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Properties and evolution of anisotropic structures in collisionless plasmas

Published online by Cambridge University Press:  19 September 2016

A. R. Karimov*
Affiliation:
Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13/19, Moscow, 127412, Russia Department of Electrophysical Facilities, National Research Nuclear University MEPhI, Kashirskoye shosse 31, Moscow, 115409, Russia
M. Y. Yu
Affiliation:
Department of Physics, Zhejiang University, 310027 Hangzhou, China Institut für Theoretische Physik I, Ruhr-Universität Bochum, D-44780 Bochum, Germany
L. Stenflo
Affiliation:
Department of Physics, Linköping University, SE-58183 Linköping, Sweden
*
Email address for correspondence: [email protected]

Abstract

A new class of exact electrostatic solutions of the Vlasov–Maxwell equations based on the Jeans’s theorem is proposed for studying the evolution and properties of two-dimensional anisotropic plasmas that are far from thermodynamic equilibrium. In particular, the free expansion of a slab of electron–ion plasma into vacuum is investigated.

Type
Research Article
Copyright
© Cambridge University Press 2016 

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References

Agren, O., Moiseenko, V., Johansson, C. & Savenko, N. 2005 Gyro center invariant and associated diamagnetic current. Phys. Plasmas 12, 122503.CrossRefGoogle Scholar
Agren, O. & Moiseenko, V. 2006 Four motional invariants in axisymmetric tori equilibria. Phys. Plasmas 13, 052501.Google Scholar
Arfken, G. B. & Weber, H. J. 2006 Mathematical Methods for Physicists, 6th edn. Elsevier.Google Scholar
Birdsall, C. K. & Langdon, A. B. 2004 Plasma Physics via Computer Simulation. Taylor & Francis.Google Scholar
Bohr, T., Jensen, M. H., Paladin, G. & Vulpiani, A. 1998 Dynamics Systems Approach to Turbulence. Cambridge University Press.Google Scholar
Buchanan, M. & Dorning, J. J. 1993 Superposition of nonlinear plasma waves. Phys. Rev. Lett. 70, 37323735.Google Scholar
Campa, A., Dauxois, T., Fanelli, D. & Ruffo, S. 2014 Physics of Long-Range Interacting Systems. Oxford University Press.CrossRefGoogle Scholar
Chavanis, P. H. 2012 Kinetic theory of Onsagers vortices in two-dimensional hydrodynamics. Physica A 391, 36573679.Google Scholar
Clemmow, P. C. & Dougherty, J. P. 1969 Electrodynamics of Particles and Plasmas. Edison-Wesley.Google Scholar
Degond, P. & Raviart, P. A. 1992 An analysis of the Darwin model of approximation to Maxwells equations. Forum Math. 4, 1327.CrossRefGoogle Scholar
Demeio, L. & Zweifel, P. F. 1990 Numerical simulations of perturbed Vlasov equilibria. Phys. Fluids B 2, 12521255.CrossRefGoogle Scholar
Demeio, L. & Holloway, J. P. 1991 Numerical simulations of BGK modes. J. Plasma Phys. 46, 6384.Google Scholar
Dorozhkina, D. S. & Semenov, V. E. 1998 Exact solution of Vlasov equations for quasineutral expansion of plasma bunch into vacuum. Phys. Rev. Lett. 81, 26912694.CrossRefGoogle Scholar
Eyink, G. L. & Sreenivasan, K. R. 2006 Onsager and the theory of hydrodynamic turbulence. Rev. Mod. Phys. 78, 87135.Google Scholar
Eliasson, B. & Shukla, P. K. 2006 Formation and dynamics of coherent structures involving phase-space vortices in plasmas. Phys. Rep. 422, 225290.CrossRefGoogle Scholar
Holloway, J. P. & Dorning, J. J. 1991 Undamped plasma waves. Phys. Rev. A 44, 38563868.Google Scholar
Karimov, A. R. & Lewis, H. R. 1999 Nonlinear solutions of the Vlasov–Poisson equations. Phys. Plasmas 6, 759761.CrossRefGoogle Scholar
Karimov, A. R. 2001 Nonlinear solutions of a Maxwellian type for the Vlasov–Poisson equations. Phys. Plasmas 8, 15331537.CrossRefGoogle Scholar
Karimov, A. R., Stenflo, L. & Yu, M. Y. 2009a Coupled azimuthal and radial flows and oscillations in a rotating plasma. Phys. Plasmas 16, 062313.Google Scholar
Karimov, A. R., Stenflo, L. & Yu, M. Y. 2009b Coupled flows and oscillations in asymmetric rotating plasmas. Phys. Plasmas 16, 102303.Google Scholar
Karimov, A. R. & Godin, S. M. 2009 Coupled radial and azimuthal oscillations in twirling cylindrical plasmas. Phys. Scr. 80, 035503.CrossRefGoogle Scholar
Karimov, A. R., Yu, M. Y. & Stenflo, L. 2011 Flow oscillations in radial expansion of an inhomogeneous plasma layer. Phys. Lett. A 375, 26292636.Google Scholar
Karimov, A. R., Yu, M. Y. & Stenflo, L. 2012 Large quasineutral electron velocity oscillations in radial expansion of an ionizing plasma. Phys. Plasmas 19, 092118.CrossRefGoogle Scholar
Karimov, A. R. 2013 Coupled electron and ion nonlinear oscillations in a collisionless plasma. Phys. Plasmas 20, 052305.CrossRefGoogle Scholar
Karimov, A. R., Yu, M. Y. & Stenflo, L. 2016 A new class of exact solutions for Vlasov–Poisson Plasmas. Phys. Scr.; (submitted).Google Scholar
Kiessling, M. K. H. 2003 The ‘Jeans swindle’: a true story mathematically speaking. Adv. Appl. Maths 31, 132149.Google Scholar
Kovalev, V. F. & Bychenkov, V. Y. 2003 Analytic solutions to the Vlasov equations for expanding plasmas. Phys. Rev. Lett. 90, 185004.CrossRefGoogle Scholar
Kozlov, V. V. 2008 The generalized Vlasov kinetic equation. Russian Math. Surveys 63, 93130.Google Scholar
Kuznetsov, E. A. 1996 Wave collapse in plasmas and fluids. Chaos 6, 381390.CrossRefGoogle ScholarPubMed
Lancellotti, C. & Dorning, J. J. 1998 Critical initial states in collisionless plasmas. Phys. Rev. Lett. 81, 51375140.Google Scholar
Lewis, H. R. & Leach, P. G. L. 1982 A direct approach to finding exact invariants for one-dimensional time-dependent classical Hamiltonians. J. Math. Phys. 23, 23712374.Google Scholar
Lewis, H. R. & Symon, K. R. 1984 Exact time-dependent solutions of the Vlasov–Poisson equations. Phys. Fluids 27, 192196.CrossRefGoogle Scholar
Levin, Y., Pakter, R., Rizzato, F. B., Teles, T. N. & Benetti, F. P. C. 2014 Nonequilibrium statistical mechanics of systems with long-range interactions. Phys. Rep. 535, 160.CrossRefGoogle Scholar
Luque, A. & Schamel, H. 2005 Electrostatic trapping as a key to the dynamics of plasmas, fluids and other collective systems. Phys. Rep. 415, 261359.CrossRefGoogle Scholar
Majda, A. J., Majda, G. & Zheng, Y. 1994 Concentrations in the one-dimensional Vlasov–Poisson equations I: temporal development and non-unique weak solutions in the single component case. Physica D 74, 268300.Google Scholar
Manfredi, G. 1997 Long-time behavior of nonlinear Landau damping. Phys. Rev. Lett. 79, 28152828.CrossRefGoogle Scholar
Nielson, C. & Lewis, H. R. 1976 Particle code models in the nonradiative limit. Meth. Comput. Phys. 16, 367388.Google Scholar
Pecseli, H. L. 2012 Waves and Oscillations in Plasmas. Taylor & Francis.Google Scholar
Saffman, P. G. 2006 Vortex Dynamics. Cambridge University Press.Google Scholar
Schamel, H. 2004 Lagrangian fluid description with simple applications in compressible plasma and gas dynamics. Phys. Rep. 392, 279319.Google Scholar
Schamel, H. 2015 Particle trapping: a key requisite of structure formation and stability of Vlasov–Poisson plasmas. Phys. Plasmas 22, 042301.CrossRefGoogle Scholar
Struckmeier, J. & Riedel, C. 2001 Invariants for time-dependent Hamiltonian systems. Phys. Rev. E 64, 026503.Google Scholar
Taranov, V. B. 1976 On the symmetry of one-dimensional high frequency motions of a collisionless plasma. Sov. Phys. Tech. Phys. 21, 720724.Google Scholar
Wang, Y.-M., Yu, M. Y., Stenflo, L. & Karimov, A. R. 2016 Evolution of a cold non-neutral electron–positron plasma slab. Chin. Phys. Lett. 33, 085205.CrossRefGoogle Scholar
Yang, S., Shi, B. & Li, M. 2011 Mean square stability of impulsive stochastic differential systems. Intl J. Diff. Equ. 2011, 613695.Google Scholar