122
A. G. Aksenov
ρε γ = aT
4
γ , P γ =
4
3
− 1
ρε γ .
(9.17)
It is possible to disregard electron heat conduction and introduce the equation of
transport for the radiation energy density as:
∂ρε γ
∂t
+ v∇
ρε γ
= div F γ − ρ Q p,e ,
(9.18)
where the flux is determined by the gradient of the zeroth moment of the photons
distribution function. In the opaque case, F
thick
γ
= −(grad ρε γ )/(3cσ T n e ), and in the
transparent case F max
γ
= cρε γ . In the arbitrary case, we can use the interpolation
(the flux limiter):
F γ =
F
thick
γ
F thick
γ
/F max
γ
+ 1
.
(9.19)
The constraint on the flux refers to the introduction of nonlinear thermal conductivity and a certain arbitrary fit of the fluxes in the intermediate case. The nonlinear
diffusion flux transfers the parabolic equation in the opaque region into hyperbolic
transport equation in the transparent region for the spectral energy densities.
The exchange of energy between radiation and matter is described by the
relaxation to a thermal distribution:
ρ Q p,e = cσ T n e
ρε γ − ρε
th
γ
,
(9.20)
where equilibrium blackbody radiation energy density ρε
th
γ should be calculated for
the total energy density of radiation and matter ρε + ρε γ .
Figure 9.2 illustrates the evaluation of profiles of the density ρ and the temperatures of gas and radiation T p,e , T γ with time. At the first time moment t = 1.70·10
−5 s,
radiation is negligible, and its role is unimportant. The density and temperature
profiles look as in the previous section for the hydrodynamic case. In the next time
moments 1.12 × 10
−5 s and 1.70 × 10
−5 s, radiation is still small due to a matter
transparency, but radiation plays considerable role in the energy losses in the relaxation zone behind SW. The maximum density becomes larger than 4 × 10
−6 g cm
−3
in the relaxation zone. At time moment more than 10
−5 s, the SW structure obtained
in the previous section changes. The density jump is still 4, but the gas temperature
decreases value 8 × 10
5 K. At time moment more than 10
−5 s, the SW structure
obtained in the previous section becomes inapplicable.
The steady solution with taking into account radiation forms at SW propagation
on the distance ∼10
8 cm during 5 s, see Fig. 9.3. This steady solution contains
nonequilibrium radiation (the space scale in Fig. 9.3 cannot resolve nonequilibrium
region near SW), slightly preheated gas before SW, and relaxation zone after SW
(the zone is not resolved in Fig. 9.3). In the relaxation zone, radiation achieves the
thermal equilibrium with matter T γ = T p,e , but the radiation energy flux from the SW
A. G. Aksenov
ρε γ = aT
4
γ , P γ =
4
3
− 1
ρε γ .
(9.17)
It is possible to disregard electron heat conduction and introduce the equation of
transport for the radiation energy density as:
∂ρε γ
∂t
+ v∇
ρε γ
= div F γ − ρ Q p,e ,
(9.18)
where the flux is determined by the gradient of the zeroth moment of the photons
distribution function. In the opaque case, F
thick
γ
= −(grad ρε γ )/(3cσ T n e ), and in the
transparent case F max
γ
= cρε γ . In the arbitrary case, we can use the interpolation
(the flux limiter):
F γ =
F
thick
γ
F thick
γ
/F max
γ
+ 1
.
(9.19)
The constraint on the flux refers to the introduction of nonlinear thermal conductivity and a certain arbitrary fit of the fluxes in the intermediate case. The nonlinear
diffusion flux transfers the parabolic equation in the opaque region into hyperbolic
transport equation in the transparent region for the spectral energy densities.
The exchange of energy between radiation and matter is described by the
relaxation to a thermal distribution:
ρ Q p,e = cσ T n e
ρε γ − ρε
th
γ
,
(9.20)
where equilibrium blackbody radiation energy density ρε
th
γ should be calculated for
the total energy density of radiation and matter ρε + ρε γ .
Figure 9.2 illustrates the evaluation of profiles of the density ρ and the temperatures of gas and radiation T p,e , T γ with time. At the first time moment t = 1.70·10
−5 s,
radiation is negligible, and its role is unimportant. The density and temperature
profiles look as in the previous section for the hydrodynamic case. In the next time
moments 1.12 × 10
−5 s and 1.70 × 10
−5 s, radiation is still small due to a matter
transparency, but radiation plays considerable role in the energy losses in the relaxation zone behind SW. The maximum density becomes larger than 4 × 10
−6 g cm
−3
in the relaxation zone. At time moment more than 10
−5 s, the SW structure obtained
in the previous section changes. The density jump is still 4, but the gas temperature
decreases value 8 × 10
5 K. At time moment more than 10
−5 s, the SW structure
obtained in the previous section becomes inapplicable.
The steady solution with taking into account radiation forms at SW propagation
on the distance ∼10
8 cm during 5 s, see Fig. 9.3. This steady solution contains
nonequilibrium radiation (the space scale in Fig. 9.3 cannot resolve nonequilibrium
region near SW), slightly preheated gas before SW, and relaxation zone after SW
(the zone is not resolved in Fig. 9.3). In the relaxation zone, radiation achieves the
thermal equilibrium with matter T γ = T p,e , but the radiation energy flux from the SW