Eikonal expansion of the Vlasov-Maxwell equations valid near cyclotron resonance

Technical Report · Tue Jan 01 04:00:00 EST 1980

DOI:https://doi.org/10.2172/5501417· OSTI ID:5501417

Weitzner, H.; Batchelor, D. B.

In the usual formulations of geometrical optics, the physics of the medium enters the equations through a conductivity tensor operator sigma. An essential assumption in the subsequent expansion is that the magnitude of sigma/sup H/, the Hermitian part of sigma, is much smaller than sigma/sup A/, the anti-Hermitian part. In a finite temperature plasma with ..omega../sub pe/ approx. absolute value ..cap omega../sub e/, this condition is always violated sufficiently close to cyclotron resonance, even though in many cases the waves are weakly damped and k is slowly varying. Simultaneously expanding the Vlasov equation and Maxwell equations and taking explicit account of the relative magnitude of the electric field components in the ordering scheme yields a formalism in terms of real rays, real eikonal function, and slowly varying amplitude that is valid at cyclotron resonance. It is assumed that ..omega../sub pe/ approx. absolute value ..cap omega../sub e/ approx. ..omega.. are large, that ..omega.. approx. = absolute value ..cap omega../sub e/, and that v/sub e/k/..omega.. is small. It is shown that when the waves are weakly damped at cyclotron resonance, the ray trajectories are to leading order exactly those of cold plasma theory.

• Research Organization: Oak Ridge National Lab., TN (USA)
• DOE Contract Number: W-7405-ENG-26
• OSTI ID: 5501417
• Report Number(s): ORNL/TM-7075
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700105* -- Fusion Energy-- Plasma Research-- Plasma Kinetics-Theoretical-- (-1987)
BOLTZMANN-VLASOV EQUATION
CYCLOTRON RESONANCE
DIFFERENTIAL EQUATIONS
EIKONAL APPROXIMATION
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
EQUATIONS
MAXWELL EQUATIONS
PHYSICAL PROPERTIES
PLASMA
PLASMA WAVES
RESONANCE
WAVE PROPAGATION