Anomalous resistivity due to lower-hybrid drift waves.

Results of Vlasov-code simulations and Cluster observations.

Ilya Silin

Department of Physics

University of Alberta

isilin@phys.ualberta.ca

Cluster results are courtesy of

A. Vaivads and Yu. KhotyaintsevIRFU,Uppsala, Sweden

K.-H. Glaßmeier TU Braunschweig

and E. PanovMPI für Sonnensystemforschung

Outline

• Thin current sheets and reconnection

• Instabilities of current sheets

• General perturbation theory

• Vlasov-code simulations

• Cluster measurements at magnetopause

• Sheared magnetopause models

Thin current sheets: dynamical regions

Magnetotail

MagnetopauseSolar corona

Current sheets - regions of plasma accumulation in magnetic “traps”.

Magnetic reconnection

E. Priest, A&A, 2001

C. T. Russell, Adv. Sp. Res., 2002

Thin current sheets: separation of regions of oppositely directed magnetic field

Biot-Savart law:

or

jc

B 4

yx j

cz

B 4

Instabilities of thin current sheets

P. Yoon et al., Phys. Plasmas, 2002

General perturbation theory

Vlasov equation 0)(1

v

fBv

cE

m

e

r

fv

t

f j

j

jjj

Wave-like perturbations

BBB

EEE

fff jjj

0

0

0

Perturbations of density and current

jj

jjj

vfdvej

vdfe

0 BEf j

jj ff ~

After ensemble averaging

General perturbation theory

v

f

c

BvE

m

e

t

f

v

fBv

cE

m

e

r

fv

t

f j

j

j

an

jj

j

jjj

0

0000 )(

1

Collision term integrated over velocities

Effective anomalous collision frequency

c

BjBjEvmn

tzjxxjz

jyan

jyjj

,,

,

c

BjBjE

vmnvmn

tvmnzjxxjz

jy

jyjjanjyjj

jyjj

eff

,,

,

,

,

11

Normalized to LH frequency

Anomalous collision rates

CeCiLH

Quasi-linear estimate (Davidson and Gladd, Phys. Fluids, 1975)

LHeff

eBLH

peeff Tnk

E

8

22

)/( 2nem effean

Anomalous resistivity

Vlasov-code simulations• initial equilibrium - Harris current sheet (Harris, Nuovo Cim., 1962)

• normalization

• distribution function moments

vdfvej

vdfe

ei

Veijei

V

eieij

ei

3,

,,

3,

,,

NrvddfRV

ei 33

,

,

Vlasov-code simulations• equations for potentials

• Coulomb gauge

• equations for electromagnetic fields

• Vlasov equation

jct

A

cA

41

4

2

2

2

0 A

AB

t

A

cE

1

0)(1 ,

,

,,,

v

fBv

cE

m

e

r

fv

t

f ei

ei

eieiei

tc

1

Vlasov-code simulations

Simulation results: lower-hybrid drift (LHD) waves

LHD waves grow at the edges of the current sheet and gradually penetrate towards the central plane.

Simulation results: kink and sausage modes

The interaction of LHD waves from the edges can trigger either global kink or sausage eigen-mode.

Simulation results: effective collision ratesions electrons

2D simulations with mi/me=100

electrostatic part

electromagnetic part

Simulation results: effective collision rates3D simulations with mi/me=16

yyean Ej 5.0

Bale et al., GRL (2002): yyean Ej 005.0

Our Vlasov-simulations:

Cluster magnetopause encounter March 30th 2002, 13:11:46

X

ZZ

Y

Cluster measurements at magnetopause

tangential magnetic fields

electric fields

normal magnetic field

LHD electric fields

plasma density

tangential magnetic fields

electric fields

average momentum

density fluctuations

electric field fluctuations

p1049 28-Nov-2004 23:04:23 Vmp=31.25*[-0.94 -0.21 -0.25]km/s, dt=[0.00 1.61 2.81 -0.50]s L=[-0.25 -0.05 0.97]N=[0.94 0.21 0.25]M=[-0.22 0.98 0.00]f

filter=[20 100].

-100

0

100

BL [

nT]

C1 C2 C3 C4

a)

0

20

40

60

NV

ps [

cc]

sc2 b)

-100

-50

0

50

En [

mV

/m]

sc2 c)

-5

0

5

dn [

cc]

sc2

d)

-100

-50

0

50

dE [

mV

/m]

sc2 e)

.6 .8 13:11:46.0 .2 .4 -50

0

50

100

dn d

E [

cc m

V/m

] sc

2

30-Mar-2002

f) product of density and electric field fluctuations

Cluster: νeff due to e/s fluctuations

Hzeff 70~ HzfLH 60~

Cluster: νeff due to e/m fluctuations

magnetic field fluctuations

current fluctuations

product of current and magnetic field fluctuations

-2

-1

0

1

2

B [

nT

]

-2

-1

0

1

2

j [u

A/m

2 ]

0

5

10

15

20

25

jxB

/e [

cc m

V/m

]

.6 .8 13:11:46.0 .2 .4 0

5

10

15

20

25

jxB

/e [

cc m

V/m

]

30-Mar-2002

Hzeff 30~

Observations of the magnetopausemagnetic field component hodographs

in local magnetopause frame:

BL and BM – tangential components, BN – normal component

(from Cluster s/c1 06.16.02, 00:54-00:58 and 01.15.03 00:30-01:30, courtesy of K.-H. Glaßmeier and E. Panov)

Magnetopause current sheet model

BxB

ByB

vxvthi

vyvthi

magnetic field hodograph

ion drift velocity hodograph

t i

zLz

BzB

LHD waves at the sheared magnetopause

zLz

BzB

Conclusions• The effective collision frequency calculated from

results of numerical simulations and Cluster measurements is of the order of νeff ~ ΩLH

• Anomalous collisions become significant only when LHD waves reach a non-linear phase

• Contributions to νeff from e/s and e/m fluctuations are comparable

• The dissipation due to microscopic kinetic effects becomes significant for large-scale processes, e.g., reconnection at Earth magnetopause

• However, for more realistic magnetopause configuration, the situation is still not quite clear