massive star collapses after running out of nuclear fuel. During the collapse, the star literally becomes a neutron star as neutrinos totally dominate in numbers of particles for a few seconds and carry off most of the energy from the implosion, more energy than radiated during the entire life of the star. For example, the neutrino flash was actually observed in Supernova 1987A. Neutrinos are also created when cosmic rays, fast moving particles from space, bombard the Earth's atmosphere producing cascades of secondary particles, which rain down on us. There are three different kinds, or 'flavors', as they are called, of neutrinos: electron, muon and tau neutrinos. There are also three anti-neutrinos of the same flavors. The neutrinos get their names from their charged lepton brethren, the electron, muon and tau, with masses of 0.511 MeV, 106 MeV and 1777 Mev, respectively. The three species of neutrinos at https://www.cambridge.org/core/terms. https://doi

Neutrino oscillations in a turbulent plasma

“…This is because of the extra term ( ω/ω) Ṗ2 in Eq. (21). In passing, we note that assuming the reduction P 1 sin 2θ + P 3 cos 2θ ≡ 0, one has exactly d 2 P 1 /dT 2 + P 1 = d 2 P 2 /dT 2 + P 2 = 0, which allows an exact solution regardless the form of the time-dependent frequency.…”

Neutrino oscillations in a turbulent plasma

“…This is because of the extra term ð _ x=xÞ _ P 2 in Eq. (21). In passing, we note that assuming the reduction P 1 sin 2h þ P 3 cos 2h 0, one has exactly d 2 P 1 =dT 2 þ P 1 ¼ d 2 P 2 =dT 2 þ P 2 ¼ 0, which allows an exact solution regardless the form of the time-dependent frequency.…”

“…The amplitude parameter can be simply interpreted as the ratio between the electron trapping frequency in the potential well of the electron plasma wave and the electron plasma frequency. 21 To avoid analytic difficulties, we will uniquely consider forward propagating waves, so that 0 < 1. Notice that from Eq.…”

Exact solution to neutrino-plasma two-flavor dynamics

“…The orthodox approach to the neutrino-plasma interaction problem is to assume specific medium properties, and then to solve the dynamical equations, either in approximate or numerical forms. In this respect, one can have sinusoidal variations of the electron density (Schafer and Koonin 1987;Krastev and Smirnov 1989;Koike et al 2009;Kneller et al 2013), general timedependent media (Hollenberg and Päs 2012), stochastic backgrounds (Torrente-Lujan 1999; Benatti and Floreanini 2005) as well as instabilities due to electron density ripples (Shukla 2011). In an inverse way, in the present work, a certain electron density profile is assumed, and then the corresponding medium properties are unveiled.…”

“…The associated neutrino charge coupling [2] leads to kinetic effects such as neutrino Landau damping [3], as well as to the generation of quasi-static magnetic fields [4] The orthodox approach to the neutrinoplasma interaction problem is to assume specific medium properties, and then to solve the dynamical equations, either in approximate or numerical forms. In this respect, one can have sinusoidal variations of the electron density [5], [6], [7], [8], general time-dependent media [9], stochastic backgrounds [10], [11] as well as instabilities due to electron density ripples [12]. In an inverse way, in the present work a certain electron density profile is assumed, and then the corresponding medium properties are unveiled.…”