The inner magnetosphere: - auroras - radiation belts - plasmasphere - ionosphere - polar wind

The inner

magnetosphere:

- auroras

- radiation belts - plasmasphere - ionosphere

- polar wind

 Viviane Pierrard

 Belgian Institute for Space Aeronomy

 Université Catholique de Louvain

The inner

magnetosphere

 The magnetic field of the Earth and other planets

 Auroras

 Radiation belts

 Motion in the terrestrial magnetic field

 Plasmasphere

 Ionosphere

 Polar wind

 Kinetic models

 Geomagnetic activity

 Space weather

B quasi-dipolar

liquid core

Angle 11° with rotation axis

Magnetic North Pole in Arctic Canada (1700 km)

N

Paleomagnetism: Magnetic poles

inversion Macedonio Melloni (1850).

normal polarity yellow inverse in blue

Magnetic dipole:

ˆ ) ˆ cos

sin 2

3

(  ^   ^

   r 

r B M

M magnetic moment

M=8 10¹⁵ T m³ =0.304 G R_T³

 magnetic latitude r radial distance

 

B r

r B M

T





2 3

2 3

sin 3 ) 1

/ (

31000

sin 3 1









=0° B=31000 nT

=90° B=62000 nT



cos

r

r 

International Geomagnetic Reference Field (IGRF)

 ^{cos sin (sin )} 

8 1

1 1







m n n

n

n m

P m

h m

r g a a

V

gradV B

 



 



 







 





 geographic latitude

 geographic longitude

P_n^m () associated Legendre polynomials g_n^m et h_n^m coefficients (80 terms)

r>4R_t: magnetospheric currents (magnetopause, neutral sheet, ring current) modify Z, H, B

Tsyganenko

Compression

Elongation

Mercure

Saturn

Jupiter

Uranus

Aurora

Auroras Photos:

Jan Curtis Alaska

6 Nov 2000, et 1 April 2000

Auroral

oval

Magnetic storm 15 July,

2000

21 October 2001 Aurora in Belgium

Saturn

Jupiter

VAN ALLEN belts

Van Allen belts Discovered 1958 Explorer 1

inner: p+ (100 keV-500 MeV) outer: p+ (<10 MeV)

e- (10 keV-10 MeV) e- (10 keV-5 MeV)

4 Rt 10 Rt

Thermonuclear bombs in 1958 and 1962

Sources:

Inner belt

CRAND (Cosmic Ray Albedo Neutron Decay) SPAND (Solar proton Albedo Neutron Decay) Outer belt

SW, radial diffusion, wave-particle interactions…

Losses :

atmospheric collisions, charge exchange, angular diffusion

) /

( f T losses

sources t

f  





AP8 Max J(E>10 MeV) AE8 Max J(E >1 MeV)

L (Re) L (Re)

Empirical models NASA

SPENVIS www.spenvis.oma.be

South Atlantic Anomaly (500 km)

2.5 km/y

0.3°/y (westward)

Temporal variations

Benck et al., Ann. Geophys., 28, 848, 2010.

Decay times

SAC-C/ICARE diff. F:

LEO 700 km inclin.:98.2°

0.19-4.11 MeV, 18 channels,

Dec 2000- Sep 2006 DEMETER/IDP:

LEO: 710 km Inclin.: 98°

0.07-2.34 MeV, 27 channels,

Aug 2004-Mar 2006

Dynamic model: SSA

Evolution in time of the flux

(in cm^-2/sr^-1/s^-1) for E=0.2-0.3 MeV in geographic

coordinate system.

The left upper graph shows the steady state at the onset of the storm (t=0 days).

SACC,

DEMETER CLUSTER

Dynamic simulation of radiation belts for SWIFF based on CLUSTER/RAPID (see poster of Kris Borremans)

Quiet Disturbed

Motion of particles

trapped in the Earth’s

magnetic field

Adiabatic invariants Magnetic moment

conservation (bêtatron) Conservation of mirror points separation (Fermi) Magnetic flux

conservation along azimutal drift

Motion T (1MeV e^-) T (10 MeV p⁺)

Giration 7 10^-6 s (r=320 m) 5 10^-3 s (r=30 km)

Oscillation 0.1 s 0.65 s

Azimutal drift 50 min. 3.2 min.

Giration

 Uniform magnetic field (no external force)

 Centrifugal force = Lorentz force:

B v qv

m

G







2

qB mv

G  

Giration radius 

Angular frequency de Larmor

m qB v

G L  ^ 

  Giration period

qB T m

L L





 2

2 



Oscillation:

Faraday

 Conservation of the magnetic moment and of the magnetic flux in the giration circle:









 _L ^ _B

q m B

v q

B m  

² ₂^{2 2 2} _constant

Conservation of energy: constantv  v_²  v_//² 

v_{= v sin}

    _  _ e

e m

m

B v B

v^{2 2} constant







e e m

m

B B



 ²

2 sin

sin

Mirror point:

_m=90°, sin _m =1

v_//=v cos _m=0 constant

Azimutal drift

Motion equation: ma  F  q(v B) Decomposition in v=v_F+v_L

v_L giration velocity around guiding center v_F drift velocity

qB

B v

F



  



) ( ^{ }











   

 n q v_F n q v_F ne v_F v_F

J    

Current density:

Drift forces:

g m F  



qB

B v

F



  



E q F  



B F   _B



B mv

2

2

R n F mv

c

 _//² 



dt v m d

F ^D





Gravitation Electric force

Magnetic force (gradient)

Curvature of magnetic field line

Inertia (polarisation)

Energetic particles (keV)

B B

v qB v

v_B  m ( _  2 )    2

2 //

2 3

Electrons East Ions West Ring current

Plasmasphere (1 eV)

0 )

(  

 ne v_F^ v_F^

J  

2

2

B

B E

B B E

q v q

v







 

 

 



p



E e

E

v

v   

3D dynamic plasmaspheric model (Pierrard and Stegen, JGR, 113, 2008)

www.spaceweather.eu ccmc.gsfc.nasa.gov

Temperatures of protons (same as electrons dayside, lower nightside)

Temperatures of electrons

Coupled to ionosphere (IRI model) Light ion trough

Plasmapause due to interchange instability

Kp=1

Kp=6

Volland-Stern E5D

Electric potential in the geomagnetic equatorial plane Erotation + Econvection (Kp)

Before substorm 9 June 2001 8h00

After substorm 10 June 2001 7h00

Comparison with EUV/IMAGE

observations

He⁺ ions at 30.4 nm

Pierrard and Cabrera, Ann.

Geophys., 23, 7, 2635, 2005.

Pierrard and Cabrera, Space Science Rev., 122, 119, doi:

10.1007/s11214-005-5670-8, 2006.

Ionosphere: UV, X, RC, solar particles

F (F1 et F2 (max)):

10⁶ ions/

cm³

150-1000km

E:

10³-10⁵ ions/

cm³

90-150 km D:

10²-10⁴ ions/

cm³

60-90 km

ground: 100 ions/

cm³

 IRI:

International Reference Ionosphere

Radio waves reflexion on the ionosphere

Marconi 1901

 D: 30-300 kHz (LF)

 E: 300 khz-3 MHz (FM)

 F: 3-300 Mhz (HF)

 VHF: not reflected

Wave attenuation

 Oscillating electrons

 Collisions with other constituants

 High attenuation when N high (D), low frequency

Electrojet ionospheri c current:

in regions D and E of the auroral ionosphere

(high

conductivity)

Resistivity

implicates heating of the upper

atmosphere

Polar wind

www.spaceweather.eu e^- +++ O⁺….. H⁺ diamonds

 Based on the velocity

distribution function of the particles

 f(r, v, t) dr dv

 number of particles with a velocity in [ v, v+dv ] and a position in [ r, r+dr ] at an instant t

 Maxwellian VDF in regions dominated by collisions

’ ’

’ ’ ’

’

’ ’

’ ’

The kinetic approach

Evolution equation

Exosphere: mfp>>H

  ^{( )[ 1 ]}

2

1 D f WPI

f v v A

v a f

r v f

t

f 

 

  



 

 

 

 

 

 

 

 

 

 



 

 

Exobase: MFP=H

(between 1.1 and 6 Rs)

Barosphere: mfp<<H Pierrard V., in “Exploring the solar wind”, 221-240, Intech, Edited by M.

Lazar, ISBN 978-953-51-0339-4, 2012

Vlasov: no interaction term (exosphere)

Fokker-Planck: Coulomb collisions MHD

P(): Legendre polynomials S(y): Speed polynomials

L(z): Modified Legendre polynomials

Advantages: Derivatives are linear function of f calculated at the quadrature points

and integrals (moments) are related to the coefficients.

i = 1,…,10 j=1,…16 k=1,…,10

At each radial distance, f(v,) is represented by 2*10*16=320 points.

Other methods: finite differences, Monte Carlo, …

) ( )

( )

( )

exp(

) , , (

1 1 1

2 ijk y z

y y

z

f ^l a P S _j L_k

i m

j n

k i 

 

  





) (

1

j m

j ij y

y

y f y D

f

i





 



 









) ( )

( ) (

1

i n

i i b

a

y G w dy

y G y

W 

 ^ _

Spectral numerical method

Pierrard V., Numerical Modeling of Space Plasma Flows, ASP, 444, 166-176, 2011.

The moments of f







 f r v dv

r

n() (, ) 

) (

) ) (

( n r

r r F

u 

 



 







 f r v v dv r

F      )

, ( )

(

Number density [m^-3] Particle flux [m^-2 s^-1] Bulk velocity [m s^-1]

Energy flux [Jm^-2 s^-1] Pressure [Pa]

Temperature [K]

v d u v u v v r f m r

P         ) )(

)(

, ( )

(  ^  





v d u v v r r f

n k r m

T   

 









 ( , ) ²

) ( ) 3

(

v d u v u v v r m f

r

E      











 ( , ) ( )

) 2

( ²

MHD approach

 Continuity equation

 Momentum eq.

 Energy eq.

 







v d  [1]

 







v d v m  [1]

 







v mv d [1] 2

2

In each equation of order n appears the moment of order n+1.

Assumptions to close the MHD system

The moments obtained from the kinetic solutions fulfill the transport equations.

 

2

1 Df WPI

f v v A

v a f r

v f t

f 



 



 

 

 

 

 

 

 

 

 

 



 

 

4 classes of orbits Escaping

Ballistic Trapped Incoming

Quasi-neutrality: n⁺=n^-

Determination of V (electric potential):

Plasmasphere: Incoming=escaping F=0 Hydrostatic equilibrium Polar (and solar wind): Incoming=0 F⁺=F^- Hydrodynamic equilibrium Auroral regions (plasmasheet): F(V) Current

Current-Voltage relationship

Pierrard et al., JASTP 69, 12, 2007.

Results of the Fokker-Planck model for polar wind protons

Pierrard and J. Lemaire, JGR, 103, 11701, 1998.

Barghouthi, Pierrard, Barakat, Lemaire, Astr. Sp. Sci., 277, 427, 2001.

Geomagnetic

storms

Magnetic storms: problem for space missions 1. Orbits modifications

2. MeV protons: Single Event Upset (micro-electronic devices, solar cells…)

3. MeV electrons: internal charging (satellite failures)

4. KeV electrons: surface charging (discharges, parasite signals…)

Limit dose of Radiation (milliSieverts = mSv

for astronauts) Time Eyes Skin

30 days 1000 1500 1 year 2000 3000 Life 4000 6000

Electricity

failures

Pipelines corrosion

Pipeline in Alaska

Image Credit:

Courtesy of Donald D. Rice

Storms

Usw

Bx By Bz

Kp Dst

Daily variations of magnetic field

Geomagnetic activity indices

 Kp Planetary geomagnetic activity Bartels index Kp.

1939 13 stations (11N, 2S 44-60°)

 AE Auroral Electrojet

1966 12 stations N (aur.)

 Dst (Disturbed storm time)

1964 4 stations (eq.)

 PC Polar Cap

1991 1 station (pol.)

Substorms B sud

Reconnexion

Reconnexion

Magnetosphere

CLUSTER

4 satellites lancés en juillet et août 2000

Orbite polaire elliptique Périgée: 19000 km (4 Re) Apogée: 119000 km (19 Re) Période: 57 h

8h00 16h00 23h00

7h00 9h00 13h00

IMAGE/UV 30.4 nm 9-6-2001 A 23 h, Kp=5.3

10-6-2001

07 mai 2002 Plume

Effet Forbush (1937)

 Rayons cosmiques 85% H+, 10% He++

 Solaires: protons et ions de 1 à 100 MeV (augmente avec activité solaire)

 Galactiques (hors système solaire: supernovae, pulsar, noyaux actifs de galaxies…): >1 MeV (diminue avec activité solaire)

Influence sur le climat:

comparaison des températures et du nombre de

taches solaires:

minimum de

Maunder associé au petit âge

glaciaire

Minimum de

Dalton

Kp Dst

Sunspot F10.7 Nsw Vsw Tsw Psw Bz

Magnetopause

Champ électrique de convection de Weimer:

Latit=90 (pôle) Equateur

Les indices d'activité aurorale (Auroral Electrojet)

 1966

 H en nT dans 12 stations aurorales N

 AU (upper): max variations

 électrojet Est, côté jour, courant magnétopause (variations du milieu interplanétaire)

 AL (lower): min variations

 Électrojet Ouest, côté nuit, sous-orage

 AE: AU-AL, puissance dissipée dans l’ionosphère aurorale

 AO: moyenne de AU et AL, asymétries entre les électrojets, courant auroral.

Indices d'activité du courant annulaire

 1964

 Dst (Disturbed storm time): courant annulaire équatorial de 3 à 5 Re

 H (moyenne) de 4 observatoires régulièrement répartis en longitude

 Variation séculaire+diurne

 Variations séculaires obtenues des moyennes annuelles pendant les 5 jours les plus calmes de chaque mois

L’équation d’une ligne de force magnétique dipolaire est donnée par :

 cos

r

r 

r_e = L R_t est la distance équatoriale exprimée en nombre de rayons terrestres.

L est le paramètre de McIlwain

La latitude invariante d’une ligne de force correspond à la latitude à laquelle la ligne de force magnétique traverse la surface de la Terre :



 



 

L arccos 1

0

Indices planétaires

d'activité magnétique

 Kp (Bartels, 1939): Indice tri-horaire, résolution 1/3, basé sur H dans 13 stations de 44 à 60° (11 N, 2 S), table de conversion pour unités [0-9]

 Subauroraux: électrojets auroraux+ courant annulaire

 an (Nord), as (Sud), am (moyen)=(an+as)/2 en nT, depuis 1968

 21 stations (12 N et 9 S) à 50°

 aa: 2 observatoires antipodaux (Angl/Austr)

Indice de flux radio solaire (1969)

 F10.7: intensité du flux radio solaire à = 10.7 cm

 en unités 10^-22 Watts m^-2 Hz^-1

 Résolution temporelle de 1 jour

 Activité solaire