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Test kinetic modelling of collisionless perpendicular shocks

Published online by Cambridge University Press:  01 June 2008

F. MACKAY
Affiliation:
Department of Physics, University of Alberta, Edmonton Alberta, T6G 2G7Canada ([email protected])
R. MARCHAND
Affiliation:
Department of Physics, University of Alberta, Edmonton Alberta, T6G 2G7Canada ([email protected])
K. KABIN
Affiliation:
Department of Physics, University of Alberta, Edmonton Alberta, T6G 2G7Canada ([email protected])
J. Y. LU
Affiliation:
Department of Physics, University of Alberta, Edmonton Alberta, T6G 2G7Canada ([email protected])

Abstract

Test kinetic simulation results are presented for perpendicular collisionless shocks in magnetized plasmas that are representative of the Earth's bow shock. In this approach, particle kinetics are described by tracing particle trajectories in prescribed electromagnetic fields obtained in the MHD approximation, and applying Liouville's theorem. This provides a first-order description of particle dynamics in complex systems, given approximate fields obtained with a low-level description of the plasma. The method also provides a useful consistency check in assessing the validity of approximate solutions such as those obtained in the ideal MHD approximation. Compared with the more familiar test particle approach, in which trajectories of randomly injected particles are followed in time, the present approach has the advantage of being numerically more efficient, and producing results without statistical errors.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

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References

Ashour-Abdalla, M., El-Alaoui, M., Peroomian, V., Walker, R. J., Raeder, J., Frank, L. A. and Paterson, W. R. 1999 Source distributions of substorm ions observed in the near-Earth magnetotail Geophys. Res. Lett., 26 955958.CrossRefGoogle Scholar
Astudillo, H. F., Livi, S., Marsch, E. and Rosenbauer, H. 1996 Evidence for nongyrotropic alpha particle and proton distribution functions: TAUS solar wind measurements. Geophys. Res. Lett. 101, 24 42324 432.CrossRefGoogle Scholar
Burgess, D. and Scholer, M. 2007 Shock front instability associated with reflected ions at the perpendicular shock. Plasma Phys. 14, 012108-1–9.CrossRefGoogle Scholar
Candy, J. and Rozmus, W. 1990 A symplectic integration algorithm for separable Hamiltonian functions. J. Comp. Phys. 92, 230256.CrossRefGoogle Scholar
Chao, J. K., Zhang, X. X. and Song, P. 1995 Geoph. Res. Lett. 22, 24092412.CrossRefGoogle Scholar
Dasgupta, B., Burrows, R., Zank, G. P. and Webb, G. M. 2006 Hydrodynamics of shock waves with reflected particles. I. Rankine–Hugoniot relations and stationary solutions. Phys. Plasmas 13, 082112-1.CrossRefGoogle Scholar
Delcourt, D. C. 2002 Particle acceleration by inductive electric fields in the inner magnetosphere. J. Atmos. Solar-terr. Phys. 64, 551559.CrossRefGoogle Scholar
Delcourt, D. C., Grimald, S., Leblanc, F., Berthelier, J.-J., Millilo, A., Mura, A., Orsini, S. and Moore, T. E. 2003 A quantitative model of the planetary Na+ contribution to Mercury's magnetosphere Annales Geoph., 21, 17231736.CrossRefGoogle Scholar
Delcourt, D. C., Malova, H. V. and Zelenyi, L. M. 2006 Quasi-adiabaticity in bifurcated current sheets. Geoph. Res. Lett. 33, 06106 doi:10.1029/2005GL025463.CrossRefGoogle Scholar
Egedal, J., Fox, W., Belonohy, E. and Porkolab, M. 2004 Kinetic simulation of the VTF magnetic reconnection experiment. Comput. Phys. Comm. 164, 2933.CrossRefGoogle Scholar
Frey, P. J. and George, P. L. 1999 Maillages: applications aux éléments finis. Hermes Sciences Publicat.Google Scholar
Gosling, J. T., Asbridge, J. R., Bame, S. J., Paschmann, G. and Sckopke, N. 1978 Solar wind stream interfaces. Geophys. Res. Lett. 5, 957.CrossRefGoogle Scholar
Haruki, T.Sakai, J. I. and Saito, S. 2006 Electromagnetic wave emission during collision between a current sheet and a fast magnetosonic shock associated with coronal mass ejections Astron. Astrophys., 455 10991103.CrossRefGoogle Scholar
Hozumi, S. 1997 A phase-space approach to collisionless stellar systems using a particle method. Astrophys. J. 487, 617624.CrossRefGoogle Scholar
Jaeger, E. F. and Speiser, T. W. 1974 Energy and pitch angle distributions for auroral ions using the current sheet acceleration model. Astrophys. Space Sci. 28, 129144.CrossRefGoogle Scholar
Jones, F. C. and Ellison, D. C. 1991 The plasma physics of shock acceleration. J. Space Sci. Rev. 58, 259346.CrossRefGoogle Scholar
Kabin, K. 2000 MHD simulation of magnetospheric interaction of planets and satellites. PhD Dissertation, University of Michigan.Google Scholar
Kantrowitz, A. and Petschek, H. E. 1966 Plasma Physics in Theory and Application. New York: McGraw-Hill.Google Scholar
Karimabadi, H., Krauss-Varban, D. and Omidi, N. 1995 Temperature anisotropy effects and the generation of anomalous slow shocks Geophys. Res. Lett., 22, 26892692.CrossRefGoogle Scholar
Lee, M. A., Shapiro, V. D. and Sagdeev, R. Z. 1996 Pickup ion energization by shock surfing. J. Geophys. Res. 101, 47774789.CrossRefGoogle Scholar
Lembege, B. and Dawson, J. M. 1987 Self-consistent study of a perpendicular collisionless and nonresistive shock. Phys. Fluids 30, 17671788.CrossRefGoogle Scholar
Lever, E. L., Quest, K. B. and Shapiro, V. D. 2001 Shock surfing vs. shock drift acceleration. Geophys. Res. Lett. 28, 13671370.CrossRefGoogle Scholar
Lin, Y. and Lee, L. C. 1994 Structure of reconnection layers in the magnetosphere. Space Sci. Rev. 65, 59179.CrossRefGoogle Scholar
Lyu, L. H. and Kan, J. R. 1986 Shock jump conditions modified by pressure anisotropy and heat flux for Earth's bowshock. J. Geophys. Res. 91, 67716775.CrossRefGoogle Scholar
Mackay, F., Marchand, R. and Kabin, K. 2006 Divergence-free magnetic field interpolation and charged particle trajectory integration. J. Geophys. Res. 111, A06205, doi:10.1029/2005JA011382.Google Scholar
McKean, M. E., Omidi, N. and Krauss-Varban, D. 1995 Wave and ion evolution downstream of quasi-perpendicular bow shocks J. Geophys. Res., 100, 34273437.CrossRefGoogle Scholar
McKean, M. E. 1996 Magnetosheath dynamics downstream of low Mach number shocks J. Geophys. Res. 101, 2001320022.Google Scholar
Meziane, K., Mazelle, C., Lin, R. P., LeQueau, D., Larson, D. E., Parks, G. K. and Lepping, R. P. 2001 Three-dimensional observations of gyrating ion distributions far upstream from the Earth's bow shock and their association with low-frequency waves J. Geophys. Res., 106, 57315742.CrossRefGoogle Scholar
Moore, T. E., Giles, B. L., Delcour, D. C. and Fok, M.-C. 2000 The plasma sheet source groove J. Atmos. Solar-terr. Phys., 62 505512.CrossRefGoogle Scholar
Moore, T. E. et al. 2005 Plasma sheet and (nonstorm) ring current formation from solar and polar wind sources. J. Geophys. Res. 110, A02210, doi:10.1029/2004JA010563.Google Scholar
Othmer, C., Glassmeier, K. H., Motschmann, U., Schule, J. and Frick, Ch. 2000 Three-dimensional simulations of ion thruster beam neutralization Phys. Plasmas, 7 52425251.CrossRefGoogle Scholar
Richard, R. L., El.-Alaoui, M., Ashour-Abdalla, M. and Walker, R. J. 2002 Interplanetary magnetic field control of the entry of solar energetic particles into the magnetosphere. J. Geophys. Res. 107, A02210, doi:10.1029/2001JA000099.Google Scholar
Sanderson, J. J. and Uhrig, R. A. Jr., 1978 Extended Rankine–Hugoniot relations for collisionless shocks J. Geophys. Res., 83 13951400.CrossRefGoogle Scholar
Sanz-Serna, J. M. 1988 Runge-Kutta schemes for Hamiltonian systems BIT Computer Science and Numerical Mathematics, 28 877883.CrossRefGoogle Scholar
Schwartz, J. S., Burgess, D. and Moses, J. J. 1996 Low-frequency waves in the Earth's magnetosheath: present status. Ann. Geophys. 14, 11341150.Google Scholar
Shimada, M. and Yoshida, H. 1996 Long-term conservation of adiabatic invariants by using symplectic integrators. Astron. Soc. Japan 48, 147155.Google Scholar
Stuchi, T. J. 2002 Symplectic integrators revisited. Brazilian J. Phys. 32, 958979.CrossRefGoogle Scholar
Suris, Yu. B. 1989 On the canonicity of mappings that can be generated by methods of Runge-Kutta type for integrating systems = −∂U/∂x Zh. Vychisl. Mat. i Mat. Fiz 29, 202211.Google Scholar
Takeuchi, S. 2005 New particle accelerations by magnetized plasma shock waves. Phys. Plasmas 12, 102901-1–6.CrossRefGoogle Scholar
Tanaka, M., Goodrich, C. C., Winske, D. and Papadopoulos, K. 1983 A source of the backstreaming ion beams in the foreshock region. J. Geophys. Res. 88, 30463054.CrossRefGoogle Scholar
Thomas, V. A. 1989 Dimensionality effects in hybrid simulations of high Mach number collisionless perpendicular shocks. J. Geophys. Res. 94, 1200912014.CrossRefGoogle Scholar
Thomas, V. A. and Winske, D. 1990 Two dimensional hybrid simulation of a curved bow shock. Geophys. Res. Lett. 17, 12471250.CrossRefGoogle Scholar
Yong, H., Hu, X., Hu, Y., Jiang, Z. and Lu, J. 2006 Rankine-Hugoniot relations of an axial shock in cylindrical non-neutral plasma. Phys. Plasmas 13, 92116-1–5.Google Scholar
Wu, C. S. et al. 1984 Microinstabilities associated with a high Mach number, perpendicular bow shock Space Sci. Rev. 37, 63109.CrossRefGoogle Scholar
Yoshida, H. 1993 Recent progress in the theory and application of symplectic integrators. Cel. Mech. Dynam. Astron. 56, 2743.CrossRefGoogle Scholar
Zank, G. P., Pauls, H. L., Cairns, I. H. and Webb, G. M. 1996 Interstellar pickup ions and quasi-perpendicular shocks: implications for the termination and interplanetary shocks. J. Geophys. Res. 101, 457477.CrossRefGoogle Scholar
Zank, G. P., Li, G., Florinski, V., Hu, Q, Lario, D. and Smith, C. W. 2006 Particle acceleration at perpendicular shock waves: Model and observations. J. Geophys. Res. 111, A06108, doi:10.1029/2005JA011524.Google Scholar