跳至主要内容

The Classical Binary and Triplet Distribution Functions for Dilute Relativistic Plasma

Read  full  paper  at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53435#.VMWoQCzQrzE

Author(s) 
 
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 parameterμ.
 
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                                                                                             eww150126lx

评论

此博客中的热门博文

Does Immigration Promote the Investment of the Monopolistic Firm?

In the present paper, we examine the effect of increasing uncertainty of immigrants’ growth on the optimal timing of investment of a firm that has a monopolistic power over the labor market. It is revealed that when the uncertainty of immigrants’ growth is more than a threshold level, increasing uncertainty of immigrants’ growth accelerates the optimal timing of firms’ investment and enhances the economic growth, even if the uncertainty of immigrants’ growth is formulated by the geometric Brownian motion, which is in sharp contrast to the standard result that an increase in the uncertainty postpones the optimal timing. With an increase in the immigrants over the past ten years, workforces in the host countries have been growing significantly to the extent that the immigrants represent 70% of the increase in the workforce in Europe, and 47% in the United States as OECD indicates. In the present paper, we attempted to investigate the effect of increased uncertainty caused by the growi...

Education Policy Implementation: A Mechanism for Enhancing Primary Education Development in Zanzibar

Education is one of the fundamental rights of individuals; therefore, the government of a country needs to develop and strengthen educational policy and quality as well as to ensure that everyone has equal access to basic education. The improvement of access and quality of education in the world is becoming as an essential factor in development, whereas the basic education (primary school), is acknowledged as a foundation of the higher educational development for every country. To fulfill this goal, governments introduce several policies and procedures; however, it requires some reforms and participation from the politician, policymakers, and other stakeholders to re-examine educational policy so that it can lead to multiplication and betterment of the reforms. Educational reforms actually focus on accountability. A positive educational development and reform is very challenging and needs more effort and strategy on how to use and utilize the resources effectively as such it can achie...