The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton’s equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.
Kaltsas, D. A., et al. "Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria." Physics of Plasmas, vol. 27, no. 1, Jan. 2020. https://doi.org/10.1063/1.5125573
Kaltsas, D. A., Throumoulopoulos, G. N., & Morrison, P. J. (2020). Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria. Physics of Plasmas, 27(1). https://doi.org/10.1063/1.5125573
Kaltsas, D. A., Throumoulopoulos, G. N., and Morrison, P. J., "Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria," Physics of Plasmas 27, no. 1 (2020), https://doi.org/10.1063/1.5125573
@article{osti_1801010,
author = {Kaltsas, D. A. and Throumoulopoulos, G. N. and Morrison, P. J.},
title = {Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria},
annote = {The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton’s equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.},
doi = {10.1063/1.5125573},
url = {https://www.osti.gov/biblio/1801010},
journal = {Physics of Plasmas},
issn = {ISSN 1070-664X},
number = {1},
volume = {27},
place = {United States},
publisher = {American Institute of Physics (AIP)},
year = {2020},
month = {01}}
Morrison, P. J.; Eliasson, Bengt; Shukla, Padma K.
NEW DEVELOPMENTS IN NONLINEAR PLASMA PHYSICS: Proceedings of the 2009 ICTP Summer College on Plasma Physics and International Symposium on Cutting Edge Plasma Physics, AIP Conference Proceedingshttps://doi.org/10.1063/1.3266810
Bernstein, I. B.; Frieman, E. A.; Kruskal, Martin David
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 244, Issue 1236, p. 17-40https://doi.org/10.1098/rspa.1958.0023