Kinetic Alfvén turbulence driven by MHD turbulent cascade Yuriy Voitenko & Space Physics team Belgian Institute for Space Aeronomy, Brussels, Belgium Multifractal and turbulence workshop - 2010 (8-11 June 2009, Space Pole, Belgium)

Aurora – multifractal? (photo by Jan Curtic) With the increasingly accepted notion that MHD turbulence cascades anisotropically towards small cross-field length scales and drives kinetic Alfvén turbulence below some threshold length scale, it has become more important to determine just what that threshold length scale is supposed to be. An accurate determination requires a calculation of the cascade rates at MHD and kinetic length-scales that are amplitude dependent, which can dramatically influence the results. Aurora – multifractal? (photo by Jan Curtic)

Outline Kinetic Alfvén waves (KAWs) are the extensions of their MHD counterparts in the range of short (kinetic) cross-field wavelengths comparable to ion gyroradius or electron inertial length (Hasegawa and Chen, 1975 ). Contrary to MHD Alfvén waves, KAWs are efficient in the field-aligned acceleration of electrons and ions and cross-field acceleration of ions. What to see: the alfvenicity determines the transition between MHD and kinetic domains where different cascade mechanisms dominate. KAWs interact nonlinearly among themselves and form power-law turbulent spectra (Voitenko, 1998a,b). KAWs interact with plasma and deposit energy in plasma species. Spectral distributions of the KAW energy provides the possibility of a spectrally localised ion heating acceleration.

At small wave lengths cascading AWs meet natural length scales reflecting plasma microstructure: ion gyroradius i (reflects gyromotion and ion pressure effects); ion gyroradius at electron temperature s (reflects electron pressure effects); ion inertial length i (reflects effects due to ion inertia), and electron inertial length e (reflects effects due to electron inertia).

due to ion polarisation drift z MHD Alfven wave: Bo Cross-field ion currents due to ion polarisation drift Wave electric field Ex vary with z but not with x x

kinetic Alfven wave: short cross-field wavelength Bo Cross-field ion currents build up ion space charges and holes Field-aligned electron currents try to compensate ion charges but fail (electron inertia and/or electron pressure effects) Parallel electric field arise

decay of a pump KAW into two co-streaming KAWs (1998b)  kzVAK(k1) P = 1 + 2; kP = k1 + k2 kzVAK(kP) P kzVAK(k2) 1 2 k1z k2z kPz kz

decay of a pump KAW in two counter-streaming KAWs (1998b) kP = k1 + k2  kzVAK(kP) kzVAK(k1) P 1 kzVAK(k2) 2 k2z kPz k1z kz

Electron energization by KAWs: effect of parallel electric field Ez || B0

Electron heating by KAWs: Landau damping Fi Fe VTi Vph1 Vph2 Vz VA KAWs are here

Super-adiabatic cross-field ion acceleration Resonant plasma heating and particle acceleration Demagnetization of ion motion Kinetic wave-particle interaction Kinetic Alfvén waves Kinetic instabilities Parametric decay Turbulent cascade Phase mixing MHD waves Unstable PVDs

Wygant et al. (2002) – evidence of parallel electron acceleration by KAWs at 4 Earth radii

Equation for cross-field ion velocity in the presence of KAWs: Specify KAW fields as: In the vicinity of demagnetizing KAW phases the solution can grow exponentially as where K is the KAW phase velocity (dispersion). In the two-fluid model

n-a/p H+ He+ O+ 0.5A (mi/qi)/(mp/qp) A-1 2A-1 1 + kx2p2 ________ 16 (mi/qi)/(mp/qp) A-1 2A-1 1 + kx2p2 ________ ___ B A = kxp K(kx) B0

Some important properties of the super-adiabatic ion acceleration by KAWs: Non-resonant, frequency independent Bulk kick-like acceleration across the magnetic field after single super-critical KAW fluctuation Depends on the parallel ion velocity Threshold-like in wave amplitude and/or cross-field wavelength

Perpendicular velocity of an ion in a super-critical KAW wave train Phase portrait of the ion’s orbit in the region of super-adiabatic acceleration (transition of the demagnetizing wave phase 3 pi)

The origin of velocity space relates to PROTON VELOCITY DISTRIBUTIONS IN THE SOLAR WIND (HELIOS MEASUREMENTS) The origin of velocity space relates to the maximum of the distribution. Isodensity contours correspond to fractions of 0.8, 0.6, 0.4, 0.2 and of 0.1, 0.03, 0.01, 0.003, 0.001 (dashed contours). The vector of solar wind flow is along VY axis, the vector of magnetic field is along dash line.

KAW turbulence (Voitenko, 1998): (i) dual perpendicular cascades; (ii) power law spectra  k-p , 2<p<4; (iii) excitation of the counter-streaming KAWs - imbalanced turbulence,  k-2 (p=2);

Hamrin et al. (2002) estimated spectral slope of the BBELF turbulence observed by Freja as p=-2,5

Spectra steepened with higher k: intermittent dissipation range acceleration occurs around spectral break Approximate condition for non-adiabatic ion acceleration Constant Nb depends on the KAW amplitudes at the spectral break

surfing acceleration of ions along Bo Effect of : surfing acceleration of ions along Bo Condition for non-adiabatic ion acceleration by power-law spectrum: Let it be satisfied for ions with initial at some , where they undergo initial cross-field acceleration. Then magnetic mirror force come into play and accelerate these ions upward along Bo, increasing upward (negative) . Increased , in turn makes more turbulent energy accessible for ions (the condition is satisfied at lower and higher perturbation amplitudes) -> positive feed-back loop spreading of the acceleration

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

Conclusions transition MHD->KAW at low k_perp ; parallel electron/ion heating; importance of KAW turbulent spectra; cross-field ion heating by KAW turbulence;