Structure of intermediate shocks in collisionless anisotropic Hall-magnetohydrodynamics plasma models

Sánchez‐Arriaga, G.

doi:10.1063/1.4824001

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“…After assuming the travelling wave ansatz, the system of partial differential equations becomes a set of ordinary differential equations that can be used to investigate the existence of solitary waves and discontinuities. This technique has been used to study the structure of intermediate shock waves in the resistive-magnetohydrodynamics (MHD) [17], the resistive Hall-MHD [18], and Hall-MHD with a double-adiabatic pressure tensor [19] systems, and also rotational discontinuities in the Hall-MHD model with finite-Larmor-radius (FLR) and scalar pressure [20].…”

Section: Introductionmentioning

confidence: 99%

“…Such organization, which was briefly suggested in Ref. [19], lies on well-known results for homoclinic orbits in reversible systems [24]. Section III introduces a numerical procedure that proves rigorously the existence of solitary waves and uses it to compute them in several parametric regimes.…”

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confidence: 99%

“…The parameters used for panels (a) and (b) [(c) and (d)] correspond to case 1 (2) inTable I. The green dotted lines in panels (a) and (c) are the velocities making p 1 = 0 in Eq (19)…”

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Structure and evolution of magnetohydrodynamic solitary waves with Hall and finite Larmor radius effects

et al. 2019

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Nonlinear and low-frequency solitary waves are investigated in the framework of the onedimensional Hall-magnetohydrodynamic model with finite Larmor effects and a double adiabatic model for plasma pressures. The organization of these localized structures in terms of the propagation angle with respect to the ambient magnetic field θ and the propagation velocity C is discussed. There are three types of regions in the θ −C plane that correspond to domains where either solitary waves cannot exist, are organized in branches, or have a continuous spectrum. A numerical method valid for the two latter cases, that rigorously proves the existence of the waves, is presented and used to locate many waves, including bright and dark structures. Some of them belong to parametric domains where solitary waves were not found in previous works. The stability of the structures has been investigated by first performing a linear analysis of the background plasma state and second by means of numerical simulations. They show that the cores of some waves can be robust but, for the parameters considered in the analysis, the tails are unstable. The substitution of the double adiabatic model by evolution equations for the plasma pressures appears to suppress the instability in some cases and to allow the propagation of the solitary waves during long times.Exact solitary waves solutions in the Hall-MHD model for cold [21] and warm plasmas with scalar [22] and double-adiabatic pressure models [12] have been also found.In the case of the Hall-MHD model with a double adiabatic pressure tensor, the traveling wave ansatz leads to a pair of coupled ordinary differential equations that governs the normalized components of the magnetic field normal to the propagation direction, named b y and b z . Such a system has a hamiltonian structure and is reversible, i.e. solutions are invariant under the transformation (ζ, b y , b z → −ζ, −b y , b z ), with ζ the independent variable. Adding FLR effects does not change the reversible character of the dynamical system but it increases the effective dimension from two to four [23]. Numerical evidence about the existence of solitary waves in the parametric domain where the upstream state is a saddle-center was also given [23]. The hamiltonian character of the dynamical system with FLR effects is an open and interesting topic, especially because an energy conservation theorem is not known for the Hall-MHD model with double adiabatic pressure and without FLR effects.This work investigates the existence and stability of solitary waves in the FLR-Hall-MHD model with double adiabatic pressure tensor. Section II follows Ref.[23] closely, and presents in a concise way the procedure to find the dynamical system that governs the solitary waves. The details of the method are given in Appendix A, where few discrepancies with the results of Ref.[23] are highlighted. Section II also discusses the main properties of the dynamical system and takes advantage of some geometrical arguments related with the dimension, reversible ...

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