Numerical modelling of the two-dimensional Fourier transformed Vlasov-Maxwell system

Journal of Computational Physics

Volumn 190, Issue 2, 2003, Pages 501-522

  Eliasson, Bengt ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Divergence problem; Maxwell equation; Vlasov equation

Indexed keywords

ELECTRONS; IONS; VLASOV EQUATION;

DIVERGENCE PROBLEMS; ELECTRIC AND MAGNETIC FIELDS; ELECTROMAGNETICS; FOURIER; LINEAR PHENOMENA; LORENTZ; MAGNETIZED ELECTRONS; MAGNETIZED IONS; TWO-DIMENSIONAL; VLASOV-MAXWELL SYSTEM;

MAXWELL EQUATIONS;

EID: 0038467183     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00295-X     Document Type: Article

References (30)

1. T.P. Armstrong, R.C. Harding, G. Knorr, D. Montgomery, Solution of Vlasov's equation by transform methods, in: Methods in Computational Physics, vol. 9, Academic Press, New York, 1970, pp. 29-86.
2. F. Assous, P. Degond, E. Heintze, P.A. Raviart, J. Segre, On a finite-element method for solving the three-dimensional Maxwell equations, J. Comput. Phys. 109 (2) (1993) 222-237.
3. C.K. Birdsall, A.B. Langdon, Plasma Physics via Computer Simulation, McGraw-Hill Inc., 1985, ISBN 0-07-005371-5.
4. F.F. Chen, Introduction to Plasma Physics, second ed., Plasma Physics, vol. 1, Plenum Press, New York, 1984, ISBN 0-306-41332-9.
5. C.Z. Cheng, The integration of the Vlasov equation for a magnetized plasma, J. Comput. Phys. 24 (1977) 348-360.
6. C.Z. Cheng, G. Knorr, The integration of the Vlasov equation in configuration space, J. Comput. Phys. 22 (1976) 330-351.
7. J. Denavit, W.L. Kruer, Comparison of numerical solutions of the Vlasov equation with particle simulations of collisionless plasmas, Phys. Fluids (1971) 1782-1791.
8. J.W. Eastwood, The virtual particle electromagnetic particle-mesh method, Comput. Phys. Commun. 64 (1991) 252-266.
9. F. Edelvik, Hybrid Solvers for the Maxwell Equations in Time-Domain. The Department of Information technology, Uppsala University. Doctoral thesis. (Uppsala Dissertations from the Faculty of Science and Technology), ISSN 1104-2516, ISBN 91-554-5354-6. Downloadable from Web site http://publications.uu.se/theses/, 2002.
10. B. Eliasson, Outflow boundary conditions for the Fourier transformed one-dimensional Vlasov-Poisson system, J. Sci. Comput. 16 (1) (2001) 1-28.
11. B. Eliasson, Outflow boundary conditions for the Fourier transformed two-dimensional Vlasov equation, J. Comput. Phys. 181 (2002) 98-125.
12. J. Feng, W.N.G. Hitchon, Self-consistent kinetic simulation of plasmas, Phys. Rev. E 61 (1999) 3160-3173.
13. F. Filbet, E. Sonnedrücker, P. Bertrand, Conservative numerical schemes for the Vlasov equation, J. Comput. Phys. 172 (2001) 166-187.
14. R.J. Goldston, P.H. Rutherford, Introduction to Plasma Physics, Institute of Physics Publishing, Bristol and Philadelphia, 1997, ISBN 0-7503-0183-X.
15. B. Gustafsson, H.-O. Kreiss, J. Oliger, Time Dependent Problems and Difference Methods, Wiley, New York, 1999, ISBN 0-471-50734-2.
16. J.D. Jackson, Classical Electrodynamics, third ed., Wiley, New York, 1999, ISBN 0-471-30932-X.
17. B. Jiang, J. Wu, L.A. Povinelli, The origin of spurious solutions in computational electromagnetics, J. Comput. Phys. 125 (1996) 104-123.
18. A.J. Klimas, W.M. Farrel, A splitting algorithm for Vlasov simulation with filamentation filtration, J. Comput. Phys. 110 (1994) 150-163.
19. A.J. Klimas, A method for overcoming the velocity space filamentation problem in collisionless plasma model solutions, J. Comput. Phys. 68 (1987) 202-226.
20. S.K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103 (1992) 16-42.
21. A. Mangeney, F. Califano, C. Cavazzoni, P. Travnicek, A numerical scheme for the integration of the Vlasov-Maxwell system of equations, J. Comput. Phys. 179 (2002) 495-538.
22. B. Marder, A method for incorporating Gauss' law into electromagntetic PIC codes, J. Comput. Phys. 68 (1987) 48-55.
23. R.L. Morse, C.W. Nielson, Numerical simulation of the Weibel instability in one and two dimensions, Phys. Fluids 14 (4) (1971) 830-840.
24. S. Puri, F. Leuterer, M. Tutter, Dispersion curves for generalised Bernstein modes, J. Plasma Phys. 9 (1) (1973) 89-100.
25. L. Råde, B. Westergren, BETA Mathematics Handbook, second ed., Studentlitteratur AB, Lund, Sweden, 2002.
26. J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Wadsworth Inc, 1989 (Chapter 1.6).
27. S.H. Strogatz, Nonlinear Dynamics and Chaos, Addison-Wesley Publishing Company, 1994.
28. B. Thidé, Electromagnetic Field Theory. Web book, downloadable from Web site: http://www.plasma.uu.se/CED/Book, 2002.
29. C.L. Wagner, J.B. Schneider, Divergent fields, charge, and capacitance in FDTD simulations, IEEE Transactions on Microwave Theory and Techniques 46 (12) (1998) 2131-2136.
30. R. Wangsness, Electromagnetic Fields, second ed., Wiley, New York, 1986.