NS  Vol.7 No.1 , January 2015
The Classical Binary and Triplet Distribution Functions for Dilute Relativistic Plasma
ABSTRACT
The aim of this paper is to calculate the binary and triplet distribution functions for dilute relativistic plasma in terms of the thermal parameter μ where , is the mass of charge; c is the speed of light; k is the Boltzmann’s constant; and T is the absolute temperature. Our calculations are based on the relativistic Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. We obtain classical binary and triplet distribution functions for one- and two-component plasmas. The excess free energy and pressure are represented in the forms of a convergent series expansions in terms of the thermal parameter μ.

Cite this paper
Hussein, N. , Eisa, D. and Sayed, E. (2015) The Classical Binary and Triplet Distribution Functions for Dilute Relativistic Plasma. Natural Science, 7, 42-54. doi: 10.4236/ns.2015.71005.
References
[1]   Droz-Vincent, P. (1997) Direct Interactions in Relativistic Statistical Mechanics. Foundations of Physics, 27, 363-387.
http://dx.doi.org/10.1007/BF02550162

[2]   Bogoliubov, N.N. (1946) Probleme der Dynamischen Theorie in der Statistischen Physik. Moskau.

[3]   Simonella, S. (2011) BBGKY Hierarchy for Hard Sphere Systems. Ph.D. Dissertation, Sapienza University of Rome, Rome.

[4]   Kraeft, W.D., Kremp, D. and Ebeling, W. (1986) Quantum Statistics of Charged Particle Systems. Akademie Verlag, Berlin.
http://dx.doi.org/10.1007/978-1-4613-2159-0

[5]   Kahlbaum, T. (1999) Density Expansions of the Reduced Distribution Functions and the Excess Free Energy for Plasma with Coulomb and Short-Range Interactions. Contributions to Plasma Physics, 39, 181-184.
http://dx.doi.org/10.1002/ctpp.2150390144

[6]   Hussein, N.A. and Eisa, D.A. (2011) The Quantum Equation of State of Fully Ionized Plasmas. Contributions to Plasma Physics, 51, 44-50.
http://dx.doi.org/10.1002/ctpp.201110003

[7]   Eisa, D.A. (2012) The Classical Binary and Triplet Distribution Functions for Two Component Plasma. Contributions to Plasma Physics, 52, 261-275.
http://dx.doi.org/10.1002/ctpp.201100030

[8]   Arendt Jr., P.N. and Eilek, J.A. (2000) The Pair Cascade in Strong and Weak Field Pulsars. Pulsar Astronomy—2000 and beyond, 202, 445-448.

[9]   Barcons, X. and Lapiedra, R. (1985) Statistical Mechanics of Classical Dilute Relativistic Plasmas in Equilibrium. Journal of Physics A: Mathematical and General, 18, 271-285.
http://dx.doi.org/10.1088/0305-4470/18/2/017

[10]   Swisdak, M. (2013) The Generation of Random Variates from a Relativistic Maxwellian Distribution. Physics of Plasmas, 20, Article ID: 062110.
http://dx.doi.org/10.1063/1.4812459

[11]   Ares de Parga, G. and Lopez-Carrera, B. (2011) Relativistic Statistical Mechanics vs. Relativistic Thermodynamics. Entropy, 13, 1664-1693.
http://dx.doi.org/10.3390/e13091664

[12]   Treumann, R.A., Nakamura, R. and Baumjohann, W. (2011) A Model of So-Called “Zebra” Emissions in Solar Flare Radio Burst Continua. Annales Geophysicae, 29, 1673-1682.
http://dx.doi.org/10.5194/angeo-29-1673-2011

[13]   Sciortino, F. and Kob, W. (2001) Debye-Waller Factor of Liquid Silica: Theory and Simulation. Physical Review Letters, 86, 648-651.
http://dx.doi.org/10.1103/PhysRevLett.86.648

[14]   Rosenfeld, Y., Levesque, D. and Weis, J.J. (1990) Free-Energy Model for the Inhomogeneous Hard-Sphere Fluid Mixture: Triplet and Higher-Order Direct Correlation Functions in Dense Fluids. The Journal of Chemical Physics, 92, 6818-6832.
http://dx.doi.org/10.1063/1.458268

[15]   Lapiedra, R. and Santos, E. (1981) Classical Relativistic Statistical Mechanics: The Case of a Hot Dilute Plasma. Physical Review D, 1, 2181-2188.
http://dx.doi.org/10.1103/PhysRevD.23.2181

[16]   Alam, M.S., Masud, M.M. and Mamun, A.A. (2014) Effects of Two-Temperature Superthermal Electrons on Dust-Ion-Acoustic Solitary Waves and Double Layers in Dusty Plasmas. Astrophysics and Space Science, 349, 245-253.
http://dx.doi.org/10.1007/s10509-013-1639-3

[17]   Masud, M.M., Kundu, N.R. and Mamun, A.A. (2013) Obliquely Propagating Dust-Ion Acoustic Solitary Waves and Their Multidimensional Instabilities in Magnetized Dusty Plasmas with Bi-Maxwellian Electrons. Canadian Journal of Physics, 91, 530-536.
http://dx.doi.org/10.1139/cjp-2012-0390

[18]   Lazar, M., Stockem, A. and Schlickeiser, R. (2010) Towards a Relativistically Correct Characterization of Counterstreaming Plasmas. I. Distribution Functions. Open Plasma Physics Journal, 3, 138-147.
http://dx.doi.org/10.2174/1876534301003010138

[19]   Lapiedra, R. and Santos, E. (1983) Classical Dilute Relativistic Plasma in Equilibrium. Two-Particle Distribution Function. Physical Review A, 27, 422-430.
http://dx.doi.org/10.1103/PhysRevA.27.422

[20]   Turski, L.A. (1974) Pair Correlation Function for a System with Velocity-Dependent Interactions. Journal of Statistical Physics, 11, 1-16.
http://dx.doi.org/10.1007/BF01019474

[21]   Kosachev, V.V. and Trubnikov, B.A. (1969) Relativistic Corrections to the Distribution Functions of Particles in a High-Temperature Plasma. Nuclear Fusion, 9, 53-56.
http://dx.doi.org/10.1088/0029-5515/9/1/006

[22]   Bel, L., Salas, A. and Sanchez, J.M. (1973) Approximate Solutions of Predictive Relativistic Mechanics for the Electromagnetic Interaction. Physical Review D, 7, 1099-1106.
http://dx.doi.org/10.1103/PhysRevD.7.1099

[23]   Kirkwood, J.G. (1935) Statistical Mechanics of Fluid Mixtures. The Journal of Chemical Physics, 3, 300-313.
http://dx.doi.org/10.1063/1.1749657

[24]   Bonitz, M., Henning, C. and Block, D. (2010) Complex Plasmas: A Laboratory for Strong Correlations. Reports on Progress in Physics, 73, Article ID: 066501.
http://dx.doi.org/10.1088/0034-4885/73/6/066501

[25]   Barrat, J.L., Hansen, J.P. and Pastore, G. (1988) On the Equilibrium Structure of Dense Fluids: Triplet Correlations, Integral Equations and Freezing. Molecular Physics, 63, 747-767.
http://dx.doi.org/10.1080/00268978800100541

[26]   Kalman, G.J., Rommel, J.M., Blagoev, K. and Blagoev, K. (1998) Strongly Coupled Coulomb Systems. Springer, Berlin.
http://www.springer.com/physics/particle+and+nuclear+physics/
book/978-0-306-46031-9


 
 
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