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

Journal Article · Tue Jul 01 04:00:00 EDT 1980 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.863150· OSTI ID:5207257

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 p/eapprox.vertical-bar..cap omega../sub e/vertical-bar, 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 functions, and slowly varying amplitude that is valid at cyclotron resonance. It is assumed that ..omega../sub p/eapprox.vertical-bar..cap omega../sub e/vertical-barapprox...omega.. are large, that ..omega..approx. =vertical-bar..cap omega../sub e/vertical-bar, 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. A Poynting theorem that can be put into the standard form is obtained by taking the expansion to first order. Care must be taken, however, to include finite temperature effects in calculating the zero-order electric field. The theory is also applied to ion cyclotron resonance.

• Research Organization: New York University, New York, New York 10012
• DOE Contract Number: W-7405-ENG-26; EY-76-C-02-3077
• OSTI ID: 5207257
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 23:7; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700108* -- Fusion Energy-- Plasma Research-- Wave Phenomena
BOLTZMANN-VLASOV EQUATION
COLD PLASMA
CYCLOTRON RESONANCE
DIFFERENTIAL EQUATIONS
EIKONAL APPROXIMATION
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
ELECTROMAGNETIC RADIATION
EQUATIONS
HEATING
INHOMOGENEOUS PLASMA
MAXWELL EQUATIONS
PHYSICAL PROPERTIES
PLASMA
PLASMA HEATING
PLASMA WAVES
POYNTING THEOREM
RADIATIONS
RESONANCE
TENSORS
WAVE PROPAGATION