We elucidate the intermediate of the macroscopic fluid model and the microscopic kinetic model by studying the Poisson algebraic structure of the one-dimensional Vlasov–Poisson system. The water-bag model helps formulating the hierarchy of sub-algebras, which interpolates the gap between the fluid and kinetic models. By analyzing the embedding of the sub-manifold of an intermediate hierarchy in a more microscopic hierarchy, we characterize the microscopic effect as the symmetry breaking pertinent to a macroscopic invariant.
References
1.
E.
Tassi
, “Hamiltonian closures in fluid models for plasmas
,” Eur. Phys. J. D
71
, 269
(2017
).2.
M.
Perin
, C.
Chandre
, P.
Morrison
, and E.
Tassi
, “Higher-order Hamiltonian fluid reduction of Vlasov equation
,” Ann. Phys.
348
, 50
–63
(2014
).3.
M.
Perin
, C.
Chandre
, P.
Morrison
, and E.
Tassi
, “Hamiltonian closures for fluid models with four moments by dimensional analysis
,” J. Phys. A: Math. Theor.
48
, 275501
(2015
).4.
C.
Chandre
, L.
De Guillebon
, A.
Back
, E.
Tassi
, and P. J.
Morrison
, “On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets
,” J. Phys. A: Math. Theor.
46
, 125203
(2013
).5.
P. J.
Morrison
, “The Maxwell–Vlasov equations as a continuous Hamiltonian system
,” Phys. Lett. A
80
, 383
–386
(1980
).6.
J.
Marsden
and A.
Weinstein
, “Reduction of symplectic manifolds with symmetry
,” Rep. Math. Phys.
5
, 121
–130
(1974
).7.
P. J.
Morrison
, “Hamiltonian description of the ideal fluid
,” Rev. Mod. Phys.
70
, 467
(1998
).8.
P. J.
Morrison
, “Poisson brackets for fluids and plasmas
,” in AIP Conference Proceedings
(American Institute of Physics
, 1982
), Vol. 88
, pp. 13
–46
.9.
Z.
Yoshida
, “Self-organization by topological constraints: Hierarchy of foliated phase space
,” Adv. Phys.: X
1
, 2
–19
(2016
).10.
Z.
Yoshida
and P. J.
Morrison
, “The kinetic origin of the fluid helicity—A symmetry in the kinetic phase space
,” J. Math. Phys.
63
, 023101
(2022
).11.
K.
Tanehashi
and Z.
Yoshida
, “Gauge symmetries and Noether charges in Clebsch-parameterized magnetohydrodynamics
,” J. Phys. A: Math. Theor.
48
, 495501
(2015
).12.
P.
Bertrand
and M.
Feix
, “Non linear electron plasma oscillation: The ‘water bag model’
,” Phys. Lett. A
28
, 68
–69
(1968
).13.
M.
Perin
, C.
Chandre
, and E.
Tassi
, “Hamiltonian fluid reductions of drift-kinetic equations and the link with water-bags
,” J. Phys. A: Math. Theor.
49
, 305501
(2016
).14.
M.
Perin
, C.
Chandre
, P.
Morrison
, and E.
Tassi
, “Hamiltonian fluid closures of the Vlasov–Ampère equations: From water-bags to N moment models
,” Phys. Plasmas
22
, 092309
(2015
).15.
J.
Tennyson
, J.
Meiss
, and P.
Morrison
, “Self-consistent chaos in the beam-plasma instability
,” Phys. D: Nonlinear Phenom.
71
, 1
–17
(1994
).16.
H.
Sato
, T.-H.
Watanabe
, and S.
Maeyama
, “Contour dynamics for one-dimensional Vlasov–Poisson plasma with the periodic boundary
,” J. Comput. Phys.
445
, 110626
(2021
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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