Генерация электростатического КНЧ шумалокализованными 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

[Golovchanskaya et al., 2013]

DE-2

FAST

Samples of electrostatic ELF noise associated with Alfvenic turbulence

FAST

Alfvénic turbulence (f < several tens of Hz in the spacecraft frame), broadband electrostatic noise (f = 0.01-1 kHz),

[Stasiewicz et al., 2000]

EIC waves?

Event of the broadband ELF turbulence observed by FAST in the near-midnight auroral zone; [Ergun et al., 1998]

Connection with TAI

FAST

AMICISTh=850 км,Vr = 2 km/s

EIC waves?

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

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

1. Heppner et al., 1993, h < 1000 km2. Golovchanskaya et al., 2013, h up to 4000

km

Inhomogeneous energy density driven instability(IEDDI) , the idea:

2

0 2 2 20

2 ( )( , ) 1 0nEIC

n i

bD kn

2 2 / 2ib k i

iti

v

)exp()( bbInn , ,

With damping terms neglected:

( )D DU

2 2 2

222 2 20

4 ( ) 0n

n

nUn

VE = 0

VE = E/B, 1 y Ek V )( 11' U,

U’ can be < 0, if ω < kyVE

Region II:

Region I:

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:

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;

In reality, in the auroral ionosphere: VE/Vti = 0.1- 0.5 instead of 2.9, and eps = 0.01 instead of 0.1;

H+

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

Growth is indicated even for individually subcritical parallel electron drift and transverse flow shear;

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;

O+

Vd(x) and E(x) are setto be in phase;

The unstable solution of Gavrishchaka et al. [1996] corresponds tovelocity shears ωs of the order of 4 s-1.Can such velocity shears be produced by Alfvenic turbulence ? Marginally, and under winter conditions only.

[Golovchanskaya et al., 2011]

jz = -ΣP ·E, ωs ~ ·E

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, especiallywith oppositely directed flows in adjacent layers;

Can actually observed electric fields of Alfvenic turbulence

be effective in excitation of EIC-like modes?

[Golovchanskaya et al., 2013]

A close-up shows the non-uniform electric field configuration adopted in the calculations

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:

22

2( ) ( ) 0k

11 1 1

|| || || ||2

' 11

|| ||

1 ( ) ( ) ( ) ( ) ( )| | | | | | | |

2( ) ( ) ( )

| | | |

in

n ti ti te te

in

n ti ti

nbk V k V k V k V

knb

k V k V

where i

x

, and

1 y Ek V for ions; 1 y E z dk V k V for electrons;

0, 1, 2n 0n

( ) ( )exp( )n nb I b b 'n nb

2,

,

( )2

y i ei e

kb

r i

,

Formulation:

1

2 2

3 3

1

2 3

4 5

2 ( 1)

..........................NL

L

ik x

ik x ik x

ik x ik x

ik xN

e

e e

e e

e

where Im k1 > 0, Im kNL > 0.

0M φ

Two matching conditions on , /x across each boundary set of 2 (Nl -1) eq:

det 0M

Nonlocal dispersion relation for EIC-like modes:

Unstable solutions for EIC-like modes:2( )

2y ik

b

Vd = 0.05Vte

ε = ρi/L= 0.02

u =k||/kperp= 0.08

τ = 0.5

Vd = 0.17Vte

ωr = 0.9 thin lineωr = 2.1 thick line

ωr = 0.95 thin lineωr = 2.1 thick line

ωr = 1.25

Vd = 0.34Vte

ωr = 1.2

ε = ρi/L= 0.005

u =k||/kperp= 0.04

Conclusions

1. Actually observed localized electric fields of Alfvernicturbulence can be effective in excitation of the EIC modes;2. Unlike solutions for the CDEIC instability, unstable solutionsof 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.

Large argument asymptotic (ion term):

ς = x + i y

Small argument asymptotic (electron term):