Nonlinear processes of whistler-mode wave-particle interactions

Transcription

1 Nonlinear processes of whistler-mode wave-particle interactions Yoshiharu Omura Research Institute for Sustainable Humanosphere, Kyoto University RBSP SWG Meeting, APL, May 16-17, 2012

2 Chorus Emission due to Injection of Energetic Electrons [Cluster, Santolik and Gurnett,]

3 VLF Triggered Emissions Rising and falling tones from the Morse code dashes [Helliwell, et al., JGR, 1964]

4 Overview Constant Frequency Wave Linear growth rate Quasi-linear diffusion Nonlinear trapping and relativistic acceleration in an inhomogeneous medium: RTA and URA Rising-tone Chorus Element Nonlinear wave growth Generation of upper-band chorus emissions (Nonlinear wave damping) Efficient acceleration by nonlinear trapping and formation of the pancake distribution

5 Test Particle Simulation of Nonlinear Wave Trapping and Acceleration of Trapped Particles ( kev) Wave Electrons [ Omura and Summers, JGR, 2006 ]

6 Resonance Velocity

7 Trajectories of Resonant Electrons (400 kev) Relativistic Turning Acceleration (RTA) Bw = 125 pt [Omura, Furuya, and Summers, JGR, 2007]

8 Trajectories of Resonant Electrons ( > 1MeV) Ultra-Relativistic Acceleration (URA) [Summers and Omura, GRL, 2007]

9 Electron Hybrid Simulation (cold electrons : fluid) = 9 Linear Growth Nonlinear Growth [Katoh and Omura,GRL, 2007]

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11 Frequency Sweep Rate Dependence on Wave Amplitude at Equator, which is controlled by Energetic Electron Density [Katoh and Omura, 2011]

12 RTA and URA in the chorus generation process [Katoh, Omura and Summers, Ann. Geophys. 2008]

13 Numerical Green s Function G(K 1, K 2 ) [Furuya et al., JGR, 2008 ]

14 Time evolution of F(K) estimated by repeating the convolution integral F 0 (K) F 1000 (K) A constant influx of F 0 (K) ( kev) is assumed.

15 for Whistler-mode Wave for Longitudinal Wave

16 Inhomogeneity Ratio for inhomogeneous density model for constant density model [Omura et al., JGR, 2008; 2009]

17 Formation of Electron Hole by Nonlinear Wave Trapping with Inhomogeneity S = -0.4

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19 Nonlinear Wave Growth due to Formation of Electromagnetic Electron Hole Maximum -J E [Omura, et al., JGR, 2008]

20 Electron Hole for Nonlinear Wave Growth [Hikishima and Omura, JGR, 2012]

21 The linear dispersion relation gives The frequency only changes at the equator realizing the condition for the maximum J E.

22 Vlasov Hybrid Simulation [Nunn et al., 2009] [Omura and Nunn, JGR, 2011]

23 Linear Dispersion Relation Nonlinear Dispersion Relation Assuming where ( > 0 : Electron Hole)

24 By calculating the resonant current J B we estimate the frequency sweep rate by dividing the frequency deviation by the nonlinear transition time T N for formation of the resonant current. where and Equating ω 1 /T N and the frequency sweep rate for the maximum nonlinear wave growth [Omura and Nunn, JGR, 2011]

25 We obtain an optimum wave amplitude for triggering a rising tone emission whereas the threshold for nonlinear wave growth through propagation is given by where we assume a parabolic variation of the dipole magnetic field as [ Omura et al., JGR, 2009; Omura and Nunn, JGR, 2011 ]

26 Electron Hybrid Code Simulation [Katoh and Omura, 2007]

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29 Rising-Tone Emissions Triggered by Waves with Different Amplitudes [Hikishima and Omura, JGR 2012]

30 Chorus Equations : Absolute Instability Threshold of Wave Amplitude B w Time Scale of Chorus T c

31 Formation of Electron Hole and Bump [Hikishima et al., JGR, 2010 ]

32 Nonlinear Wave Growth through Propagation : Convective Instability Equator [Hikishima et al., JGR, 2010] Self-sustaining Mechanism h B w

33 Simulations : parallel propagation Observations: oblique propagation [Omura et al., JGR, 2008 ] [Hikishima et al., JGR, 2009 ] [Santolik, et al., JGR, 2003 ] [Hosphodarsky et al., JGR, 2008 ]

34 Quasi-parallel Propagation (Oblique) : Wavenormal Angle With

35 Nonlinear Resonant Damping in the dipole magnetic field [Omura et al., JGR, 2009]

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37 [ Burtis and Helliwell, PSS, 1976 ]

38 [Kurita et al., to be submitted JGR]

39 [Kurita et al., to be submitted JGR]

40 Summary The nonlinear wave growth takes place near the equator through formation of an electromagnetic electron hole for a rising tone triggered emission with an optimum wave amplitude above the threshold of the absolute instability. The self-sustaining mechanism results in the nonlinear wave growth through propagation away from the equator. Oblique propagation in a dipole field induces strong nonlinear resonant damping at half the gyro-frequency due to trapping by the parallel wave electric field, resulting in the lower and upper band chorus emissions. Resonant electrons trapped by chorus emissions are accelerated to higher pitch angles, forming a pancake distribution. Some of them are effectively accelerated to relativistic energy by RTA and URA, resulting in formation of relativistic electron flux of the radiation belts.

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42 Linear Dispersion Relation Nonlinear Dispersion Relation Assuming where ( J B < 0 : Electron Hole) ( J B > 0 : Electron Hill )

43 Electron Hole for Rising Tone Electron Hill for Falling Tone

44 Nonlinear Wave Growth Rising Tone Emission 0 < Q < 1 Falling Tone Emission -1< Q < 0

45 Whistler-mode Triggered Emissions EMIC Triggered Emissions [Kimura et al., JGG, 1990] [Pickett et al., GRL, 2010]

46 Cluster Spacecraft Observation EMIC Triggered Emissions Hybrid Code Simulation [Omura et al., JGR, 2010] [Shoji and Omura, JGR, 2011]

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