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Nonlinear Hall MHD and electrostatic ion–cyclotron stationary waves: a Hamiltonian-geometric viewpoint

Published online by Cambridge University Press:  01 October 2007

J. F. McKENZIE ,
R. L. MACE  and
T. B. DOYLE
J. F. McKENZIE
Affiliation:
School of Physics, University of KwaZulu-Natal, Westville Campus, University Road, Westville, Private Bag x 54001, Durban 4000, South Africa (macer@ukzn.ac.za) Senior Member of King's College, Cambridge CB2 IST, UK
R. L. MACE
Affiliation:
School of Physics, University of KwaZulu-Natal, Westville Campus, University Road, Westville, Private Bag x 54001, Durban 4000, South Africa (macer@ukzn.ac.za)
T. B. DOYLE
Affiliation:
School of Physics, University of KwaZulu-Natal, Westville Campus, University Road, Westville, Private Bag x 54001, Durban 4000, South Africa (macer@ukzn.ac.za)
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Abstract

Some supplementary results and interpretations on the theory of Hall MHD solitons (McKenzie and Doyle 2002 Phys. Plasmas9, 55) are presented. It is shown that the Hall MHD soliton reduces, in the appropriate limit, to an electrostatic ion–cyclotron soliton. It is also shown how the dynamical equations governing the Hall MHD soliton can be obtained from a Hamiltonian H. Soliton solutions correspond to H = 0, periodic solutions to H < 0 and rotation-type solutions to H >0. Possible applications are discussed. A non-canonical Hamiltonian picture is developed and compared to the well-known example of a free rigid body.

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Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 5 , October 2007 , pp. 687 - 700
Copyright
Copyright © Cambridge University Press 2007

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