Numerical thermodynamic analysis of alloys for plasma electronics and advanced technologies
Thermodynamic properties (pressure, specific internal energy and entropy) of the ionized gas mixture are obtained on the basis of the Thomas-Fermi theory and Saha model. The calculations was made for the lithium-indium alloy (Li + 10% In), which has various applications in plasma electronics and tec...
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irk-123456789-1122352017-01-19T03:02:46Z Numerical thermodynamic analysis of alloys for plasma electronics and advanced technologies Kuzenov, V.V. Ryzhkov, S.V. Shumaev, V.V. Нерелятивистская электроника Thermodynamic properties (pressure, specific internal energy and entropy) of the ionized gas mixture are obtained on the basis of the Thomas-Fermi theory and Saha model. The calculations was made for the lithium-indium alloy (Li + 10% In), which has various applications in plasma electronics and technology. Термодинамічні властивості (тиск, питома внутрішня енергія і ентропія) суміші іонізованих газів отримані на основі теорії Томаса-Фермі та моделі Саха. Розрахунки були зроблені для сплаву літій-індій (Li + 10%In), який має різні застосування в плазмових технологіях. Термодинамические свойства (давление, удельная внутренняя энергия и энтропия) смеси ионизованных газов получены на основе теории Томаса-Ферми и модели Саха. Расчеты были сделаны для сплава литий-индий (Li + 10%In), который имеет различные применения в плазменных технологиях. 2015 Article Numerical thermodynamic analysis of alloys for plasma electronics and advanced technologies / V.V. Kuzenov, S.V. Ryzhkov, V.V. Shumaev // Вопросы атомной науки и техники. — 2015. — № 4. — С. 53-56. — Бібліогр.: 30 назв. — англ. 1562-6016 PACS: 52.25.Kn, 31.15.Bs http://dspace.nbuv.gov.ua/handle/123456789/112235 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Нерелятивистская электроника Нерелятивистская электроника |
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Нерелятивистская электроника Нерелятивистская электроника Kuzenov, V.V. Ryzhkov, S.V. Shumaev, V.V. Numerical thermodynamic analysis of alloys for plasma electronics and advanced technologies Вопросы атомной науки и техники |
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Thermodynamic properties (pressure, specific internal energy and entropy) of the ionized gas mixture are obtained on the basis of the Thomas-Fermi theory and Saha model. The calculations was made for the lithium-indium alloy (Li + 10% In), which has various applications in plasma electronics and technology. |
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| author |
Kuzenov, V.V. Ryzhkov, S.V. Shumaev, V.V. |
| author_facet |
Kuzenov, V.V. Ryzhkov, S.V. Shumaev, V.V. |
| author_sort |
Kuzenov, V.V. |
| title |
Numerical thermodynamic analysis of alloys for plasma electronics and advanced technologies |
| title_short |
Numerical thermodynamic analysis of alloys for plasma electronics and advanced technologies |
| title_full |
Numerical thermodynamic analysis of alloys for plasma electronics and advanced technologies |
| title_fullStr |
Numerical thermodynamic analysis of alloys for plasma electronics and advanced technologies |
| title_full_unstemmed |
Numerical thermodynamic analysis of alloys for plasma electronics and advanced technologies |
| title_sort |
numerical thermodynamic analysis of alloys for plasma electronics and advanced technologies |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2015 |
| topic_facet |
Нерелятивистская электроника |
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http://dspace.nbuv.gov.ua/handle/123456789/112235 |
| citation_txt |
Numerical thermodynamic analysis of alloys for plasma electronics and advanced technologies / V.V. Kuzenov, S.V. Ryzhkov, V.V. Shumaev // Вопросы атомной науки и техники. — 2015. — № 4. — С. 53-56. — Бібліогр.: 30 назв. — англ. |
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ISSN 1562-6016. ВАНТ. 2015. №4(98) 53
NUMERICAL THERMODYNAMIC ANALYSIS OF ALLOYS FOR
PLASMA ELECTRONICS AND ADVANCED TECHNOLOGIES
V.V. Kuzenov1,2, S.V. Ryzhkov1, V.V. Shumaev1
1Bauman Moscow State Technical University, Moscow, Russia;
2A.Yu. Ishlinsky Institute for Problems in Mechanics RAS, Moscow, Russia
E-mail: kuzenov@ipmnet.ru; svryzhkov@bmstu.ru; shumaev@student.bmstu.ru
Thermodynamic properties (pressure, specific internal energy and entropy) of the ionized gas mixture are ob-
tained on the basis of the Thomas-Fermi theory and Saha model. The calculations was made for the lithium-indium
alloy (Li + 10% In), which has various applications in plasma electronics and technology.
PACS: 52.25.Kn, 31.15.Bs
INTRODUCTION
Nowadays it is explored the possibility of combina-
tion of two nuclear power production methods and the
possibility of creation fission-fusion hybrid reactors.
Fusion devices can be used for the destruction of long-
lived radioactive wastes from fission reactors. In the
nearest future perspective technologies and high-
energy-density systems, in particular, neutron and pro-
ton sources, will be important for the material science,
analysis and non-destructive control, medical isotope
production, chemical waste destruction, personnel train-
ing and etc.
However, the hybrid way of fusion exists. It is
known as magneto-inertial fusion (MIF) [1 - 4], where
are used as drivers the capacitor and inductive stores
(electrodynamic method), magneto-explosive genera-
tors, explosive charges (explosive method) and the en-
ergy of the compressed gas (gas dynamics method). We
consider the compression and heating of plasmoid
which is confined by the ultra-strong external magnetic
field, high-speed plasma jets and laser beams with high-
energy impulse. Ultra-strong magnetic fields reduce
electronic thermal losses and provide sufficient plasma
confinement.
The calculation of thermal processes in MIF sys-
tems, powerful and compact fusion neutron sources and
experimental prototypes of perspective systems and
devices based on the fusion plasma in the magnetic field
requires to develop methods of computational and theo-
retical justification of the energy efficiency and optimi-
zation of alternative systems and perspective ways of
power production. Moreover, it is important to deter-
mine magneto-inertial regimes for perspective devices:
fusion reactors with plasma (argon or xenon) liner and
neutron generators and to optimize these regimes con-
sidering specifications which allow creating economi-
cally viable industrial plants.
The critical part of magneto-inertial system for
plasma confinement is the final stage of compression
where the corresponding isolation and plasma confine-
ment, rotational speed for hydrodynamic stability are
necessary. Authors have developed the two-dimensional
radiation-magneto gas dynamics code PLUM which is
the part of the nonstationary instruments and codes for
fusion applications (NICA) and includes radiation
transport in multi group diffusion approach and gas dy-
namics with dynamic adaptive grid and finite difference
scheme with the increased order of accuracy, and also
the influence on hydrodynamics of plasma by the ener-
gy release [5]. The possibility of the hydrodynamics
instability suppression with the external magnetic field
is represented in papers [6 - 8].
The important problem for the hydrodynamics cal-
culations of processes in plasma is to determine its
thermodynamic (the pressure, specific internal energy
and entropy) and transport properties (electrical conduc-
tivity and heat conductivity coefficients, optical proper-
ties). Authors have developed the computational code
for evaluation the thermodynamic properties of ionized
gases mixture in the magnetic field based on the Thom-
as-Fermi (TF) model. It is called TERMAG [9, 10].
Nowadays the code is supplemented with ionization
equilibrium model (Saha model) which will allow ex-
panding the region of the code applicability to lower
temperatures and densities.
The TF theory has different applications [11 - 13].
The Thomas-Fermi-Firsov energy transfer calculations
are used for the analysis of the emission of electrons
from a metal surface [14], the Thomas-Fermi von
Weizsacker theory is used to investigate the properties
of metal surfaces (the work function and surface energy)
[15] and it can be also used in the theory of metallic
clusters [16]. The TF screening length is used in the
isolated ferroelectric domain walls analysis [17].
The analysis we made are related to the question of
lithium and indium applicability in fusion [18], electri-
cal engineering [19] and electronic [20] systems.
1. THERMODYNAMIC AND GAS-DYNAMIC
ASPECTS OF PLASMA TECHNOLOGIES
In high-energy-density systems, e.g. neutron and
pro-ton sources based on inertial plasma confinement it
is important to compress the target in such a way that
only its central part reaches the temperature of the igni-
tion while the rest parts of the fuel is cold. This mode
can be characterized by the minimum driver energy be-
cause the energy is used only for compressing the fuel
to a high density [21]. To provide such energy efficient
fusion burning, it is necessary to compress the core of
the target in the isentropic regime to the value
ρR > 1 g/cm2, where ρ is the plasma density; R is the
radius of the target. Note that in the presence of the
strong magnetic field typical for MIF devices this condi-
tion changes. For the cylindrical target it looks like [22]:
5
7...10 keV
(4.5...6.5) 10 G cm
T
B R
≥
⋅ ≥ ⋅ ⋅
,
where B is the magnetic induction.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 54
The common formulation of the computational prob-
lem for the MIF processes requires taking into consider-
ation the influence of the external magnetic field with
induction to 104 T [23, 24] on the plasma thermodynam-
ic and transport properties. Evaluations have been made
by authors show that the magnetic field of such induc-
tion influences only the transport properties of plasma
but it does not change the shape of internal atom or ion
shells [25].
It is required to consider the processes of the isentrop-
ic compression of the target by converging shock waves
together with the thermal and caloric equations of state
for the substance on different stages including the stage
of the high compression i.e. in a wide range of densities
(from gas-like up to 103…104 g/cm3) and temperatures
(from a few thousands K to a hundred millions K).
Nowadays the obtaining equations of state for sub-
stance in such wide range of parameters are connected
with the problem of joining the solutions. The TF model
is rather simple and precise. It can be used in the area of
high temperatures and densities (temperatures T >105 K,
densities of solid body and higher) [26, 27]. The Saha
model is used for lower temperatures and densities [26 -
28].
Methods for calculating thermodynamic properties
(the pressure, specific internal energy and entropy) of
ionized gases mixtures are described in the following
papers: for the TF model [25 - 27, 29], for Saha equa-
tions [26 - 28, 30]. Authors performed calculations by
the TF model, but values of thermodynamic functions
according the Saha model were taken from [30].
2. CALCULATION RESULTS
The graphical correlation between temperature and
pressure P, specific internal energy E and entropy S for
mixture Li + 10% In at average densities ρ = 2.94∙10-6,
2.94·10-4, and 2.94·10-2 g/cm3 obtained by computation-
al code TERMAG (TF model) and Saha model literature
data are shown in the Figs. 1,a-c. Note, that the smooth
conjugation of the calculation results according these
models haven’t been carried out in this paper.
a
b
c
Fig. 1. Thermodynamic functions of the Li + 10% In
mixture depending on the temperature calculated
by Saha (dotted line) and Thomas-Fermi (solid line)
models: the pressure (a); specific internal energy (b);
specific entropy (c). The average density of mixture:
1 – 2.94·10-6 g/cm3; 2 – 2.94·10-4 g/cm3;
3 – 2.94·10-2 g/cm3
With increasing average density increases the pres-
sure, but the specific internal energy and entropy de-
crease. A decrease in the average density causes the
decrease in the difference between the results obtained
by the TF model and Saha model at T = 105 K. This can
be explained as the increase of the plasma ideality so the
accuracy of Saha equations also increases (the TF model
is not as sensitive to the changes in the density).
The Saha and TF models describe the transition area
of thermodynamics parameters 10-7 < ρ < 10-1 g/cm3,
103 < Т < 106 K. Figs. 2,a-c represents thermodynamic
functions P(T), E(T), S(T) in this region of parameters.
a
b
c
Fig. 2. Thermodynamic functions of the Li + 10% In
mixture depending on the temperature in the region
where both models can work. The average density
of mixture is 2.94·10-6 g/cm3
ISSN 1562-6016. ВАНТ. 2015. №4(98) 55
On the Figs. 2,a-c. TF model represents a smooth
curve, because this model averages the effects of the
atomic shell structure. Fig. 2,a shows two areas of good
result agreement: at T ~ 104 and ~ 105 K. At the same
time Fig. 2,b and c show that the result agreement grows
when the temperature increases. It is known that the
accuracy of the TF increases with temperature [26, 29].
Therefore the increase in the model results difference at
T ~ 3·105 K can be explained as the fact that the Saha
model reaches its boundary of the applicability area.
The difference between these model results at
T~103…104 K is intolerably huge. This happens, be-
cause the thermodynamic properties, obtained by the TF
model, are inaccurate in this temperature range [29].
CONCLUSIONS
It is necessary to solve the systems of magnetohy-
drodynamics equations including Maxwell's equations
and wide-range equation of state for the calculation of
thermal physical processes in perspective high-energy-
density systems like magneto-inertial fusion devices.
Wide-range equation of state can be found by conjuga-
tion the solutions of the TF model for rather high tem-
peratures Т and densities ρ and the Saha model for low
Т and ρ.
This paper illustrates the calculation results of the
ionized gas mixture thermodynamic properties (the
pressure, specific internal energy and entropy) on the
basis of the TF theory and Saha equations. These calcu-
lations was made for the lithium-indium alloy
(Li+10% In) for temperatures T = 3·103…108 K and
densities ρ = (10-6…10-2) g·cm-3 by the computational
code for evaluation the thermodynamic properties of
ionized gases mixture in the magnetic field based on the
TF model (TERMAG) and the published data on the
Saha model. Analysis we made is related to the question
of lithium and indium application in energy (fusion de-
vice first wall), electric (lithium-indium alloy compound
in batteries) and electronics (indium layer or additive on
the lithium base) systems. The TF model can be also
used for energy transfer calculations in the analysis of
the electron emission from a metal surface, to investi-
gate the properties of metal surfaces (the work function
and surface energy), and also in the theory of metallic
clusters.
This work was supported by the Ministry of Educa-
tion and Science of the Russian Federation (Project
№ 13.79.2014/K).
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Article received 05.05.2015
ЧИСЛЕННЫЙ ТЕРМОДИНАМИЧЕСКИЙ АНАЛИЗ СПЛАВОВ ДЛЯ ПЛАЗМЕННОЙ
ЭЛЕКТРОНИКИ И ПЕРЕДОВЫХ ТЕХНОЛОГИЙ
В.В. Кузенов, С.В. Рыжков, В.В. Шумаев
Термодинамические свойства (давление, удельная внутренняя энергия и энтропия) смеси ионизованных
газов получены на основе теории Томаса-Ферми и модели Саха. Расчеты были сделаны для сплава литий-
индий (Li + 10%In), который имеет различные применения в плазменных технологиях.
ЧИСЕЛЬНИЙ ТЕРМОДИНАМІЧНИЙ АНАЛІЗ СПЛАВІВ ДЛЯ ПЛАЗМОВОЇ ЕЛЕКТРОНІКИ
І ПЕРЕДОВИХ ТЕХНОЛОГІЙ
В.В. Кузенoв, С.В. Рижков, В.В. Шумаєв
Термодинамічні властивості (тиск, питома внутрішня енергія і ентропія) суміші іонізованих газів отри-
мані на основі теорії Томаса-Фермі та моделі Саха. Розрахунки були зроблені для сплаву літій-індій (Li +
10%In), який має різні застосування в плазмових технологіях.
INTRODUCTION
Nowadays it is explored the possibility of combination of two nuclear power production methods and the possibility of creation fission-fusion hybrid reactors. Fusion devices can be used for the destruction of long-lived radioactive wastes from fission...
However, the hybrid way of fusion exists. It is known as magneto-inertial fusion (MIF) [1 - 4], where are used as drivers the capacitor and inductive stores (electrodynamic method), magneto-explosive genera-tors, explosive charges (explosive method) a...
The calculation of thermal processes in MIF systems, powerful and compact fusion neutron sources and experimental prototypes of perspective systems and devices based on the fusion plasma in the magnetic field requires to develop methods of computation...
The critical part of magneto-inertial system for plasma confinement is the final stage of compression where the corresponding isolation and plasma confinement, rotational speed for hydrodynamic stability are necessary. Authors have developed the two-d...
The important problem for the hydrodynamics calculations of processes in plasma is to determine its thermodynamic (the pressure, specific internal energy and entropy) and transport properties (electrical conductivity and heat conductivity coefficients...
1. Thermodynamic and gas-dynamic aspects of plasma technologies
2. Calculation results
CONCLUSIONS
references
|