Hamiltonian theory of guiding centre motion revisited

Weyssow, Boris; Balescu, Radu

doi:10.1017/s0022377800011454

Cited by 31 publications

(39 citation statements)

References 17 publications

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“…Simply put, it provides a means for deforming the single-particle phase space so as to illuminate the approximate symmetry associated to the magnetic moment, the gyrosymmetry, while keeping the Hamiltonian structure of the particle dynamics in focus. However, in spite of its importance and the number of years it has been studied [1][2][3][4][5][6][7][8][9][10][11][12] , there are still poorly understood subtleties in the theory.…”

Section: Introductionmentioning

confidence: 99%

Gyrosymmetry: Global considerations

Burby

Qin

2012

Physics of Plasmas

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In the guiding center theory, smooth unit vectors perpendicular to the magnetic field are required to define the gyrophase. The question of global existence of these vectors is addressed using a general result from the theory of characteristic classes. It is found that there is, in certain cases, an obstruction to global existence. In these cases, the gyrophase cannot be defined globally. The implications of this fact on the basic structure of the guiding center theory are discussed. In particular, it is demonstrated that the guiding center asymptotic expansion of the equations of motion can still be performed in a globally consistent manner when a single global convention for measuring gyrophase is unavailable. The latter fact is demonstrated directly by deriving a new expression for the guiding-center Poincaré-Cartan form exhibiting no dependence on the choice of perpendicular unit vectors.

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Section: Introductionmentioning

confidence: 99%

Gyrosymmetry: Global considerations

Burby

Qin

2012

Physics of Plasmas

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“…The appropriate generalization of GK theory allowing for the presence of strong gravitational fields should in principle be based on a covariant formulation [see [23][24][25][26]]. However, for non-relativistic plasmas within a gravitational field, the appropriate formulation can also be directly recovered via a suitable reformulation of the standard non-relativistic theory holding for magnetically confined plasmas [27][28][29][30][31][32][33][34][35].…”

Section: Basic Assumptions and Definitionsmentioning

confidence: 99%

Kinetic description of quasi-stationary axisymmetric collisionless accretion disk plasmas with arbitrary magnetic field configurations

Cremaschini¹,

Miller²,

Tessarotto³

2011

Physics of Plasmas

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A kinetic treatment is developed for collisionless magnetized plasmas occurring in hightemperature, low-density astrophysical accretion disks, such as are thought to be present in some radiatively-inefficient accretion flows onto black holes. Quasi-stationary configurations are investigated, within the framework of a Vlasov-Maxwell description. The plasma is taken to be axisymmetric and subject to the action of slowly time-varying gravitational and electromagnetic fields. The magnetic field is assumed to be characterized by a family of locally nested but open magnetic surfaces. The slow collisionless dynamics of these plasmas is investigated, yielding a reduced gyrokinetic Vlasov equation for the kinetic distribution function. For doing this, an asymptotic quasi-stationary solution is first determined, represented by a generalized bi-Maxwellian distribution expressed in terms of the relevant adiabatic invariants. The existence of the solution is shown to depend on having suitable kinetic constraints and conditions leading to particle trapping phenomena. With this solution one can treat temperature anisotropy, toroidal and poloidal flow velocities and finite Larmor-radius effects. An asymptotic expansion for the distribution function permits analytic evaluation of all of the relevant fluid fields. Basic theoretical features of the solution and their astrophysical implications are discussed. As an application, the possibility of describing the dynamics of slowly time-varying accretion flows and the self-generation of magnetic field by means of a "kinetic dynamo effect" is discussed. Both effects are shown to be related to intrinsically-kinetic physical mechanisms.

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“…The first term of the right-hand side of equation (6) describes the pitch-angle scattering while the second term describes the slowing down whereby the v 3 term is due to fast-ion-electron interactions while the v 3 c comes from fast-ion-ion interactions. From the collision operator (equation (6)) the slowing-down equation:…”

Section: Slowing-down and Pitch-angle Scatteringmentioning

confidence: 99%