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International Journal of Theoretical Physics, "Col. 27, No. 7, 1988High-Frequency Sum Rules for ClassicalOne-Component Plasma in a Magnetic FieldR. O. Genga ~Received September 16, 1987A high-frequency sum-rule expansion is derived for all elements of a classicalplasma dielectric tensor in the presence of an external magnetic field. 124~3 isfound to be the only coefficient of to -4 that has no correlational and finite-radiation-temperaturecontributions. The finite-radiation-temperatureeffectresults in an upward renormalization of the frequencies of the modes; it alsoleads to either reduction of the negative correlational effect on the positivethermal dispersion or, together with correlation, enhancement of the positivethermal dispersion for finite k, depending on the direction of propagation.Further, for the extraordinary mode, the finite-radiation-temperature effectincreases the positive refractive dispersion for finite k.1. INTRODUCTIONThe high-frequency sum rule provide the coefficient of the inversepowers of to in the high-frequency asymptotic expansions of ~t(k). Sumrules follow from the equations of motion (i.e., conservation laws) via thefluctuation-dissipation theorems (FDT) and the Kramers-Kronig (KK)relations for the response functions (Kalman, 1978).In this work we consider an anisotropic system in the presence of anexternal magnetic field, since the result for an isotropic system is alreadyknown (Kalman and Genga, 1986). In this system the dielectric tensor hassix independent elements. Also, the relationship between the elements ofthe external and current-current response function and the elements of thedielectric tensor become quite involved.The high-frequency expansion is carried out to order to -5. The methodof derivation is similar to the standard approach (de Gennes, 1959) andrelies heavily on the Hamiltonian formalism. It is known (Kalman and~Department of Physics, University of Nairobi, Nairobi, Kenya.8190020-7748/88/0700-0819506.00/01988 Plenum Publishing Corporation
820GengaGenga, 1986) that in order to describe the transverse interaction, the particleHamiltonian has to be enlarged to include the photon degrees of freedom.In so doing we encounter, in addition to the particle contribution to thesum-rule coefficients, the photon gas coexistent with the high-temperatureplasma, which generates its own contribution. As in the magnetic field-freecase (Kalman and Genga, 1986), the evaluation of the contribution ishampered by two circumstances; the first is the well-known classical ultravio-let divergence, which requires that even within the framework of a classicaltheory one describe the photons via the quantum Bose-Einstein distribution,while the second difficulty arises from the fact that the equilibrium descrip-tion implies the existence of one single temperature for the combinedparticle-photon system. Such an equilibrium, however, seldom prevails inany but astrophysical situations. Thus, a reasonablead hocapproximation,described in Section 2, is used to decouple the photons from the particlesystem.

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Term
Fall
Professor
NoProfessor
Tags
Photon, Magnetic Field, Fundamental physics concepts, Longitudinal mode, dispersion relation

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