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Генерация электростатического КНЧ шума
локализованными электрическими полями
и продольными токами
И.В. Головчанская, Б.В. Козе лов, О.В. Мингалёв
Полярный геофизический институт КНЦ РАН
Alfvenic turbulence and electrostatic ELF noise
DE-2
FAST
[Golovchanskaya et al., 2013]
Samples of electrostatic ELF noise associated with
Alfvenic turbulence
Alfvénic turbulence (f < several tens of Hz in the spacecraft frame),
broadband electrostatic noise (f = 0.01-1 kHz),
FAST
[Stasiewicz et al., 2000]
EIC waves?
FAST
Event of the
broadband ELF
turbulence observed
by FAST
in the near-midnight
auroral zone;
[Ergun et al., 1998]
Connection with TAI
EIC waves?
AMICIST
h=850 км,
Vr = 2 km/s
Bonnell et al., 1996:
Interferometric determination of BBELF wave phase velocity within a
region of transversely accelerated ions (TAI);
v|| , k||/kperp, electrostatic character are relevant to EHC waves;
But:
(1) PSD is not ordered by Ω of H+, He+ or O+ = 600 Hz, 160 Hz and
40 Hz, respectively; (2) j|| is subcritical for Kindel and Kennel
mechanism; (3) occurrence during TAI (i.e., Ti/Te is not << 1).
Imaginary part DI of the local dispersion relation for CDEIC
instability (negative DI indicating the growth)
as a function of u= k||/kperp, Vd,  = Ti/Te
[Ganguli and Bakshi, 1982]
Why does the character of the electrostatic ELF emission
change so crucially in the presence of Alfvenic turbulence?
FAST
Seasonal asymmetry of the electrostatic ELF noise has
the same sense as the electric fields of Alfvenic turbulence
1. Heppner et al., 1993, h < 1000 km
2. Golovchanskaya et al., 2013, h up to 4000 km
Over 100 summertime and 100 wintertime
events, h = 3000-4000 km,
all ne
Over 61 summertime and 33 wintertime
events, h = 3000-4000 km,
ne is fixed
Can the electric fields of Alfvenic turbulence be effective in
excitation of electrostatic ion-cyclotron (EIC) modes?
Theory of Ganguli et al. [1985] in the simplest form:
one sheared flow layer, Vd = 0:
Inhomogeneous energy density driven instability
(IEDDI) , the idea:
With damping terms neglected:
DEIC ( , k )  1  0  
n0
n  I n (b)  exp( b) ,
U
bk  /2
2

2
i
, i 
vt i
i
 D 
 ( D)



  
Region II: V = 0
E
Region I:
2 2  n (b)
0
2
2 2
  n i


42n n22 

2
U   
    ( )  0
2
2 2 2
n  0   n   
VE = E/B,
1    k yVE ,
U '   1(1 )
U’ can be < 0, if ω < kyVE
Unstable solutions of the nonlocal dispersion relation for EIC
modes of Ganguli et al. [1985] in case of pure IEDDI
are narrowband, coherent and requires too large velocity shears;
H+
In reality, in the auroral ionosphere:
VE/Vti = 0.1- 0.5 instead of 2.9, and eps = 0.01 instead of 0.1;
EIC instability driven by combination of a parallel electron
drift and a transverse localized electric field:
the single-layer theory of Gavrishchaka et al. [1996]
with a smooth velocity profile
O+
Vd(x) and E(x) are set
to be in phase;
Growth rate as a function of peak E×B
velocity in the region of velocity shear:
L = 25 ρi (ε = 0.04),
b=(kyρi)2/2 =0.15, τ = 0.5, Vd=0.17 Vte,
u=kparall/kperp = 0.16; ωr depends on E×B;
Growth is indicated even for individually subcritical
parallel electron drift and transverse flow shear;
The unstable solution of Gavrishchaka et al. [1996] corresponds to
velocity shears ωs of the order of 4 s-1.
Can such velocity shears be produced by Alfvenic turbulence ?
Marginally, and under winter conditions only.
j = -Σ ·E,
z
P
ωs ~ ·E
[Golovchanskaya et al., 2011]
Reynolds and Ganguli [1998] considered two transverse flow
layers (without j||):
Conclusion:
•The requirement of strong velocity shears can be significantly
relaxed if the theory includes multiple sheared flows, especially
with oppositely directed flows in adjacent layers;
Can actually observed electric fields of Alfvenic turbulence
be effective in excitation of EIC-like modes?
A close-up shows the non-uniform electric field configuration
adopted in the calculations
[Golovchanskaya et al., 2013]
Formulation:
For small kx and inhomogeneity in the x direction,
kx  -i/ x.
Then, instead of a local dispersion relation, we have a second
order differential (eigenvalue) equation for  in each layer:
2
( 2  k 2 ) ( )  0

x
where    , and n (b)  I n (b) exp(b) ,
i
k  2
1      n (b) (
2
n
1
| k|| | Vti
) (
1  ni
)  (
1
| k|| | Vte
1  ni
1
'
n n (b) (| k | V ) ( | k | V )
||
ti
||
ti
n  0,  1,  2
1    k yVE for ions;
| k|| | Vti
(k  )

   n bi ,e  y i ,e
b
2
2
'
n
) (
1
| k|| | Vte
)
n0
1    k yVE  k zVd for electrons;   r  i

Formulation:

1e  ik1x 
  ik2 x

 ik2 x
  3e
 2 e



   4 e  ik3 x   5e  ik3 x 
.......................... 


 ik N L x
 2( N 1) e

L


where Im k1 > 0, Im kNL > 0.
Two matching conditions on , /x across each boundary 
set of 2 (Nl -1) eq:
M φ  0
Nonlocal dispersion relation for EIC-like modes:
det M  0
Unstable solutions for EIC-like modes:
ωr = 0.9 thin line
ωr = 2.1 thick line
b
Vd = 0.17Vte
ωr = 1.25
( k y i ) 2
2
Vd = 0.05Vte
ε = ρi/L= 0.02
u =k||/kperp= 0.08
τ = 0.5
ωr = 0.95 thin line
ωr = 2.1 thick line
ε = ρi/L= 0.005
Vd = 0.34Vte
ωr = 1.2
u =k||/kperp= 0.04
Conclusions
1. Actually observed localized electric fields of Alfvernic
turbulence can be effective in excitation of the EIC modes;
2. Unlike solutions for the CDEIC instability, unstable solutions
of the nonlocal dispersion relation indicate a variety of
frequencies and perpendicular wavelengths;
3. Unlike solutions for the CDEIC instability, the above solutions
are persistent to variations of the parameters, e.g., τ ;
Благодарность:
• Выражаем благодарность Программе 22
Президиума РАН за поддержку данной работы
Plasma dispersion function Z(ς). Asymptotic.
ς=x+iy
Large argument asymptotic (ion term):
Small argument asymptotic (electron term):