References
- Bauer S. and Kunze M. (2005): The Darwin approximation of the relativistic Vlasov-Maxwell system. Annales Henri Poincaré, Vol. 6, No. 2, pp. 283-308.
- Bégué M.L., Ghizzo A. and Bertrand P. (1999): Two-dimensional Vlasov simulation of Raman scattering and plasma beatwave acceleration on parallel computers. Journal of Computational Physics, Vol. 151, No. 2, pp. 458-478.
- Benachour S., Filbet F., Laurençcot P. and Sonnendrücker E. (2003): Global existence for the Vlasov-Darwin system in R3 for small initial data. Mathematical Methods in the Applied Sciences., Vol. 26, No. 4, pp. 297-319.
- Besse N. (2004): Convergence of a semi-Lagrangian scheme for the one-dimensional Vlasov-Poisson system. SIAM Journal on Numerical Analysis, Vol. 42, No. 1, pp. 350-382.
- Besse N. and Mehrenberger M. (2006): Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system. Mathematics of Computation, (in print).
- Besse N. and Sonnendrücker E. (2003): Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space. Journal of Computational Physics, Vol. 191, No. 2, pp. 341-376.
- Borodachev L.V. (2005): Elliptic formulation of discrete Vlasov-Darwin model with the implicit finite-difference representation of particle dynamics. Proceedings of 7-th International School/Symposium for Space Simulations, Kyoto, Japan.
- Califano F., Prandi R., Pegoraro F. and Bulanov S.V. (1998): Nonlinear filamentation instability driven by an inhomogeneous current in a collisionless plasma. Physical Review E, Vol. 58, No. 6, pp. 19-24.
- Cheng C.Z. and Knorr G. (1976): The integration of the Vlasov equation in configuration space. Journal of Computational Physics, Vol. 22, No. 3, pp. 330-351.
- Coppi B., Laval G. and Pellat R. (1996): Dynamics of the geomagnetic tail. Physical Review Letters, Vol. 16, No. 26, pp. 1207-1210.
- Degond P. and Raviart P.-A. (1992): An analysis of Darwin model of approximation to Maxwell's eqautions. Forum Mathematics, Vol. 4, pp. 13-44.
- Fijalkow E. (1999): A numerical solution to the Vlasov equation. Computer Physics Communications, Vol. 116, No. 2, pp. 319-328.
- Filbet F., Sonnendrücker E. and Bertrand P. (2000): Conservative numerical schemes for the Vlasov equation. Journal of Computational Physics, Vol. 172, No. 1, pp. 166-187.
- Gibbons M.R. and Hewett D.W. (1995): The Darwin direct implicit particle-on-cell (DADIPIC) method for simulation of low frequency plasma phenomena. Journal of Computational Physics, Vol. 120, No. 2, pp. 231-247.
- Gibbons M.R. and Hewett D.W. (1997): Characterization of the Darwin direct implicit particle-in-cell method an resulting guidelines for operation. Journal of Computational Physics, Vol. 130, No. 1, pp. 54-66.
- Kulsrud R.M. (1998): Magnetic reconnection in a magnetohydrodynamic plasma. Physics of Plasmas, Vol. 5, No. 5, pp. 1599-1606.
- Lee W.W.L., Startsev E., Hong Q. and Davidson R.C. (2001): Electromagnetic (Darwin) model for threedimensional perturbative particle simulation of high intensity beams. Proceedings of the Particle Accelerator Conference, PACS'2001, Chicago, USA, IEEE Part, Vol. 3, p. 1906.
- Masmoudi N. and Mauser N.J. (2001): The selfconsistent Pauli equation. Monatshefte für Mathematik, Vol. 132, No. 1, pp. 19-24.
- Omelchenko Y.A. and Sudan R.N. (1997): A 3-D Darwin-EM Hybrid PIC code for ion ring studies. Journal of Computational Physics, Vol. 133, No. 1, pp. 146-159.
- Ottaviani M. and Porcelli F. (1993): Nonlinear collisionless magnetic reconnection. Physical Review Letters, Vol. 71, No. 23, pp. 3802-3805.
- Pallard C. (2006): The initial value problem for the relativistic Vlasov-Darwin system. International Mathematics Research Notices, Vol. 2006, Article ID 57191, available at: DOI:100.1155/IMRN/2006/57191.
- Raviart P.-A. and Sonnendrücker E. (1996): A Hierarchy of Approximate Models for the Maxwell Equations. Numerische Mathematik, Vol. 73, No. 3, pp. 329-372.
- Schmitz H. and Grauer R. (2006): Darwin-Vlasov simulations of magnetised plasmas. Journal of Computational Physics, Vol. 214, No. 2, pp. 738-756.
- Sabatier M., Such N., Mineau P., Feix M., Shoucri M., Bertrand P. and Fijalkow E. (1990): Numerical simulations of the Vlasov equation using a flux conservation scheme; comparaison with the cubic spline interpolation code. Technical Report No. 330e, Centre Canadien de Fusion Magnetique, Varennes, Canada.
- Sonnendrücker E., Ambrosiano J.J. and Brandon S.T. (1995): A finite element formulation of the Darwin PIC model for use on unstructured grids. Journal of Computational Physics, Vol. 121, No. 2, pp. 281-297.
- Taguchi T., Antonsen T.M. Jr., Liu C.S. and Mima K. (2001): Structure formation and tearing of an MeV cylindrical electron beam in a laser-produced plasma. Physical Review Letters, Vol. 86, No. 2, pp. 5055-5058.