ArticlePDF Available

INVESTIGATION OF CONCENTRATION INFLUENCE ON ELECTRONIC COEFFICIENTS OF HE:NE PLASMA BY PREDICTING A MATHEMATICAL MODEL

Authors:

Abstract and Figures

In this work a comprehensive investigation of specific electron transport coefficients in plasma state He-Ne gas mixtures has been carried out. Theoretical calculations and estimated data are presented that enable us to measure the influence of He:Ne concentration on plasma electronic coefficients based on the variation in a plasma field resistance situated in a varied electric field and under a thermodynamic equilibrium. The Boltzmann equation was used to calculate several concentrations of energy mobility and momentum frequency and varied electric fields. Utilisation of the BOLSIG+ simulation verified the results that the Boltzmann distribution analysis revealed. By using a simulation process, appropriated equations which indicate the variation of plasma electronic coefficients according to the variation of mixture concentration and reduced electric field (E/N) have been obtained. The applied reduced electric field has been chosen to be in the limited range of (0-100) Td, and for several concentrations in the limited range of (0.1-0.7) mol. The between unique information (utilizing BOLSIG+) and our estimated data. The results show a stark resemblance involving original data (using BOLSIG+) and our estimated data, our simulation data, where root mean square of (νe-i /N,) = 4.2×10-7 , root mean square of µƐN = 1.5×10-6 and root mean square of <> = 9.4×10-5. This improvement in electronic coefficients assume a significant part in the development of energy for He:Ne laser
Content may be subject to copyright.
Journal of Engineering Science and Technology
Vol. 17, No. 2 (2022) 1550 - 1560
© School of Engineering, Taylor’s University
1550
INVESTIGATION OF CONCENTRATION INFLUENCE
ON ELECTRONIC COEFFICIENTS OF HE:NE PLASMA BY
PREDICTING A MATHEMATICAL MODEL
BAIDAA HAMED*, RAFID ABBAS ALI, MAYSAM T. AL-OBAIDI
Mustansiriyah University, Baghdad, Iraq
*Corresponding Author: baidaa800@uomustansiriyah.edu.iq,
Abstract
In this work a comprehensive investigation of specific electron transport
coefficients in plasma state He-Ne gas mixtures has been carried out. Theoretical
calculations and estimated data are presented that enable us to measure the
influence of He:Ne concentration on plasma electronic coefficients based on the
variation in a plasma field resistance situated in a varied electric field and under
a thermodynamic equilibrium. The Boltzmann equation was used to calculate
several concentrations of energy mobility and momentum frequency and varied
electric fields. Utilisation of the BOLSIG+ simulation verified the results that the
Boltzmann distribution analysis revealed. By using a simulation process,
appropriated equations which indicate the variation of plasma electronic
coefficients according to the variation of mixture concentration and reduced
electric field (E/N) have been obtained. The applied reduced electric field has
been chosen to be in the limited range of (0-100) Td, and for several
concentrations in the limited range of (0.1-0.7) mol. The between unique
information (utilizing BOLSIG+) and our estimated data. The results show a stark
resemblance involving original data (using BOLSIG+) and our estimated data,
our simulation data, where root mean square of (νe-i /N,) = 4.10-7, root mean
square of µƐN = 1.5×10-6 and root mean square of <
> = 9.4×10-5. This
improvement in electronic coefficients assume a significant part in the
development of energy for He:Ne laser
Keywords: Elastic and inelastic collisions, Electron-ion momentum frequency,
Energy mobility, Mean energy, Plasma electronic coefficients.
Investigation of Concentration Influence on Electronic Coefficients of . . . . 1551
Journal of Engineering Science and Technology April 2022, Vol. 17(2)
1. Introduction
Plasma, which represents one of the four essential states of matter had been firstly
defined in the 1920s by Irving Langmuir as a ‘mouldable substance [1, 2]. It is
primarily comprised of a gas of atoms and molecules bearing a small number of
electrons within orbitals displaced, and free electrons [3]. Plasma is a state of matter
wherein an electrical condensation conducted upon ionized gaseous to the point that
long fields command the conduct of the matter by a range electric and attractive [4, 5].
Plasma medium possesses unbound moving negatively and positively charged
particles, therefore it is an electrically neutralised buffer with a net charge of about
nothing. Albeit these particles are unrestrained, they still have the capability of
experiencing forces to the sense that they are not “free.” An electrical current within
a magnetic field is generated by the movement of a charged also, any development
of a plasma molecule which is charged affects and is also directly affected by the
created by the other present charges. In turn, this results in varying degrees of
control collective behaviour [6, 7].
Plasma’s properties are remarkably dependent upon its particle interactions and
electron transport coefficients. Collective effects help to identify plasma’s
behaviour as being entirely unique towards that of liquids. Every charged molecule
of plasma influence instantaneously alongside a substantial amount of related
charged particles because of the vast scope of present electromagnetic powers. The
resulting effects can be represented by elastic and inelastic collisions provides a
rich variation of physical phenomena that occur in plasma [8, 9].
There has been widespread interest in plasma sciences over the past two decades
and several breakthroughs regarding the field has been made. Developing advanced
new sources of plasma was the core of this progress of new. This progress is
generally the result of advancement of current plasma sources in light of plasma
creation in electrical releases in vacuum, magnetrons and in gases with high or low
pressures and is in many ways a part of the progress made. The plasma technique
resulting from this processing is used in aerospace movement and largely within
fields of nanoscience revolving around plasma and on particular in areas where
meticulous control is necessitated. These applications involve, but are not limited
to Plasma Chemistry, lighting systems revolving around Plasma, Plasma Spray and
lighting systems [10-12].
The Boltzmann equation is one of the most powerful tools for investigating the
plasma state, from the electron kinetics in weakly ionized gases [10] to fusion [13,
14] and astrophysical plasmas. Boltzmann equation introduced into physics the idea
of probability, which was then used some years later in quantum physics [15]. The
development of models and simulation techniques for electrical discharges has
been going for more than five decades. In present paper, theoretical calculations for
several electronic coefficients in a mixture of He:Ne gas (using several gas mixture
concentrations) are presented by creating mathematical models utilizing Boltzmann
distribution function and appropriated simulation process.
In present paper, theoretical investigation of electron transport coefficients in
plasma state He-Ne gas mixtures has been introduced using BOLSIG+ simulation
method as a Boltzmann equation solver often employed in plasma modelling
community. Origin program has been utilized in a simulation process resulting
appropriated equations for theoretical calculations of electronic coefficients. Each
1552 B. Hamed et al.
Journal of Engineering Science and Technology April 2022, Vol. 17(2)
of mean energy <
>, energy mobility µ and momentum frequency ν at several
concentrations of He-Ne gas mixture and under varied reduced electric field has
been theoretically calculated.
2. The Boltzmann Equation
The Boltzmann condition portrays the factual way of behaving of a nonequilibrium
thermodynamic framework designed in 1872 by Ludwig Boltzmann. What defines the
Boltzmann equation in modern day and particularly its uses in a wider sense are any
alteration of a perceptible amount within a system of thermodynamics for example,
particle number, charge, energy. might be utilized to decide how actual amounts change
when a fluid is in transport, such as heat energy and momentum [16, 17].
Certain behaviours trademark of liquids like consistency, heat-based
conductivity, and electric-powered conductivity can also be extracted (through
influencing the bearers of charges within a liquid like a gas). The mathematical
unknown of the equation is a function of likelihood amount within the space
revolving around particle position and momentum. This means that the equation
becomes a nonlinear integral differential equation [18].
Boltzmann equation gives the ratio of number per unit volume (the numeral
mass) of molecules, ions or atoms, denoted by N2, in a certain level of energy
comparable to the numeral mass within another lower energy level which shows as
N1, and it is given by [19]:


 (1)
where, g1 and g2 represent the multiplicity of the two energy levels, in another ward
the degeneracies of the energy levels with the same energy, E is the required energy
to excite particles, K represents Boltzmann constant and T represents
thermodynamic temperature, so as T increases a greater number of particles will be
excited [20].
Boltzmann kinetic equation
The kinetic Boltzmann equation highlights the distribution function of gas
molecules f (v, r, t) in this case v becomes the velocity and r is coordinates (as
mathematic equations of time shown as t) which showcases non-equilibrium
operations within low density. The mathematical process of f helps to showcase the
mean molecules with speed between the scope of v to v, and include the coordinate
between the scope of r to r. This Boltzmann (kinetic) equation has the form only
when the distribution function x and the velocity component of v. speeds inside a
little reach from ν to ν + Δν and facilitates inside a little reach from one r to r + Δr.
In the event that the dispersion work relies just upon the direction x and the speed
part vx, then the Boltzmann (active) condition has the structure [21]:





 (2)
where m is the mass of the molecule. The pace of progress of the appropriation
work is addressed by the fractional subordinate ∂f/∂t. The second term in the
situation assesses the adjustment of f because of the development of particles in
space. Third term in this situation decides the adjustment of dissemination work
that is alluding to impact of an outer power F.
Investigation of Concentration Influence on Electronic Coefficients of . . . . 1553
Journal of Engineering Science and Technology April 2022, Vol. 17(2)
The right term represents changes in the function of distribution which is
referring to particle collision. This term is reliant on each of f as well as the idea of
interaction powers among particles and this is show by [21]:


 (3)
where, f, f1, and fʹ, f1ʹ represent functions of particle distribution prior to and
following collision; v1, v2 represent the velocities of the particles before collision;
and dσ dΩ is the differential powerful dissipating cross area into the strong point
(depending on coordinate system of laboratory) and it depends on the law of
molecular interaction [22].
The kinetic or transport equations are generalizations of the Boltzmann equation
and showcase electron gas behaviors in crystal lattice phonons and in metals [23, 24].
3. Mean Energy
3.1. Influence of reduced electric field and concentration on mean energy
The concentration affects obviously on discharge process can be noticed in Fig. 1.
and it can be also noticed the dependence of mean energy <
> on reduced electric
field (E/N), where the increasing of mean energy according to the increasing of (E/N)
is observed also note that the mean energy values increase when moving from the
low concentration (0.1) mole to the high concentration (0.9) mole with respect to the
confined area from (0-68) Td as in Table 1, while the behavior becomes reversed in
relation to the confined region between (69 - 100) Td as in Table 2. This is because
the cross-section area is directly influenced by the reduced electric area - this impact
is high form low to high concentrations (0,1 to 0,7) mole for when E over N is
(0 - 68) Td. This behavior becomes opposite in the case of E over N= (69 - 100)Td,
wherein all of the mean energy is highly sensitive to the concentration of the gas
mixture, and as a result it will increase the rate of elastic-inelastic collisions.
Fig. 1. Mean Energy as a function of reduced electric field (E/N).
020 40 60 80 100
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Mean Energy (eV)
E/N (Td)
A1(C=0.1)
A1(C=0.2)
A1(C=0.3)
A1(C=0.4)
A1(C=0.5)
A1(C=0.6)
A1(C=0.7)
1554 B. Hamed et al.
Journal of Engineering Science and Technology April 2022, Vol. 17(2)
Table 1. The correlation between mean
energy and Ne concentration (E/N= (0-68) Td).
E/N=45.38 Td
E/N= (0-68) Td
Concentration
(Mol.)
0.1
0.3
0.5
0.6
Mean Energy
(eV)
2.63
2.71
2.81
2.87
Table 2. The relationship between mean
energy and concentration of Ne, E/N= (69-100) Td.
E/N=100 Td
E/N= (69-100) Td
Concentration
(Mol.)
0.1
0.3
0.5
0.6
Mean Energy
(eV)
4.88
2.71
2.81
2.87
3.2. Mean energy modelling
For all concentrations, the fitting relationship could be obtained as shown in Fig. 1.
This relationship addresses a matching between the BOLSIG+ program values and
present model (Fig. 2) that based of utilizing strategic capacity and it can be
represented by Eq. (4):



 (4)
Fig. 2. Represents percent and BOLSIG+ data
(using mathematical model) of mean energy.
Investigation of Concentration Influence on Electronic Coefficients of . . . . 1555
Journal of Engineering Science and Technology April 2022, Vol. 17(2)
From Eq. (4) for all concentrations, parameters (A1, A2, X0, P) can be shown
through calculation of function of logistic and polynomial to determine the required
concentration calculated in Eq. (4). The equations of these parameters:
 (5)
 (6)
 (7)
 (8)
where C is concentration.
4. Energy Mobility
4.1. Influence of reduced electric field and concentration on energy mobility
The relationship between energy mobility μεN and E/N is shown in Fig. 3., where
sharp decreasing in energy mobility can be observed particularly in the limited
region between E/N= (0-50) Td. This decreasing is referred to energy losing by
ionization and excitation processes inside He:Ne mixture which is highly
influenced by reduced electric field. While in the limited region between E/N= (50-
100) Td energy mobility is almost steady.
Fig. 3. Energy mobility as a capacity of decreased electric field (E/N).
Dependences of energy mobility on gas mixture concentration can be observed,
where increasing of mobility according to the increasing of E/N can be noticed as
in Table 3, the reason for this, is the increase electron drift by increasing the
concentration with increasing the reduced electric field [10].
Table 3. The correlation between energy mobility *N and mass of Ne.
E/N =65.86Td
Concentration
(Mol.)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Energy mobility
*N×1024 (1/m/V/s)
3.74
3.97
4.23
4.53
4.89
5.32
5.84
1556 B. Hamed et al.
Journal of Engineering Science and Technology April 2022, Vol. 17(2)
4.2. Energy mobility modeling
The following Eq. (9) illustrates the behavior of energy mobility according to the
change of E/N based of using logistic function:
 


 (9)
where B1, B2, r0, and r are parameters, C is gas mixture concentration. This
relationship addresses a close link between the BOLSIG+ programming numbers
and percent model Fig. 4.
Fig. 4. Estimated/simulated data (using mathematical
model) of Energy mobility and calculated data.
From Eq. (9) for all concentrations, parameters (B1, B2, r0, r) can be shown
mathematically by function of numerical and mathematical to determine the
required concentration calculated in Eq. (9). The equations of these parameters are:
 
  (10)
 
 (11)
 (12)
 (13)
where C concentration.
5. e-i Momentum Frequency
5.1. Influence of reduced electric field and concentration on e-i
momentum frequency
The increasing of E/N produce sharp decreasing of (νe-i) particularly in the limited
region between (0-63) Td as shown in Fig. 5. It is clearly approved that the electron-
ion momentum frequency (νe-i) values increase when changing position from the
greater concentration (0.1) mole to the reduced concentration (0, 9) mole with
Investigation of Concentration Influence on Electronic Coefficients of . . . . 1557
Journal of Engineering Science and Technology April 2022, Vol. 17(2)
respect to the confined area from (0-63) Td as in Table 4, while the behavior
becomes reversed in relation to the confined region between (63 - 100) Td as in
Table 5. This is because the electron-ion momentum frequency has an inverse
proportion with temperature (e-i).
Fig.5. e-i momentum frequency /N as
part of an equation of reduced electric field.
Table 4. The relationship between e-i momentum
frequency /N and concentration of Ne E/N= (0-63) Td.
E/N= 48.79 Td
E/N= (0-63) Td
Concentration
(Mol.)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
e-i momentum
frequency
/N×10-15 (m3/s)
1.53
1.51
1.48
1.45
1.42
1.39
1.35
Table 5. The relationship between e-i momentum
frequency /N and concentration of Ne E/N= (65-100) Td.
E/N=100Td
E/N= (65-100) Td
Concentration
(Mol.)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
e-i momentum
frequency
/N×10-16 (m3/s)
7.2
7.45
7.7
7.95
8.2
8.47
8.75
5.2. e-i momentum frequency /N modeling
The following Eq. (14) illustrates the behavior of e-i momentum frequency ν/N
according to the change of E/N based of using logistic function:


 (14)
1558 B. Hamed et al.
Journal of Engineering Science and Technology April 2022, Vol. 17(2)
where, , ,, are parameters, C is gas mixture concentration.
This relationship showcases a correlation between the BOLSIG+ values and
percent model (Fig. 6.):
Fig. 6. Assessed/recreated information (utilizing numerical
model) of e-i Momentum Prevalence and calculated data.
From Eq. (14) for all concentrations, parameters (, ,,) can be shown
mathematically by function of numerical and mathematical to determine the required
concentration calculated in Eq. (14). The equations of these parameters are:

 (15)
  
 (16)

 (17)

  (18)
Figure 6 represents the high matching between BOLSIG+ data and our estimated
data, where root mean square is in the range of (4.2×10-7). Also, Eqs. (15-18) are
used to calculate concentration in Eq. (14).
6. Conclusions
A comprehensive investigation of specific electron transport coefficients in plasma
state He-Ne gas mixtures has been carried out using the solution of Boltzmann
equation, adopting BOLSIG+ program. Through this investigation the influence of
mixture concentration on the electronic coefficients (νe-i/N, µƐN, and <
>) can be
observed. It can be also observed that by changing the reduced electric field, each
of versatile inelastic crashes and cross-area of collisions has a significant role in
discharge process.
In addition to, this investigation introduced appropriated equations of electronic
coefficients of He:Ne plasma field utilizing a simulation process for each of these
Investigation of Concentration Influence on Electronic Coefficients of . . . . 1559
Journal of Engineering Science and Technology April 2022, Vol. 17(2)
coefficients. Also simplified equations for concentration calculation have been
introduced. In general, the obtained equations through our simulation process are
shown high matching between BOLSIG+ data and our simulation data, where root
mean square of (νe-i /N,) = 4.2×10-7, root mean square of µƐN = 1.5×10-6 and root
mean square of <
> = 9.4×10-5.
Acknowledgments
Creators would want to express gratitude toward Mustansiriyah University
(www.uomustansiriyah.edu.iq) Baghdad-Iraq for its help in the current work, and
we are grateful to G. B. Ragimkhanov Dagestan State University.
Nomenclatures
E/N
Reduce electric field, 10-21 Vm2
F
External force, N

󰐗
Distribution function before and after collision, (e.V)-3/2

Multiplicity of two energy level
K
Boltzmann constant, J/K
m
Particle mass, kg
Density of charge, m-3

Number of densities, m-3
T
Thermodynamic temperature, K
v
Velocity of electron, m/s2
Greek Symbols

Differential effective scattering

Solid angle
f/t
Rate of the change of the distribution rate of the change of the
distribution function
<
>
Mean energy, e.V
µ
Mobility, m2 /vs.

Momentum frequency, m3/s
References
1. Li, Y. (2017). Engineering plasmonic nanostructures for Fano resonance-
based biosensor. Graduate theses, Johns Hopkins University, Goldstone.
2. Liu, L. (2017). Physics of electrical discharge transitions in air. KTH Royal
Institute of Technology.
3. Morozov, A.I. (2012). Introduction to plasma dynamics. CRC Press.
4. Ali, R.A.; Hamed, B.; Al-obaidi, M.T.; and Abbas, A.M. (2021). Estimation
of a Mathematical Model for Theoretical Measuring of Plasma Electrons
Mobility at Different Concentrations of He-Cu Mixture, in Journal of Physics:
Conference Series, 1999(1), 12132.
5. Francis, F. (1984). Introduction to plasma physics and controlled fusion. Springer.
6. Freidberg, J.P. (2008). Plasma physics and fusion energy. Cambridge
University Press.
1560 B. Hamed et al.
Journal of Engineering Science and Technology April 2022, Vol. 17(2)
7. Sturrock, P.A. (1994). Plasma physics: An introduction to the theory of
astrophysical, geophysical & laboratory plasmas. Cambridge University Press.
8. Smirnov, B.M. (2015). Theory of gas discharge plasma. Springer.
9. Othman, M.M.; Taha, S.A.; Mohammad, J.J. (2017). Electron transport parameters
in hydrogen-argon mixtures. AIP Conference Proceedings, 1888, 020040.
10. Yang, W.; Meng, X.; Zhou, Q.; and Dong, Z. (2019). Boltzmann equation
studies on electron swarm parameters in Townsend breakdown of copper vapor
plasma using independently assessed electron-collision cross sections. AIP
Advances, 9(3), 035041.
11. Kurbanismailov, V.S., Omarov, O.A., Ragimkhanov, G.B., Abakarova, K.M.;
and Ali, A.R.A. (2016). Formation of shock waves in a discharge plasma in the
presence of a magnetic field. Plasma Physics Reports, 2016, 42(7), 687-698.
12. Köhn, C.; Chanrion, O.; and Neubert, T. (2017). The influence of
Bremsstrahlung on electric discharge streamers in N2, O2 gas mixtures. Plasma
Sources Science and Technology, 26, 015006.
13. Colonna, G. (2016). Plasma modeling: Methods and applications. Iop
Publishing Ltd, 1-23.
14. Villani, C. (2002). A review of mathematical topics in collisional kinetic
theory. In Friedlander, S.; and Serre D. (Eds.). Handbook of Mathematical
Fluid Dynamics (Vol. 1), Elsevier Science.
15. Rockwood, S.D. (1973). Elastic and inelastic cross sections for Electron-Hg
scattering from Hg transport data. Physical Review A, 8, 2348-2360.
16. Chiavazzo, E.; Gorban, A.N.; and Karlin, I.V. (2007). Comparison of invariant
manifolds for model reduction in chemical kinetics. Communications in
Computational Physics, 2(5), 964-992.
17. Rita, G.; and Trigg, G.L. (1991). Encyclopedia of Physics (2nd ed.). VHC publishers.
18. Hadi, F.M.; Ali, R.A.; and Al-Rubaiee, A.A. (2020). Mathematical model of the
electronic coefficients for different concentrations of argon and mercury mixture.
IOP Conference Series: Materials Science and Engineering, 928, 072072.
19. Sukhinin, G.I.; Salnikov, M.V.; and Fedoseev, A.V. (2018). The effect of the
type of ion-neutral collisions on ion cloud formation. AIP Conference
Proceedings, 1925(1), 20029.
20. Debbasch, F.; and van Leeuwen, W.A. (2009). General relativistic Boltzmann
equation, I: Covariant treatment. Physica A: Statistical Mechanics and its
Applications, 388(7), 1079-1104.
21. Drewes, M.; Mendizabal, S.; and Weniger, C. (2013). The Boltzmann equation
from quantum field theory. Physics Letters B, 718 (3), 1119-1124.
22. Hadi, F.M.; Ali, R.A.; and Al-Rubaiee A. A. (2020). Simulation analyses and
investigation of the induced electric field and Ar-Hg mixture on the gas
discharge processes. Al-Mustansiriyah Journal of Science, 31(3), 126-136.
23. Al-obaidi, M.T.; Ali, R.A.; and Hamed, B. (2021). Modelling of Reduced
Electric Field and Concentration Influence on Electron Transport Coefficients
of He-Ne Plasma. Acta Phys. Pol. A., 140(4).
24. Kurbanismailov, V.S., Maiorov, S.A., Ragimkhanov, G.B., Khalikova, Z.R.
(2020). Monte Carlo simulation of mercury ion drift characteristics in an inert
gas. Journal of Physics: Conference Series, 2020, 1697, 012234.
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
In this work, theoretical calculations and simulated data are presented that enable us to calculate the effect of Ar: Hg on the plasma electronic coefficients depending on the variance in the plasma field resistance, which presents in a varied electrical field and under thermodynamic equilibrium. The electric field was chosen in the limited range (1-1000) Td, and the concentrations in the limited range (0.01-0.09) mol. Results show a good agreement between the original data (using BOLSIG +) and that estimated data. There are a large number of applications, for example, material technology that uses flare discharge, thin-film deposition, invasive laser beams, and plasma screen TV. Other technological applications such as gas circuit breakers and L. of particle detectors have also been developed. The work includes calculating the effect of c variation on plasma electronic coefficients and different mercury concentrations of the argon and mercury mixture, and secondly, calculating the effect of the electric field (E / N) on electronic coefficients (mobility, the mean energy of electron, momentum frequency) by solving the Boltzmann equation using BOLSIG + where It was noticed that there is a clear effect of reducing the electric field (E / N) on the electronic transactions where the low electric field increases.
Article
Full-text available
In this work, theoretical calculations and simulated data were presented to investigate the effect of the Ar: Hg mixture on electronic plasma coefficients, in addition to study the influence of the electric field and focus on electronic coefficients. The low electric field was chosen in the range (1-1000) Td, and concentrations in a limited range (0.01-0.09) mol. The results showed a clear effect of the electric field on electronic transactions, especially at low levels. These parameters values are higher for high concentrations due to the effect of the electric field on the excitation and ionization energy. In compare to elastic and inelastic collision, and cross-section collision of gas discharges. The results showed good agreement between the original data (using BOLSIG +) and the estimated data in the current work.
Article
Full-text available
Electron transport coefficients in copper vapor plasma are calculated both by two-term expansion of electron Boltzmann equation Bolsig+ and tracking the random motion of electrons using Monte Carlo collision code METHES based upon recently evaluated cross section sets. The copper atoms are evaporated from hot electrode during the post-arc phase of vacuum circuit breakers, in which Townsend breakdown between electrode gaps is probable. The electron energy probability function, electron mean energy, flux/transport mobility and diffusion coefficients, as well as Townsend ionization coefficients are shown in reduced fields 10∼1000 Td at a typical vapor temperature 2000 K. The validity of two-term approximation is checked by comparison to well benchmarked METHES code. If the electrode temperature varies between 1500∼2500 K, the influence of vapor temperature on ionization coefficients is about 5% at 200.4 Td, and drops to 0.5% at 493 Td according to Bolsig+ results. Similar to classic gas discharge theory, the Paschen curve is proposed for Townsend breakdown of metal vapor. Using the calculated ionization coefficient and a constant secondary electron yield, the Paschen minimum is determined to be 106∼122 V at a critical value of the product of vapor density and gap length (4.7∼5.7)×10 ¹⁹ m ⁻² . A satisfactory agreement was found with the previously measured ignition voltage between vacuum interrupter contacts after the arcing.
Thesis
Full-text available
Electrical discharges with a variety of different forms (streamers, glow corona, leaders, etc.) broadly exist in nature and in industrial applications. Under certain conditions, one electrical discharge can be transformed into another form. This thesis is aimed to develop and use numerical simulation models in order to provide a better physical understanding of two of such transitions, namely the glow-to-streamer and the streamer-to-leader transitions in air. In the first part, the thesis includes the two-dimensional simulation of the glow-to-streamer transition under a fast changing background electric field. The simulation is performed with a fluid model taking into account electrons. An efficient semi-Lagrangian algorithm is proposed to solve the convection-dominated continuity equations present in the model. The condition required for the glow-to-streamer transition is evaluated and discussed. In order to enable such simulations for configurations with large interelectrode gaps and long simulation times, an efficient simplified model for glow corona discharges and their transition into streamers is also proposed. The second part of the thesis is dedicated to investigate the dynamics of the streamer-to-leader transition in long air gaps at atmospheric pressure. The transition is studied with a one-dimensional thermo-hydrodynamic model and a detailed kinetic scheme for N2/O2/H2O mixtures. In order to evaluate the effect of humidity, the kinetic scheme includes the most important reactions with the H2O molecule and its derivatives. The analysis includes the simulation of the corresponding streamer bursts, dark periods and aborted leaders that may occur prior to the inception of a stable leader. The comparison between the proposed model and the widely-used model of Gallimberti is also presented.
Article
Full-text available
Streamers are ionization filaments of electric gas discharges. Negative polarity streamers propagate primarily through electron impact ionization, whereas positive streamers in air develop through ionization of oxygen by UV photons emitted by excited nitrogen; however, experiments show that positive streamers may develop even for low oxygen concentrations. Here we explore if bremsstrahlung ionization facilitates positive streamer propagation. To discriminate between effects of UV and bremsstrahlung ionization, we simulate the formation of a double headed streamer at three different oxygen concentrations: no oxygen, 1 ppm O2 and 20% O2, as in air. At these oxygen levels, UV-relative to bremsstrahlung ionization is zero, small, and large. The simulations are conducted with a particle-in-cell code in a cylindrically symmetric configuration at ambient electric field magnitudes three times the conventional breakdown field. We find that bremsstrahlung induced ionization in air, contrary to expectations, reduces the propagation velocity of both positive and negative streamers by about 15%. At low oxygen levels, positive streamers stall; however, bremsstrahlung creates branching sub-streamers emerging from the streamer front that allow propagation of the streamer. Negative streamers propagate more readily forming branching sub-streamers. These results are in agreement with experiments. At both polarities, ionization patches are created ahead of the streamer front. Electrons with the highest energies are in the sub-streamer tips and the patches.
Article
Full-text available
The effect of an external magnetic field on the dynamics of shock waves generated in an argon plasma due to both explosive processes on the cathode and expansion of the spark channel has been studied experimentally. It is shown that the expanding plasma of the cathode spot forms a shock wave and that the application of a longitudinal magnetic field decelerates the radial expansion of the cathode plasma. It is found that the intensities of some argon spectral lines increase in the presence of a magnetic field.
Book
As the twenty-first century progresses, plasma technology will play an increasing role in our lives, providing new sources of energy, ion–plasma processing of materials, wave electromagnetic radiation sources, space plasma thrusters, and more. Studies of the plasma state of matter not only accelerate technological developments but also improve the understanding of natural phenomena. Beginning with an introduction to the characteristics and types of plasmas, Introduction to Plasma Dynamics covers the basic models of classical diffuse plasmas used to describe such phenomena as linear and shock waves, stationary flows, elements of plasma chemistry, and principles of plasma lasers. The author presents specific examples to demonstrate how to use the models and to familiarize readers with modern plasma technologies. The book describes structures of magnetic fields—one- and zero-dimensional plasma models. It considers single-, two-, and multi-component simulation models, kinetics and ionization processes, radiation transport, and plasma interaction with solid surfaces. The text also examines self-organization and general problems associated with instabilities in plasma systems. In addition, it discusses cosmic plasma dynamic systems, such as Earth’s magnetosphere, spiral nebulas, and plasma associated with the Sun. This text provides wide-range coverage of issues related to plasma dynamics, with a final chapter addressing advanced plasma technologies, including plasma generators, plasma in the home, space propulsion engines, and controlled thermonuclear fusion. It demonstrates how to approach the analysis of complex plasma systems, taking into account the diversity of plasma environments. Presenting a well-rounded introduction to plasma dynamics, the book takes into consideration the models of plasma phenomena and their relationships to one another as well as their applications.
Book
http://iopscience.iop.org/book/978-0-7503-1200-4 Plasma Modeling: Methods and Applications presents and discusses the different approaches that can be adopted for plasma modeling, giving details about theoretical and numerical methods. The book is intended to assist and direct students and researchers, who want to develop research activity in the field of plasma physics, in the choice of the best model for the problem of interest. The book is organised in three parts. The first describes kinetic models used in plasma investigations, consisting of the solution of the Boltzmann equation using different approaches. The second part develops the theory of fluid equations and of hybrid models, and the third part is devoted to applications, considering some practical problems of interest in different fields.
Article
1. Introduction 2. Basic concepts 3. Orbit theory - uniform fields 4. Adiabatic invariants 5. Orbit theory 6. Electromagnetic waves in a cold electron plasma 7. Electromagnetic waves in an electron-ion plasma 8. Two-stream instability 9. Electrostatic oscillations in a plasma of non-zero temperature 10. Collision theory 11. MHD equations 12. Magnetohydrodynamics 13. Force-free magnetic configurations 14. Waves in MHD systems 15. Magnetohydrodynamic stability 16. Variational principle for MHD systems 17. Resistive instabilities 18. Stochastic processes 19. Interaction of particles and waves.