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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 BBB = 0. Those modes, which consist of transverse oscillations, are called transverse plasmons. The relation between the frequency of transverse plasmons ω and their wave-number k = 2π ∕λ (where λ is the wavelength) for the simplest case of nonrelativistic electrons is
∘ ---------- ω = ω2 + k2c2, (262 ) pe
where ωpe is the electron plasma frequency (12View Equation). Only plasmons with ω > ωpe can propagate in the crust. At a given temperature T, the number density of plasmons is given by the Bose–Einstein formula
∫ 2 n γ ∝ dp ----p------. (263 ) eℏω∕kBT − 1
While a photon in vacuum cannot decay into a neutrino-antineutrino pair, a plasmon in a plasma can,
γ → νx + ¯νℓ, ℓ = e,μ,τ . (264 )
This process of neutrino emission was first considered in detail by Inman & Ruderman [209]. For T ≪ T pe, the value of Qplas ν is strongly temperature dependent,
Qplas∝ exp(− T ∕T ), (265 ) ν pe
where Tpe is the electron plasma temperature defined by Equations (12View Equation) and (13View Equation). For T ≪ Tpe, the plasmon decay process is therefore negligible. It is also strongly density dependent through Tpe in Equation (265View Equation). Generally, Qplas ν is switched-off by decreasing temperature and increasing density. Detailed formulae for plas Q ν can be found in [428Jump To The Next Citation Point].

The plasmon decay is influenced by a strong magnetic field, because BBB modifies the plasma dispersion relation (relation between plasmon frequency ω and its wavenumber k). In particular, new plasma modes may appear. The effects of magnetic fields are important if ωB ≡ eB ∕(m ∗ec) > ωpe. At ρ ∼ 1011 g cm −3 this requires B ≳ 3 × 1015 G. The magnitude of B required to modify the plasmon dispersion relation grows as 2∕3 ρ.


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