General aspects of whistler wave generation in space plasmas K. Sauer and R. Sydora

Transcription

1 General aspects of whistler wave generation in space plasmas K. Sauer and R. Sydora Institute of Geophysics, University of Alberta, Canada ISSS-10, Banff, Canada, July 24-30, 2011

2 General aspects of whistler wave generation in space plasmas Introduction: whistler wave observations in space and laboratory Two kinds of whistler waves: - unstable waves, - stationary nonlinear waves: oscillitons (Sauer et al., 2002) Results of PIC simulations showing the transition from unstable waves to oscillitons Summary

3 HF electromagnetic waves in an electron-proton plasma G=Ω e /ω e < 1 (solar wind) and G=Ω e /ω e > 1 (auroral regions)

4 Whistler waves in an electron-proton plasma with G=Ω e /ω e < 1

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6 Power spectral density of the magnetic field versus the generalized McIllwain coordinate L * The black line marks f ce /2 Polar spacecraft measurements, adapted from Santolik et al. (2010).

7 Large-amplitude whistlers observed in Earth s radiation belt by STEREO Cattel et al., 2008 ω ~ 0.2 Ω e V ph ~ 0.2V Ae θ ~ 50 0

8 Large-amplitude whistlers observed in Earth s radiation belt by Wind Wilson III et al., 2011 B 0 ~400nT db y /B 0 ~0.02 f/f ce 0.5 mostly oblique propagation

9 Auroral hiss near Saturn s moon Enceladus: Cassini observations Gurnett et al., 2011 Parameters: f ce =9 khz, B~300 nt f pe = 65 khz, n~45 cm - G=f ce /f pe ~0.15 V Ae = cm/s, V Te = cm/s (T e ~40eV) β e ~0.007 V b ~ cm/s (~100eV) V b /V Ae ~ 0.1 (0.2) The frequency is terminated at f/f ce ~0.75.

10 Electron beam experiment aboard Spacelab 2 Farrell et al., 1998 Parameters: f ce =1 MHz, B~ nt f pe = 3 MHz, n~10 5 cm -3 G=f ce /f pe ~0.33 V Ae ~ cm/s, V Te ~ 10 8 cm/s (Te~10eV), V Ae ~100 V Te : β e ~ V b ~10 9 cm/s (~1 kev) V b /V Ae ~0.1 (0.2)

11 Parameters: Laboratory experiment, Stenzel 1977 f ce ~220 MHz, B~30 G f pe ~ 1 GHz, n~ cm -3 G=f ce /f pe ~ V Ae ~ cm/s, V Te ~ 10 8 cm/s (Te~2eV), V Ae ~100 V Te : β e ~10-4 V b ~ cm/s ( 50 ev) V b /V Ae ~0.1 (0.2) n b /n 0 =0.005

12 G=Ω e /ω e <1 Two kinds of whistler waves Unstable waves driven by beams or electron temperature anisotropy Nonlinear stationary waves: whistler oscillitons (nonlinear Gendrin mode waves)

13 θ=0 0 ω = f(θ)

14 Unstable whistler waves driven by temperature anisotropy a) Warm plasma (β e = ) with temperature anisotropy (T /T // =2), parallel propagation (θ=0 0 ). b) Cold (β e = ) and hot anisotropic population (n h /n c =0.15, T h /T c =7, T /T // =10, θ=40 0 )

15 Unstable whistler waves driven by electron beams c) Cold plasma (βe= ) with sub-alfvenic beam (n b /n c =0.01, V b /V Ae =0.2, T b /T c =1), θ=40 0 ): Cherenkov-type instability ω=k V b d) Cold plasma (β e = ) with super-alfvenic beam (n b /n c =0.01, V b /V Ae =2.5, T b /T c =1), θ=60 0 : Doppler-shifted cyclotron mode ω = -Ω e + k V b

16 Unstable whistler waves: maximum growth rate at oblique propagation a) Cold plasma and hot anisotropic population b) Cold plasma and super-alfvenic beam

17 Gendrin mode waves propagating obliquely to the magnetic field Gendrin mode waves: kc/ω e =1, ω/ω e =(1/2)cosθ V ph =V ph /cosθ=v gr =V Ae /2 The component of the phase velocity parallel to B 0 and the group velocity have the same value! Gendrin, 1961; Helliwell, 1995 z magnetic field direction B 0 θ k wave propagation direction x

18 Whistler wave dispersion, stationary waves and oscillitons θ=0 0 Gendrin point Sauer et al., 2002 θ=70 0 Whistler wave dispersion at parallel and oblique propagation, θ=0 0,70 0 ω = ω(k) Dispersion of stationary waves: ω k U k = k(u) Whistler oscillitons (nonlinear Gendrin mode waves): B y, E z = f(x)

19 Nonlinear stationary waves(whistler oscillitons), nonlinear Gendrin mode waves; Basic equations are: Sauer et al., 2002 (1) Equation of motion for electrons and protons : (2) Ampere s law and t U x (3) Faraday s law

20 Governing equations of whistler oscillitons Equations of motion for electrons and protons: i=e,p u u iy x u x ez iz = = 1 m i 1 = ( E z m ei (E ( E + y z + u u u B ix B ex ex ixy B z y y + u u u iz B B B ey ey iyx x )/(M - v ) /(M v ) x/(m x v ix ) ) ex ix ) Ampere s law: B y x = n v + n e ez p v pz, B z x =+ n v + n e ey p v py Faraday s law: E = + M y B z, E = M z B y B o x Conservation of longitudinal momentum: u px u ex = 1 2Mµ p (B 2 1) M=U/V Ae

21 Waveform of nonlinear Gendrin mode waves (whistler oscillitons) Sauer, Sydora; 2010 θ=70 0, U=0.172V Ae

22 Particle in-cell (PIC) simulations of the evolution of unstable whistler waves

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24 Temporal evolution of unstable whistler waves, transition to oscillitons magnetic energy 8 T T/ 4 0 temperature ratio T /T (transition from T /T =9 to ~3) wave number (transition from kc/ω e ~2 to 1)

25 Wave number shift from unstable waves to oscillitons oscillitons unstable waves

26 Transition to oscillitons: nonlinear Gendrin waves Spatial profiles from oscilliton theory (Sauer et al., 2002, 2010) kc/ω e ~1 Spatial profiles from PIC simulations (Sydora et al., 2007)

27 two electron populations: cold+hot anisotropic 10-2 Time: / Magnetic Energy ω t e

28 Wave number shift of unstable waves ω e t log B y x 10-3 kc/ω e

29 Wave number shift seen in other studies Schriver et al., Whistler wave generation PIC simulation Silin et al., EMIC waves Vlasov simulation Usanova, EMIC waves (thesis, Univ. Alberta) - Hybrid code simulation

30 Wave number shift due to nonlinear wave-wave interaction Schriver et al., 2010

31 Superposition of two anisotropic populations: cool and hot one Gendrin mode β c =0.003 n c /n e =0.9 A c =5 θ max ~ 45 0 β h =0.01 n h /n e =0.1 A h =7 θ max ~10 0 Gary et al., AGU Radiation belt physics conference, St. John s, July 2011

32 Explanation of banded structure of whistler wave emission The spectrum of whistler waves is essentially determined by the electron plasma beta (β e ): Only one warm population (β e >0.01) whistler emission only in the lower frequency band: ω=(1/2)ω e cos(θ) Only one cool population (β e <<0.01) whistler emission only in the upper frequency band: ω=ω e cos(θ)

33 Explanation of frequency bands and gaps at whistler wave emission Nunn et al., 2009 Schriver et al., 2011

34 Summary There are two kinds of whistler waves: a) unstable waves with kc/ω e >1, b) whistler oscillitons (nonlinear Gendrin modes) PIC simulations have shown that oscillitons can be excited by unstable waves owing to nonlinear wave number shift, obviously caused by wavewave interaction. Frequency bands and gaps in observed whistler wave spectra and the particular role of one-half the cyclotron frequency (Ω e /2) can be explained by the transition from unstable waves to oscillitons.

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