ASTROPHYSICAL AND LABORATORY PLASMAS: HF PROPERTIES UNDER EXTREME CONDITIONS
arXiv:1612.04760v2 [physics.plasm-ph] 20 Jun 2017
Vladimir A. Sre´ckovi´c,∗ Anatolij.A. Mihajlov, Nenad. M. Sakan, and Ljubinko.M. Ignjatovi´c Institute of physics, University of Belgrade, P.O. Box 57 11001, Belgrade, Serbia Darko Jevremovi´c, Veljko Vujˇci´c, and Milan S. Dimitrijevi´c Astronomical Observatory, Volgina 7 11060, Belgrade 74, Serbia (Received 6 August 2007)
Abstract The values of electrical conductivity of plasma of stars with a magnetic field or moving in the magnetic field of the other component in a binary system could be of significant interest, since they are useful for the study of thermal evolution of such objects, cooling, nuclear burning of accreted matter, and the investigation of their magnetic fields. So, on the basis of numerically calculated values for the dense plasma conductivity in an external HF electric field, we determine the HF characteristics of astrophysical plasmas under extreme conditions. The examined range of frequencies covers the IR, visible and near UV regions and consider electronic number density and temperature are in the ranges of 1021 cm−3 ≤ N e and 20 000 ≤ T , respectively. The method developed here represents a powerful tool for research into white dwarfs with different atmospheric compositions (DA, DC etc.), and for investigation of some other stars (M-type red dwarfs, Sun etc.). PACS numbers: 52.25.Fi, 52.27.Gr, 96.30.Iz Keywords: Strongly-coupled plasmas, Transport properties, Dwarf Planets
∗
Electronic address:
[email protected]
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I.
INTRODUCTION
Exploring and improving the new calculation possibilities, simulation techniques and the extension of numerous models in connection with the dynamic properties of nonideal plasma is in the focus of investigators nowadays [1–5]. In this paper it is considered a highly ionized plasma in a homogenous and monochro~ matic external electric field E(t) = E~0 exp {−iωt}. According to [6], the dynamic electric conductivity of a strongly coupled plasma σ(ω) = σRe (ω) + iσIm (ω) is presented by the expressions
4e2 σ(ω) = 3m
Z
dw(E) ρ(E)EdE, τ (E) − dE
∞
0
4e2 σRe (ω) = 3m
Z
∞
4e2 σIm (ω) = 3m
Z
∞
0
0
(1)
τ (E) dw(E) ρ(E)EdE − 1 + (ωτ (E))2 dE
(2)
ωτ 2 (E) dw(E) ρ(E)EdE − 1 + (ωτ (E))2 dE
(3)
where ρ(E) is the density of a electron states in the energy space and w(E) is the Fermi-Dirac distribution function, τ (E) is the relaxation time
τ (E) =
τ (E) , 1 − iωτ (E)
(4)
τ (E) being the ’static’ relaxation time. The method of determination of τ (E) is described in the previous papers [6–11] in detail. Other HF plasma characteristics can be expressed in terms of the quantities σRe (ω) and σIm (ω). Thus the plasma dielectric permeability is
ε(ω) = 1 + i
4π σ(ω) = εRe (ω) + iεIm (ω), ω
1
(5)
where εRe (ω) and εIm (ω) are given as
εRe (ω) = 1 −
4π σIm (ω), ω
εIm (ω) =
4π σRe (ω). ω
(6)
The coefficients of refraction, n(ω), and reflection, R(ω), are determined as
n(ω) =
p ε(ω) = nRe (ω) + inIm (ω),
(7)
n(ω) − 1 2 R(ω) = n(ω) + 1
(8)
where, bearing in mind that
|ε(ω)| =
q
ε2Re (ω) + ε2Im (ω),
(9)
the real and imaginary pert of refractivity, nRe (ω) and nIm (ω), are given by
nRe (ω) =
r
1 (|ε(ω)| + εRe (ω)), 2
nIm (ω) =
r
1 (|ε(ω)| − εRe (ω)). 2
(10)
From here the equation for the plasma reflectivity could be expressed as
R(ω) =
(
)1/2 √ p 2 |ε(ω)| + εRe (ω) √ p 1 + |ε(ω)| + 2 |ε(ω)| + εRe (ω)
1 + |ε(ω)| −
(11)
The other parameter of interest is the penetration depth of electromagnetic radiation into plasma, ∆(ω). This quantity is just the skin-layer width determined as the inverse imaginary part of the electromagnetic field wave number
∆(ω) =
1 c . ω nIm (ω)
(12)
where c is the speed of light.
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FIG. 1: The dynamic conductivity real σRe (ω) and imaginary part σIm (ω) for N e = 5 · 1022 cm−3 and 20000K < T < 100000K. II.
RESULTS AND DISCUSSION
We here continue our previous investigations of plasma static electrical conductivity which are of interest for DB white dwarf atmospheres (see e.g. [12, 13]). So, in accordance with the aim of this work, we calculated HF plasma characteristics for vide plasma conditions in order to apply our results on the atmospheres of different stellar types. Figures 1-3 illustrates the behavior of the HF conductivity for various plasma conditions which gives possibility to calculate other transport properties. The figures 1-3, demonstrate the regular behavior of σRe (ω), i.e. the convergence to the corresponding values of σ0 (ne , T ) when ω → 0, and the existence of the interval of variation of ω where σRe (ω) is practically constant. We observe the tendency of this interval to decrease when temperature T increases. Similarly, the figures 1-3, demonstrate a regular behavior of σIm (ω), i.e. the convergence to zero when ω → 0, and the presence of a maximum in the interval 0 < ω < 0.5ωp . Our plane is to present the results obtained during this investigation in database which can be accessed directly through http://servo.aob.rs as a web service similarly to the existing MOL-D and E-MOL databases http://servo.aob.rs/mold, http://servo.aob.rs/emol/ (see e.g. [14, 15]). The method developed in this paper represents a powerful tool for research white dwarfs with different atmospheric compositions (DA, DC etc.), and some other stars (M-type red dwarfs, Sun etc.). Finally, the presented method provides a basis for the development of 3
FIG. 2: The dynamic conductivity real σRe (ω) and imaginary part σIm (ω) for N e = 1 · 1023 cm−3 and 20000K < T < 100000K.
FIG. 3: The dynamic conductivity real σRe (ω) and imaginary part σIm (ω) for N e = 5 · 1023 cm−3 and 20000K < T < 100000K.
methods to describe other transport characteristics which are important for the study of all mentioned astrophysical objects, such as the electronic thermo-conductivity in the stellar atmosphere layers with large electron density, and electrical conductivity in the presence of strong magnetic fields or plasma reflectivity [16] in high energy and high density plasma.
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Acknowledgments
The authors are thankful to the MESTD of RS for support of this work within projects 176002 and III44002.
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