Integrable, oblique travelling waves in quasi-charge-neutral two-fluid plasmas

Webb, G. M.; Ko, C. M.; Mace, R. L.; McKenzie, J. F.; Zank, G. P.

doi:10.5194/npg-15-179-2008

Cited by 7 publications

(8 citation statements)

References 28 publications

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“…Example of oblique travelling wave solutions for whistler oscillitons in which the electron momentum can be of the same order as that of the protons is described in Webb et al (2008). However, the further consideration of such higher frequency effects is out of the scope of this review, and is not addressed in the following discussion.…”

Section: Classification and Signatures Of Periodic Snwsmentioning

confidence: 99%

Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas

Дубинов

Kolotkov

2018

Rev. Mod. Plasma Phys.

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The review summarises recent theoretical achievements and observational manifestations of a new, recently discovered type of nonlinear oscillations in multi-component plasmas, namely super-nonlinear periodic waves and super-nonlinear solitary waves (supersolitons). Both are characterised by a non-trivial topology of their phase portraits, highly anharmonic profile shapes, extremely long periods, and large amplitudes. Based upon multi-fluid magnetohydrodynamic plasma models, examples of ion-acoustic and Alfvén super-nonlinear waves are considered. A multi-component nature of the plasma was revealed to be a crucial condition for the existence of these super-nonlinear waves, with the complexity of the system growing with the number of plasma species accounted for in the model. A minimum number of plasma components which allow for the existence of supernonlinear waves are also discussed. From the observational point of view, typical signatures of periodic super-nonlinear waves are manifested, for example, in the oscillatory processes operating in the magnetised plasma of the solar corona and ground-based plasma machines. Super-nonlinear solitary structures (supersolitons) of an electrostatic origin are recognised in the Earth's magnetosphere, laboratory experiments with chemically active plasmas, and numerical simulations.

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Section: Classification and Signatures Of Periodic Snwsmentioning

confidence: 99%

Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas

Дубинов

Kolotkov

2018

Rev. Mod. Plasma Phys.

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“…This is useful in the formulation of travelling wave problems, where two distinct Hamiltonian formulations of the equations are possible with, distinct Hamiltonians (e.g. Bridges (1992), Webb et al ( , 2007Webb et al ( , 2008Webb et al ( , 2014d). For systems in one Cartesian space variable x and one time variable t, both x and t can be regarded as the evolution variable.…”

Section: Introductionmentioning

confidence: 99%

Multi-symplectic, Lagrangian, one-dimensional gas dynamics

Webb

2015

Journal of Mathematical Physics

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The equations of Lagrangian, ideal, one-dimensional (1D), compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate m and time t as independent variables, and in which the Eulerian position of the fluid element x = x(m, t) is one of the dependent variables. This approach differs from the Eulerian, multi-symplectic approach using Clebsch variables. Lagrangian constraints are used to specify equations for x m , x t and S t consistent with the Lagrangian map, where S is the entropy of the gas. We require S t = 0 corresponding to advection of

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“…Multi-symplectic Hamiltonian systems have been studied by Marsden and Shkoller (1999) and Bridges et al (2005). Webb et al (2007); Webb et al (2008Webb et al ( , 2014d discuss travelling waves in multi-fluid plasmas using a multi-symplectic formulation analogous to Bridges (1992) paper on travelling water waves. Holm et al (1998) give an overview of Hamiltonian systems, semi-direct product Lie algebras and Euler-Poincaré equations.…”

Section: Introductionmentioning

confidence: 99%

Multi-symplectic magnetohydrodynamics

2014

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A multi-symplectic formulation of ideal magnetohydrodynamics (MHD) is developed based on a Clebsch variable variational principle in which the Lagrangian consists of the kinetic minus the potential energy of the MHD fluid modified by constraints using Lagrange multipliers, that ensure mass conservation, entropy advection with the flow, the Lin constraint and Faraday's equation (i.e the magnetic flux is Lie dragged with the flow). The analysis is also carried out using the magnetic vector potentialÃ where α =Ã·dx is Lie dragged with the flow, and B = ∇ ×Ã. The multi-symplectic conservation laws give rise to the Eulerian momentum and energy conservation laws. The symplecticity or structural conservation laws for the multi-symplectic system corresponds to the conservation of phase space. It corresponds to taking derivatives of the momentum and energy conservation laws and combining them to produce n(n − 1)/2 extra conservation laws, where n is the number of independent variables. Noether's theorem for the multi-symplectic MHD system is derived, including the case of non-Cartesian space coordinates, where the metric plays a role in the equations.

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Integrable, oblique travelling waves in quasi-charge-neutral two-fluid plasmas

Cited by 7 publications

References 28 publications

Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas

Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas

Multi-symplectic, Lagrangian, one-dimensional gas dynamics

Multi-symplectic magnetohydrodynamics

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