An implicit Vlasov-Fokker-Planck code to model non-local electron transport in 2-D with magnetic fields

Journal of Computational Physics

Volumn 194, Issue 1, 2004, Pages 1-34

  Kingham, R J ^a   Bell, A R ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Electron transport; Finite difference scheme; Fokker Planck; Implicit; Magnetic field; Maxwell's equations; Non local; Plasma; Sparse matrix; Vlasov

Indexed keywords

COLLISIONAL PLASMAS; CYLINDERS (SHAPES); ELECTROMAGNETIC FIELDS; ELECTRON TRANSPORT PROPERTIES; FINITE DIFFERENCE METHOD; FOKKER PLANCK EQUATION; LASER PRODUCED PLASMAS; MAGNETIC FIELDS; MAGNETOPLASMA; VLASOV EQUATION;

ELECTRON TRANSPORT; FINITE DIFFERENCE SCHEME; FOKKER PLANCK; FOKKER-PLANCK-EQUATION; IMPLICIT; IMPLICIT FINITE-DIFFERENCE SCHEMES; MAGNETIC-FIELD; NONLOCAL; SPARSE MATRICES; VLASOV;

MAXWELL EQUATIONS;

EID: 0842312310     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.08.017     Document Type: Article

References (63)

1. S.I. Braginskii, Transport processes in a plasma, in: Reviews of Plasma Physics, Consultants Bureau, New York, vol. 1, p. 205.
2. L. Spitzer Jr., R. Härm, Transport phenomena in a completely ionized gas, Phys. Rev. 89 (1953) 977.
3. L. Biermann, Uber den Ursprung der Magnetfelder auf Sternen und im interstellaren Raum, Z. Naturf. A 5 (1950) 65.
4. J.A. Stamper et al., Spontaneous magnetic fields in laser-produced plasmas, Phys. Rev. Lett. 26 (1971) 1012.
5. M.G. Haines, Magnetic-field generation in laser fusion and hot-electron transport, Can. J. Phys. 64 (1986) 912.
6. M. Zepf et al., Fast particle generation and energy transport in laser-solid interactions, Phys. Plasmas 8 (2001) 2323.
7. J.T. Mendonca, J.R. Davies, M. Eloy, Proton and neutron sources using terawatt lasers, Meas. Sci. Technol. 12 (2001) 1801.
8. M. Tabak et al., Ignition and high gain with ultrapowerful lasers, Phys. Plasmas 1 (1994) 1626.
9. M.G. Haines, Review of inertial confinement fusion, Astrophys. Space Sci. 256 (1998) 125.
10. R.J. Kingham, A.R. Bell, Nonlocal magnetic-field generation in plasmas without density gradients, Phys. Rev. Lett. 88 (2002) 045004.
11. S.H. Glenzer et al., Thomson scattering from laser plasmas, Phys. Plasmas 6 (1999) 2117.
12. R.M. Kulsrud, R. Cen, J.P. Ostriker, D. Ryu, The protogalactic origin for cosmic magnetic fields, Astrophys. J. 480 (1997) 481.
13. N.Y. Gnedin, A. Ferrara, E.G. Zweibel, Generation of the primordial magnetic fields during cosmological reionization, Astrophys. J. 539 (2000) 505.
14. G. Davies, L.M, Widrow, A possible mechanism for generating galactic magnetic fields, Astrophys. J. 540 (2000) 755.
15. A.R. Bell, J.R. Davies, S. Guérin, H. Ruhl, Fast-electron transport in high-intensity short-pulse laser-solid experiments, Plasma Phys. Control. Fusion 39 (1997) 653.
16. S.M. Guérin, A.R. Bell, J.R. Davies, M.G. Haines, One-dimensional particle simulations of fast electron transport in solid targets, Plasma Phys. Control. Fusion 41 (1999) 285.
17. A.R. Bell, R.G. Evans, D.J. Nicholas, Electron energy transport in steep temperature gradients in laser-produced plasmas, Phys. Rev. Lett. 46 (1981) 243.
18. J.P. Matte, J. Virmont, Electron heat transport down steep temperature gradients, Phys. Rev. Lett. 49 (1982) 1936.
19. E.M. Epperlein, G.J. Rickard, A.R. Bell, Two-dimensional nonlocal electron transport in laser-produced plasmas, Phys. Rev. Lett. 61 (1988) 2453.
20. G.J. Rickard, A.R. Bell, E.M. Epperlein, 2D Fokker-Planck simulations of short-pulse laser-plasma interactions, Phys. Rev. Lett. 62 (1989) 2687.
21. E.M. Epperlein, G.J. Rickard, A.R. Bell, A code for the solution of the Vlasov-Fokker-Planck equation in 1-D or 2-D, Comput. Phys. Commun. 52 (1988) 7.
22. E.M. Epperlein, Fokker-Planck modeling of electron transport in laser-produced plasmas, Laser Part. Beams 12 (1994) 257.
23. T.H. Kho, M.G. Haines, Nonlinear kinetic transport of electrons and magnetic field in laser-produced plasmas, Phys. Rev. Lett. 55 (1985) 825.
24. T.H. Kho, M.G. Haines, Nonlinear electron transport in magnetized laser plasmas, Phys. Fluids 29 (1986) 2665.
25. R.S. Craxton, M.G. Haines, Hot spots in laser plasmas, Phys. Rev. Lett. 35 (1975) 1336.
26. R.S. Craxton, M.G. Haines, J × B acceleration of fast ions in laser-target interactions, Plasma Phys. 20 (1979) 487.
27. D.G. Colombant, N.K. Winsor, Thermal-force terms and self-generated magnetic fields in laser-produced plasmas, Phys. Rev. Lett. 38 (1977) 697.
28. J.U. Brackbill, S.R. Goldman, Magnetohydrodynamics in laser fusion: fluid modeling of energy transport in laser targets, Comm. Pure Appl. Math. 36 (1983) 415.
29. J. Dawson, One-dimensional plasma model, Phys. Fluids 5 (1962) 445.
30. C.K. Birdsall, A.B. Langdon, Plasma Physics Via Computer Simulation, McGraw-Hill, New York, 1985.
31. C.Z. Cheng, G. Knorr, The integration of the Vlasov equation in configuration space, J. Comput. Phys. 22 (1976) 330.
32. J.U. Brackbill, D.W. Forslund, An implicit method for electromagnetic plasma simulation in two dimensions, J. Comput. Phys. 46 (1982) 271.
33. A.B. Langdon, B.L. Cohen, A. Fiedman, Direct implicit large time-step particle simulation of plasmas, J. Comput. Phys. 51 (1983) 107.
34. M. Honda, J. Meyer-ter-Vehn, A. Pukhov, Two-dimensional particle-in-cell simulation for magnetized transport of ultra-high relativistic currents in plasma, Phys. Plasmas 7 (2000) 1302.
35. J.M. Wallace et al., Collisional effects on the Weibel instability, Phys. Fluids 30 (1987) 1085.
36. R.J. Mason, Monte Carlo hybrid modeling of electron transport in laser produced plasmas, Phys. Fluids 23 (1980) 2204.
37. R.J. Mason, An electromagnetic field algorithm for 2D implicit plasma simulation, J. Comput. Phys. 71 (1987) 429.
38. J.R. Davies, A.R. Bell, M.G. Haines, S. Guérin, Short-pulse high-intensity laser-generated fast electron transport into thick solid targets, Phys. Rev. E 56 (1997) 7193.
39. L. Gremillet, G. Bonnaud, F. Amiranoff, Filamented transport of laser-generated relativistic electrons penetrating a solid target, Phys. Plasmas 9 (2002) 941.
40. R.J. Mason, Double-diffusion hot-electron transport in self-consistent E and B fields, Phys. Rev. Lett 42 (1979) 239.
41. R.J. Mason, M. Tabak, Magnetic field generation in high-intensity-laser-matter interactions, Phys. Rev. Lett. 80 (1998) 524.
42. I.P. Shkarofsky, Heat conduction and magnetic field induction in the presence of cold and hot-electron Maxwellian distributions, Phys. Rev. Lett. 42 (1979) 1342.
43. G.P. Schurtz, Ph.D. Nicolai, M. Busquet, A nonlocal electron conduction model for multidimensional radiation hydrodynamic codes, Phys. Plasmas 7 (2000) 4238.
44. J.C. Whitney, Finite difference methods for the Fokker-Planck equation, J. Comput. Phys. 6 (1970) 483.
45. S. Jorna, L. Wood, Fokker-Planck calculations on relaxation of anisotropic velocity distributions in plasmas, Phys. Rev. A 36 (1987) 397.
46. L. Chacón, D.C. Barnes, D.A. Knoll, G.H. Miley, An implicit energy-conservative 2D Fokker-Planck algorithm, J. Comput. Phys. 157 (2000) 618.
47. C. Buet, S. Cordier, P. Degond, M. Lemou, Fast algorithms for numerical, conservative, and entropy approximations of the Fokker-Planck-Landau equation, J. Comput. Phys. 133 (1997) 310.
48. T.W. Johnston, Cartesian tensor scalar product and spherical harmonic expansions in Boltzmann's equation, Phys. Rev. 120 (1960) 1103.
49. I.P. Shkarofsky, T.W. Johnston, M.P. Bachynski, The Particle Kinetics of Plasmas, Addison-Wesley, Reading, MA, 1966.
50. A.B. Langdon, Nonlinear inverse Bremsstrahlung and heated-electron distributions, Phys. Rev. Lett. 44 (1980) 575.
51. J.S. Chang, G. Cooper, A practical difference scheme for Fokker-Planck equations, J. Comput. Phys. 6 (1970) 1.
52. E.M. Epperlein, Implicit and conservative difference scheme for the Fokker-Planck equation, J. Comput. Phys. 112 (1994) 291.
53. A.B. Langdon, Conservative differencing of the electron Fokker-Planck transport equation, in: CECAM Report of Workshop on The Flux Limiter and Heat Flow Instabilities in Laser-Fusion Plasmas, Universite Paris Sud, France, 1981, p. 69.
54. H.A. Van der Vorst, Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 13 (1992) 631.
55. R. Fletcher, Conjugate gradient methods for indefinite systems, in: G. Watson (Ed.), Proceedings of the Dundee Biennial Conference on Numerical Analysis, Springer-Verlag, New York, 1975.
56. E.M. Epperlein, M.G. Haines, Plasma transport coefficients in a magnetic field by direct numerical solution of the Fokker-Planck equation, Phys. Fluids 29 (1986) 1029.
57. E.M. Epperlein, J. Phys. D 17 (1984) 1823.
58. W.M. MacDonald, M.N. Rosenbluth, W. Chuck, Relaxation of a system of particles with Coulomb interactions, Phys. Rev. 107 (1957) 350.
59. T.H. Kho, Relaxation of a system of charged particles, Phys. Rev. A 32 (1985) 666.
60. R.P.J. Town, A.R. Bell, S.J. Rose, Fokker-Planck simulations of short-pulse-laser-solid experiments, Phys. Rev. E 50 (1994) 1413.
61. R.P.J. Town, A.R. Bell, S.J. Rose, Fokker-Planck calculations with ionization dynamics of short-pulse laser-solid interactions, Phys. Rev. Lett. 74 (1995) 924.
62. S. Ethier, J.P. Matte, Electron kinetic simulations of solid density A1 plasmas produced by intense subpicosecond laser pulses. I. Ionization dynamics in 30 femtosecond pulses, Phys. Plasmas 8 (2001) 1650.
63. A.R. Bell, R.J. Kingham, Resistive collimation of electron beams in laser-produced plasmas, Phys. Rev. Lett. 91 (2003) 035003.