Адиабатический нагрев электронов в хвосте магнитосферы.

Физика плазмы в солнечной системе» 6 - 10 февраля 2012 г., ИКИ РАН

Зеленый Л.М., Артемьев А.В., Петрукович А.А.

ИКИ РАН

Model of electron heating in the course of Earthward convection

and formation of electron temperature profiles

Guiding center equation

Formation of electron temperature profiles

z

x

Magnetic field lines

z, Bx

Te

0Te

x

Lyons 19842~ , ~1 3a

e zT B a

Tverskoy 19722 5~e zT B For particles with

distant mirror points

The growth of the electron temperature corresponds to the growth of Bz

Adiabatic modelz

xconvection

Bz

x

The pointof observation

Tverskoy 1972,Zelenyi et al. 1990

Electron heating during the earthward convection due to the conservation of the first and second adiabatic invariants

Single electron dynamics

InvariantsInvariants 2

23 2

2

~ const

1 ~ const

v

B

vB

v

2

21 1

a a ba b db

b

2 5~e zT B

~e zT B

Electrons with mirror points far from the neutral plane

Near equatorial mirroring electrons

Evolution of electron distribution function

2 2

, ~ exp2 2e e

ee e

m v m vf v v

T T

Velocity distribution in the point of observation (Bz = Bz0)

“In situ” observed values

0

, ,

, ,

h

z z xB B x L

u u v v x

u u v v x

Assumption

Expressions obtained from and JII conservation

0ˆ, , , ,e ef v v x f u u x

Velocity distribution in the neutral plane (Bx~0)

2 22 2

2 2 2 2

x z

z

B z B xw u

B x

w u u w

Projection along field lines

Point in the neutral plane

x as a function of zalong field line

ˆ , , , ,e ef u u x f w w z

Velocity distribution in dependence on Bx~z coordinate

X

Z

,ef v v

observation point

ˆ , ,ef u u x

tracing

field line

downstream tail

, ,ef w w z

Integration of obtained function , ,ef w w z gives temperature profile

13( ) 2e e eT z T T

3

2

, ,

, ,

e e

e e

T w f w w z dw dw

T w w f w w z dw dw

x0

)()( xB

dz

zB

dx

zx

The vertical profiles of electron temperature and anisotropyAnisotropic heating:

Projection of velocity distribution along field lines gives the profiles of electron temperature anisotropy: TeII/Te ~ const

~e zT B

2/5~e zT B

Bz/Bnprofile downstream the tail

Electron anisotropy decays towards the Earth.Electron anisotropy is almost constant across the tail

To Earth

TeII/Te

Te /T

emax

IN THE EQUATORIAL PLANE

Observed profiles of temperature anisotropy

Profiles of electron temperature: Te=(TeII+2Te)/3

Te decreases toward the TCS boundary

Profiles of electron anisotropy: TeII/Te TeII/Te is approximately constant

Comparison of model profiles Te(Bx) and observations

Electron temperature Electron temperature as a function of the local magnetic field for four TCS crossings

Spacecraft (Cluster 2) observations

Model profiles Te(Bx) with h=-0.8

Electron energy distribution in TCS

Difference of energy distribution for =90o and for =0o

Anisotropy of temperature is produced by electron population with energy ~ 1keV. Cold core of distribution (<100 ev) and hot tails (>3 keV) are isotropic: f(=0o)=f(=90o)

1/4~ 5 [eV]e

For TCS

e~1 e~1e~1

Statistics of observationsStatistics for 70 TCS crossings

Anisotropy of electron temperature is constant inside TCS

Lyons 1984

Anisotropic heating:

2/5~ , ~e z e zT B T B

Tverskoy 1969, Zelenyi et al. 1991

Isotropisation of electron distribution due to scattering at small-scale magnetic field fluctuations

2/3~ ~e e zT T B Who is right?

(SMALL ) ELECTRON ANISOTROPY DO !! EXISTS

Simple model based on conservation of adiabatic invariants explains: 1.Temperature anisotropy do exist 2. Anisotropy profile across the tail~ const

The estimates of current sheet parameters from comparison of observations and model profiles Te(Bx)

Input model parameters: B0 – amplitude of TCS magnetic field Bz – normal component of magnetic fieldBext - magnetic field magnitude at the lobeLz – current sheet thicknessLx – spatial scale along Earth-Sun direction

direct observationdirect observation

direct observation~B0/jcurl from mutlispacecraft observations

free model parameter

Output model parameters: Te(Bx) profilesComparison of model Te(Bx) profiles and observed Te(Bx) can give estimates of Lx

We vary the model input Lx to approximate the observed

profiles Te(Bx)

We use the statistics of 62 TCS crossings from 2001, 2002

and 2004 years

As a result, we obtain the statistics of Lx

Distribution of Lx estimates

Distribution of Lx/Lz ratio

The most TCSs The most TCSs have have LLxx/L/Lzz~25~25

The most TCSs The most TCSs have Lhave Lxx [5, 20] R [5, 20] REE..

Distribution of Lx

The ratio Lx/L and pressure balance in TCS

For 2D current sheet =1, and longitudinal pressure balance could be maintained only by the gradient along x (Schindler 1972, Lembege and Pellat 1982).

For TCS >1>1 and part of pressure balance corresponds to the inertia of Speiser ion motion which create the off-diagonal terms of the pressure tensor.

=2BzLx/B0Lz

z

z

x

x

1D TCS with >1 and nongyrotropic pressure

2D isotropic current sheet with =1

Effect of ion nongyrotropy

1y z

pj B

x c

Electrons help us to prove that Speiser ions are main

players in pressure balance in thin current sheets!

Conclusions:

• Adiabatic electrons can gain energy during the Earthward convection with the rate:

• The model of electron adiabatic heating during earthward convection can describe the observed profiles of Te(Bx) with the reasonable accuracy

• The comparison between model and observed profiles Te(Bx) allows to estimate the longitudinal spatial scale of current sheet Lx~(∂lnBz/∂x)-1:

• Stretched magnetotail equilibria could be supported only by nongyrotropic ion distributions (Te<<Ti)

and principal future task is the careful examination of ion pressure tensor

2 5~ zH B ~ zH B

For equatorial particlesFor particles with far mirror points

5 RE<Lx<20 RE <Lx/Lz>25 <2BzLx/B0Lz>~5

0

ˆ 0 0

0

xx xz

yy

zx zz

p p

p p

p p