2010-07-25
Covariant Constitutive Relations, Landau Damping and Non-Stationary Inhomogeneous Plasmas
By
Progress In Electromagnetics Research M, Vol. 13, 145-156, 2010
Abstract
Models of covariant linear electromagnetic constitutive relations are formulated that have wide applicability to the computation of susceptibility tensors for dispersive and inhomogeneous media. A perturbative framework is used to derive a linear constitutive relation for a globally neutral plasma enabling one to describe in this context a generalized Landau damping mechanism for non-stationary inhomogeneous plasma states.
Citation
Jonathan Gratus, and Robin W. Tucker, "Covariant Constitutive Relations, Landau Damping and Non-Stationary Inhomogeneous Plasmas," Progress In Electromagnetics Research M, Vol. 13, 145-156, 2010.
doi:10.2528/PIERM10051310
References

1. O'Sullivan, R. A. and H. Derfler, "Relativistic theory of electromagnetic susceptibility and its application to plasmas," Physical Review A, Vol. 8, No. 5, 2645-2656, 1973.
doi:10.1103/PhysRevA.8.2645        Google Scholar

2. Beskin, V. S., A. V. Gurevich, and I. N. Istomin, "Permittivity of a weakly inhomogeneous plasma," Soviet Physics JETP, Vol. 65, 715-726, 1987.        Google Scholar

3. Fo, R. A. C., R. S. Schneider, and L. F. Ziebell, "The dispersion relation and the dielectric tensor of inhomogeneous magnetized plasmas," Journal of Plasma Physics, Vol. 42, 165-175, 1989.
doi:10.1017/S0022377800014240        Google Scholar

4. Obukhov, Y. N., "Electromagnetic energy and momentum in moving media," Annalen der Physik, Vol. 17, No. 9, 10, 2008.
doi:10.1002/andp.200810313        Google Scholar

5. Itin, Y., "On light propagation in premetric electrodynamics," Journal of Physics A: Mathematical and Theoretical, Vol. 42, 475402, 2009.
doi:10.1088/1751-8113/42/47/475402        Google Scholar

6. Lindell, I. V., "Class of electromagnetic SD media," Metamaterials, Vol. 2, No. 2-3, 54-70, 2008.
doi:10.1016/j.metmat.2008.02.001        Google Scholar

7. Vladimirov, S. V. and D. B. Melrose, "Covariant electromagnetic forces in a time-dependent and inhomogeneous medium," Physica Scripta, Vol. 57, 298-300, 1998.
doi:10.1088/0031-8949/57/2/028        Google Scholar

8. Melrose, D. B., "A covariant formulation of wave dispersion," Plasma Physics, Vol. 15, No. 2, 99-106, 1973.
doi:10.1088/0032-1028/15/2/002        Google Scholar

9. Lamalle, P. U., "Kinetic theory of plasma waves-part I: Introduction," Fusion Science and Technology, Vol. 41, No. 2, SUPP, 135-140, 2002.        Google Scholar

10. Lamalle, P. U., "Kinetic theory of plasma waves-part III: Inhomogeneous plasma," Fusion Science and Technology, Vol. 41, No. 2, SUPP, 151-154, 2002.        Google Scholar

11. Weibel, E. S., "Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution," Physical Review Letters, Vol. 2, No. 3, 83-84, 1959.
doi:10.1103/PhysRevLett.2.83        Google Scholar

12. Schaefer-Rolffs, U., I. Lerche, and R. Schlickeiser, "The relativistic kinetic weibel instability: General arguments and specific illustrations," Physics of Plasmas, Vol. 13, No. 1, 012107, 2006.
doi:10.1063/1.2164812        Google Scholar

13. Yoon, P. H., "Electromagnetic weibel instability in a fully relativistic bi-maxwellian plasma," Physics of Fluids B: Plasma Physics, Vol. 1, No. 6, 1336-1338, 1989.
doi:10.1063/1.858961        Google Scholar

14. Brambilla, M., "The high-frequency constitutive relation of axisymmetric toroidal plasmas," Plasma Physics and Controlled Fusion, Vol. 41, 775-800, 1999.
doi:10.1088/0741-3335/41/6/307        Google Scholar

15. Bernstein, I. B., J. M. Greene, and M. D. Kruskal, "Exact nonlinear plasma oscillations," Physical Review, Vol. 108, No. 3, 546-550, 1957.
doi:10.1103/PhysRev.108.546        Google Scholar

16. Manfredi, G., "Long-time behavior of nonlinear Landau damping," Physical Review Letters, Vol. 79, No. 15, 2815-2818, 1997.
doi:10.1103/PhysRevLett.79.2815        Google Scholar

17. Nicholson, D. R., Introduction to Plasma Theory, Wiley, New York, 1983.

18. Feix, M. R., P. Bertrand, and A. Ghizzo, Advances in Kinetic Theory and Computing, B. Perthame (ed.), 4581, World Scientific, Singapore, 1994.

19. Brodin, G., "Nonlinear landau damping," Physical Review Letters, Vol. 78, No. 7, 1263-1266, 1997.
doi:10.1103/PhysRevLett.78.1263        Google Scholar

20. Petri, J. and J. G. Kirk, "Numerical solution of the linear dispersion relation," Plasma Physics and Controlled Fusion, Vol. 49, 297-308, 2007.
doi:10.1088/0741-3335/49/3/008        Google Scholar