Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T12:20:29.122Z Has data issue: false hasContentIssue false

A drift of Langmuir waves in a magnetized inhomogeneous plasma

Published online by Cambridge University Press:  11 January 2019

Vasily I. Erofeev*
Affiliation:
Institute of Automation and Electrometry, Russian Academy of Sciences, 1 Koptyug Prosp., 630090, Novosibirsk, Russia Novosibirsk State University, 2 Pirogova Str., Novosibirsk, Russia
*
Email address for correspondence: [email protected]

Abstract

The concept of informativeness of nonlinear plasma physics scenarios is explained. Natural ideas of developing highly informative models of plasma kinetics are spelled out. They are applied to develop a formula that governs the drift of long Langmuir waves in spatial positions and wave vectors in a magnetized plasma due to the plasma inhomogeneity. Together with previous findings (Erofeev, Phys. Plasmas, vol. 22, 2015, 092302), the formula evidences the need for an intelligent generalization of the notion of wave energy density from usual homogeneous plasmas to inhomogeneous ones.

Type
Research Article
Copyright
© Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akhiezer, I. A., Danelia, I. A. & Tsintsadze, N. L. 1964 Theory of transformation and scattering of electromagnetic waves in a nonequilibrium plasma. Sov. Phys. JETP 19, 208.Google Scholar
Al’tshul’, L. M. & Karpman, V. I. 1965 The kinetics of waves in a weakly turbulent plasma. Sov. Phys. JETP 20 (4), 10431056.Google Scholar
Andrés, N. & Sahraoui, F. 2017 Alternative derivation of exact law for compressible and isothermal magnetohydrodynamics turbulence. Phys. Rev. E 96, 053205.Google Scholar
Araki, K. 2015 Helicity-based particle-relabeling operator and normal mode expansion of the dissipationless incompressible hall magnetohydrodynamics. Phys. Rev. E 92, 063106.Google Scholar
Banks, J. W., Brunner, S., Berger, R. L., Arrighi, W. J. & Tran, T. M. 2017 Collisional damping rates for electron plasma waves reassessed. Phys. Rev. E 96, 043208.Google Scholar
Belyi, V. V. 2018 Theory of Thomson scattering in inhomogeneous plasmas. Phys. Rev. E 97, 053204.Google Scholar
Bhattacharjee, C., Das, R., Stark, D. J. & Mahajan, S. M. 2015 Beltrami state in black-hole accretion disk: a magnetofluid approach. Phys. Rev. E 92, 063104.Google Scholar
Bogoliubov, N. N. 1962 Problems of a dynamical theory in a statistical physics. In Studies in Statistical Mechanics (ed. deBoer, J. & Uhlenbeck, G. E.), vol. 1. North-Holland.Google Scholar
Born, M. & Green, H. S. 1949 A General Kinetic Theory of Liquids. Cambridge University Press.Google Scholar
Dupree, T. H. 1963 Kinetic theory of plasma and the electromagnetic field. Phys. Fluids 6, 17141729.Google Scholar
Erofeev, V. 2011a High-Informative Plasma Theory. LAP.Google Scholar
Erofeev, V. 2013 Printsipy Razrabotki Visokoinformativnikh Modelei Plazmennoi Kinetiki. Publishing House of the Siberian Branch of RAS.Google Scholar
Erofeev, V. 2016 Coulomb collisions in a ‘single’ ionized plasma. AIP Conf. Proc. 1771 (1), 040004.Google Scholar
Erofeev, V. I. 1997 Derivation of an equation for three-wave interactions based on the Klimontovich–Dupree equation. J. Plasma Phys. 57 (2), 273298.Google Scholar
Erofeev, V. I. 2000 Langmuir wave scattering induced by electrons in a single collisionless plasma. J. Fusion Energy 19 (2), 99113.Google Scholar
Erofeev, V. I. 2002a Collisionless dissipation of Langmuir turbulence. Phys. Plasmas 9 (4), 11371149.Google Scholar
Erofeev, V. I. 2002b Impossibility of Zakharov’s short-wavelength modulational instability in plasmas with intense Langmuir turbulence. J. Plasma Phys. 68 (1), 125.Google Scholar
Erofeev, V. I. 2003 Influence of Langmuir turbulence on plasma electron distribution during the induced wave scattering. J. Fusion Energy 22 (4), 259275.Google Scholar
Erofeev, V. I. 2004a Derivation of an evolution equation for two-time correlation function. J. Plasma Phys. 70 (3), 251270.Google Scholar
Erofeev, V. I. 2004b Impossibility of Vedenov–Rudakov’s plasma modulational instability as one more illustration of the inappropriateness of the recipes of nonequilibrium statistical mechanics. Phys. Plasmas 11 (6), 32843295.Google Scholar
Erofeev, V. I. 2009 Key ideas for heightening the informativeness of plasma physical theorizing. J. Plasma Fusion Res. Ser. 8, 5964.Google Scholar
Erofeev, V. I. 2010 Thermalization of Langmuir wave energy via the stochastic plasma electron acceleration. J. Fusion Energy 29, 337346.Google Scholar
Erofeev, V. I. 2011b A decay of Langmuir wave quanta in their scatter by plasma electrons. J. Fusion Energy 30, 157168.Google Scholar
Erofeev, V. I. 2011c High-informative theorizing in plasma physics: basic principles and importance for researches on beam-plasma heating, plasma confinement and transport phenomena. Fusion Sci. Technol. 59 (1T), 316319.Google Scholar
Erofeev, V. I. 2014 High-informative version of nonlinear transformation of Langmuir waves to electromagnetic waves. J. Plasma Phys. 80, 289318.Google Scholar
Erofeev, V. I. 2015a Dissipation of Langmuir waves in the process of their nonlinear conversion into electromagnetic waves. J. Plasma Phys. 81, 905810322.Google Scholar
Erofeev, V. I. 2015b A maximally informative version of inelastic scattering of electromagnetic waves by Langmuir waves. Phys. Plasmas 22 (9), 092302.Google Scholar
Gibbs, J. W. 1902 Elementary Principles in Statistical Mechanics, Developed with Especial Reference to the Rational Foundation of Thermodynamics. Yale University Press.Google Scholar
Hau-Riege, S. P. & Weisheit, J. 2017 Microfield dynamics in dense hydrogen plasmas with high- $z$ impurities. Phys. Rev. E 95, 013204.Google Scholar
Hill, D. W. & Kingham, R. J. 2018 Enhancement of pressure perturbations in ablation due to kinetic magnetized transport effects under direct-drive inertial confinement fusion relevant conditions. Phys. Rev. E 98, 021201.Google Scholar
Keenan, B. D., Simakov, A. N., Chacón, L. & Taitano, W. T. 2017 Deciphering the kinetic structure of multi-ion plasma shocks. Phys. Rev. E 96, 053203.Google Scholar
Kirkwood, J. G. 1946 The statistical mechanical theory of transport processes. J. Chem. Phys. 14, 180201.Google Scholar
Klimontovich, Y. L. 1958 On the method of ‘second quantization’ in phase space. Sov. Phys. JETP 6, 753.Google Scholar
Klimontovich, Y. L. 1967 The Statistical Theory of Nonequilibrium Processes in a Plasma. MIT Press.Google Scholar
Maxwell, J. C. 1865 A dynamical theory of the electromagnetic field. Phil. Trans. R. Soc. Lond. 155, 459512.Google Scholar
Plunk, G. G. 2013 Landau damping in a turbulent setting. Phys. Plasmas 20 (3), 032304.Google Scholar
Rozmus, W., Brantov, A., Fortmann-Grote, C., Bychenkov, V. Y. & Glenzer, S. 2017 Electrostatic fluctuations in collisional plasmas. Phys. Rev. E 96, 043207.Google Scholar
Sagdeev, R. Z. & Galeev, A. A. 1969 Nonlinear Plasma Theory. Benjamin.Google Scholar
Schoeffler, K. M., Loureiro, N. F. & Silva, L. O. 2018 Fully kinetic Biermann battery and associated generation of pressure anisotropy. Phys. Rev. E 97, 033204.Google Scholar
Shi, Y., Qin, H. & Fisch, N. J. 2017 Three-wave scattering in magnetized plasmas: from cold fluid to quantized lagrangian. Phys. Rev. E 96, 023204.Google Scholar
Squire, J. & Bhattacharjee, A. 2015 Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence. Phys. Rev. E 92, 053101.Google Scholar
Stawarz, J. E. & Pouquet, A. 2015 Small-scale behavior of hall magnetohydrodynamic turbulence. Phys. Rev. E 92, 063102.Google Scholar
Taguchi, M. 2010 Theory of particle diffusion in electrostatic turbulent plasma using extended direct-interaction approximation. J. Plasma Phys. 76 (05), 681697.Google Scholar
Terashima, Y. & Yajima, N. 1963 Radiation by plasma waves in a homogeneous plasma. Prog. Theor. Phys. 30, 443459.Google Scholar
Tsytovich, V. N. 1970 Nonlinear Effects in Plasma. Plenum.Google Scholar
Viciconte, G., Gréa, B.-J. & Godeferd, F. S. 2018 Self-similar regimes of turbulence in weakly coupled plasmas under compression. Phys. Rev. E 97, 023201.Google Scholar
Vlasov, A. A. 1945 On the kinetic theory of an assembly of particles with collective interaction. J. Phys. (U.S.S.R.) 9 (1), 2540.Google Scholar
Wang, S. 2013 Kinetic theory of weak turbulence in plasmas. Phys. Rev. E 87 (6), 063103.Google Scholar
Willes, A. J., Robinson, P. A. & Melrose, D. B. 1996 Second harmonic electromagnetic emission via Langmuir wave coalescence. Phys. Plasmas 3 (1), 149159.Google Scholar
Yoon, P. H. 2000 Generalized weak turbulence theory. Phys. Plasmas 7, 48584872.Google Scholar
Yoon, P. H. 2005a Effects of spontaneous fluctuations on the generalized weak turbulence theory. Phys. Plasmas 12 (4), 042306.Google Scholar
Yoon, P. H. 2005b Nonlinear electromagnetic susceptibilities of unmagnetized plasmas. Phys. Plasmas 12 (11), 112306.Google Scholar
Yoon, P. H. 2006 Statistical theory of electromagnetic weak turbulence. Phys. Plasmas 13 (2), 022302.Google Scholar
Yoon, P. H. & Fang, T.-M. 2008 Kinetic theory for low-frequency turbulence in magnetized plasmas including discrete-particle effects. Phys. Plasmas 15 (12), 122312.Google Scholar
Yoon, P. H., Ziebell, L. F., Gaelzer, R. & Pavan, J. 2012 Electromagnetic weak turbulence theory revisited. Phys. Plasmas 19 (10), 102303.Google Scholar
Yoon, P. H., Ziebell, L. F., Kontar, E. P. & Schlickeiser, R. 2016 Weak turbulence theory for collisional plasmas. Phys. Rev. E 93, 033203.Google Scholar
Yvon, J. 1935 La théorie des fluids et l’équation d’état: actualités, scirntifigues et industrielles. Hermann and Cie.Google Scholar
Ziebell, L. F., Yoon, P. H., Gaelzer, R. & Pavan, J. 2012 Langmuir condensation by spontaneous scattering off electrons in two dimensions. Plasma Phys. Control. Fusion 54 (5), 055012.Google Scholar