Alfv é nic turbulence at

1. Alfvénic turbulence at ion kinetic scalesYuriy VoitenkoSolar-Terrestrial Centre of Excellence, BIRA-IASB, Brussels, Belgium Recent results obtained in collaboration with J. De Keyser, V. Pierrard, J. S. Zhao, D. J. Wu STORM annual meeting (25-26 November 2013, Graz, Austria)

2. OUTLINE 1. MHD Alfvénic turbulence evolves anisotropically toward large wavenumbers (perpendicular to the mean magnetic field) [Goldreich and Sridhar,1996] 2. Alfvén waves at ion (proton) kinetic scales (KAWs with finite differ drastically from MHD Alfvén waves [Hasegawa and Chen, 1974] 3. Alfvén turbulence at ion kinetic scales is much less known [see however Voitenko, 1998; Voitenko and De Keyser, 2011]

3. k || ICW _ - 1 d i I o n – c y c l o t r o n m i c r o ( k i n e t i c ) C h e r e n k o v N o n – a d I a b a t I c KAW M A C R O ( M H D ) | | - 1 k r R - 1 ç ^ i

4. KINETIC ALFVEN WAVES - KAWs Kinetic Alfvén wave (KAW) - extension of Alfvén mode in the range of high perpendicular wavenumbers. Padé approximation for the KAW dispersion: - proton gyroradius.

5. THEORY (Howes; Schekochihin et al., 2008-2013) -5/3 Power Spectral Density -7/3 MHD RANGE KAW RANGE =1

6. SOLAR WIND TURBULENCE ? MHD RANGE KAW RANGE ( f ~ k_perp ) Sahraoui et al. (2010): high-resolution magnetic spectrum exhibits 4 different slopes (!)

7. MHD VS KINETIC ALFVÉN TURBULENCE AT MHD SCALES (MHD AWs): Only counter-propagating MHD AWs interact (Goldreich and Sridhar, 1995) AT KINETIC SCALES (KAWs): Counter-propagating KAWs interact (Voitenko, 1998): Co-propagating KAWs interact (Voitenko, 1998):

8. ALFVÉNIC TURBULENCE SPECTRA (THEORY) Non-dispersive range (MHD):  weak turbulence;  strong turbulence; Weakly dispersive range (WDR kinetic):  weak turbulence; STEEPEST!  strong turbulence; Strongly dispersive range (SDR kinetic):  weak turbulence;  strong turbulence;

9. DOUBLE-KINK SPECTRAL PATTERN (Voitenko and De Keyser, 2011) Three possible interpretations: (1) dissipative (left), or (2) dispersive (right), or (3) =(1)+(3)

10. ALFVÉNIC TURBULENCE IN SOLAR WIND WDR kinetic MHD RANGE SDR KINETIC ( f ~ k_perp ) KAW range = WDR KAW range + SDR KAW range

11. PUZZLE 1: KAWs VERSUS OTHER WAVE MODES AT ION SCALES

12. RECENT OBSERVATIONS OF WAVE MODES Wave-vector inclination (top) and frequency (bottom) versus wavenumber [Narita et al., 2011]. The dispersion analysis suggests whistlers/magnetosonic waves rather than kinetic Alfven waves.

13. RECENT OBSERVATIONS OF WAVE MODES Exploiting BIIBo component to discriminate KAWs vs. FW/whistlers: He et al. (2012):DO KINETIC ALFVEN/ION-CYCLOTRON OR FAST-MODE/WHISTLER WAVES DOMINATE? Salem et al. (2012) :IDENTIFICATION OF KINETIC ALFVEN TURBULENCE IN THE SOLAR WIND FW/whistlers are not supported by these observations: He et al. (2012) Salem et al. (2012)

14. PUZZLE 2: PARALLEL AGAINST PERPENDICULAR ION HEATING

15. PROTON VELOCITY DISTRIBUTIONS WITH SUPRATHRMAL TAILS AND ANISOTROPIC CORES IN THE SOLAR WIND (after E. Marsch, 2006) Kinetic-scale Alfvénic turbulence covers the tails’ velocity ranges

16. Use kinetic Fokker-Planck equation for protons with diffusion terms due to KAWs Calculate proton diffusion (plateo formation) time Use observed turbulence levels and spectra Estimate generated tails in the proton VDFs and compare with observed ones VELOCITY-SPACE DIFFUSION OF PROTONS: ANALYTICAL THEORY (Voitenko and Pierrard, 2013) NUMERICAL SIMULATIONS Pierrard and Voitenko, 2013)

17. VELOCITY-SPACE DIFFUSION OF SW PROTONS: ANALYTICAL THEORY (Voitenko and Pierrard, 2013)

18. VELOCITY-SPACE DIFFUSION OF PROTONS: KINETIC SIMULATIONS (Pierrard and Voitenko, 2013) Proton velocity distributions with tails are reproduced not far from the boundary KAW velocities cover this range Proton VDF obtained at 17 Rs assuming a displaced Maxwellian as boundary condition at14 Rs by the Fokker-Planck evolution equation including Coulomb collisions and KAW turbulence

19. Fp VTp Vph2 Vz proton diffusion occurs here Generation of proton tails by turbulence MHD RANGE WDR kinetic SDR kinetic ( f ~ k_perp ~ Vz) DIFFUSION VA

20. PUZZLE 3: REDUCED INTERMITTENCY AT ION SCALES

21. FLATNESS DECREASES AT ION SCALES, WHICH IS COUNTER-INTUITIVE Alexandrova et al. (2008)

22. SPECTRALLY LOCALIZED SELECTIVE DISSIPATION acceleration AW turbulent spectrum (solid line) and ”threshold” spectrum for non-adiabatic ion acceleration (dashed line).Cross-field non-adiabatic ion acceleration is associated with the first spectral kink, where the turbulent spectral power raises above the threshold spectrum.

23. SUMMARY • Nonlinear kinetics becomes important at scales that are still larger than the ion gyroradius • Alfvenic turbulence is formed by weakly/mildly dispersive KAWs • Main dissipation mechanisms: nonlinear Landau damping and non-adiabatic ion acceleration • This explains many phenomena revealed by the field and particle observations: • Steepest spectra at ion scales and double-kink spectral pattern • Suprathermal ion tails and beams along MF • Proton heating across MF • spectrally localized selective dissipation removing highest amplitudes in the vicinity of the spectral break •  Reduced intermittency observed by Alexandrova et al. (2008) •  switch to weak turbulence and steepest spectra (were observed by Smith et al. 2006 and Sahraoui et al. 2010)