Hamiltonian formalism of extended magnetohydrodynamics

被引：48

作者：

Abdelhamid, H. M. ^{[1
,2
]}

Kawazura, Y. ^{[1
]}

Yoshida, Z. ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Frontier Sci, Kashiwa, Chiba 2778561, Japan

[2] Mansoura Univ, Fac Sci, Dept Phys, Mansoura 35516, Egypt

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2015年 / 48卷 / 23期

关键词：

extended magnetohydrodynamics; Hamiltonian dynamics; Jacobi's identity; HALL-MAGNETOHYDRODYNAMICS; WHISTLER OSCILLITONS; PLASMAS; WAVES; FORMULATION; CONSTANTS; MOTION; FLUID;

D O I：

10.1088/1751-8113/48/23/235502

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The extended magnetohydrodynamics (MHD) system, including the Hall effect and the electron inertia effect, has a Hamiltonian structure embodied by a noncanonical Poisson algebra on an infinite-dimensional phase space. A nontrivial part of the formulation is the proof of Jacobi's identity for the Poisson bracket. We unearth a basic Lie algebra that generates the Poisson bracket. A class of similar Poisson algebra may be generated by the same Lie algebra, which encompasses the Hall MHD system and inertial MHD system.

引用

页数：19

共 28 条

[11] THE HAMILTONIAN-STRUCTURE OF THE MAXWELL-VLASOV EQUATIONS [J].

MARSDEN, JE ;

WEINSTEIN, A .

PHYSICA D, 1982, 4 (03) :394-406

[12] SEMIDIRECT PRODUCTS AND REDUCTION IN MECHANICS [J].

MARSDEN, JE ;

RATIU, T ;

WEINSTEIN, A .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 281 (01) :147-177

[13] The application of the constants of motion to nonlinear stationary waves in complex plasmas: a unified fluid dynamic viewpoint [J].

McKenzie, JF ;

Dubinin, E ;

Sauer, K ;

Doyle, TB .

JOURNAL OF PLASMA PHYSICS, 2004, 70 :431-462

[14]

Morrison P J, 1982, PHYS REV LETT, V48, P7596

[15] NON-CANONICAL HAMILTONIAN DENSITY FORMULATION OF HYDRODYNAMICS AND IDEAL MAGNETOHYDRODYNAMICS [J].

MORRISON, PJ ;

GREENE, JM .

PHYSICAL REVIEW LETTERS, 1980, 45 (10) :790-794

[16]

MORRISON PJ, 1982, AIP CONF PROC, P13

[17] Hamiltonian description of the ideal fluid [J].

Morrison, PJ .

REVIEWS OF MODERN PHYSICS, 1998, 70 (02) :467-521

[18] Hamiltonian canonical formulation of Hall-magnetohydrodynamics: Toward an application to weak turbulence theory [J].

Sahraoui, F ;

Belmont, G ;

Rezeau, L .

PHYSICS OF PLASMAS, 2003, 10 (05) :1325-1337

[19] Wave emission by whistler oscillitons: Application to "coherent lion roars" [J].

Sauer, K ;

Dubinin, E ;

McKenzie, JF .

GEOPHYSICAL RESEARCH LETTERS, 2002, 29 (24)

[20] GENERALIZED 2-FLUID THEORY OF NONLINEAR MAGNETIC-STRUCTURES [J].

SCHEP, TJ ;

PEGORARO, F ;

KUVSHINOV, BN .

PHYSICS OF PLASMAS, 1994, 1 (09) :2843-2852

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