Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena

Bauer S. and Kunze M. (2005): The Darwin approximation of the relativistic Vlasov-Maxwell system. Annales Henri Poincaré, Vol. 6, No. 2, pp. 283-308.10.1007/s00023-005-0207-ySearch in Google Scholar

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. 458-478.10.1006/jcph.1999.6193Search in Google Scholar

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. 297-319.10.1002/mma.355Search in Google Scholar

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. 350-382.10.1137/S0036142902410775Search in Google Scholar

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).Search in Google Scholar

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. 341-376.10.1016/S0021-9991(03)00318-8Search in Google Scholar

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.Search in Google Scholar

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. 19-24.10.1103/PhysRevE.58.7837Search in Google Scholar

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. 330-351.10.1016/0021-9991(76)90053-XSearch in Google Scholar

Coppi B., Laval G. and Pellat R. (1996): Dynamics of the geomagnetic tail. Physical Review Letters, Vol. 16, No. 26, pp. 1207-1210.Search in Google Scholar

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.Search in Google Scholar

Fijalkow E. (1999): A numerical solution to the Vlasov equation. Computer Physics Communications, Vol. 116, No. 2, pp. 319-328.10.1016/S0010-4655(98)00146-5Search in Google Scholar

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.Search in Google Scholar

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. 231-247.10.1006/jcph.1995.1160Search in Google Scholar

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. 54-66.10.1006/jcph.1996.5475Search in Google Scholar

Kulsrud R.M. (1998): Magnetic reconnection in a magnetohydrodynamic plasma. Physics of Plasmas, Vol. 5, No. 5, pp. 1599-1606.10.1063/1.872827Search in Google Scholar

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.Search in Google Scholar

Masmoudi N. and Mauser N.J. (2001): The selfconsistent Pauli equation. Monatshefte für Mathematik, Vol. 132, No. 1, pp. 19-24.10.1007/s006050170055Search in Google Scholar

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. 146-159.10.1006/jcph.1997.5670Search in Google Scholar

Ottaviani M. and Porcelli F. (1993): Nonlinear collisionless magnetic reconnection. Physical Review Letters, Vol. 71, No. 23, pp. 3802-3805.10.1103/PhysRevLett.71.3802Search in Google Scholar

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/2006/57191.10.1155/IMRN/2006/57191Search in Google Scholar

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.Search in Google Scholar

Schmitz H. and Grauer R. (2006): Darwin-Vlasov simulations of magnetised plasmas. Journal of Computational Physics, Vol. 214, No. 2, pp. 738-756.10.1016/j.jcp.2005.10.013Search in Google Scholar

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.Search in Google Scholar

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. 281-297.10.1016/S0021-9991(95)90119-1Search in Google Scholar

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. 5055-5058.10.1103/PhysRevLett.86.505511384419Search in Google Scholar