volume | PIER Journals

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.

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

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.

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

Dr. Jonathan Gratus

Dr. Robin W. Tucker