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Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

Part of: Focus on Plasma Astrophysics

Published online by Cambridge University Press:  05 April 2018

Anton V. Artemyev ,
Anatoly I. Neishtadt ,
Alexei A. Vasiliev  and
Didier Mourenas
Anton V. Artemyev*
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA Space Research Institute, Moscow, Russia
Anatoly I. Neishtadt
Affiliation:
Space Research Institute, Moscow, Russia Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK
Alexei A. Vasiliev
Affiliation:
Space Research Institute, Moscow, Russia
Didier Mourenas
Affiliation:
CEA, DAM, DIF, Arpajon, France
*
†Email address for correspondence: [email protected]
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Abstract

Accurately modelling and forecasting of the dynamics of the Earth’s radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave–particle resonant interaction. Energetic electron acceleration or scattering into the Earth’s atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave–particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Keywords

wave-particle interaction
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 2 , April 2018 , 905840206
Copyright
© Cambridge University Press 2018 

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References

Agapitov, O., Artemyev, A., Krasnoselskikh, V., Khotyaintsev, Y. V., Mourenas, D., Breuillard, H., Balikhin, M. & Rolland, G. 2013 Statistics of whistler mode waves in the outer radiation belt: Cluster STAFF-SA measurements. J. Geophys. Res. 118, 3407–3420.CrossRefGoogle Scholar
Agapitov, O., Artemyev, A., Mourenas, D., Krasnoselskikh, V., Bonnell, J., Le Contel, O., Cully, C. M. & Angelopoulos, V. 2014 The quasi-electrostatic mode of chorus waves and electron nonlinear acceleration. J. Geophys. Res. 119, 1606–1626.CrossRefGoogle Scholar
Agapitov, O. V., Artemyev, A. V., Mourenas, D., Mozer, F. S. & Krasnoselskikh, V. 2015 Nonlinear local parallel acceleration of electrons through Landau trapping by oblique whistler mode waves in the outer radiation belt. Geophys. Res. Lett. 42, 10.Google Scholar
Agapitov, O., Blum, L. W., Mozer, F. S., Bonnell, J. W. & Wygant, J. 2017 Chorus whistler wave source scales as determined from multipoint Van Allen Probe measurements. Geophys. Res. Lett. 44, 2634–2642.Google Scholar
Agapitov, O., Krasnoselskikh, V., Zaliznyak, Y., Angelopoulos, V., Le Contel, O. & Rolland, G. 2011 Observations and modeling of forward and reflected chorus waves captured by THEMIS. Ann. Geophys. 29, 541–550.Google Scholar
Agapitov, O. V., Mourenas, D., Artemyev, A. V. & Mozer, F. S. 2016 Exclusion principle for very oblique and parallel lower band chorus waves. Geophys. Res. Lett. 43 (21), 11112–11120.Google Scholar
Albert, J. M. 2002 Nonlinear interaction of outer zone electrons with VLF waves. Geophys. Res. Lett. 29, 1275.Google Scholar
Albert, J. M. 2010 Diffusion by one wave and by many waves. J. Geophys. Res. 115, A14.Google Scholar
Albert, J. M. & Bortnik, J. 2009 Nonlinear interaction of radiation belt electrons with electromagnetic ion cyclotron waves. Geophys. Res. Lett. 36, 12110.Google Scholar
Albert, J. M., Tao, X. & Bortnik, J. 2013 Aspects of nonlinear wave-particle interactions. In Dynamics of the Earth’s Radiation Belts and Inner Magnetosphere (ed. Summers, D., Mann, I. U., Baker, D. N. & Schulz, M.), Geophysical Monograph Series. American Geophysical Union.Google Scholar
Albert, J. M. & Young, S. L. 2005 Multidimensional quasi-linear diffusion of radiation belt electrons. Geophys. Res. Lett. 32, 14110.CrossRefGoogle Scholar
Arnold, V. I., Kozlov, V. V. & Neishtadt, A. I. 2006 Mathematical Aspects of Classical and Celestial Mechanics, 3rd edn. Springer.CrossRefGoogle Scholar
Artemyev, A., Krasnoselskikh, V., Agapitov, O., Mourenas, D. & Rolland, G. 2012 Non-diffusive resonant acceleration of electrons in the radiation belts. Phys. Plasmas 19, 122901.Google Scholar
Artemyev, A. V., Mourenas, D., Agapitov, O. V., Vainchtein, D. L., Mozer, F. S. & Krasnoselskikh, V. V. 2015 Stability of relativistic electron trapping by strong whistler or electromagnetic ion cyclotron waves. Phys. Plasmas 22, 082901.CrossRefGoogle Scholar
Artemyev, A. V., Neishtadt, A. I., Vasiliev, A. A. & Mourenas, D. 2016 Kinetic equation for nonlinear resonant wave-particle interaction. Phys. Plasmas 23 (9), 090701.CrossRefGoogle Scholar
Artemyev, A. V., Neishtadt, A. I., Vasiliev, A. A. & Mourenas, D.2017a Kinetic equation for systems with resonant captures and scatterings. Preprint, arXiv:1710.04489.Google Scholar
Artemyev, A. V., Neishtadt, A. I., Vasiliev, A. A. & Mourenas, D. 2017b Probabilistic approach to nonlinear wave-particle resonant interaction. Phys. Rev. E 95 (2), 023204.Google Scholar
Artemyev, A. V., Vasiliev, A. A., Mourenas, D., Agapitov, O. & Krasnoselskikh, V. 2013 Nonlinear electron acceleration by oblique whistler waves: Landau resonance versus cyclotron resonance. Phys. Plasmas 20, 122901.Google Scholar
Artemyev, A. V., Vasiliev, A. A., Mourenas, D., Agapitov, O., Krasnoselskikh, V., Boscher, D. & Rolland, G. 2014 Fast transport of resonant electrons in phase space due to nonlinear trapping by whistler waves. Geophys. Res. Lett. 41, 5727–5733.Google Scholar
Bell, T. F. 1984 The nonlinear gyroresonance interaction between energetic electrons and coherent VLF waves propagating at an arbitrary angle with respect to the earth’s magnetic field. J. Geophys. Res. 89, 905–918.Google Scholar
Bortnik, J., Inan, U. S. & Bell, T. F. 2006 Landau damping and resultant unidirectional propagation of chorus waves. Geophys. Res. Lett. 33, L03102.Google Scholar
Bortnik, J., Thorne, R. M. & Inan, U. S. 2008 Nonlinear interaction of energetic electrons with large amplitude chorus. Geophys. Res. Lett. 35, 21102.Google Scholar
Breuillard, H., Zaliznyak, Y., Agapitov, O., Artemyev, A., Krasnoselskikh, V. & Rolland, G. 2013 Spatial spreading of magnetospherically reflected chorus elements in the inner magnetosphere. Ann. Geophys. 31, 1429–1435.CrossRefGoogle Scholar
Brinca, A. L. 1980 On the evolution of the geomagnetospheric coherent cyclotron resonance in the midst of noise. J. Geophys. Res. 85, 4711–4714.CrossRefGoogle Scholar
Cattell, C., Wygant, J. R., Goetz, K., Kersten, K., Kellogg, P. J., von Rosenvinge, T., Bale, S. D., Roth, I., Temerin, M., Hudson, M. K. et al. 2008 Discovery of very large amplitude whistler-mode waves in Earth’s radiation belts. Geophys. Res. Lett. 35, 1105.Google Scholar
Chen, L., Thorne, R. M., Li, W. & Bortnik, J. 2013 Modeling the wave normal distribution of chorus waves. J. Geophys. Res. 118, 1074–1088.CrossRefGoogle Scholar
Cully, C. M., Bonnell, J. W. & Ergun, R. E. 2008 THEMIS observations of long-lived regions of large-amplitude whistler waves in the inner magnetosphere. Geophys. Res. Lett. 35, 17.Google Scholar
Demekhov, A. G., Trakhtengerts, V. Y., Hobara, Y. & Hayakawa, M. 2000 Cyclotron amplification of whistler waves by nonstationary electron beams in an inhomogeneous magnetic field. Phys. Plasmas 7, 5153–5158.Google Scholar
Demekhov, A. G., Trakhtengerts, V. Y., Rycroft, M. & Nunn, D. 2009 Efficiency of electron acceleration in the Earth’s magnetosphere by whistler mode waves. Geomagn. Aeron. 49, 24–29.Google Scholar
Demekhov, A. G., Trakhtengerts, V. Y., Rycroft, M. J. & Nunn, D. 2006 Electron acceleration in the magnetosphere by whistler-mode waves of varying frequency. Geomagn. Aeron. 46, 711–716.Google Scholar
Dolgopyat, D. 2012 Repulsion from resonances. In Memoires De La Societe Mathematique De France, vol. 128. Amer Mathematical Society.Google Scholar
Drozdov, A. Y., Shprits, Y. Y., Orlova, K. G., Kellerman, A. C., Subbotin, D. A., Baker, D. N., Spence, H. E. & Reeves, G. D. 2015 Energetic, relativistic, and ultrarelativistic electrons: comparison of long-term VERB code simulations with Van Allen Probes measurements. J. Geophys. Res. 120, 3574–3587.Google Scholar
Drummond, W. E. & Pines, D. 1962 Nonlinear stability of plasma oscillations. Nucl. Fusion Suppl. 3, 1049–1058.Google Scholar
Foster, J. C., Erickson, P. J., Omura, Y., Baker, D. N., Kletzing, C. A. & Claudepierre, S. G. 2017 Van allen probes observations of prompt mev radiation belt electron acceleration in nonlinear interactions with vlf chorus. J. Geophys. Res. 122 (1), 324–339.Google Scholar
Glauert, S. A., Horne, R. B. & Meredith, N. P. 2014 Three-dimensional electron radiation belt simulations using the BAS Radiation Belt Model with new diffusion models for chorus, plasmaspheric hiss, and lightning-generated whistlers. J. Geophys. Res. 119, 268–289.Google Scholar
Hsieh, Y.-K. & Omura, Y. 2017a Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere. J. Geophys. Res. 122, 675–694.Google Scholar
Hsieh, Y.-K. & Omura, Y. 2017b Study of wave-particle interactions for whistler mode waves at oblique angles by utilizing the gyroaveraging method. Radio Sci. 52 (10), 1268–1281.Google Scholar
Itin, A. P., Neishtadt, A. I. & Vasiliev, A. A. 2000 Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave. Physica D 141, 281–296.Google Scholar
Karpman, V. I. 1974 Nonlinear effects in the ELF waves propagating along the magnetic field in the magnetosphere. Space Sci. Rev. 16, 361–388.CrossRefGoogle Scholar
Karpman, V. I., Istomin, J. N. & Shklyar, D. R. 1974 Nonlinear theory of a quasi-monochromatic whistler mode packet in inhomogeneous plasma. Plasma Phys. 16, 685–703.Google Scholar
Karpman, V. I., Istomin, J. N. & Shklyar, D. R. 1975 Effects of nonlinear interaction of monochromatic waves with resonant particles in the inhomogeneous plasma. Phys. Scr. 11, 278–284.Google Scholar
Kennel, C. F. & Engelmann, F. 1966 Velocity space diffusion from weak plasma turbulence in a magnetic field. Phys. Fluids 9, 2377–2388.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1988 Mechanics, vol. 1. Pergamon Press.Google Scholar
Leoncini, X., Vasiliev, A. & Artemyev, A. 2018 Resonance controlled transport in phase space. Physica D 364, 22–26.Google Scholar
Le Queau, D. & Roux, A. 1987 Quasi-monochromatic wave-particle interactions in magnetospheric plasmas. Solar Rephys. 111, 59–80.CrossRefGoogle Scholar
Li, W., Bortnik, J., Thorne, R. M. & Angelopoulos, V. 2011a Global distribution of wave amplitudes and wave normal angles of chorus waves using THEMIS wave observations. J. Geophys. Res. 116, 12205.Google Scholar
Li, W., Thorne, R. M., Bortnik, J., Shprits, Y. Y., Nishimura, Y., Angelopoulos, V., Chaston, C., Le Contel, O. & Bonnell, J. W. 2011b Typical properties of rising and falling tone chorus waves. Geophys. Res. Lett. 38, L14103.Google Scholar
Lyons, L. R. & Williams, D. J. 1984 Quantitative Aspects of Magnetospheric Physics. D. Reidel Publishing Company.Google Scholar
Ma, Q., Li, W., Thorne, R. M., Nishimura, Y., Zhang, X.-J., Reeves, G. D., Kletzing, C. A., Kurth, W. S., Hospodarsky, G. B., Henderson, M. G. et al. 2016 Simulation of energy-dependent electron diffusion processes in the Earth’s outer radiation belt. J. Geophys. Res. 121, 4217–4231.CrossRefGoogle Scholar
Mourenas, D., Artemyev, A. V., Agapitov, O. V., Mozer, F. S. & Krasnoselskikh, V. V. 2016 Equatorial electron loss by double resonance with oblique and parallel intense chorus waves. J. Geophys. Res. 121, 4498–4517.Google Scholar
Mozer, F. S., Artemyev, A., Agapitov, O. V., Mourenas, D. & Vasko, I. 2016 Near-relativistic electron acceleration by Landau trapping in time domain structures. Geophys. Res. Lett. 43, 508–514.Google Scholar
Neishtadt, A. I. 1999 On adiabatic invariance in two-frequency systems. In Hamiltonian Systems with Three or More Degrees of Freedom (ed. Sim, C.), NATO ASI Series C, vol. 533, pp. 193–213. Kluwer.CrossRefGoogle Scholar
Neishtadt, A. I., Petrovichev, B. A. & Chernikov, A. A. 1989 Particle entrainment into unlimited acceleration. Sov. J. Plasma Phys. 15, 1021–1023.Google Scholar
Nunn, D. 1971 Wave-particle interactions in electrostatic waves in an inhomogeneous medium. J. Plasma Phys. 6, 291.Google Scholar
Nunn, D. 1974 A self-consistent theory of triggered VLF emissions. Planet. Space Sci. 22, 349–378.CrossRefGoogle Scholar
Nunn, D. 1986 A nonlinear theory of sideband stability in ducted whistler mode waves. Planet. Space Sci. 34, 429–451.CrossRefGoogle Scholar
Nunn, D. & Omura, Y. 2015 A computational and theoretical investigation of nonlinear wave-particle interactions in oblique whistlers. J. Geophys. Res. 120, 2890–2911.Google Scholar
Omura, Y., Furuya, N. & Summers, D. 2007 Relativistic turning acceleration of resonant electrons by coherent whistler mode waves in a dipole magnetic field. J. Geophys. Res. 112, 6236.Google Scholar
Omura, Y., Miyashita, Y., Yoshikawa, M., Summers, D., Hikishima, M., Ebihara, Y. & Kubota, Y. 2015 Formation process of relativistic electron flux through interaction with chorus emissions in the Earth’s inner magnetosphere. J. Geophys. Res. 120, 9545–9562.Google Scholar
Omura, Y. & Zhao, Q. 2012 Nonlinear pitch angle scattering of relativistic electrons by EMIC waves in the inner magnetosphere. J. Geophys. Res. 117, 8227.Google Scholar
Omura, Y. & Zhao, Q. 2013 Relativistic electron microbursts due to nonlinear pitch angle scattering by EMIC triggered emissions. J. Geophys. Res. 118, 5008–5020.Google Scholar
Santolík, O., Kletzing, C. A., Kurth, W. S., Hospodarsky, G. B. & Bounds, S. R. 2014 Fine structure of large-amplitude chorus wave packets. Geophys. Res. Lett. 41, 293–299.Google Scholar
Schulz, M. & Lanzerotti, L. J. 1974 Particle Diffusion in the Radiation Belts. Springer.Google Scholar
Shapiro, V. D. & Sagdeev, R. Z. 1997 Nonlinear wave-particle interaction and conditions for the applicability of quasilinear theory. Phys. Rep. 283, 49–71.Google Scholar
Sheeley, B. W., Moldwin, M. B., Rassoul, H. K. & Anderson, R. R. 2001 An empirical plasmasphere and trough density model: CRRES observations. J. Geophys. Res. 106, 25631–25642.Google Scholar
Shklyar, D. & Matsumoto, H. 2009 Oblique whistler-mode waves in the inhomogeneous magnetospheric plasma: resonant interactions with energetic charged particles. Surv. Geophys. 30, 55–104.Google Scholar
Shklyar, D. R. 1981 Stochastic motion of relativistic particles in the field of a monochromatic wave. Sov. Phys. JETP 53, 1197–1192.Google Scholar
Shklyar, D. R. 2011 On the nature of particle energization via resonant wave-particle interaction in the inhomogeneous magnetospheric plasma. Ann. Geophys. 29, 1179–1188.Google Scholar
Shklyar, D. R. 2017 Energy transfer from lower energy to higher-energy electrons mediated by whistler waves in the radiation belts. J. Geophys. Res. 122 (1), 640–655.Google Scholar
Shprits, Y. Y., Kellerman, A. C., Drozdov, A. Y., Spence, H. E., Reeves, G. D. & Baker, D. N. 2015 Combined convective and diffusive simulations: VERB-4D comparison with 17 March 2013 Van Allen Probes observations. Geophys. Res. Lett. 42, 9600–9608.Google Scholar
Solovev, V. V. & Shklyar, D. R. 1986 Particle heating by a low-amplitude wave in an inhomogeneous magnetoplasma. Sov. Phys. JETP 63, 272–277.Google Scholar
Stix, T. H. 1962 The Theory of Plasma Waves. McGraw-Hill.Google Scholar
Su, Z., Zheng, H. & Wang, S. 2010 Three-dimensional simulation of energetic outer zone electron dynamics due to wave-particle interaction and azimuthal advection. J. Geophys. Res. 115, 6203.Google Scholar
Summers, D. & Omura, Y. 2007 Ultra-relativistic acceleration of electrons in planetary magnetospheres. Geophys. Res. Lett. 34, 24205.Google Scholar
Summers, D., Thorne, R. M. & Xiao, F. 1998 Relativistic theory of wave-particle resonant diffusion with application to electron acceleration in the magnetosphere. J. Geophys. Res. 103, 20487–20500.Google Scholar
Tao, X., Bortnik, J., Albert, J. M. & Thorne, R. M. 2012a Comparison of bounce-averaged quasi-linear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations. J. Geophys. Res. 117, 10205.Google Scholar
Tao, X., Bortnik, J., Albert, J. M., Thorne, R. M. & Li, W. 2013 The importance of amplitude modulation in nonlinear interactions between electrons and large amplitude whistler waves. J. Atmos. Sol.-Terr. Phys. 99, 67–72.Google Scholar
Tao, X., Bortnik, J., Thorne, R. M., Albert, J. M. & Li, W. 2012b Effects of amplitude modulation on nonlinear interactions between electrons and chorus waves. Geophys. Res. Lett. 39, 6102.Google Scholar
Thorne, R. M., Li, W., Ni, B., Ma, Q., Bortnik, J., Chen, L., Baker, D. N., Spence, H. E., Reeves, G. D., Henderson, M. G. et al. 2013 Rapid local acceleration of relativistic radiation-belt electrons by magnetospheric chorus. Nature 504, 411–414.Google Scholar
Thorne, R. M., Ni, B., Tao, X., Horne, R. B. & Meredith, N. P. 2010 Scattering by chorus waves as the dominant cause of diffuse auroral precipitation. Nature 467, 943–946.Google Scholar
Trakhtengerts, V. Y. 1966 Stationary states of the Earth’s outer radiation zone. Geomagn. Aeron. 6, 827–836.Google Scholar
Tsurutani, B. T., Falkowski, B. J., Verkhoglyadova, O. P., Pickett, J. S., Santolík, O. & Lakhina, G. S. 2011 Quasi-coherent chorus properties: 1 implications for wave-particle interactions. J. Geophys. Res. 116, 9210.Google Scholar
Turner, D. L., Lee, J. H., Claudepierre, S. G., Fennell, J. F., Blake, J. B., Jaynes, A. N., Leonard, T., Wilder, F. D., Ergun, R. E., Baker, D. N. et al. 2017 Examining coherency scales, substructure, and propagation of whistler-mode chorus elements with magnetospheric multiscale (mms). J. Geophys. Res. 122, 11201–11226.Google Scholar
Vasiliev, A., Neishtadt, A. & Artemyev, A. 2011 Nonlinear dynamics of charged particles in an oblique electromagnetic wave. Phys. Lett. A 375, 3075–3079.CrossRefGoogle Scholar
Vedenov, A. A., Velikhov, E. P. & Sagdeev, R. Z. 1962 Quasilinear theory of plasma oscillations. Nucl. Fusion Suppl. 2, 465–475.Google Scholar
Wilson, L. B. III, Cattell, C. A., Kellogg, P. J., Wygant, J. R., Goetz, K., Breneman, A. & Kersten, K. 2011 The properties of large amplitude whistler mode waves in the magnetosphere: propagation and relationship with geomagnetic activity. Geophys. Res. Lett. 38, 17107.Google Scholar
Yoon, P. H., Pandey, V. S. & Lee, D.-H. 2013 Relativistic electron acceleration by oblique whistler waves. Phys. Plasmas 20 (11), 112902.Google Scholar