Longitudinal traveling waves bifurcating from Vlasov plasma equilibria

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:6039047

Holloway, J P

The kinetic equations governing longitudinal motion along a straight magnetic field in a multi-species collisionless plasma are investigated. A necessary condition for the existence of small amplitude spatially periodic equilibria and traveling waves near a given spatially uniform background equilibrium is derived, and the wavelengths which such solutions must approach as their amplitude decreases to zero are discussed. A sufficient condition for the existence of these small amplitude waves is also established. This is accomplished by studying the nonlinear ODE for the potential which arises when the distribution functions are represented in a BGK form; the arbitrary functions of energy that describe the BGK representation are tested as an infinite dimensional set of parameters in a bifurcation theory for the ODE. The positivity and zero current condition in the wave frame of the BGK distribution functions are maintained. The undamped small amplitude nonlinear waves so constructed can be made to satisfy the Vlasov dispersion relation exactly, but in general they need only satisfy it approximately. Numerical calculations reveal that even a thermal equilibrium electron-proton plasma with equal ion and electron temperatures will support undamped traveling waves with phase speeds greater than 1.3 times the electron velocity; the dispersion relation for this case exhibits both Langmuir and ion-acoustic branches as long wavelength limits, and shows how these branches are in fact connected by short wavelength waves of intermediate frequency. In apparent contradiction to the linear theory of Landau, these exact solutions of the kinetic equations do not damp; this contradiction is explained by observing that the linear theory is, in general, fundamentally incapable of describing undamped traveling waves.

• Research Organization: Virginia Univ., Charlottesville, VA (USA)
• OSTI ID: 6039047
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700108* -- Fusion Energy-- Plasma Research-- Wave Phenomena
AMPLITUDES
BOLTZMANN-VLASOV EQUATION
COLLISIONLESS PLASMA
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
DISTRIBUTION FUNCTIONS
ELECTRON TEMPERATURE
EQUATIONS
EQUILIBRIUM
FUNCTIONS
ION TEMPERATURE
KINETIC EQUATIONS
MAGNETIC FIELDS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
TRAVELLING WAVES