Asymptotic Behavior of Spectral Energy Distribution Function of Equilibrium Radiation in Maxwell Plasma at Low Frequencies

Radiation in a plasma and applications to cosmic microwave background

“…[11,12] The part e 2 (𝜔) of e(𝜔) corresponding to the second term in the square brackets is a new one. [14] As is shown in [17] for the collisionless model of TDP [16] the asymptotic behavior of the part e 1 (𝜔) of the SEDER for the Maxwellian electrons is singular e 1 (𝜔) ≃ f 1 (Γ e , 𝜂 e ) ln(T∕ℏ𝜔). Here, Γ e = e 2 n 1∕3 ∕T is the interaction parameter, 𝜂 e = n e Λ 3 e is proportional to the degeneration parameter, and Λ e = ℏ √ 2𝜋∕m e T is the de Broglie electron wave length.…”

Primordial plasma: influence of non-ideality on equilibrium radiation

“…Let us introduce the dimensionless SEDER e(ω) determined by the equalities E(ω)=(VT 3 /π 2 c 3 ÿ 2 )e(ω). As is known [10,11] the low-frequency asymptotic of the part e (1) (ω) of the SEDER for the dimensionless variable W=1 has the logarithmic singularity where γ=0,577 is the Euler's constant. The term W 3 /2 in e (1) (ω) corresponding to zero vacuum oscillations is omitted as negligible in e (1) (ω) in the low-frequency limit.…”

“…The term W 3 /2 in e (1) (ω) corresponding to zero vacuum oscillations is omitted as negligible in e (1) (ω) in the low-frequency limit. The low-frequency asymptotic W=1 of the part e (2) (ω) of the full SEDER [12] for electron gas can be found analytically by the method similar to that proposed in [10] for the part e (1) (ω) and reads where α≡Ryη 2/3 /πm e c 2 Γ (Ry is the Rydberg constant equals m e e 4 /2ÿ 2 ).…”

“…In these works, the consideration was carried out both for a completely equilibrium system of non-relativistic charged particles and photons [7,8] in the quantum electrodynamic (QED) approximation, and based on a generalization of a more traditional approach using the fluctuation-dissipation theorem [9]. In [10,11], based on [7,8], the frequency-asymptotic behavior of SEDER was studied. It was found that at low frequencies the SEDER in a plasma medium has a logarithmic (integrable) singularity.…”

“…In this case, the radiation energy remains finite. However, the works [10,11] were based on the part of the SEDER that is related to the influence of plasma on the photon distribution function through the transverse permittivity of charged particles. At the same time, as was shown in [12], there is one more contribution to the SEDER, which must be taken into account.…”