Damping models in the truncated derivative nonlinear Schroedinger equation

Journal Article · Wed Aug 15 04:00:00 EDT 2007 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.2768513· OSTI ID:21072615

Sanchez-Arriaga, G; Sanmartin, J R; Elaskar, S A ^[1]

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1. Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Madrid (Spain)

Four-dimensional flow in the phase space of three amplitudes of circularly polarized Alfven waves and one relative phase, resulting from a resonant three-wave truncation of the derivative nonlinear Schroedinger equation, has been analyzed; wave 1 is linearly unstable with growth rate {gamma}, and waves 2 and 3 are stable with damping {gamma}{sub 2} and {gamma}{sub 3}, respectively. The dependence of gross dynamical features on the damping model (as characterized by the relation between damping and wave-vector ratios, {gamma}{sub 2}/{gamma}{sub 3}, k{sub 2}/k{sub 3}), and the polarization of the waves, is discussed; two damping models, Landau ({gamma}{proportional_to}k) and resistive ({gamma}{proportional_to}k{sup 2}), are studied in depth. Very complex dynamics, such as multiple blue sky catastrophes and chaotic attractors arising from Feigenbaum sequences, and explosive bifurcations involving Intermittency-I chaos, are shown to be associated with the existence and loss of stability of certain fixed point P of the flow. Independently of the damping model, P may only exist for {gamma}<2({gamma}{sub 2}+{gamma}{sub 3})/3, as against flow contraction just requiring {gamma}<{gamma}{sub 2}+{gamma}{sub 3}. In the case of right-hand (RH) polarization, point P may exist for all models other than Landau damping; for the resistive model, P may exist for RH polarization only if {gamma}<({gamma}{sub 2}+{gamma}{sub 3})/2.

• OSTI ID: 21072615
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 8 Vol. 14; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ALFVEN WAVES
AMPLITUDES
ATTRACTORS
BIFURCATION
CHAOS THEORY
FOUR-DIMENSIONAL CALCULATIONS
LANDAU DAMPING
NONLINEAR PROBLEMS
PHASE SPACE
PLASMA
PLASMA WAVES
POLARIZATION
SCHROEDINGER EQUATION
STABILITY
VECTORS