Research References: Kinetic Theory
Vlasov-Poisson and Vlasov-Maxwell
Francis E. Low: A Lagrangian Formulation of the Boltzmann-Vlasov Equation for Plasmas (1958)
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 248, p. 282-287Philip J. Morrison: The Maxwell-Vlasov Equations as a Continuous Hamiltonian System (1980)
Physics Letters A, Vol. 80, p. 383-386Alan Weinstein and Philip J. Morrison: Comments on: The Maxwell-Vlasov Equations as a Continuous Hamiltonian System (1981)
Physics Letters A, Vol. 86, p. 235-236Jerrold E. Marsden and Alan Weinstein: The Hamiltonian Structure of the Maxwell-Vlasov Equations (1982)
Physica D: Nonlinear Phenomena, Vol. 4, p. 394-406Allan N. Kaufman and Robert L. Dewar: Canonical Derivation of the Vlasov-Coulomb Noncanonical Poisson Structure (1983)
Fluids and Plasmas: Geometry and Dynamics, p. 51-54John D. Crawford and Peter D. Hislop: Vlasov Equation on a Symplectic Leaf (1988)
Physics Letters A , Vol. 134, p. 19-24Huanchun Ye, Philip J. Morrison and John D. Crawford: Poisson Bracket for the Vlasov Equation on a Symplectic Leaf (1991)
Physics Letters A, Vol. 156, p. 96-100Huanchun Ye and Philip J. Morrison: Action Principles for the Vlasov Equation (1992)
Physics of Fluids B, Vol. 4, p. 771Jonas Larsson: An action principle for the Vlasov equation and associated Lie perturbation equations. Part 1. The Vlasov-Poisson system (1992)
Journal of Plasma Physics, Vol. 48, p. 13-35Jonas Larsson: An action principle for the Vlasov equation and associated Lie perturbation equations. Part 2. The Vlasov-Maxwell system (1993)
Journal of Plasma Physics, Vol. 49, p. 255-270Tor Flå: Action Principle and the Hamiltonian Formulation for the Maxwell-Vlasov Equations on a Symplectic Leaf (1994)
Physics of Plasmas, Vol. 1, p. 2409Hernán Cendra, Darryl D. Holm, Mark J. W. Hoyle, and Jerrold E. Marsden: The Maxwell-Vlasov Equations in Euler-Poincare Form (1998)
Journal of Mathematical Physics, Vol. 39, p. 3138, arXiv:chao-dyn/9801016
Lie Perturbation Analysis and Guiding Centre Theory
André Deprit: Canonical Transformations Depending on a Small Parameter (1969)
Celestial Mechanics and Dynamical Astronomy, Vol. 1, p. 12-30Ali Hasan Nayfeh: Perturbation Methods, Chapter 5.7, Averaging by Using the Lie Series and Transforms (2000)
Wiley-VCH, ISBN: 978-0-471-39917-9, doi: 10.1002/9783527617609Robert G. Littlejohn: A Guiding Center Hamiltonian - A New Approach (1979)
Journal of Mathematical Physics, Vol. 20, p. 2445Robert G. Littlejohn: Hamiltonian Formulation of Guiding Center Motion (1981)
Physics of Fluids, Vol. 24, p. 1730Robert G. Littlejohn: Hamiltonian Perturbation Theory in Noncanonical Coordinates (1982)
Journal of Mathematical Physics, Vol. 23, p. 742John R. Cary and Allan N. Kaufman: Ponderomotive Effects in Collisionless Plasma - A Lie Transform Approach (1981)
Physics of Fluids, Vol. 24, p. 1238John R. Cary: Lie Transform Perturbation Theory for Hamiltonian Systems (1981)
Physics Reports, Vol. 79, p. 129-159John R. Cary and Robert G. Littlejohn: Noncanonical Hamiltonian Mechanics and its Application to Magnetic Field Line Flow (1983)
Annals of Physics, Vol. 151, p. 1-34Robert G. Littlejohn: Variational Principles of Guiding Centre Motion (1983)
Journal of Plasma Physics, Vol. 29, p. 111-125John R. Cary and Alain J. Brizard: Hamiltonian Theory of Guiding Center Motion (2009)
Reviews of Modern Physics, Vol. 81, p. 693-738, doi: 10.1103/RevModPhys.81.693Naoaki Miyato et al.: A Modification of the Guiding-Centre Fundamental 1-Form with Strong ExB Flow (2009)
Journal of the Physical Society of Japan, Vol. 78, 104501Jens Madsen: Second Order Guiding Center Vlasov-Maxwell Equations (2010)
Physics of Plasmas, Vol. 17, 082107
Gyrokinetic Theory
John A. Krommes: The Gyrokinetic Description of Microturbulence in Magnetized Plasmas (2011)
Annual Review of Fluid Mechanics, Vol. 4, p.: 175-201John A. Krommes: Nonlinear Gyrokinetics: A Powerful Tool for the Description of Microturbulence in Magnetized Plasmas (2010)
Physica Scripta 2010, 014035Alain J. Brizard and Taik Soo Hahm: Foundations of Nonlinear Gyrokinetic Theory (2007)
Reviews of Modern Physics, Vol. 79, p. 421-468Hong Qin: A Short Introduction to General Gyrokinetic Theory (2005)
Topics in Kinetic Theory Vol. 46 p. 171, PPPL Report 4052Hong Qin et al.: Geometric Gyrokinetic Theory for Edge Plasmas (2007)
Physics of Plasmas, Vol. 14, 056110Taik Soo Hahm et al.: Fully Electromagnetic Nonlinear Gyrokinetic Equations for Tokamak Edge Turbulence (2009)
Physics of Plasmas Vol. 16, 022305Bruce D. Scott and Juri Smirnov: Energetic Consistency and Momentum Conservation in the Gyrokinetic Description of Tokamak Plasmas (2010)
Physics of Plasmas, Vol. 17, 112302, arXiv:1008.1244
Gyrokinetic Field Theory
Hideo Sugama: Gyrokinetic Field Theory (2000)
Physics of Plasmas, Vol. 7, p. 466-480, doi: 10.1063/1.873832Hideo Sugama et al.: Extended Gyrokinetic Field Theory for Time-Dependent Magnetic Confinement Fields (2014)
Physics of Plasmas, Vol. 21, 012515, doi: 10.1063/1.4863426Alain J. Brizard: New Variational Principle for the Vlasov-Maxwell Equations (2000)
Physical Review Letters, Vol. 84, p. 5768-5771, doi: 10.1103/PhysRevLett.84.5768Alain J. Brizard: Variational Principle for Nonlinear Gyrokinetic Vlasov-Maxwell Equations (2000)
Physics of Plasmas, Vol. 7, p. 4816, doi: 10.1063/1.1322063Alain J. Brizard: Variational Formulations of Exact and Reduced Vlasov-Maxwell Equations (2005)
Topics in Kinetic Theory Vol. 46 p. 151, arXiv:physics/0409119
Gyrofluid Theory
William Dorland and Greg W. Hammett: Gyrofluid Turbulence Models with Kinetic Effects (1993)
Physics of Fluids B, Vol. 5, p. 812Mike A. Beer and Greg W. Hammett: Toroidal Gyrofluid Equations for Simulations of Tokamak Turbulence (1996)
Physics of Plasmas, Vol. 3, p. 4046Bruce D. Scott: Derivation via Free Energy Conservation Constraints of Gyrofluid Equations with Finite-Gyroradius Electromagnetic Nonlinearities (2010)
Physics of Plasmas, Vol. 17, 102306, arXiv:0710.4899