Hostname: page-component-6898cfcb55-w5hgh Total loading time: 0 Render date: 2026-11-11T13:23:36.744Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiple spatial scaling and the weak-coupling approximation. Part 1. General formulation and equilibrium theory

Published online by Cambridge University Press:  13 March 2009

Paul E. Kleinsmith
Paul E. Kleinsmith
Affiliation:
Chemical Engineering Department, Carnegie-Mellon University
Get accessRights & Permissions [Opens in a new window]

Abstract

Multiple spatial scaling is incorporated in a modified form of the Bogoliubov plasma cluster expansion; then this proposed reformulation of the plasma weak- coupling approximation is used to derive, from the BBGKY Hierarchy, a decoupled set of equations for the one- and two-particle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential two-particle collisional information in the limiting equations, while simultaneously retaining the well-established Debye-scale relative ordering of the correlation functions, decoupling of the Hierarchy is accomplished without introduction of the divergence problems encountered in the Bogoliubov theory, as is indicated by an exact solution of the limiting equations for the equilibrium case. To establish additional links with existing plasma equilibrium theories, the two-particle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium three-particle correlation function is then developed, and a formal solution is obtained.

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 15 , Issue 2 , April 1976, pp. 223 - 238
Copyright
Copyright © Cambridge University Press 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Abe, R. 1959 Prog. Theor. Phys., Kyoto, 22, 213.CrossRefGoogle Scholar
Abramowitz, M., & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.Google Scholar
Balescu, R. 1960 Phys. Fluids, 3, 52.CrossRefGoogle Scholar
Balescu, R. 1963 The Statistical Mechanics of Charged Particles. Wiley.Google Scholar
Bogoliubov, N. N. 1946 Problems of a Dynamical Theory in Statistical Mechanics as translated in Studies in Statistical Mechanics vol. 1 (ed. DeBoer, J. and Uhlenbeck, G. E., 1962) North Holland.Google Scholar
Bowers, D. L., & Salpeter, E. E. 1960 Phys. Rev., 119, 1180.CrossRefGoogle Scholar
Friedman, H. L. 1959 Mol. Phys. 2, 23.Google Scholar
Frieman, E. A. 1963 J. Math. Phys. 4, 410.CrossRefGoogle Scholar
Frieman, E. A., & Book, D. L. 1963 Phys. Fluids, 6, 1700.CrossRefGoogle Scholar
Gradsteyn, I. S., & Ryzhic, I. M. 1965 Table of Integrals, Series and Products. Academic.Google Scholar
Guernsey, R. L. 1964 a Phys. Fluids, 7, 792.Google Scholar
Guernsey, R. L. 1964 b Phys. Fluids, 7, 1600.CrossRefGoogle Scholar
Henline, W. D., & Condiff, D. W. 1970 J. Chem. Phys. 54, 5346.CrossRefGoogle Scholar
Kahn, B. 1938 On the Theory of the Equation of State as translated in Studies in Sta. tistical Mechanics vol. 3 (ed. DeBoer, J. and Uhlenbeck, G. E.) North Holland.Google Scholar
Lenard, A. 1960 Ann. Phys. N.Y. 10, 390.Google Scholar
Meeron, E. 1958 J. Chem. Phys. 28, 630.Google Scholar
Meeron, E. 1958 Phys. Fluids, 1, 139.CrossRefGoogle Scholar
Montgomery, D. C., & Tidman, D. A. 1964 Plasma Kinetic Theory. McGraw Hill.Google Scholar
Sandri, G. 1963 Ann. Phys. N.Y. 13, 332.Google Scholar
Trulio, J. G., & Brush, S. G. 1961 Phys. Rev. 121, 940.CrossRefGoogle Scholar
Ursell, H. D. 1927 Proc. Camb. Phil. Soc. 23, 685.CrossRefGoogle Scholar