Relativistic Non-linear Theory of Plasma Oscillations

Journal Article · Sun Jul 01 04:00:00 EDT 1962 · Journal of Electronics and Control

DOI:https://doi.org/10.1080/00207216208937416· OSTI ID:4772968

GOLD, LOUIS

Nonlinear theory of plasma oscillations is extended into the threshold relativistic region where radiation damping can be neglected. A general characterization of the stationary oscillatory modes is performed in terms of a phase-space analysis with a comparison of the nonrelativistic behavior. Two procedures are offered for delineation of the ampiitude-dependent frequency of the fundamental vibration. One of these is readily adopted to the zero-current limit, allowing a development already featured for the relativistic harmonic oscillator. Thus regimes requiring relativistic classical or quantum mechanical treatment are identified. In general, very-highdensity plasmas require classical relativistic treatment, although tenuous astrophysical plasmas, where extremely large amplitudes of ion-electron motion can be accommodated, also may be included. The relativistic quantum analysis enters when the plasmon energy approaches the rest of the mass energy of the vibrating charge. A critique of studies of nonlinear plasma oscillations is set forth, and a method for solution of a related class of nonlinear differential equations is presented.

• Research Organization: Univ. of Michigan, Ann Arbor
• Sponsoring Organization: USDOE
• NSA Number: NSA-17-004189
• OSTI ID: 4772968
• Journal Information: Journal of Electronics and Control, Journal Name: Journal of Electronics and Control Journal Issue: 1 Vol. 13; ISSN 0368-1947
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ASTROPHYSICS
CHARGED PARTICLES
CURRENTS
DENSITY
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC WAVES
ELECTRONS
ENERGY
FREQUENCY
IONS
LOSSES
MASS
MATHEMATICS
MECHANICS
MOTION
OSCILLATIONS
PLASMA
QUANTUM MECHANICS
RELATIVITY THEORY