Conductivity Tensor and Dispersion Equation for a Plasma

Journal Article · Mon Jan 01 04:00:00 EST 1962 · Physics of Fluids (New York)

DOI:https://doi.org/10.1063/1.1706512· OSTI ID:4755768

Lewis, Robert M.; Keller, Joseph B.

Periodic plane waves are considered in a plasma pervaded by a uniform magnetic field. The appropriate linearized Boltzmann equations for the distribution functions of the electrons and of each type of ion are solved exactly. Collisions are taken into account by the inclusion of a simplified collision term. The solutions are used to compute the electric current, from which the conductivity tensor of each ionic species is found. The total conductivity is then used in Maxwell's equations to determine the electromagnetic field, and this leads to the dispersion equation for plane waves. This equation is solved in various parameter ranges for the case of longitudinal waves when the conductivity of only one species is taken into account. The solutions of Landau, Gordeyev, Gross, Bernstein, and others are recovered when the collision frequency vanishes. In addition, various power series and asymptotic expansions for the conductivity tensor are given, and it is shown to reduce to that of the magneto- ionic theory under suitable conditions. The Appendix contains a systematic study of a function which plays a central role in the theory.

• Research Organization: New York Univ., New York
• Sponsoring Organization: USDOE
• NSA Number: NSA-17-005470
• OSTI ID: 4755768
• Journal Information: Physics of Fluids (New York), Journal Name: Physics of Fluids (New York) Journal Issue: 10 Vol. 5; ISSN 0031-9171
• Publisher: American Institute of Physics
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BOLTZMANN EQUATION
CURRENTS
DIFFERENTIAL EQUATIONS
DISPERSION THEORY
DISTRIBUTION
ELECTRIC CONDUCTIVITY
ELECTRODYNAMICS
ELECTROMAGNETIC FIELDS
ELECTROMAGNETIC WAVES
ELECTRONS
EQUATIONS
FREQUENCY
HOMOGENEOUS REACTORS
INTERACTIONS
IONS
MAGNETIC FIELDS
MATHEMATICS
MAXWELL EQUATIONS
PHYSICS
PLASMA
STATISTICS
TENSORS
VECTORS