CENTER-MANIFOLD THEORY FOR LOW-FREQUENCY EXCITATIONS IN MAGNETIZED PLASMAS

For the dissipative trapped-ion mode, a simple one-dimensional nonline ar model equation, including the effects of instability, dissipation, and dispersion, is investigated. The center-manifold theory is applied to the situation of more than one marginally stable mode, and the dyn amics in the neighborhood of the onset of instability is elucidated. D epending on the (three) relevant parameters, stable solitary waves, mi xed modes, heteroclinic orbits, etc., can exist; a scenario for the no nlinear dynamical behavior is developed. The bifurcation diagrams are drawn with quantitative predictions in parameter space. An important c onclusion is that the codimension-two analysis utilized can predict su ccessive bifurcations which cannot be captured by simple analysis of o ne unstable mode. The analytical calculations are checked by numerical simulations.