Analytical Solving a Nonlinear Model of the Glow Discharge
DOI:
https://doi.org/10.14311/ppt.2021.3.23Keywords:
cw glow discharge, nonlinear differential equation, pure gas environment.Abstract
A nonlinear model has been introduced for the positive column of DC glow discharge in apure sealed, or low flow, gas media by including the diffusion, recombination, attachment, detachment,process and having the two-step ionization process of the metastable excited states, too. By thecombination of the system of the nonlinear continuity equations of the system, using some physicalestimations, and degrading the resulted nonlinear PDE in polar and rectangular systems of coordinatethe steady-state nonlinear ODE have been derived. Using a series-based solution, an innovativenonlinear recursion relation has been proposed for calculating the sentence of series. Using the stateof elimination of free charge on the outer boundary of the discharge vessel, the universal equation ofthe characteristic energy of the electrons versus the similarity variable, using the maximum degree ofionization as the parameter, has been derived.
References
B. M. Smirnov.Theory of Gas Discharge Plasma.Springer International Publishing, 2014. ISBN978-3-319-11064-6.
B. E. Cherrington.Gaseous Electronics and GasLasers. Pergamon Press, 2014. ISBN 978-1-483-23400-7.
Y. P. Raizer.Gas Discharge Physics. 1st Editionreprint. Springer-Verlag Berlin Heidelberg, 2011. ISBN978-3-642-64760-4.
M. P. Jahan, editor.Electrical Discharge Machining(EDM): Types, Technologies and Applications. NovaScience Publishers, Incorporated, 2015. ISBN978-1-634-83591-6.
M. C. Jones, D. J. Ampleford, M. E. Cuneo, et al.X-ray power and yield measurements at the refurbishedZ machine.Review of Scientific Instruments,85(8):083501, 2014.doi:10.1063/1.4891316.
M. Thompson.Handbook of Inductively CoupledPlasma Spectrometry. 2nd Edition. Springer US, 2012.ISBN 978-1-4612-8037-8.
G. Colonna and A. D’Angola, editors.PlasmaModeling, Methods and Applications. IOP PublishingLtd, 2016. ISBN 978-0-7503-1200-4.
M. Aram, N. Morshedian, S. Behrouzinia, andM. Namnabat. An innovative simple method for studyof the characteristics of the trigatron plasma switch.Contributions to Plasma Physics, 56(10):982–986, 2016.doi:10.1002/ctpp.201600023.
A. Bogaerts, E. Neyts, R. Gijbels, and J. van derMullen. Gas discharge plasmas and their applications.Spectrochimica Acta Part B: Atomic Spectroscopy,57(4):609–658, 2002.doi:10.1016/S0584-8547(01)00406-2.
A. Bogaerts and R. Gijbels. Fundamental aspectsand applications of glow discharge spectrometrictechniques.Spectrochimica Acta Part B: AtomicSpectroscopy, 53(1):1–42, 1998.doi:10.1016/S0584-8547(97)00122-5.
M. R. Kenneth, editor.Glow Discharge Spectroscopies.Springer US, 2013. ISBN 978-1-489-92396-7.
W. J. Witteman, editor.The CO2Laser. 1st Editionreprint. Springer-Verlag Berlin Heidelberg, 2013. ISBN978-3-662-13617-1.
D. Basting and G. Marowsky, editors.Excimer LaserTechnology. Springer-Verlag Berlin Heidelberg, 2005.ISBN 978-3-642-05749-6.
T. J. Killian. The uniform positive column of anelectric discharge in mercury vapor.Physical Review,35(10):1238–1252, 1930.doi:10.1103/PhysRev.35.1238.
V. Granovsky. On the applicability of similarity lawsto the positive column in mercury discharges.Proceedingsof the USSR Academy of Science, 28:37, 1940.
B. A. Anicin. A theory of the low-pressure positivecolumn in a transverse magnetic field.The Physics ofFluids, 10(11):2377–2383, 1967.doi:10.1063/1.1762046.
K. Chandrakar. Electron temperature in an a.c. glowdischarge in air.British Journal of Applied Physics,16(4):449–451, 1965.doi:10.1088/0508-3443/16/4/305.
U. Kortshagen and L. D. Tsendin, editors.ElectronKinetics and Applications of Glow Discharges. SpringerUS, 2006. ISBN 978-0-306-47076-9.
S. Ono and S. Teii. Negative ion formations and theireffects on the electron temperature in CO2-N2-hemixture gas discharges.Journal of Physics D: AppliedPhysics, 17(10):1999–2008, 1984.doi:10.1088/0022-3727/17/10/011.
C. Leys, C. van Egmond, and E. Desoppere.Ionization equilibrium in flowing CO2laser mixtures.Journal of Physics D: Applied Physics, 30(4):573–581,1997.doi:10.1088/0022-3727/30/4/011.
H. T. Davis.Introduction to Nonlinear Differentialand Integral Equations. 1st Edition. U.S. AtomicEnergy Commission, 1960.
A. Plastino and M. C. Rocca. From thehypergeometric differential equation to a non-linearschrödinger one.Physics Letters A, 379(42):2690–2693,2015.doi:10.1016/j.physleta.2015.08.015.
J. Guckenheimer and P. J. Holmes.NonlinearOscillations, Dynamical Systems, and Bifurcations ofVector Fields. Corrected 7th Edition. Springer-VerlagNew York, 2013. ISBN 978-1-4612-1140-2.
A. S. Al-Johani and M. A.-A. El-Beltagy. Numericalsolution of stochastic nonlinear differential equationsusing wiener-hermite expansion. InProceedings of theInternational Conference on Numerical Analysis andApplied Mathematics 2013 (ICNAAM 2013), volume1558 ofAIP Conference Proceedings, Rhodes, Greece,2013. AIP Publishing. ISBN 978-0-7354-1184-5.
C. V. Pao.Nonlinear Parabolic and EllipticEquations. Springer US, 2012. ISBN 978-1-461-53034-3.
H. K. Avetissian.Relativistic NonlinearElectrodynamics: Interaction of Charged Particles withStrong and Super Strong Laser Fields, volume 120 ofSpringer Series in Optical Sciences. Springer-VerlagNew York, 2007. ISBN 978-1-4419-2135-2.
B.-Y. Guo and C.-L. Xu. Hermite pseudospectralmethod for nonlinear partial differential equations.ESAIM: Mathematical Modelling and NumericalAnalysis, 34(4):859–872, 2000.doi:10.1051/m2an:2000100.
J. R. de Oliveira and M. A. de Moura. Analyticalsolution for the modified nonlinear Schrödingerequation describing optical shock formation.PhysicalReview E, 57(4):4751–4756, 1998.doi:10.1103/PhysRevE.57.4751.
W. Elenbaas. Der gradient derquecksilber-hochdruckentladung als funktion von druck,durchmesser und stromstärke.Physica, 2(1–12):787–792,1935.doi:10.1016/S0031-8914(35)90158-6.
A. Lompe, R. Seeliger, and E. Wolter.Untersuchungen an Hohlkathoden.Annalen der Physik,428(1):9–37, 1939.doi:10.1002/andp.19394280103.
R. Radtke and K. Gunther. Electrical conductivity ofhighly ionized dense hydrogen plasma. I. Electricalmeasurements and diagnostics.Journal of Physics D:Applied Physics, 9(7):1131–1138, 1976.doi:10.1088/0022-3727/9/7/007.
G. E. Norman and A. A. Valuev. Electricalconductivity of nonideal plasma.Plasma Physics,21(6):531–544, 1979.doi:10.1088/0032-1028/21/6/002.
Y. K. Kurilenkov and A. A. Valuev. The electricalconductivity of plasma in wide range of charge densities.Beiträge aus der Plasmaphysik, 24(3):161–171, 1984.doi:10.1002/ctpp.19840240304.
M. R. Zaghloul, M. S. Al Na’imi, and M. A.Bourham. Measurement of electrical conductivity ofweakly nonideal multicomponent plasma mixturesgenerated from dielectric materials.IEEE Transactionson Plasma Science, 37(8):1626–1631, 2009.doi:10.1109/TPS.2009.2024423.
R. J. Zollweg and R. W. Liebermann. Electricalconductivity of nonideal plasmas.Journal of AppliedPhysics, 62(9):3621–3627, 1987.doi:10.1063/1.339265.
T. Ramazanov, K. Galiyev, K. N. Dzhumagulova,et al. Scattering processes and electrical conductivity ofpartially ionized hydrogen plasma.Contributions toPlasma Physics, 43(1):39–46, 2003.doi:10.1002/ctpp.200310005.
M. Baus, J.-P. Hansen, and L. Sjögren. Electricalconductivity of a strongly coupled hydrogen plasma.Physics Letters A, 82(4):180–182, 1981.doi:10.1016/0375-9601(81)90115-8.
B. Chervy and A. Gleizes. Electrical conductivity inSF6thermal plasma at low temperature (1000-5000 K).Journal of Physics D: Applied Physics, 31(19):2557–2565, 1998.doi:10.1088/0022-3727/31/19/029.
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