### 11.3 Plasmon decay

Quanta of electromagnetic waves in a plasma have different properties than in vacuum. They are called
(electron) plasmons, and appear in two basic modes. We first consider the case . Those modes,
which consist of transverse oscillations, are called transverse plasmons. The relation between the frequency
of transverse plasmons and their wave-number (where is the wavelength) for the
simplest case of nonrelativistic electrons is
where is the electron plasma frequency (12). Only plasmons with can propagate in the
crust. At a given temperature , the number density of plasmons is given by the Bose–Einstein formula
While a photon in vacuum cannot decay into a neutrino-antineutrino pair, a plasmon in a plasma can,
This process of neutrino emission was first considered in detail by Inman & Ruderman [209]. For
, the value of is strongly temperature dependent,
where is the electron plasma temperature defined by Equations (12) and (13). For , the
plasmon decay process is therefore negligible. It is also strongly density dependent through in
Equation (265). Generally, is switched-off by decreasing temperature and increasing density.
Detailed formulae for can be found in [428].
The plasmon decay is influenced by a strong magnetic field, because modifies the plasma dispersion
relation (relation between plasmon frequency and its wavenumber ). In particular, new plasma
modes may appear. The effects of magnetic fields are important if . At
this requires . The magnitude of required to modify the plasmon
dispersion relation grows as .