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An exponential integrator for a highly oscillatory vlasov equation
Application of Lie transform techniques for simulation of a charged particle beam
| 1. | Inria Nancy-Grand Est, CALVI Project, & IRMA (UMR CNRS 7501), Université de Strasbourg, 7, rue René-Descartes, 67084, Strasbourg, France |
References:
| [1] |
J. A. Brizard, Nonlinear gyrokinetic Vlasov equation for toroidally rotating axisymmetric tokamaks, Physics of Plasmas, 2 (1995), 459-471.
doi: 10.1063/1.871465. |
| [2] |
N. Crouseilles, M. Lemou and F. Méhats, Asymptotic preserving schemes for highly oscillatory kinetic equations, J. Comp. Phys., 248 (2013), 287-308.
doi: 10.1016/j.jcp.2013.04.022. |
| [3] |
D. H. E. Dubin, J. A. Krommes, C. Oberman and W. W. Lee, Nonlinear gyrokinetic equations, Physics of Fluids, 26 (1983), 3524-3535.
doi: 10.1063/1.864113. |
| [4] |
F. Filbet and E. Sonnendrücker, Modeling and numerical simulation of space charge dominated beams in the paraxial approximation, Mathematical Models and Methods in Applied Sciences, 16 (2006), 763-791.
doi: 10.1142/S0218202506001340. |
| [5] |
E. Frénod, F. Salvarani and E. Sonnendrücker, Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method, Mathematical Models and Methods in Applied Sciences, 19 (2009), 175-197.
doi: 10.1142/S0218202509003395. |
| [6] |
E. Frénod and E. Sonnendrücker, The finite larmor radius approximation, SIAM J. Math. Anal., 32 (2001), 1227-1247.
doi: 10.1137/S0036141099364243. |
| [7] |
E. A. Frieman and L. Chen, Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria, Physics of Fluids, 25 (1982), 502-508.
doi: 10.1063/1.863762. |
| [8] |
T. S. Hahm, Nonlinear gyrokinetic equations for tokamak microturbulence, Physics of Fluids, 31 (1988), 2670-2673.
doi: 10.1063/1.866544. |
| [9] |
T. S. Hahm, W. W. Lee and A. Brizard, Nonlinear gyrokinetic theory for finite-beta plasmas, Physics of Fluids, 31 (1988), 1940-1948.
doi: 10.1063/1.866641. |
| [10] |
R. G. Littlejohn, A guiding center Hamiltonian: A new approach, Journal of Mathematical Physics, 20 (1979), 2445-2458.
doi: 10.1063/1.524053. |
| [11] |
R. G. Littlejohn, Hamiltonian formulation of guiding center motion, Physics of Fluids, 24 (1981), 1730-1749.
doi: 10.1063/1.863594. |
| [12] |
R. G. Littlejohn, Hamiltonian perturbation theory in noncanonical coordinates, Journal of Mathematical Physics, 23 (1982), 742-747.
doi: 10.1063/1.525429. |
| [13] |
J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, Springer, 1999.
doi: 10.1007/978-0-387-21792-5. |
| [14] |
K. R. Meyer and G. R. Hall, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Applied Mathematical Sciences, 90, Springer-Verlag, New York, 1992.
doi: 10.1007/978-1-4757-4073-8. |
| [15] |
P. J. Olver, Applications of Lie Groups to Differential Equations, Second edition, Graduate Texts in Mathematics, 107, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4350-2. |
| [16] |
F. I. Parra and P. J. Catto, Limitations of gyrokinetics on transport time scales, Plasma Physics and Controlled Fusion, 50 (2008), 065014.
doi: 10.1088/0741-3335/50/6/065014. |
| [17] |
F. I. Parra and P. J. Catto, Gyrokinetic equivalence, Plasma Physics and Controlled Fusion, 51 (2009), 065002.
doi: 10.1088/0741-3335/51/6/065002. |
| [18] |
F. I. Parra and P. J. Catto, Turbulent transport of toroidal angular momentum in low flow gyrokinetics, Plasma Physics and Controlled Fusion, 52 (2010), 045004.
doi: 10.1088/0741-3335/52/4/045004. |
| [19] |
H. Qin, R. H. Cohen, W. M. Nevins and X. Q. Xu, General gyrokinetic equations for edge plasmas, Contributions to Plasma Physics, 46 (2006), 477-489.
doi: 10.1002/ctpp.200610034. |
show all references
References:
| [1] |
J. A. Brizard, Nonlinear gyrokinetic Vlasov equation for toroidally rotating axisymmetric tokamaks, Physics of Plasmas, 2 (1995), 459-471.
doi: 10.1063/1.871465. |
| [2] |
N. Crouseilles, M. Lemou and F. Méhats, Asymptotic preserving schemes for highly oscillatory kinetic equations, J. Comp. Phys., 248 (2013), 287-308.
doi: 10.1016/j.jcp.2013.04.022. |
| [3] |
D. H. E. Dubin, J. A. Krommes, C. Oberman and W. W. Lee, Nonlinear gyrokinetic equations, Physics of Fluids, 26 (1983), 3524-3535.
doi: 10.1063/1.864113. |
| [4] |
F. Filbet and E. Sonnendrücker, Modeling and numerical simulation of space charge dominated beams in the paraxial approximation, Mathematical Models and Methods in Applied Sciences, 16 (2006), 763-791.
doi: 10.1142/S0218202506001340. |
| [5] |
E. Frénod, F. Salvarani and E. Sonnendrücker, Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method, Mathematical Models and Methods in Applied Sciences, 19 (2009), 175-197.
doi: 10.1142/S0218202509003395. |
| [6] |
E. Frénod and E. Sonnendrücker, The finite larmor radius approximation, SIAM J. Math. Anal., 32 (2001), 1227-1247.
doi: 10.1137/S0036141099364243. |
| [7] |
E. A. Frieman and L. Chen, Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria, Physics of Fluids, 25 (1982), 502-508.
doi: 10.1063/1.863762. |
| [8] |
T. S. Hahm, Nonlinear gyrokinetic equations for tokamak microturbulence, Physics of Fluids, 31 (1988), 2670-2673.
doi: 10.1063/1.866544. |
| [9] |
T. S. Hahm, W. W. Lee and A. Brizard, Nonlinear gyrokinetic theory for finite-beta plasmas, Physics of Fluids, 31 (1988), 1940-1948.
doi: 10.1063/1.866641. |
| [10] |
R. G. Littlejohn, A guiding center Hamiltonian: A new approach, Journal of Mathematical Physics, 20 (1979), 2445-2458.
doi: 10.1063/1.524053. |
| [11] |
R. G. Littlejohn, Hamiltonian formulation of guiding center motion, Physics of Fluids, 24 (1981), 1730-1749.
doi: 10.1063/1.863594. |
| [12] |
R. G. Littlejohn, Hamiltonian perturbation theory in noncanonical coordinates, Journal of Mathematical Physics, 23 (1982), 742-747.
doi: 10.1063/1.525429. |
| [13] |
J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, Springer, 1999.
doi: 10.1007/978-0-387-21792-5. |
| [14] |
K. R. Meyer and G. R. Hall, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Applied Mathematical Sciences, 90, Springer-Verlag, New York, 1992.
doi: 10.1007/978-1-4757-4073-8. |
| [15] |
P. J. Olver, Applications of Lie Groups to Differential Equations, Second edition, Graduate Texts in Mathematics, 107, Springer-Verlag, New York, 1993.
doi: 10.1007/978-1-4612-4350-2. |
| [16] |
F. I. Parra and P. J. Catto, Limitations of gyrokinetics on transport time scales, Plasma Physics and Controlled Fusion, 50 (2008), 065014.
doi: 10.1088/0741-3335/50/6/065014. |
| [17] |
F. I. Parra and P. J. Catto, Gyrokinetic equivalence, Plasma Physics and Controlled Fusion, 51 (2009), 065002.
doi: 10.1088/0741-3335/51/6/065002. |
| [18] |
F. I. Parra and P. J. Catto, Turbulent transport of toroidal angular momentum in low flow gyrokinetics, Plasma Physics and Controlled Fusion, 52 (2010), 045004.
doi: 10.1088/0741-3335/52/4/045004. |
| [19] |
H. Qin, R. H. Cohen, W. M. Nevins and X. Q. Xu, General gyrokinetic equations for edge plasmas, Contributions to Plasma Physics, 46 (2006), 477-489.
doi: 10.1002/ctpp.200610034. |
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