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

2. 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)

3. 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.

5. 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).

6. due to ion polarisation driftz
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

7. kinetic Alfven wave: short cross-field wavelengthBo
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

11. 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

12. 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

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

19. Electron heating by KAWs: Landau dampingFi Fe
VTi
Vph1
Vph2 Vz VA
KAWs are here

21. 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

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

23. 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

25. 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

26. 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

27. 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)

28. 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, (dashed
contours). The vector of solar wind
flow is along VY axis, the vector of
magnetic field is along dash line.

29. 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);

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

31. 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

32. 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

33. 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

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