Abstract
Extensive theoretical work has been performed on the equilibrium structure of tangential discontinuities (TDs) in collisionless plasmas. This paper reviews kinetic models based on steady-state solutions of the Vlasov equation. It is shown that most of the existing models are special cases of a generalized multi-species model. In this generalized model all particle populations -from both outer regions and from inside the layer — are described using a unique formalism for the velocity distribution functions. Because of their historical importance, the Harris and Sestero models are reviewed and deduced from the generalized model. The Lee and Kan model is also a special case of the generalized model. The generalized model, however, is also able to describe TDs with velocity shear and large angles of magnetic field rotation. Such a multi-species model with a large number of free parameters and different gradient scales illustrates many observable features of TDs, including their multiscale fine structure. Particular attention is paid to the magnetopause. Observed magnetopause crossings are simulated. The effects of the relative flow velocity and asymmetrical magnetic field profiles on the structure of the magnetopause and on its stability with respect to tearing perturbations are discussed. We also present calculations that demonstrate the potential of the generalized model in explaining the origin of discrete auroral arcs. Numerical simulations of solar wind TDs with heavy ions and a large spectrum of thicknesses are also feasible. This indicates that such a model is of fundamental importance for understanding the detailed structure of solar wind TDs, like those observed by the interplanetary spacecraft ULYSSES. The problems associated with the one-dimensional, time-independent Vlasov approach are discussed and a variational principle is suggested to reduce the arbitrariness resulting from the large number of free parameters.
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References
Alfvén, H.: 1981, Cosmic Plasma, D. Reidel Publ. Co., Dordrecht, Holland.
Alpers W.: 1969, ‘Steady State Charge Neutral Models of the Magnetopause’, Astrophys. Space Sci. 5, 425.
Anderson, R. R., Harvey, C. C., Hoppe, M. M., Tsurutani, B. T., Eastman, T. E., and Etcheto, J.: 1982, ‘Plasma Waves Near the Magnetopause’, J. Geophys. Res. 87, 2087.
Balogh, A., Hedgecock, P. C., Smith, E. J., and Tsurutani, B. T.: 1983, ‘The Magnetic Field Investigation on ISPM’ in K.-P. Wenzel, R. G. Marsden, and B. Battrick, ed(s)., The International Solar Polar Mission —Its Scientific Investigations, European Space Agency, ESA SP-1050, p. 27.
Behannon, K. W., Neubauer, F. M., and Barnstorf, H.: 1981, ‘Fine-Scale Characteristics of Interplanetary Sector Boundaries’, J. Geophys. Res. 86, 3273.
Berchem, J. and Okuda, H.: 1990, ‘A Two-Dimensional Particle Simulation of the Magnetopause Current Layer’, J. Geophys. Res. 95, 8133.
Berchem, J. and Russell, C. T.: 1982a, ‘The Thickness of the Magnetopause Current Layer: ISEE 1 and 2 Observations’, J. Geophys. Res. 87, 2108.
Berchem, J. and Russell, C.T.: 1982b, ‘Magnetic Field Rotation through the Magnetopause: ISEE 1 and 2 Observations’, J. Geophys. Res. 87, 8139.
Berchem, J. and Russell, C.T.: 1984, ‘Flux Transfer Events on the Magnetopause: Spatial Distributions and Controlling Factors’, J. Geophys. Res. 89, 6689.
Burlaga, L. F., Lemaire, J. F., and Turner, J. M.: 1977, ‘Interplanetary Currents Sheets at 1 AU’, J. Geophys. Res. 82, 3191.
Cargill, P. J. and Eastman, T. E.: 1991, ‘The Structure of Tangential Discontinuities. 1. Results of Hybrid Simulations’, J. Geophys. Res. 96, 13763.
Channell, P. J.: 1976, ‘Exact Vlasov-Maxwell Equilibria with Sheared Magnetic Field’, Phys. Fluids 19, 1541.
Coppi, B., Mark, J. W.-K., Sugiyama, L., and Bertin, G.: 1979, ‘Reconnecting Modes in Collisionless Plasmas’, Phys. Rev. Letters 42, 1058.
Davidson, R. C., Gladd, N. T., Wu, C. S., and Huba, J. D.: 1977, ‘Effects of Finite Plasma Beta on the Lower Hybrid Drift Instability’, Phys. Fluids 20, 301.
De Keyser, J., Roth, M., Lemaire, J. L., Tsurutani, B. T., Ho, C. M., and Hammond, C. M.: 1995, ‘Theoretical Plasma Distributions Consistent with Ulysses Magnetic Field Observations in a Solar Wind Tangential Discontinuity’, Aeronomica Acta, Belgian Institute for Space Aeronomy, Brussels.
Drake, J. F. and Lee, Y. C.: 1977, ‘Kinetic Theory of Tearing Instabilities’, Phys. Fluids 20, 1341.
Drake, J. F., Gerber, J., and Kleva, R. G.: 1994, ‘Turbulence and Transport in the Magnetopause Current Layer’, J. Geophys. Res. 99, 211.
Dubinin, E. M., Podgorny, I. M., and Potanin, Y. N.: 1980, ‘Structure of the Magnetic Field at the Boundary of the Magnetosphere: Analysis of a Simulation Experiment’, Cosmic Res., Engl. Transl. 18, 99.
Eastman, T. E., Frank, L. A., Peterson, W. K., and Lennartsson, W.: 1984, ‘The Plasma Sheet Boundary Layer’, J. Geophys. Res. 89, 1553.
Elphinstone, R. D., Hearn, D., Murphree, J. S., and Cogger, L. L.: 1991, ‘Mapping Using the Tsyganenko Long Magnetospheric Model and Its Relationship to Viking Auroral Images’, J. Geophys. Res. 96, 1467.
Fälthammar, C.-G., Akasofu, S.-I., and Alfvén, H.: 1978, ‘The Significance of Magnetospheric Research for Progress in Astrophysics’, Nature 275, 185.
Furth, H. P., Killeen, J., and Rosenbluth, M. N.: 1963, ‘Finite-Resistivity Instabilities in a Sheet Pinch’, Phys. Fluids 6, 459.
Galeev, A. A. and Zelenyi, L. M.: 1977, ‘The Model of Magnetic Field Reconnection in a Slab Collisionless Plasma Sheath’, Pis'ma Zh. Eksperim. Tear. Fiz. 25, 407.
Galeev, A. A., Kuznetsova, M. M., and Zelenyi, L. M.: 1986, ‘Magnetopause Stability Threshold for Patchy Reconnection’, Space Sci. Rev. 44, 1.
Gary, S. P. and Eastman, T. E.: 1979, ‘The Lower Hybrid Drift Instability at the Magnetopause’, J. Geophys. Res. 84, 7378.
Gladd, N. T.: 1990, ‘Collisionless Drift-Tearing Modes in the Magnetopause’, J. Geophys. Res. 95, 889.
Gosling, J. T., Thomsen, M. F., Bame, S. J., Elphic, R. C., and Russell, C. T.: 1990, ‘Plasma Flow Reversals at the Dayside Magnetopause and the Origin of Asymmetric Polar Cap Convection’, J. Geophys. Res. 95, 8073.
Grad, H.: 1961, ‘Boundary Layer between a Plasma and a Magnetic Field’, Phys. Fluids 4, 1366.
Greenly, J. B. and Sonnerup, B. U. Ö.: 1981, ‘Tearing at the Magnetopause’, J. Geophys. Res. 86, 1305.
Gurnett, D. A., Anderson, R. R., Tsurutani, B. T., Smith, E. J., Paschmann, G., Haerendel, G., Bame, S. J., and Russell, C. T.: 1979, ‘Plasma Wave Turbulence at the Magnetopause: Observations from ISEE 1 and 2’, J. Geophys. Res. 84, 7043.
Harris, E. G.: 1962, ‘On a Plasma Sheath Separating Regions of Oppositely Directed Magnetic Field’, Nuovo Cimento 23, 115.
Huba, J. D., Gladd, N. T., and Papadopoulos, K.: 1978, ‘Lower Hybrid Drift Turbulence in the Distant Magnetotail’, J. Geophys. Res. 83, 5217.
Hudson, P. D.: 1970, ‘Discontinuities in an Anisotropic Plasma and Their Identification in the Solar Wind’, Planetary Space Sci. 18, 1611.
Kan, J. R.: 1972, ‘Equilibrium Configurations of Vlasov Plasmas Carrying a Current Component Along an External Magnetic Field’, J. Plasma Phys. 7, 445.
Kuznetsova, M. M. and Roth, M.: 1995, ‘Thresholds for Magnetic Percolation through the Magnetopause Current Layer in Asymmetrical Magnetic Fields’, J. Geophys. Res. 100, 155.
Kuznetsova, M. M. and Zelenyi, L. M.: 1985, ‘Stability and Structure of the Perturbations of the Magnetic Surfaces in the Magnetic Transitional Layers’, Plasma Phys. Controlled Fusion 27, 363.
Kuznetsova, M. M. and Zelenyi, L. M.: 1990a, ‘The Theory of FTE: Stochastic Percolation Model’ in C. T. Russell, E. R. Priest, and L. C. Lee, ed(s)., Physics of Magnetic Flux Ropes, Geophys. Monogr. Ser., Vol. 58, AGU, Washington, D.C., p. 473.
Kuznetsova, M. M. and Zelenyi, L. M.: 1990b, ‘Nonlinear Evolution of Magnetic Islands in a Sheared Magnetic Field with Uniform Plasma Background’, Plasma Phys. Controlled Fusion 32, 1183.
Kuznetsova, M. M., Roth, M., and Zelenyi, L. M.: 1995, ‘Kinetic Structure of the Magnetopause: Equilibrium and Percolation’ in P. Song, B. U. Ö. Sonnerup, and M. F. Thomsen, ed(s)., Physics of the Magnetopause, Geophys. Monogr. Ser., Vol. 90, AGU, Washington, D.C., p. 99.
Kuznetsova, M. M., Roth, M., Wang, Z., and Ashour-Abdalla, M.: 1994, ‘Effect of the Relative Flow Velocity on the Structure and Stability of the Magnetopause Current Layer’, J. Geophys. Res. 99, 4095.
Lakhina, G. S., and Schindler, K.: 1983a, ‘Collisionless Tearing Modes in the Presence of Shear Flow’, Astrophys. Space Sci. 89, 293.
Lakhina, G. S. and Schindler, K.: 1983b, ‘Tearing Modes in the Magnetopause Current Sheet’, Astrophys. Space Sci. 97, 421.
Laval, G., Pellat, R., and Vuillemin, M.: 1966, ‘Instabilités électromagnétiques des plasmas sans collisions’, Plasma Phys. and Contr. Fusion Res., IAEA, Vienna 2, p. 259.
Lee, L. C. and Kan, J. R.: 1979, ‘A Unified Kinetic Model of the Tangential Magnetopause Structure’, J. Geophys. Res. 84, 6417.
Lemaire, J. and Burlaga, L. F.: 1976, ‘Diamagnetic Boundary Layers: a Kinetic Theory’, Astrophys. Space Sci. 45, 303.
Lemaire, J., Roth, M., Scherer, M., and Schulz, M.: 1983, ‘Interdisciplinary Study of Directional Discontinuities in the Solar Wind with ISPM’ in K.-P. Wenzel, R.G. Marsden, and B. Battrick, ed(s)., The International Solar Polar Mission —Its Scientific Investigations, European Space Agency, ESA SP-1050, p. 263.
Lembege, B. and Pellat, R.: 1982, ‘Stability of a Thick Two-Dimensional Quasi-Neutral Sheet’, Phys. Fluids 25, 1995.
Lyons, L. R.: 1981, ‘Discrete Aurora as the Direct Result of an Inferred, High-Altitude Generating Potential Distribution’, J. Geophys. Res. 86, 1.
Lyons, L. R., Evans, D. S., and Lundin, R.: 1979, ‘An Observed Relation Between Magnetic Field Aligned Electric Fields and Downward Electron Energy Fluxes in the Vicinity of Auroral Forms’, J. Geophys. Res. 84, 457.
McBride, J. B., Ott, E., Boris, J. P., and Orens, J. H.: 1972, ‘Theory and Simulation of Turbulent Heating by the Modified Two-Stream Instability’, Phys. Fluids 15, 2367.
Morse, R. L.: 1965, ‘Adiabatic Time Development of Plasma Sheaths’, Phys. Fluids 8, 308.
Nicholson, R. B.: 1963, ‘Solution of the Vlasov Equations for a Plasma in a Uniform Magnetic Field’, Phys. Fluids 6, 1581.
Parks, G. K., Fitzenreiter, R., Ogilvie, K. W., Huang, C., Anderson, K. A., Dandouras, J., Frank, L. A., Lin, R. P., McCarthy, M., Rème, H., Sauvaud, J. A., and Werden, S.: 1992, ‘Low-Energy Particle Layer Outside of the Plasma Sheet Boundary’, J. Geophys. Res. 97, 2943.
Paschmann, G., Sckopke, N., Haerendel, G., Papamastorakis, J., Bame, S. J., Asbridge, J. R., Gosling, J. T., Hones, E. W., Jr., and Tech, E. R.: 1978, ‘ISEE Plasma Observations Near the Subsolar Magnetopause’, Space Sci. Rev. 22, 717.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T.: 1986, Numerical Recipes. The Art of Scientific Computing, Cambridge University Press, Cambridge.
Quest, K. B. and Coroniti, F. V.: 1981a, ‘Tearing at the Dayside Magnetopause’, J. Geophys. Res. 86, 3289.
Quest, K. B. and Coroniti, F. V.: 1981b, ‘Linear Theory of Tearing in a High-Beta Plasma’, J. Geophys. Res. 86, 3299.
Ralston, A. et Wilf, H. S.: 1965, Méthodes mathématiques pour calculateurs arithmétiques, Dunod, Paris, p. 482.
Rosenbluth, M. N., Sagdeev, R. Z., Taylor, J. B., and Zaslavsky, G. M.: 1966, ‘The Destruction of Magnetic Surfaces’, Nucl. Fusion 6, 297.
Roth, M.: 1976, ‘The Plasmapause as a Plasmasheath: a Minimum Thickness’, J. Atmospheric Terrest. Phys. 38, 1065.
Roth, M.: 1978, ‘Structure of Tangential Discontinuities at the Magnetopause: the Nose of the Magnetopause’, J. Atmospheric Terrest. Phys. 40, 323.
Roth, M.: 1979, ‘A Microscopic Description of Interpenetrated Plasma Regions’ in B. Battrick and J. Mort, ed(s)., Magnetospheric Boundary Layers, European Space Agency, ESA SP-148, pp. 295–309.
Roth, M.: 1984, ‘La structure interne de la magnétopause’, Mém. Cl. Sci. Acad. R. Belg. Collect. 8° 44(7), 222. Also in: Aéronomica Acta A, 221, Belgian Institute for Space Aeronomy, 1980.
Roth, M.: 1983, ‘Boundary Layers in Space Plasmas: a Kinetic Model of Tangential Discontinuities’ in W. Botticher, H. Wenk, and E. Schulz-Gulde, ed(s)., Phenomena in Ionized Gases, XVI International Conference, Dusseldorf, pp. 139–147.
Roth, M.: 1986, ‘A Computer Simulation Study of the Microscopic Structure of a Typical Current Sheet in the Solar Wind’ in R. G. Marsden, ed(s)., The Sun and the Heliosphere in Three Dimensions, ASSL123, D. Reidel Publ. Co., Dordrecht, Holland, pp. 167–171.
Roth, M., Evans, D. S., and Lemaire, J.: 1993, ‘Theoretical Structure of a Magnetospheric Plasma Boundary: Application to the Formation of Discrete Auroral Arcs’, J. Geophys. Res. 98, 411.
Roth, M., Lemaire, J., and Misson, A.: 1990, ‘An Iterative Method to Solve the Nonlinear Poisson's Equation in the Case of Plasma Tangential Discontinuities’, J. Comput. Phys. 86, 466.
Russell, C. T. and Elphic, R. C.: 1978, ‘Initial ISEE Magnetometer Results: Magnetopause Observations’, Space Sci. Rev. 22, 681.
Sestero, A.: 1964, ‘Structure of Plasma Sheaths’, Phys. Fluids 7, 44.
Sestero, A.: 1966, ‘Vlasov Equation Study of Plasma Motion Across Magnetic Fields’, Phys. Fluids 9, 2006.
Sonnerup, B. U. Ö. and Cahill, L. J., Jr.: 1968, ‘Explorer 12 Observations of the Magnetopause Current Layer’, J. Geophys. Res. 73, 1757.
Southwood, D. J., Saunders, M. A., Dunlop, M. W., Mier-Jedrzejowicz, W. A. C., and Rijnbeek, R. P.: 1986, ‘A Survey of Flux Transfer Events Recorded by the UKS Spacecraft Magnetometer’, Planetary Space Sci. 34, 1349.
Su, S. Y. and Sonnerup, B. U. Ö.: 1968, ‘First-Order Orbit Theory of the Rotational Discontinuity’, Phys. Fluids 11, 851.
Szabo, A., Lepping, R. P., Peredo, M., and Byrnes, J.: 1995, ‘Improvements and Extensions of the Heliospheric Current Sheet Study with the WIND Magnetometer Measurements’ in, ed(s)., EOS Supplement, Transactions, American Geophysical Union, Vol. 76, AGU, p. 218. Abstract of paper SH21B-2 presented at the Spring Meeting of the American Geophysical Union, Baltimore, 1995.
Treumann, R. A., LaBelle, J., and Bauer, T. M.: 1995, ‘Diffusion Processes: an Observational Perspective’ in P. Song, B. U. Ö. Sonnerup, and M. F. Thomsen, ed(s)., Physics of the Magnetopause, Geophys. Monogr. Ser., Vol. 90, AGU, Washington, D.C., p. 331.
Tsurutani, B. T., Ho, C. M., Smith, E. J., Neugebauer, M., Goldstein, B. E., Mok, J. S., Arballo, J. K., Balogh, A., Southwood, D. J., and Feldman, W. C.: 1994, ‘The Relationship between Interplanetary Discontinuities and Alfvén Waves: Ulysses Observations’, Geophys. Res. Letters 21, 2267.
Wang, Z. and Ashour-Abdalla, M.: 1992, ‘Topological Variation in the Magnetic Field Line at the Dayside Magnetopause’, J. Geophys. Res. 97, 8245.
Wang, Z. and Ashour-Abdalla, M.: 1994, ‘Magnetic Field Line Stochasticity at the Magnetopause’, J. Geophys. Res. 99, 2321.
Whipple, E. C., Hill, J. R., and Nichols, J. D.: 1984, ‘Magnetopause Structure and the Question of Particle Accessibility’, J. Geophys. Res. 89, 1508.
Winske, D., Thomas, V. A., and Omidi, N.: 1995, ‘Diffusion at the Magnetopause: a Theoretical Perspective’ in P. Song, B. U. Ö. Sonnerup, and M. F. Thomsen, ed(s)., Physics of the Magnetopause, Geophys. Monogr. Ser., Vol. 90, AGU, Washington, D.C., p. 321.
Wu, C. S., Zhou, Y. M., Tsai, S. T., Guo, S. C., Winske, D., and Papadopoulos, K.: 1983, ‘A Kinetic Cross-Field Streaming Instability’, Phys. Fluids 26, 1259.
Zelenyi, L. M. and Kuznetsova, M. M.: 1984, ‘Large-scale Instabilities of the Plasma Sheet Driven by Particle Fluxes at the Boundary of the Magnetosphere’, Fiz. Plasmy Moscow 10, 190.
Zelenyi, L., Kovrazkhin, R., and Bosqued, J.: 1990, ‘Velocity-Dispersed Ion Beams in the Nightside Auroral Zone: AUREOL 3 Observations’, J. Geophys. Res. 95, 119.
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Roth, M., De Keyser, J. & Kuznetsova, M.M. Vlasov theory of the equilibrium structure of tangential discontinuities in space plasmas. Space Sci Rev 76, 251–317 (1996). https://doi.org/10.1007/BF00197842
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DOI: https://doi.org/10.1007/BF00197842