Models of Plasma Kinetics and Problems with Their Interpretation in the Current Paradigm



Series: Physics Research and Technology
BISAC: SCI055000

Proposed by A.A. Vlasov in 1938, the kinetic equation with a self-consistent electromagnetic field led to a fundamentally new perspective in plasma physics. This equation represents the most profound approach to the description of plasma because it operates directly with plasma particles using the distribution function. Plasma is found everywhere in space; that is why this equation has an extensive application. A large number of works where the study of plasma properties based on the solution of the Vlasov equation have appeared.

However, the results based on the solution of the Vlasov equation should be assumed with caution. As noted in the manuscript, the Vlasov equation has a set of formal solutions. The researcher must have the ability to select the correct solutions, correct in the sense of their adequacy to the processes under investigation.

Some aspects of the polarization of a magnetoactive plasma are investigated. It is shown that neglecting the electric field in problems of such sharply inhomogeneous structures as a boundary or current layers leads to an inadequate model. Thus, the successive solution of the kinetic equation taking into account the electric polarization field indicates that the equations describing the equilibrium of these sharply inhomogeneous structures become nonlinear and exhibit the property of structural instability.

Natural science over time included the expansion of the field of numbers from natural to real. Now, physics is in the stage of semi-recognition of complex numbers. On the one hand, when solving the differential equation, the physicist finds the value of the roots of the characteristic equation in a complex field. However, at the final stage, all imaginary parts are discarded, and only real values of physical quantities are passed in response. In this case, the complex field has a fundamental feature that distinguishes it: it is algebraically closed. The restriction of physical quantities only to the field of real numbers seems logically unsatisfactory since often mathematical operations derive them from the field of the original definition. In this manuscript, some problems of the complexification of physics are investigated.

Table of Contents

Table of Contents


Chapter 1. On the Theory of Type III Radio Bursts in the Inhomogeneous Interplanetary Space

Chapter 2. Kinetic Theory of the Current Sheet and Effect of Plasma Polarization on Its Equilibrity and Stability

Chapter 3. The Equilibrium and Stability of the Magnetopause. Kinetic Theory

Chapter 4. The Charge on the Magnetopause and Transfer of the Impulse and Energy into the Magnetosphere

Chapter 5. Research of the Instability Nonelectroneutrality Current Sheets in a Quasi-Linear Approximation

Chapter 6. Role of Complex Numbers in the Electrodynamics of Plasma

Chapter 7. Complex Numbers and Physical Reality

Summary and Conclusions




Akasofu, S. I. & Chapman, S. (1974). “Solar-Terrestrial physics. Vol. I., Solar-terrestrial physics. Part 1. Translated from the English edition,” Moscow: Mir, (in Russian).
Aleksandrov, A. S., Bogdankevich, L. S. & Rukhadze, A. A. (1988). “Fundamentals of Plasma Electrodynamics,” Moscow: Visshaj shkola, (in Russian).
Alpers, W. (1969). “Steady state charge neutral models of the magnetopause,” J. Astrophysics and Space Sci. Springer, 5(4), pp. 425–437.
Alpers, W. (1971). “On the equilibrium of an exact charge neutral magnetopause,” J. Astrophysics and Space Sci. Springer, 11(3), pp. 471–474.
Amata, E., Savin, S. P., André, M., Dunlop, M., Khotyaintsev, Y., Marcucci, M. F., Fazakerley, A., Bogdanova, Y. V., Décréau, P. M. E., Rauch, J. L., Trotignon, J. G., Skalsky, A., Romanov, S., Büchner, J., Blecki, J. & Rème, H. (2006). “Experimental study of nonlinear interaction of plasma flow with charged thin current sheets: 1. Boundary structure and motion,” J. Nonlinear Proc. Geophys. European Geosciences Union, 13(4), pp. 365–376.
Antonelli, P. L. (2003). Handbook of Finsler geometry. Kluwer Aca. Dordrecht: Springer Science & Business Media.
Antonov, A. A. (2008). “Physical Reality of Resonance on Complex Frequencies,” European Journal of Scientific Research, 21(4), pp. 627–641.
Antonov, A. A. (2009). “Resonance on Real and Complex Frequencies,” European Journal of Scientific Research, 28(2), pp. 193–204.
Antonov, A. A. (2010). “Solution of algebraic quadratic equations taking into account transitional processes in oscillation systems,” General Mathematics Notes, 1(2), pp. 11–16.
Arkhipov, Y. V. & Lyahov, V. V. (1992). “About natural modes of the uncompensated relativistic electron beam in a plasma-filled waveguide,” J. Plasma Phys., 18(10), p. 1363.
Artemyev, A. V., Neishtadt, A. I., Vasiliev, A. A. & Zelenyi, L. M. (2015). “Nonresonant Charged-Particle Acceleration by Electrostatic Waves Propagating across Fluctuating Magnetic Field,” Phys. Rev. Lett., 115(15), p. 155001.
Benz, A. O., Grigis, P. C., Csillaghy, A. & Saint-Hilaire, P. (2005). “Survey on solar X-ray flares and associated coherent radio emissions,” J. Solar Phys. Springer, 226(1), pp. 121–142.
Berestetskiy, V. B. (1962). “Dinamicheskie svoystva elementarnykh chastits i teoriya matritsy rasseyaniya. (Dynamic properties of elementary particles and theory of the scattering matrix),” UFN, 76(1), pp. 25–77.
Birn, J., Schindler, K. & Hesse, M. (2004). “Thin electron current sheets and their relation to auroral potentials,” J. Geophys. Res., 109(A2).
Bogdankevich, L. S., Kuzelev, M. V. & Rukhadze, A. A. (1981). “Plasma microwave electronics,” UFN, 133(1–16).
Braginsky, V. B., Mitrofanov, V. P. & Popov, V. Y. (1981). “Systems with low dissipation. Moscow: Nauka, (in Russian).
Brittnacher, M., Quest, K. B. & Karimabadi, H. (1994). “On the energy principle and ion tearing in the magnetotail,” J. Geophys. Res. Lett., 21(15), pp. 1591–1594.
Brittnacher, M., Quest, K. B. & Karimabadi, H. (1998). “A study of the effect of pitch angle and spatial diffusion on tearing instability using a new finite element based linear code,” J. Geophys. Res., 103(A3), pp. 4587–4596.
Büchner, J. & Kuska, J. P. (1999). “Sausage mode instability of thin current sheets as a cause of magnetospheric substorms,” in Ann. Geophysicae, pp. 604–612.
Camporeale, E. & Lapenta, G. (2005). “Model of bifurcated current sheets in the Earth s magnetotail : Equilibrium and stability,” J. Geophys. Res.: Space Physics. Wiley Online Library, 110(A7), pp. 1–21.
Camporeale, E., Lapenta, G., Daughton, W., Brackbill, J. & Ricci, P. (2004). “A comparative study of Cluster observations and 3D kinetic simulations of current sheet configuration and stability in the Earth’s magnetotail,” in American Geophysical Union, Fall Meeting, abstract #SM13C-05.
Cane, H. V., Erickson, W. C. & Prestage, N. P. (2002) “Solar flares, type III radio bursts, coronal mass ejections, and energetic particles,” J. Geophys. Res.: Space Physics. Wiley Online Library, 107(A10), p. 12/1-14/19.
Cartwright, D. G. & Kellogg, P. J. (1971). “Controlled Experiment on Wave–Particle Interactions in the Ionosphere,” J. Nature. Nature Publishing Group, 231(18), pp. 11–30.
Chandrasekhar, S., Gurov, K. P. & Bogolyubov, N. N. (1947). “Stochastic Problems in Physics and Astronomy,” Moscow: Inostrannaja Literatura, (in Russian).
Coppi, B., Laval, G. & Pellat, R. (1966). “Dynamics of the geomagnetic tail,” J. Phys. Rev. Lett., 16(26), p. 1207.
Daughton, W. (1998). “Kinetic theory of the drift kink instability in a current sheet,” J. Geophys. Res., 103(A12).
Daughton, W. (1999). “The unstable eigenmodes of a neutral sheet,” J. Phys. Plasm. AIP Publishing, 6(4), pp. 1329–1343.
Davis, M. (1980). “Applied nonstandard analysis,” Moscow: Mir, (in Russian).
Dobrovolny, M. S. (1968). “Instability of a neutral sheet,” J. II Nuovo Cimento B Series, 10, 55(2), pp. 427–442.
Dorman, L. I. & Miroshnichenko, L. I. (1968). “Solar Cosmic Rays,” NAUKA, (in Russian).
Faddeeva, V. N. & Terentyev, N. M. (1954). “Tables of the probability integral values,” Moscov: State Technical Press, (in Russian).
Génot, V., Mottez, F., Fruit, G., Louarn, P., Sauvaud, J. A. & Balogh, A. (2005). “Bifurcated current sheet: Model and Cluster observations,” J. Planetary and Space Science. Elsevier, 53(1–3), pp. 229–235.
Gilbert, D. (1948). “Foundations of Geometry,” Moscow-Leningrad: State Technical Press, (in Russian).
Ginzburg, V. L. & Zhelezniakov, V. V. (1958). “On the possible mechanisms of sporadic solar radio emission (radiation in anisotropic plasma),” Astronomicheskii Zhurnal, 35(5), p. 694.
Grad, H. (1961). “Boundary Layer between a Plasma and a Magnetic Field,” J. Physics of Fluids (1958-1988). AIP Publishing, 4(11), pp. 1366–1375.
Harris, E. G. (1962). “On a plasma sheet separation regions of oppositely directed magnetic field,” J. Nuovo Cim., XXIII(1), pp. 115–121.
Harrison, M. G. & Neukirch, T. (2009). “Some remarks on one-dimensional force-free Vlasov–Maxwell equilibria,” J. Phys. Plasm., 16(2), pp. 22106–1 – 22106–9.
Hendrickson, R. A., McEntire, R. W. & Winckler, J. R. (1971). “Electron echo experiment: A new magnetospheric probe,” J. Nature, 230, pp. 564–566.
Heppner, J. P., Ness, N. F., Skillman, T. L. & Scearce, C. S. (1962). “Magnetic Field Measurements with the Explorer X Satellite,” J. Phys. Soc. Japan Suppl. A-II, 17, pp. 546–558.
Hess, W. N., Trichel, M. C., Davis, T. N., Beggs, W. C., Kraft, G. E., Stassinopoulos, E. & Maier, E. J. (1971). “Artificial aurora experiment: Experiment and principal results,” J. Geophys. Res. Wiley Online Library, 76(25), pp. 6067–6097.
Hoshino, M., Nishida, A., Mukai, T., Saito, Y., Yamamoto, T. & Kokubun, S. (1996). “Structure of plasma sheet in magnetotail: Double-peaked electric current sheet,” J. Geoph. Res.: Space Physics. Wiley Online Library, 101(A11), pp. 24775–24786.
De Jager, C. (1962). Structure and Dynamics of Solar Atmosphere. Moscow: Izd-vo inostr. lit.-ri.
Kaplan, S. A., Pikelner, S. B. & Tsytovich, V. N. (1977). Physics of Solar Atmospheric Plasma. Moscow: Nauka, Moscow.
Kaplan, S. A. & Tsytovich, V. N. (1972). Plasma Astrophysics. Moscow: Nauka.
Karimabadi, H., Dorelli, J., Roytershteyn, V., Daughton, W. & Chacon, L. (2011). “Flux pileup in collisionless magnetic reconnection: Bursty interaction of large flux ropes,” J. Phys. Rev. Lett. APS, 107(2).
Kline, M. (1988). “Mathematics. Search for truth,” Moscow: Mir, (in Russian).
Kolmogorov, A. I. (1990). On the concepts of quantity and number. Collection Historical and mathematical investigations, Proc. Historical and mathematical investigations. Moscow: Nauka, Moscow.
Kontorovich, V. M., Pimenov, S. F. & Tsvyk, N. A. (1993). “On the Cascade theory of type III radio bursts (fast and slow beams in the solar corona),” J. Astronomy, 70(3), p. 571.
Korn, G. & Korn, T. (1974). Reference book on mathematics. Nauka, Moscow.
Krimigis, S. M. (1965). “Interplanetary diffusion model for the time behavior of intensity in a solar cosmic ray event,” J. Geophys. Res. Wiley Online Library, 70(13), pp. 2943–2960.
Kropotkin, A. P. & Domrin, V. I. (1996). “Theory of a thin one-dimensional current sheet in collisionless space plasma,” J. Geophys. Res., 101(A9), pp. 19893–19902.
Kuznetsova, M. M., Hesse, M. & Winske, D. (2001). “Collisionless reconnection supported by nongyrotropic pressure effects in hybrid and particle shnulations,” J. Geophys. Res., 106(A3).
Landau, L. D. (1946). “Oscillations of the electron plasma,” ZhETF, 16(7), pp. 574–586, (in Russian).
Landau, L. D. & Lifshitz, E. M. (1967). “Field Theory,” Moscow: Nauka, (in Russian).
Lazutin, L. L., Gotselyuk, Y. V., Muravyova, E. A., Myagkova, I. N., Panasyuk, M. I., Starostin, L. I., Yushkov, B. Y., Kudela, K., Hasebe, N. & Sukurai, K. (2010). “Dynamics of solar protons in the Earth’s magnetosphere during magnetic storms in November 2004–January 2005,” Geomagnetism and Aeronomy. Springer, 50(2), pp. 168–180.
Ledenev, V. G. & Starygin, A. P. (2002). “Relaxation of electron fluxes generating type III bursts,” in European Space Agency, (Special Publication) ESA SP, pp. 323–326.
Lee, L. C. & Kan, J. R. (1979). “A unified kinetic model of the tangential magnetopause structure,” J. Geoph. Res. Wiley Online Library, 84(A11), p. 6417.
Lembege, B. & Pellat, R. (1982). “Stability of a thick two-dimensional quasineutral sheet,” J. Phys. Fluids., 25(11), pp. 1995–2004.
Li, B., Robinson, P. A. & Cairns, I. H. (2006a). “Numerical modeling of type III solar radio bursts in the inhomogeneous solar corona and interplanetary medium,” J. Phys. Plasm. AIP Publishing, 13(9), p. 92902.
Li, B., Robinson, P. A. & Cairns, I. H. (2006b). “Quasilinear calculation of Langmuir wave generation and beam propagation in the presence of density fluctuations,” J. Phys. Plasm. AIP Publishing, 13(8), p. 82305.
Lundin, R. & Dubinin, E. M. (1985). “Solar wind energy transfer regions inside the dayside magnetopause: Accelerated heavy ions as tracers for MHD-processes in the dayside boundary layer,” Planetary and Space Science. Elsevier, 33(8), pp. 891–907.
Lyahov, V. V. (2008). “Theory of type III radio bursts in the interplanetary space: I. Derivation of permittivity tensor for the system consisting of the electron beam and solar wind plasma,” Space research. Springer, 46(5), pp. 412–417.
Lyahov, V. V. & Neshchadim, V. M. (1995a). “On the method of studying the structure of the transition layer between thermal plasma and the magnetic field in the complex plane. Dep. in Kazgos INTI, 10.10.96, N 6395-KA95.,” NIIETF KSU, Kazgos INTI, Almaty, p. 9.
Lyahov, V. V. & Neshchadim, V. M. (1995b). “On the structure of the research methodology of the boundary sheet between the plasma flow and magnetic field in the complex plane. Dep. in Kazgos INTI, 10.10.95, N 6394-KA95.,” NIIETF KSU, Kazgos INTI, Almaty, p. 13.
Lyahov, V. V. & Neshchadim, V. M. (1998). “Non-Archimedean complex numerical axis. Space and time. Dep. in VINITI, 01.04.98, № 1076-V98,” NIIETF KSU, Kazgos INTI, Almaty.
Lyahov, V. V. & Neshchadim, V. M. (2001a). “Complex Numbers and Physical Reality,” arXiv preprint physics/0102047.
Lyahov, V. V. & Neshchadim, V. M. (2001b). “On Stability of Physics Systems,” arXiv preprint physics/0111052.
Lyahov, V. V. & Neshchadim, V. M. (2001c). “The Landau Damping Effect and Complex-valued Nature of Physical Quantities,” arXiv preprint physics/0111176.
Lyahov, V. V. & Neshchadim, V. M. (2006). “The role of complex magnitudes in plasma electrodynamics,” Advances in Plasma Physics Research. Nova Science Publishers, Inc, 5.
Lyahov, V. V. & Neshchadim, V. M. (2009). “On the theory of type III radio bursts in the nonhomogeneous interplanetary space (quasi-linear approximation),” Planetary and Space Science, 57(3), pp. 415–423.
Lyahov, V. V. & Neshchadim, V. M. (2012a). “About the Structural Stability of the Model of the Nonelectroneutral Current Sheath,” Proceedings of World Academy of Science, Engineering and Technology (WASET), 71(11), pp. 880–883.
Lyahov, V. V. & Neshchadim, V. M. (2012b). “Kinetic theory of the current sheath. I. On polarization of an equilibrium current sheath,” Advances in Space Research, 50(3), pp. 318–326.
Lyahov, V. V. & Neshchadim, V. M. (2012c). “On the Theory of Generation of Radio Bursts of III Type during Solar Flares,” Horizons in World Physics. Nova Science Publishers, Inc, 274.
Lyahov, V. V. & Neshchadim, V. M. (2013). “Kinetic theory of the current sheath. II. Effect of polarization on the stability of a current sheath,” Advances in Space Research, 51(5), pp. 730–741.
Lyahov, V. V. & Neshchadim, V. M. (2014a). “About the equilibrium and stability of non-electroneutral current sheaths,” in Advances in Space Research, pp. 901–907.
Lyahov, V. V. & Neshchadim, V. M. (2014b). “About the equilibrium and stability of the magnetopause,” Advances in Space Research, 54(1), pp. 1–13.
Lyapunov, A. M. (1956). “General problem of the stability of motion,” Collected Works, Moscow, 1956, (in Russian).
Lyu, L. H. & Kan, J. R. (1989). “Structures of Alfven shocks: S-shaped magnetic hodogram observed at the magnetopause,” Geophys. Res. Lett., 16(5), pp. 349–352.
Medvedev, F. A. (1993). Luzin about non-Archimedean time. Moscow: Nauka, Moscow.
Mingalev, O. V., Mingalev, I. V., Malova, H. V. & Zelenyi, L. M. (2007). “Numerical simulations of plasma equilibrium in a one-dimensional current sheet with a nonzero normal magnetic field component,” J. Plasm. Phys. Rep. Springer, 33(10).
Mottez, F. (2003). “Exact nonlinear analytic Vlasov–Maxwell tangential equilibria with arbitrary density and temperature profiles,” J. Phys. Plasm. AIP Publishing, 10(6), pp. 2501–2508.
Mozer, F. S., Bale, S. D., Phan, T. D. & Osborne, J. A. (2003). “Observations of electron diffusion regions at the subsolar magnetopause.,” J. A., Phys. Rev. Lett. APS, 91(24), p. 245002.
Nakamura, R., Baumjohann, W., Runov, A., Volwerk, M., Zhang, T. L., Klecker, B., Bogdanova, Y., Roux, A., Balogh, A., Reme, H., Sauvaud, J. A. & Frey, H. U. (2002). “Fast flow during current sheet thinning,” J. Geophys. Res. Lett. Wiley Online Library, 29(2), pp. 51–55.
Neukirch, T., Wilson, F. & Harrison, M. G. (2009). “A detailed investigation of the properties of a Vlasov-Maxwell equilibrium for the force-free Harris sheet,” J. Phys. Plasm., 16(12).
Nicholson, R. B. (1963). “Solution of the Vlasov Equations for a Plasma in an Externally Uniform Magnetic Field,” Physics of Fluids. AIP Publishing, 6(11), p. 1581.
Nikutowski, B., Büchner, J., Wiechen, H., Auster, U., Fornacon, K. H., Rustenbach, J., Klimov, S. L. & Savin, S. P. (1998). “A high-latitude boundary layer crossing-INTERBALL measurements and MHD model results,” Advances in Space Research, 22(1), pp. 161–165.
Panchelyuga, V. A. (2010). “Benoit Mandelbrot: the path to the fractal geometry of nature,” Hypercomplex numbers in geometry and physics, 7(2(14)), p. 172.
Panov, E. V., Artemyev, A. V., Nakamura, R. & Baumjohann, W. (2011). “Two types of tangential magnetopause current sheets: Cluster observations and theory,” J. Geoph. Res.: Space Physics. Blackwell Publishing Ltd, 116(12).
Parker, E. N. (1959). “Plasma Dynamic Determination of Shock Thickness in an Ionized Gas.,” Astrophys. J., 129, p. 217.
Parker, E. N. (1965). “Dynamic processes in the interplanetary medium,” Moscow: Mir, (in Russian).
Pavlov, D. G. (2010). “About the V International school-seminar Fundamentals of Finsler geometry and its applications in physics.,” Hypercomplex numbers in geometry and physics, 7(2(14)), p. 4.
Pellat, R., Coroniti, F. V. & Pritchett, P. L. (1991). “Does Ion Tearing Exist?,” J. Geophys. Res. Lett., 18(2), pp. 143–146.
Plaschke, F., Glassmeier, K. H., Auster, H. U., Angelopoulos, V., Constantinescu, O. D., Fornacon, K. H., Georgescu, E., Magnes, W., McFadden, J. P. & Nakamura, R. (2009). “Statistical study of the magnetopause motion: First results from THEMIS,” J. Geophys. Res.: Space Physics: Space Physics. Wiley Online Library, 114(1).
Plaschke, F., Glassmeier, K. H., Auster, H. U., Constantinescu, O. D., Magnes, W., Angelopoulos, V., Sibeck, D. G. & McFadden, J. P. (2009). “Standing Alfvén waves at the magnetopause,” J. Geophys. Res. Lett. Wiley Online Library, 36(2).
Robinson, P. A. (1992). “Clumpy Langmuir waves in type III radio sources,” J. Sol. Phys. Springer, 139(1), pp. 147–163.
Robinson, P. A. (1997). “Nonlinear wave collapse and strong turbulence,” J. Rev. Mod. Phys. APS, 69(2), pp. 507–574.
Robinson, P. A. & Benz, A. O. (2000). “Bidirectional Type III Solar Radio Bursts,” J. Sol. Phys. Springer, 194(2), pp. 345–369.
Robinson, P. A. & Cairns, I. H. (1994) “Fundamental and harmonic radiation in type III solar radio bursts,” J. Sol. Phys. Springer, 154(2), pp. 335–360.
Robinson, P. A., Cairns, I. H. & Willes, A. J. (1994). “Dynamics and efficiency of type III solar radio emission,” Astrophys. J., 422, pp. 870–882.
Roth, M., De Keyser, J. & Kuznetsova, M. M. (1996). “Vlasov theory of the equilibrium structure of tangential discontinuities in space plasmas,” J. Space Sci. Rev. Springer, 76(3–4), pp. 251–317.
Round, X. (1981) Differential Geometry of Finsler spaces. Moscow: Science, Moscow.
Runov, A. (2003) “Current sheet structure near magnetic X-line observed by Cluster,” J. Geophys. Res. Lett. Wiley Online Library, 30(11), pp. 10–13.
Runov, A., Nakamura, R., Baumjohann, W., Zhang, T. L., Volwerk, M., Eichelberger, H. U. & Balogh, A. (2003) “Cluster observation of a bifurcated current sheet,” J. Geophys. Res. Lett. Wiley Online Library, 30(2).
Savin, S. P., Amata, E., André, M., Dunlop, M., Khotyaintsev, Y., Marcucci, M. F., Fazakerley, A., Bogdanova, Y. V., Décréau, P. M. E., Rauch, J. L., Trotignon, J. G., Skalsky, A., Romanov, S., Büchner, J., Blecki, J. & Rème, H. (2006). “Experimental study of nonlinear interaction of plasma flow with charged thin current sheets: 2. Hall dynamics, mass and momentum transfer,” J. Nonlinear Proc. Geophys. Europinion Geosciences Union, 13(4), pp. 377–392.
Savin, S. P., Budaev, V. P., Zelenyi, L. M., Amata, E., Sibeck, D. G., Lutsenko, V., Borodkova, N., Zhang, H., Angelopoulos, V. & Safrankova, J. (2011). “Anomalous interaction of a plasma flow with the boundary layers of a geomagnetic trap,” JETP Lett. Springer, 93(12), p. 754.
Savin, S. P., Lyahov, V. V., Neshchadim, V. M., Amata, E., Roche, J. L., Silin, V. P., Popov, V. Y., Budaev, V. P., Klimov, S. I., Skalsky, A. A., Lezhen, L. A. & Blentski, J. (2017). “Magnetopause Charging and Transfer of Momentum and Energy into Magnetosphere,” Bulletin of the Lebedev Physics Institute, 44(4), p. 99-105.
Schindler, K. & Birn, J. (2002). “Models of two-dimensional embedded thin current sheets from Vlasov theory,” J. Geophys. Res., 107(A8), p. 1193.
Sergeev, V. A., Mitchell, D. G., Russell, C. T. & Williams, D. J. (1993) “Structure of the Tail Plasma/Current Sheet at -11 RE and Its Changes in the Course of a Substorm,” J. Geophys. Res. Wiley Online Library, 98(A10), pp. 345–365.
Sergeev, V. A., Runov, A., Baumjohann, W., Nakamura, R., Zhang, T. L., Volwerk, M., Balogh, A., Rème, H., Sauvaud, J. A., André, M. & Klecker, B. (2003). “Current sheet flapping motion and structure observed by Cluster,” J. Geophys. Res. Lett. Wiley Online Library, 30(6), p. 1327.
Sestero, A. (1964). “Structure of plasma sheaths,” Phys. Fluids (1958-1988). AIP Publishing, 7(1), pp. 44–51.
Sestero, A. (1965). “Charge Separation Effects in the Ferraro-Rosenbluth Cold Plasma Sheath Model,” Phys. Fluids (1958-1988). AIP Publishing, 8(4), pp. 739–744.
Shabansky, V. P. (1961) “Structure of the transition layer between plasma and magnetic field,” ZHETF, 40(4).
Shabansky, V. P. (1972) “Phenomena in near-Earth space,” Moscow: Nauka, (in Russian).
Shen, Z. (2001). “Differential geometry of spray and Finsler spaces,” Dordrecht: Kluwer Academic Publishers, Dordrecht.
Silin, V. P. (2011). “Theory of ion-acoustic turbulence in plasma with anisotropically heated ions,” Plasma physics reports, 37(8), p. 739.
Silin, V. P., Büchner, J. & Zelenyi, L. M. (2002). “Instabilities of collisionless current sheets: Theory and simulations,” Physics of Plasmas, 9(4), p. 1104.
Silin, V. P. & Ruhadze, A. A. (1961). The electromagnetic properties of plasma and plasma-like media, Gosatomizdat, Moscow. Moscow: Gosatomizdat, Moscow.
Sitnov, M. I., Guzdar, P. N. & Swisdak, M. (2003). “A model of the bifurcated current sheet,” J. Geophis. Res. Lett., 30(13), pp. 10–13.
Sitnov, M. I. & Lui, A. (1999). “Cross-field current instability as a catalyst of the explosive reconnection in the geomagnetotail,” J. Geophys. Res., 104(A4).
Sitnov, M. I., Malova, H. V. & Sharma, A. S. (1999). “On the question of the stability of the linear tearing modes in quasineutral current sheet,” J. Phys. plasma, 25(2), pp. 1–10, (in Russian).
Sitnov, M. I., Zelenyi, L. M., Malova, H. V. & Sharma, A. S. (2000). “Thin current sheet embedded within a thicker plasma sheet- Self-consistent kinetic theory,” J. Geophys. Res., 105(A6), p. 13029.
Snyder, C. W. & Neugebauer, M. (1964). “Interplanetary solar-wind measurements by mariner ii.,” J. Space Res., 4, pp. 89–97.
Taktakishvili, A., Zimbardo, G., Amata, E., Savin, S. P., Greco, A., Veltri, P. & Lopez, R. E. (2007). “Ion escape from the high latitude magnetopause: analysis of oxygen and proton dynamics in the presence of magnetic turbulence,” in Annales Geophysicae, pp. 1877–1885.
Tikhonov, A. N. & Samarsky, A. A. (1966). “Equations of mathematical physics,” NAUKA, p. 724, (in Russian).
Vaisberg, O. L., Galeev, A. A., Zelenyi, L. M., Zastenker, G. N., Omelchenko, A. N., Klimov, S. L., Savin, S. P., Yermolaev, Y. I., Smirnov, V. N. & Nozdrachev, M. N. (1983). “The fine structure of the magnetopause according to Prognoz-7 and Prognoz-8 satellite measurements,” Kosmicheskie Issledovaniia, 21, pp. 57–63.
Van Allen, J. A. & Krimigis, S. M. (1965). “Impulsive Emission of ∼40-kev Electrons from the Sun,” J. Geophys. Res. Wiley Online Library, 70(23), pp. 5737–5751.
Vasguez, A. M. & Gomez, D. O. (1965). “Electrostatic decay of beam-generated plasma turbulence,” J. Geophys. Res., 70, pp. 5737–5753.
Veselovsky, I. S. (1975). “On some equilibrium configurations of anisotropic plasma in a magnetic field,” ZhTF, 45, pp. 797–802, (in Russian).
Vlasov, A. A. (1938). “About the vibration properties of the electron gas,” ZhETF, 8(3), pp. 291–318, (in Russian).
Vlasov, A. A. (1945). “On the Kinetic Theory of an Assembly of Particles with Collective Interaction,” J. Physics USSR, 9(1), pp. 25–40.
Yoon, P. H. & Lui, A. T. Y. (2004). “Model of the ion-or electron-dominated current sheet,” J. Geophys. Res. Wiley Online Library, 109(A11).
Zelenyi, L. M., Dolgonosov, M. S., Bykov, A. A., Popov, V. Y. & Malova, H. V. (2002) “About influence of the trapped plasma on structure of collisionless thin current layers,” Space research, 40(4), pp. 385–394, (in Russian).

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