Kinetic Alfvén waves in space plasmas Yuriy Voitenko Belgian Institute for Space Aeronomy, Brussels, Belgium Solar-Terrestrial Center of Excellence, Space Pole, Belgium Recent results obtained in collaboration with V. Pierrard, J. De Keyser, P. Shukla CHARM kick-of meeting (8-9 October 2012, Leuven, Belgium)
Solar-terrestrial example: solar atmosphere à solar wind à magnetosphere ALFVEN WAVES AND TURBULENCE! à space weather
Super-adiabatic cross-field ion acceleration Resonant plasma heating and particle acceleration Demagnetization of ion motion Kinetic wave-particle interaction KAWs Phase mixing Turbulent cascade Kinetic instabilities Parametric decay MHD AWs Unstable PVDs
Existence of electromagnetic hydrodynamic waves (H. Alfvén, Nature 150, 405 406, 1942)
MHD VS. KINETIC ALFVÉN WAVE Kinetic Alfvén wave (KAW) - extension of Alfvén mode in the range of small perpendicular wavelength (Hasegawa and Chen, 1974-1980) [ ] 2 V 2 2 K 2 ( 2 ) B ( z; r ; t) = 0 t A z KAW dispersion: ω = k V K( k ) z A Padé approximation for the KAW dispersion function: 2 2 K ( k ) 1+ k ρ ( 1+ T / T ); = p e p ρ p - proton gyroradius.
EXAMPLE 1: KAW turbulence in the solar wind
RECENT PROGRESS IN TURBULENCE (1) MHD Alfvénic turbulence evolves anisotropically towards large wavenumbers perpendicular to the mean magnetic field: e.g. J. Shebalin, P. Goldreich, S. Sridhar, G. Howes, A. Schekochihin (2) Alfvén waves with finite (kinetic Alfvén waves - KAWs) differ drastically from MHD Alfvén waves: e.g. A. Hasegawa, L. Chen, J. Hollweg, D.-J. Wu, Y. Voitenko, WE STILL DO NOT KNOW: where and how (1) transforms into (2) what are transition scales and spectra dissipative effects and velocity distributions of particles turbulence in kinetic vs. inertial regime
k - 1 δ i _ I o n c y c l o t r o n N o n a d I a b a t I c N o n l i n e a r C h e r e n k o v KA W - 1 R ç ρ i - 1 k
RECENT OBSERVATIONAL EVIDENCES FOR KAWs He et al. (2011,2012); Podesta & Gary (2011): AT THE PROTON KINETIC SCALES THERE ARE TWO COMPONENTS: ION-CYCLOTRON (20 %) AND (DOMINANT) KINETIC ALFVEN (80%) Follows MHD slab component? Follows MHD 2D component? He et al. (2011,2012)
RECENT OBSERVATIONAL EVIDENCES FOR KAWs Exploiting B II Bo component to discriminate KAWs vs. whistlers: He et al. (2012) : DO KINETIC ALFVEN / ION-CYCLOTRON OR FAST-MODE/WHISTLER WAVES DOMINATE THE DISSIPATION OF SOLAR WIND TURBULENCE NEAR THE PROTON INERTIAL LENGTH? Salem et al. (2012) : IDENTIFICATION OF KINETIC ALFVEN WAVE TURBULENCE IN THE SOLAR WIND Theoretical predictions for whistlers are not supported by observations: He et al. (2012) Salem et al. (2012)
SOLAR WIND TURBULENCE MHD AW RANGE? KINETIC RANGE ( f ~ k_perp ) Sahraoui et al. (2010): high-resolution magnetic spectrum exhibits 4 different slopes (!) in different ranges.
MHD VS KINETIC ALFVÉN TURBULENCE AT MHD SCALES (MHD AWs): Only counter-propagating MHD AWs interact: (Goldreich and Sridhar, 1995; Boldyrev, 2005; Gogoberidze, 2007) AT KINETIC SCALES (KAWs): Co-propagating KAWs interact (Voitenko, 1998): Counter-propagating KAWs interact (Voitenko, 1998):
ALFVÉNIC TURBULENCE SPECTRA (THEORY) Non-dispersive range (MHD): à à weak turbulence; strong turbulence; Weakly dispersive range (kinetic): à à weak turbulence; strong turbulence; Strongly dispersive range (kinetic): à à weak turbulence; strong turbulence;
DOUBLE-KINK SPECTRAL PATTERN (Voitenko and De Keyser, 2011) Two interpretations: dissipative (left) and dispersive (right) Left cannot exist without right! But right can exist without left!
ALFVÉNIC TURBULENCE IN SOLAR WIND MHD RANGE WDR kinetic SDR KINETIC ( f ~ k_perp ) Sahraoui et al. (2010): high-resolution magnetic spectrum
EXAMPLE 2: proton energization in the solar wind by KAW turbulence
VELOCITY-SPACE DIFFUSION OF PROTONS: ANALYTICAL THEORY (Voitenko and Pierrard, 2012) 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 SW PROTONS: ANALYTICAL THEORY (Voitenko and Pierrard, 2012)
VELOCITY-SPACE DIFFUSION OF PROTONS: KINETIC SIMULATIONS (Pierrard and Voitenko, 2012) We use the kinetic Fokker-Planck equation with diffusion terms due to Coulomb collisions and KAW turbulence Set boundary at 14 Rs (above the Alfvén point) Use a model Alfvénic spectrum as observed at >0.3 AU and project it back to 14 Rs following ~ 1/ r^2 radial profile for the turbulence amplitude Plug the obtained spectrum in the diffusion term for wave-particle Cherenkov interactions Solve numerically using spectral method Observe tails in the obtained proton VDFs
VELOCITY-SPACE DIFFUSION OF PROTONS: KINETIC SIMULATIONS (Pierrard and Voitenko, 2012) 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 at 14 Rs by the Fokker-Planck evolution equation including Coulomb collisions and KAW turbulence
PROTON VELOCITY DISTRIBUTIONS WITH TAILS IN THE SOLAR WIND (after E. Marsch, 2006) Kinetic-scale Alfvénic turbulence covers the tails velocity ranges
NON-MAXWELLIAN LANDAU DAMPING F s V ph1 V ph2 V z KAW velocities
PARALLEL PROTON ACCELERATION BY KAWs: NON-LINEAR CHERENKOV RESONANCE MOTIVATION:
COLLISIONLESS TRAPPING CONDITION:
Generation of proton beams by KAWs Stage 1: proton trapping by KAWs F p V Tp V ph1 V z proton trapping occurs here
Generation of proton beams by KAWs Stage 2: acceleration due to increasing V ph F p ACCELERATION V Tp V ph V z
Generation of proton beams by KAWs F p ACCELERATION V Tp V ph1 V ph2 V z KAWs trap protons here and release/maintain here
PARALLEL PROTON ACCELERATION BY KAWs: NON-LINEAR CHERENKOV RESONANCE KAW pulse Passing by (free) protons Reflected protons set up a beam
B/Bo = 0.2 0.12 0.09 0.06 0.03 Normalised velocity of reflected protons as function of thermal/alfven velocity ratio. The relative KAW amplitude =0.03, 0.06, 0.09, 0.12, and 0.2 (from bottom to top). Linkage to local Alfven velocity + good coverage of typical values.
β_{p } = 0.49 0.36 0.25 0.16 Number density of reflected protons as function of the relative KAW amplitude B/B₀. The proton beta β_{p }=0.16, 0.25, 0.36, and 0.49 (from bottom to top). Trend: large relative beam density with larger plasma beta compatible with observations.
PROTON VELOCITY DISTRIBUTIONS WITH BEAMS (after E. Marsch, 2006) KAW velocities are here
SUMMARY MHD-kinetic turbulence transition occurs in the weakly dispersive range (WDR): <1 Steepest spectra occur in WDR up to Hence: universal double-kink spectral pattern Hence: quasi-linear proton diffusion à producing suprathermal proton tails locally in the solar wind Hence: nonlinear Cherenkov resonance with protons: à producing proton beams locally in the solar wind spectrally localized selective dissipation removing highest amplitudes in the vicinity of the spectral break à intermittency reduction (observed by Alexandrova et al. 2008) à switch to weak turbulence and steepest spectra (was observed by Smith et al. 2006)
FURTHER DIRECTIONS à Nature of quasi-perpendicular versus quasi-parallel components of turbulence at MHD and kinetic scales à à Are they related? à à Their respective cascades? à Role of anisotropy in the MHD-kinetic transition à Dissipation versus dispersion shaping of kinetic spectra à Correlations between nonthermal features in particles VDFs and turbulence characteristics à KAW turbulence driven by non-local interactions à
EXAMPLE 3: inertial Alfvén turbulence in the auroral zones
Aurora multiscale Alfvén wave flux (photo by Jan Curtic)
Simultaneous observations of Alfvén waves at altitudes 7 RE (Polar) and 1.5 RE (FAST) in the main phase of a major geomagnetic storm on 22 October 1999 (Dombeck et al., 2005): wave energy flux decreased from 45 to 10 erg/cm2/s between Polar and FAST electron energy flux increased to 20 erg/cm2/s most wave flux is carried by large MHD-scale Alfvén waves
W W ~ k MHD ~ k MHD -p -p PROBLEMS Injected wave spectrum kinetic k Depleted spectrum kinetic Not enough energy in kinetic-scale waves Depletion at kinetic scales is not observed How the most energetic MHD part of spectrum is dissipated? k
Possible solution - turbulent cascade to kinetic scales: Ø ion gyroradius ρ i (reflects gyromotion and ion pressure effects); Ø ion gyroradius at electron temperature ρ s (reflects electron pressure effects); Ø ion inertial length δ i (reflects effects due to ion inertia); Ø electron inertial length δ e (reflects effects due to electron inertia). If δ e larger than other microscales --> --> inertial regime; Ø parallel wave electric field develop at such length scales --> particle acceleration.
NONLINEAR IKAW INTERACTION AND TURBULENCE (Voitenko, Shukla, De Keyser, 2012)
MHD / INERTIAL KAW TRANSITION MHD nonlinear rate (Boldyrev 2005; Gogoberidze 2007): Compare with nonlinear interaction rates of IKAWs: MHD/kinetic transition occurs when MHD/kinetic rate = 1: < 0.1 for counter-propagating KAWs = 0.3 for co-propagating KAWs
TURBULENCE SPECTRA IN KINETIC RANGE strong turbulence: nonlinear time scales of perturbations are comparable to the linear ones critical balance condition in spectral representation: equivalent frequency = nonlinear interaction rate resulting spectra: à for co-propagating IKAWs; à for counter-propagating IKAWs; counter-propagating interaction is stronger and dominate spectra
(a) UV auroral image from Polar UVI instrument and FAST spacecraft trajectory. (b) FAST Ex (red) and By (black) fields. (c),(d) FAST electron and ion spectrograms. From: Chaston et al. (2008): Phys.Rev.Lett 100, 175003.
FAST measurements from August 6 to September 9, 1998 at 1.6 ER MHD k i n e t i c (a) Average B 2 (fsp=kx) spectra. (b) Average E 2 (fsp=kx) spectra. From: Chaston et al. (2008): Phys.Rev.Lett 100, 175003,