Download Presentation - Multifractal

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)
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).
z
Bo
MHD Alfven wave:
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)
P = 1 + 2;
kP = k1 + k2

P
1
2
k1z
k2z
Час розпаду   [(VA/р)(kPρi)3(Bk/B0)]-1.
kPz
kz
decay of a pump KAW in two counter-streaming
KAWs (1998b)
P = 1 + 2;
kP = k1 + k2

P
1
2
k2z
Час розпаду   [(VA/р)(kPρi)2(Bk/B0)]-1.
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
VA
KAWs are here
Vz
Super-adiabatic cross-field
ion acceleration
Demagnetization of ion motion
Phase
mixing
Turbulent
cascade
Resonant plasma heating and
particle acceleration
Kinetic wave-particle interaction
Kinetic
instabilities
Parametric
decay
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
1
2
A-1
16
2A-1
1________
+ kx2p2 ___
B
A = kxp
K(kx)
B0
(mi/qi)/(mp/qp)
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
t
Phase portrait of the ion’s orbit in the region of super-adiabatic
acceleration (transition of the demagnetizing wave phase 3 pi)
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
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||
-1
i _
I o n- c y c l o t r o n
|
-1
R
N
o
n
a
d
i
a
b
a
t
i
c
KA
W
L
a
n
d
a
u
|
i-1
k
Conclusions
•
•
•
•
transition MHD->KAW at low k_perp ;
parallel electron/ion heating;
importance of KAW turbulent spectra;
cross-field ion heating by KAW turbulence;