Hopf bifurcation and plasma instabilities

Technical Report · Tue Nov 01 04:00:00 EST 1983

OSTI ID:5371934

Crawford, J D

Center manifold theory and the theory of normal forms are applied to examples of Hopf bifurcation in two models of plasma dynamics. A finite dimensional model of a 3-wave system with quadratic nonlinearities provides a simple example of both supercritical and subcritical Hopf bifurcation. In the second model, the electrostatic instabilities of a collisional plasma correspond to Hopf bifurcations. In this problem, the Vlasov-Poisson equations with a Krook collision term describe the electron dynamics in a weakly ionized gas. The one mode in instability is analyzed in detail; near criticality it always saturates in a small amplitude nonlinear oscillation.

• Research Organization: Lawrence Berkeley Lab., CA (USA)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 5371934
• Report Number(s): LBL-17015; ON: DE84006055
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700107* -- Fusion Energy-- Plasma Research-- Instabilities
BOLTZMANN-VLASOV EQUATION
COLLISIONAL PLASMA
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
EQUATIONS
INSTABILITY
KINETIC EQUATIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
PLASMA INSTABILITY
POISSON EQUATION