Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T13:54:37.736Z Has data issue: false hasContentIssue false
  • English
  • Français

Time asymptotic statistics of the Vlasov equation

Published online by Cambridge University Press:  13 March 2009

Georg Knorr
Georg Knorr
Affiliation:
Department of Physics, Ruhr-Universität Bochum†
Get access Rights & Permissions [Opens in a new window]

Extract

A statistical description of the Vlasov equation is made possible by truncation of phase space in the velocity co-ordinates and writing the equation in terms of Fourier components in configuration and velocity space. Invariants of the resulting nonlinear turbulence equations are discussed. Expectation values and in particular an electric field spectrum of the form (β+ ακ2)-1 are derived. α and β are constants; α is always positive; β may be negative, depending on the initial conditions of the plasma. The spectrum is in reasonable agreement with available experiments and simulations.

Type
Research Article
Information
Journal of Plasma Physics , Volume 17 , Issue 3 , June 1977 , pp. 553 - 569
Copyright
Copyright © Cambridge University Press 1977

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.)

References

REFERENCES

Armstrong, T. P., Harding, R. C., Knorr, G. & Montgomery, D. 1970 Methods in computational Physics vol. IX, ed. Alder, B., Fernbach, S. & Rotenberg, M.. Academic Press.Google Scholar
Berk, H. L., Nielson, C. E. & Roberts, K. V. 1970 Phys. Fluids, 13, 980.CrossRefGoogle Scholar
Degroot, J. S. & Katz, J. I. 1973 Phys. Fluids, 16, 401.CrossRefGoogle Scholar
Dory, R. A. 1953 Bull. Am. Phys. Soc. 8, 378.Google Scholar
Elsässer, K. & Schamel, H. 1976 J. Plasma Phys.Google Scholar
Fjortoft, R. 1953 Tellus, 5, 25.Google Scholar
Grenander, U. & Szegö, G. 1958 Toeplitz forms and their applications. Berkeley.CrossRefGoogle Scholar
Hara, T., Honzawa, T., Kawai, Y., Watanabe, S. & Fujita, J. M. 1974 Phys. Lett. A, 48a, 203.CrossRefGoogle Scholar
Harries, L. 1970 Phys. Fluids, 13, 175.Google Scholar
Joyce, G. & Montgomery, D. 1973 J. Plasma Phys. 10, 107.Google Scholar
Kapetanakos, C. A., Hammer, D. A., Striffler, C. D. & Davidson, R. C. 1973 Phys. Rev. Lett. 30, 1303.CrossRefGoogle Scholar
Katz, J. I., DeGroot, J. S. & Faehl, R. J. 1974 Phys. Fluids, 18, 1173.CrossRefGoogle Scholar
Knorr, G. 1963 Z. Naturforsch. 18a, 1304.Google Scholar
Kraichnan, R. H. 1967 Phys. Fluids, 10, 1417.Google Scholar
Kraichnan, R. H. 1975 J. Fluid Mech. 67, 155.CrossRefGoogle Scholar
Lee, T. D. 1952 Q. Appl. Math. 10, 69.Google Scholar
Miller, R. H. 1970 Proc. IVth Conf. on Numerical Simulation of Plasmas, ed. Boris, J. P. & Shanny, R. A., Naval Research Laboratory, Washington D.C.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, Vol. 2, chapter 10. MIT Press.Google Scholar
Montgomery, D. 1972 Phys. Lett. 39A.Google Scholar
Montgomery, D. & Joyce, G. 1974 Phys. Fluids, 17, 1139.Google Scholar
Onsager, L. 1949 Nuovo Cimento Suppl. 6, 279.Google Scholar
Seyler, C. E. Jr, Salu, Y., Montgomery, D. & Knorr, G. 1975 Phys. Fluids, 18, 803.Google Scholar
Thompson, J. J., Faehl, R. J., Kruer, W. L. & Bodner, S. 1974 Phys. Fluids, 17, 1973.Google Scholar
Weinstock, J. & Bezzerides, B. 1975 Phys. Fluids, 18, 251.Google Scholar
Wilf, H. S. 1970 Finite Sections of Some Classical Inequalities, chapter 1. Springer.Google Scholar