Abstract
Linear stability of equilibrium states with flow is studied by means of the variational principle in Hall magnetohydrodynamics (MHD). The Lagrangian representation of the linearized Hall MHD equation is performed by considering special perturbations that preserves some constants of motion (the Casimir invariants). The resultant equation has a Hamiltonian structure which enables the variational principle. There is however some difficulties in showing the positive definiteness of the quadratic form in the presence of flow. The dynamically accessible variation is a more restricted class of perturbations which, by definition, preserves all the Casimir invariants. For such variations, the quadratic form (the second variation of Hamiltonian) can be positive definite. Some conditions for stability are derived by applying this variational principle to the double Beltrami equilibrium.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
