Vlasov and Drift Kinetic Simulation Methods Based on the Symplectic Integrator

References

• Arber , T. D. and Vann , R. G. L. 2002 . A critical comparison of eulerian‐grid‐based Vlasov solvers . J. Comput. Phys. , 180 : 339 – 357 .
   Web of Science ®Google Scholar
• Besse , N. and Sonnendrücker , E. 2003 . Semi‐Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space . J. Comput. Phys. , 191 : 341 – 376 .
   Web of Science ®Google Scholar
• Birdsall , C. K. and Langdon , A. B. 1985 . Plasma Physics via Computer Simulation New York : McGraw‐Hill .
   Google Scholar
• Blanes , S. and Moan , P. 2001 . Splitting methods for non‐autonomous Hamiltonian equations . J. Comput. Phys. , 170 : 205 – 230 .
   Web of Science ®Google Scholar
• Canuto , C. , Hussaini , M. Y. , Quarteroni , A. and Zang , T. A. 1988 . Spectral Methods in Fluid Dynamics New York : Springer‐Verlag .
   Google Scholar
• Cheng , C. Z. and Knorr , G. 1976 . The integration of the Vlasov equation in configuration space . J. Comput. Phys. , 22 : 330 – 351 .
   Web of Science ®Google Scholar
• deFrutos , J. and Sanz‐Serna , J. M. 1992 . An easily implementable fourth‐order method for the time integration of wave problems . J. Comput. Phys. , 103 : 160 – 168 .
   Google Scholar
• Dubin , D. H. E. , Krommes , J. A. , Oberman , C. and Lee , W. W. 1983 . Nonlinear gyrokinetic equations . Phys. Fluids , 26 ( 12 ) : 3524 – 3535 .
   Google Scholar
• Fijalkow , E. 1999 . A numerical solution to the Vlasov equation . Comput. Phys. Comm. , 116 : 319 – 328 .
   Web of Science ®Google Scholar
• Filbet , F. and Sonnendrücker , E. 2003 . Comparison of eulerian Vlasov solvers . Comput. Phys. Comm. , 150 : 247 – 266 .
   Web of Science ®Google Scholar
• Filbet , F. , Sonnendrücker , E. and Bertrand , P. 2001 . Conservative numerical schemes for the Vlasov equation . J. Comput. Phys. , 172 : 166 – 187 .
   Web of Science ®Google Scholar
• Forest , E. and Ruth , R. D. 1990 . Fourth‐order symplectic integration . Physica D , 43 : 105 – 117 .
   Web of Science ®Google Scholar
• Ghizzo , A. , Izrar , B. , Bertrand , P. , Fijalkow , E. , Feix , M. R. and Shoucri , M. 1988 . Stability of Bernstein‐Green‐Kruskal plasma equilibria. Numerical experiments over a long time . Phys. Fluids , 31 ( 1 ) : 72 – 82 .
   Google Scholar
• Ghizzo , A. , Bertrand , P. , Shoucri , M. , Fijalkow , E. and Feix , M. R. 1993 . An eulerian code for the study of the drift‐kinetic Vlasov equation . J. Comput. Phys. , 108 : 105 – 121 .
   Web of Science ®Google Scholar
• Izar , B. , Ghizzo , A. , Bertrand , P. , Fijalkow , E. and Feix , M. R. 1989 . Integration of Vlasov equation by a fast fourier eulerian code . Comput. Phys. Comm. , 52 : 375 – 382 .
   Google Scholar
• Klimas , A. J. and Farrell , W. M. 1994 . A splitting algorithm for Vlasov simulation with filamentation filtration . J. Comput. Phys. , 110 : 150 – 163 .
   Web of Science ®Google Scholar
• Lifshitz , E. M. and Pitaevskii , L. P. 1981 . Physical Kinetics New York : Pergamon Press .
   Google Scholar
• Manfredi , G. , Shoucri , M. , Feix , M. R. , Bertrand , P. , Fijalkow , E. and Ghizzo , A. 1995 . The numerical integration of the Vlasov equation possessing an invariant . J. Comput. Phys. , 121 : 298 – 313 .
   Web of Science ®Google Scholar
• Manfredi , G. , Shoucri , M. , Dendy , R. O. , Ghizzo , A. and Bertrand , P. 1996 . Vlasov gyrokinetic simulations of ion‐temperature‐gradient driven instabilities . Phys. Plasmas , 3 ( 1 ) : 202 – 217 .
   Google Scholar
• Mangeney , A. , Califano , F. , Cavazzoni , C. and Travnicek , P. 2002 . A numerical scheme for the integration of the Vlasov‐Maxwell system of equations . J. Comput. Phys. , 179 : 495 – 538 .
   Web of Science ®Google Scholar
• Nakamura , T. and Yabe , T. 1999 . Cubic interpolated propagation scheme for solving the hyper‐dimensional Vlasov‐Poisson equation in phase space . Comput. Phys. Comm. , 120 : 122 – 154 .
   Web of Science ®Google Scholar
• Sanz‐Serna , J. M. 1992 . Symplectic Runge‐Kutta and related methods: Recent Results . Physica D , 60 : 293 – 302 .
   Google Scholar
• Shoucri , M. 2001 . Numerical simulation of plasma edge turbulence due to E×B flow velocity shear . Czech. J. Phys. , 51 : 1139 – 1151 .
   Google Scholar
• Shoucri , M. and Knorr , G. 1976 . Linear instabilities in the quasistatic guiding‐center plasmas . Plasma Phys. , 18 : 187 – 204 .
   Google Scholar
• Shoucri , M. and Gagné , R. 1978 . A Multistep technique for the numerical solution of a two‐dimensional Vlasov equation . J. Comput. Phys. , 27 : 315 – 322 .
   Google Scholar
• Sonnendrücker , E. , Roche , J. , Bertrand , P. and Ghizzo , A. 1999 . The semi‐Lagrangian method for the numerical resolution of the Vlasov equation . J. Comput. Phys. , 149 : 201 – 220 .
   Web of Science ®Google Scholar
• Staniforth , A. and Côté , J. 1991 . Semi‐Lagrangian integration schemes for atmospheric models—A review . Mon. Weather Rev. , 119 : 2206 – 2223 .
   Web of Science ®Google Scholar
• Watanabe , T.‐H. and Sugama , H. 2002 . Kinetic simulation of a quasisteady state in collisionless ion temperature gradient driven turbulence . Phys. Plasmas , 9 : 3659 – 3662 .
   Google Scholar
• Watanabe , T.‐H. , Sugama , H. and Sato , T. 2000 . Nondissipative kinetic simulation and analytical solution of three‐mode equations of the ion temperature gradient instability . Phys. Plasmas , 7 ( 3 ) : 984 – 990 .
   Google Scholar
• Watanabe , T.‐H. , Sugama , H. and Sato , T. 2001 . A nondissipative simulation method for the drift kinetic equation . J. Phys. Soc. Jpn , 70 ( 12 ) : 3565 – 3576 .
   Google Scholar
• Yoshida , H. 1990 . Construction of higher order symplectic integrators . Phys. Lett. , 150 : 262 – 268 .
   Web of Science ®Google Scholar