Noncanonical Hamiltonian mechanics and its application to magnetic field line flow

Cary, John R.; Littlejohn, Robert G.

doi:10.1016/0003-4916(83)90313-5

Cited by 341 publications

(325 citation statements)

References 15 publications

Supporting

Mentioning

323

Contrasting

Order By: Relevance

“…In the usual way in mechanics, the-Hamiltonian H may be derived from L. The result is (4) The theory of phase space Lagrangians is presented in Ref. 8 …”

Section: Relativistic Guiding Center Motionmentioning

confidence: 99%

Relativistic ponderomotive Hamiltonian

Grebogi

Littlejohn

1984

The Physics of Fluids

View full text Add to dashboard Cite

LBL-17877The relativistic ponderomotive hamiltonian is derived under as general conditions as possible. Arbitrary kp, E,,/E..L' w/Q, vic < 1, wave polarization, spatial modulation of the wave, and nonuniformities in the background electric and magnetic fields are introduced in a systematic way. This calculation is a modification of guiding center theory, because in addition to averaging over gyration, there is also an averaging over rapid oscillations of the wave. Therefore, as a by-product of our objective, we derive a new formulation of the relativistic guiding center motion •

show abstract

“…In the usual way in mechanics, the-Hamiltonian H may be derived from L. The result is (4) The theory of phase space Lagrangians is presented in Ref. 8 …”

Section: Relativistic Guiding Center Motionmentioning

confidence: 99%

Relativistic ponderomotive Hamiltonian

Grebogi

Littlejohn

1984

The Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…Linear and nonlinear gyrokinetic equations for particle distribution functions were originally derived by recursive techniques combined with the WKB representation (Hazeltine and Meiss 1992;Rutherford and Frieman 1968;Taylor and Hastie 1968;Antonsen and Lane 1980;Catto et al 1981;Frieman and Chen 1982). Another modern derivation of the gyrokinetic equations based on the Lagrangian and/or Hamiltonian formulations (Cary and Littlejohn 1983;Brizard and Hahm 2007;Dubin et al 1983;Hahm 1988;Brizard 1989) was presented to ensure conservation laws for the phase space volume and the magnetic moment from Liouville's theorem and Noether's theorem (Goldstein et al 2002), respectively. Later, conservation of the total energy and momentum was obtained in the gyrokinetic field theory (Sugama 2000) where all governing equations for the distribution functions and the electromagnetic fields are derived from the Lagrangian which describes the whole system consisting of particles and fields.…”

Section: Introductionmentioning

confidence: 99%

Modern gyrokinetic formulation of collisional and turbulent transport in toroidally rotating plasmas

Sugama

2017

Rev. Mod. Plasma Phys.

View full text Add to dashboard Cite

Collisional and turbulent transport processes in toroidal plasmas with large toroidal flows on the order of the ion thermal velocity are formulated based on the modern gyrokinetic theory. Governing equations for background and turbulent electromagnetic fields and gyrocenter distribution functions are derived from the Lagrangian variational principle with effects of collisions and external sources taken into account. Noether's theorem modified for collisional systems and the collision operator given in terms of Poisson brackets are applied to derivation of the particle, energy, and toroidal momentum balance equations in the conservative forms which are desirable properties for long-time global transport simulation. The resultant balance equations are shown to include the classical, neoclassical, and turbulent transport fluxes which agree with those obtained from the conventional recursive formulations.

show abstract

“…According to Eqs. (18)(19), the consitutive relations defining the auxiliary electric field and auxiliary magnetic field are given by…”

Section: Example: Relativistic Vlasov-maxwell With Spinmentioning

confidence: 99%

Finite-dimensional collisionless kinetic theory

Burby

2017

Physics of Plasmas

View full text Add to dashboard Cite

A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finite-dimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems: the relativistic Vlasov-Maxwell system with spin, and a gyrokinetic Vlasov-Maxwell system.

show abstract

Noncanonical Hamiltonian mechanics and its application to magnetic field line flow

Cited by 341 publications

References 15 publications

Relativistic ponderomotive Hamiltonian

Relativistic ponderomotive Hamiltonian

Modern gyrokinetic formulation of collisional and turbulent transport in toroidally rotating plasmas

Finite-dimensional collisionless kinetic theory

Contact Info

Product

Resources

About