Hamiltonian Approach to Nonlinear Travelling Whistler Waves

Details Hamiltonian Approach to Nonlinear Travelling Whistler Waves Hamiltonian Approach to Nonlinear Travelling Whistler Waves

Aug 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005aipc..781..141w&link_type=abstract

THE PHYSICS OF COLLISIONLESS SHOCKS: 4th Annual IGPP International Astrophysics Conference. AIP Conference Proceedings, Volume

Astronomy and Astrophysics

Astrophysics

3

Whistlers, Plasma Nonlinear Waves, Plasma Solitons, Magnetosphere, Electromagnetic Waves, Solitons, Bgk Modes, Two-Fluid And Multi-Fluid Plasmas, Electromagnetic Wave Propagation

Scientific paper

A Hamiltonian formulation of nonlinear, parallel propagating, travelling whistler waves is discussed. The model is based on the equations of two-fluid electron-proton plasmas. In the cold gas limit, the complete system of equations reduces to two coupled differential equations for the transverse electron speed u and a phase variable φ = φp - φe representing the difference in the phases of the transverse complex velocities of the protons and the electrons. Two integrals of the equations are obtained. The Hamiltonian integral H, is used to classify the trajectories in the (φ, w) phase plane, where φ and w = u2 are the canonical coordinates. Periodic, oscilliton solitary wave and compacton solutions are obtained, depending on the value of the Hamiltonian integral H and the Alfvén Mach number M of the travelling wave. The individual electron and proton phase variables φe and φp are determined in terms of φ and w. An alternative Hamiltonian formulation in which φ~ = φp + φe is the new independent variable replacing x is used to write the travelling wave solutions parametrically in terms of φ~.

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