Quasi-linear theory of fast flavor instabilities in homogeneous environments

Abstract

Dense neutrino plasmas can develop instabilities that drive collisionless flavor exchange, equivalent to the emission of flavomons, the quanta of flavor waves. We treat these waves, for the first time, as independent linear degrees of freedom and develop a quasi-linear theory (QLT), including backreaction on the neutrino distribution and nonresonant neutrino--flavomon interactions, while neglecting wave--wave processes. In a homogeneous, axisymmetric model, the saturated neutrino and flavomon distributions agree closely with periodic-box solutions of the original quantum kinetic equation. These results support the use of QLT, well established in plasma physics, to bypass nonlinear small-scale effects that challenge direct simulations.

Figures (1)

• Figure 1: Comparison of quasi-linear theory (QLT) with simulations of the original quantum kinetic equation (QKE), averaged over the full periodic box, as well as over 20 realizations from the ensemble described in the text. Top: DLN spectrum (electron--muon lepton number difference) derived with the indicated methods, with an initial distributions defined by Eq. \ref{['eq:example_distribution']}, for the shown values of $a$, left to right ranging from weak to strong instability. Bottom: Final flavomon spatial power spectrum (upper lines) and at an intermediate time step (lower lines), chosen so that $|\tilde{\psi}_{0,K}|^2=10^{-2}$ at the maximum.