Magnetic Field - Ionosphere
Modeling the Space Environment
Manuel Ruiz Delgado
European Masters in Aeronautics and Space
E.T.S.I. Aeronáuticos
Universidad Politécnica de Madrid
April 2008
Magnetic Field - Ionosphere– p. 1/37
Modeling the Space Environment
Particle Dynamics: Basics of Orbital Mechanics:
Two-Body problem: Keplerian Motion
KEPLER.FOR
Equations for Perturbed Motion
COWELL.FOR
Perturbations:
Models
Gravitational
Real Earth Gravitational Field:
JGM2S
Third body perturbation:
ECSS/DE200
Non-Gravitational
Air Drag: Static and Dynamic Models:
MSISE00
Radiation Pressure
ECSS-E-10-04A/DE200
Magnetic Field:
IGRF
Ionospheric Effects:
IRI
Debris and Meteoroid Impact:
MASTER/ORDEM
Attitude Dynamics: Gravitational and Non-Gravitational torques
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Effects of Space Environment
Vacuum
Neutral
atmosphere
(∼ eV)
UV ray degradation
Contamination (outgassing)
Mechanical
Air Drag
Sputtering (abrasion)
Chemical
Atomic Oxygen attack (AO)
Spacecraft glow
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Effects of Space Environment
Micro-Meteoroid
and Space Debris
(MMOD)
Plasma (∼ 1 KeV)
Hypervelocity impact
Charging: shift in the ground potential
Interaction charge-geomagnetic
field: Lorenz force
Electrodynamic Tether propulsion
Electrostatic discharge:
Dielectric breakdown
Arc discharge
Enhanced sputtering
Reatraction of contaminants
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Effects of Space Environment
Radiation
(∼ MeV)
Mechanical: radiation pressure
Total dose effects:
Solar panel degradation
Sensor degradation
Electronics degradation
Single event effects (solar storms):
Latchup CMOS does not respond
Upset CMOS anomalous response
Effects on human beings
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Earth’s Magnetic Field
Earth has a solid metal core, mostly
iron, surrounded by a liquid iron
core, and this by the mantle.
Convective and Coriolis motion in
the ferromagnetic molten core
produces the Earth’s magnetic
field: dynamo effect
To first approximation, it is a N-S
dipole (30000nT equator, 60000nT
poles)
Magnetic field varies with time, and
has changed polarity in the past through a complex process.
Images courtesy NASA
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Battle of the Magnetic Fields
The Sun has a Strong magnetic field,
IMF, carried by solar wind
Thus interplanetary space is filled with
magnetized plasma
Interaction of Geomagnetic field with
Solar magnetized plasma (both
rotating) produces a complex
fast-changing structure:
Magnetosphere
The outer part, where both interact, is
the Outer field
The inner part, where Earth’s field dominates, is the inner field: >90 % from
the core, the rest from the mantle.
Images courtesy NASA
Magnetic Field - Ionosphere– p. 7/37
Inner field
Image courtesy NASA/Modified by Aaron Kase and Manuel Ruiz
Magnetosphere Structure
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Geomagnetic Field
Geomagnetic field: Only Earth magnetic sources
Magnetosphere:
Interaction Geomagnetic/IMF & Solar wind
Satellite atmospheric drag depends on the density of the upper
atmosphere (thermosphere)
Influence in thermospheric density:
• Geomagnetic fields: Kp /Ap indices
→ T∞ → ρ
• Solar activity: F10,7 index
Solar wind collision with charged particles interacting with the
magnetic field heat the upper atmosphere and increase “air” density
Sun → Inonosphere ← Geomagnetic F.
Geomagnetic field:
Direct influence on satellites small
(Magnetotorquers: ↑↑)
Indirect influence: large
Magnetic Field - Ionosphere– p. 9/37
Geomagnetic Field Effects
Indirect
Large
Acts on the charged particles of the
Ionosphere, influencing density, and therefore satellite drag.
Direct
Charged particles: Electrostatic forces on satellites.
Small
Ionization: Affects satellite tracking and communications
Interference with magnetotorquers: Magnets or coils for attitude
control
Large
Force on conducting wires: dF = dxI ∧ B
Electrodynamic tethers
Masts charged by ionospheric plasma
Charged structures
Small to Large
Magnetic perturbation:
Magnetic Field - Ionosphere– p. 10/37
Application: Magnetotorquers
Some satellites use magnetotorquers for cheap attitude control
—often together with reaction wheels or RCS
Magnetotorquers are just N coils of wire around one side of the
satellite, of Area A; with a current intensity I they produce a dipole
of magnetic moment
µ = I N A Am2
Moving in the Geomagnetic field of intensity B, the satellite
experiences a torque
M=µ∧B
Three torquers can control satellite attitude. An effective model for
the Geomagnetic field is needed.
Not used in the outer field: intensity drops with distance.
Magnetic Field - Ionosphere– p. 11/37
Magnetic Field Activity Indices
Kp Geomagnetic Planetary Index. Quasi-logarithmic average of the
daily sub-auroral magnetic activity over the whole planet.
Low: 0.0
High: 9.0
Input to the Jacchia model.
Magnetic Field Activity Indices
Kp Geomagnetic Planetary Index. Quasi-logarithmic average of the
daily sub-auroral magnetic activity over the whole planet.
Low: 0.0
High: 9.0
Input to the Jacchia model.
ap Geomagnetic planetary amplitude, 3-hour measure. 50◦ N. diff.
Ap Daily average of ap . Inputs to MSISE and JB2006 model
Range: 0-400
Average: 10-20
Rarely: >100
Unit: gamma = 10−9 Tesla = 10−9 kg s/m
ap = e(Kp +1,6)/1,75
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Causes of the Geomagnetic Field
From surface to about 4 Earth radii.
Convection currents in the nucleus (most)
Magnetic rocks in the crust (decays fast with height)
External Field: From about 4 ER to Magnetopause
Ionospheric
Ionospheric plasma winds (electrojet)
Auroral electrojet at higher latitudes
Magnetospheric
Geomagnetic field and interplanetary IMF
Solar Wind motion
Magnetopause currents, cross-tail currents, ring currents
Inner field:
Magnetic Field - Ionosphere– p. 13/37
Crust Magnetic Anomalies
Image courtesy NASA
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Models of the Geomagnetic Field
Inner Field (Geomagnetic: Earth)
Aligned Dipole
Tilted Dipole
Eccentric Dipole
Multipolar Expansion
(IGRF-9 (2000): 10 × 10)
(IGRF-10 (2005): 13 × 13)
External Field (Magnetosphere)
Image courtesy Dr. James L. Green, NASA
IGRF + Solar Wind: Tsiganenko
ESA recommends Tsiganenko 96 (or 01, or 06) for the external
field, or else Alexeev 2001.
IGRF-10 is recommended for the inner field (issued 2005, valid till
2010). IGRF-11 is expected in 2010. For lower precision, dipole
models could be used.
Magnetic Field - Ionosphere– p. 15/37
Aligned Dipole
um · r
Φ = −µm 3
B = −∇Φ
r
µm
B(r) = 3 [um − 3 (um · ur ) ur ]
r
Φ Magnetic Potential
B Intensity of the Magnetic Field (nTesla, gamma)
µm Magnetic moment of the dipole (including the factor µ0 /4π = 10−7
Hr/m)
um Unit vector in the direction of the dipole: (0, 0, 1)
ur Unit vector in the direction of the point:(λ, φ)
Magnetic Field - Ionosphere– p. 16/37
Tilted Dipole, Eccentric Dipole
Tilted Dipole: The dipole is tilted in the direction:
N
um = [cos φm cos λm , cos φm sin λm , sin φm ]
φm
According to IGRF-9 (2000):
λm = 71◦ 34′ W
φm = 79◦ 32′ N (Tilt: 10,53◦ )
Eccentric Dipole: The dipole center is offset from the
origin of the reference system:
x = −401,86 km
y = 300,25 km
z = 200,61 km
(Data from IGRF-9, 2000)
S
z
b
y
x
Magnetic Field - Ionosphere– p. 17/37
IGRF: Expansion in Spherical Harmonics
Intensity of the magnetic field:
Magnetic potential:
V = R⊕
l+1 X
∞ l
X
R⊕
l=1
r
m=0
B = −∇V
P lm [cos (90◦ − φgc )]·
· g lm cos mλ + hlm sin mλ
Linear variation of Coefficients, SV: ∆glm /year
Unnormalized glm , hlm : Gauss Coefficients
Normalized P̄lm , ḡlm , h̄lm : Schmidt functions (Normalized
Legendre associtated functions) and coefficients
Earth parameters from WGS-84
Magnetic Field - Ionosphere– p. 18/37
Normalization of Legendre A.F. Plm(x)
Schmidt-complete normalization
Rlm
P lm
schm
=
= Klm
=
Plm
Plm
Gravity
s
km (2l + 1) (l − m)!
(l + m)!
Schmidt-quasi-normalized
Plm
P lm
q−s
=
= Klm
=
Plm
Plm
Geomagnetism
s
km (l − m)!
(l + m)!
Keeps IGRF sectorial and tesseral terms of the same order.
1 m=0
As usual, km =
2 m>0
glm
glm
q−s
Normalization of coefficients:
= m = Klm
g lm
gl
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Relations between Models
Degree 1 coeffs ⇒ Centered dipole
−g10
h11
cos θm = sin φm =
tan λm =
g11
B0
3 4πR⊕
2
2
2
µm =
g10 + g11 + h11
µ0
B0 : geomagnetic constant, the value of B in the Equator:
µm
µ0 M q 2
2 + h2
B0 = 3 =
g
+
g
10
11
11
3
R⊕
4πR⊕
For the IGRF-10 (2005) model:
Field intensity B0 = 3,003595 · 104 nT
Dipole moment µm = 7,793 · 1015 Wb m
Magnetic moment M = 7,793 · 1022 A m2
θm = 10,25◦
λm = −71,78◦
Magnetic Field - Ionosphere– p. 20/37
Relations between Models
Degree 2 coeffs ⇒ Eccentric Dipole
ξ=
(L0 − g10 E) /3B02
η = (L1 − g11 E) /3B02
ζ = (L2 − h11 E) /3B02
p
δ = ξ 2 + η 2 + ζ 2 R⊕
√
L0 = 2g10 g20 + 3(g11 g21 + h11 h21 )
√
L1 = −g11 g20 + 3(g10 g21 + g11 g22 + h11 h22 )
√
L2 = −h11 g20 + 3(g10 h21 − h11 g22 + g11 h22 )
E = (L0 g10 + L1 g11 + L2 h11 )/4B02
IGRF-10 (2005) Model:
x = −401,23 km
y = 317,54 km
z = 208,94 km
Same moment and inclination as the centered dipole
[Compare with the IGRF-9 (2000) values in p. 17]
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Magnetic Pole evolution
Northern Pole of the Tilted Dipole Model
Model
Year Latitude Longitude
B0 (nT)
DGRF 1945
78.47
291.47
31224.51
DGRF 1950
78.47
291.15
31183.71
DGRF 1955
78.46
290.84
31129.22
DGRF 1960
78.51
290.53
31043.16
DGRF 1965
78.53
290.15
30951.64
DGRF 1970
78.59
289.82
30829.18
DGRF 1975
78.69
289.53
30696.38
DGRF 1980
78.81
289.24
30573.69
DGRF 1985
78.97
289.10
30434.77
DGRF 1990
79.13
288.89
30318.16
IGRF 1995
79.30
288.59
30215.08
IGRF 2000
79.54
288.43
30119.61
IGRF 2005
79.75
288.22
30036.74
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Earth’s Magnetosphere
Magnetosphere: region between ionosphere and Interplanetary Magnetic Field
(IMF). Comprises:
Bow shock: Supersonic shock wave due
to collision of solar wind with Earth’s
magnetosphere/ionosphere. Penetrating
plasma is subsonic and hotter (mechanic
→ thermic).
Image courtesy NASA
Magnetopause: Magnetospheric boundary. Equilibrium of dynamic
pressure of solar wind and geomagnetic field pressure (cf. Pisacane).
Magnetosheath: Region between bowshock and magnetopause.
Turbulent, weaker field; hotter at subsolar spot.
Magnetotail: Portion of magnetosphere away from the Sun. Stretched
and highly dynamic; large energy changes.
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Earth’s Magnetosphere
Neutral Point: where several field
lines converge; only possible near
zero flux. Plasmas can separate
and reconnect. Reconnection releases energy and particles can be injected into the atmosphere.
Image courtesy NASA
Neutral sheet: Thin surface, N-S boundary of magnetosfere,
“equatorial”. Divides magnetosphere into northern and southern lobes.
Dynamic, due to Earth’s field rotation.
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Earth’s Magnetosphere
Plasma mantle: boundary layer just
inside the magnetopause, coming
from the polar cusps, where solar
wind and ionospheric plasma and
magnetic field lines mix.
Current or plasma sheet: layer of hot
plasma and low field on both sides
of neutral sheet. In high solar activity and magnetic storms, becomes
unstable.
Image courtesy Dr. James L. Green, NASA GSFC
Usually solar wind plasma; in magnetic storms ionspheric plasma may
predomintate. Magnetically linked to auroral field lines.
Plasmasphere: Toroidal region of cold dense plasma between ionosphere
and magnetopause. Contains ionospheric plasma moving around
magnetic field lines.
Magnetic Field - Ionosphere– p. 25/37
Earth’s Magnetosphere
Polar cusps: Funnel-shaped regions
leading to Geomagnetic poles; both
magnetic fields add. Solar wind penetrates to plasma mantle, and inside to interact with ionosphere and atmosphere aut the Aurora oval.
Image courtesy Dr. James L. Green, NASA GSFC
Tail lobes: northern ans southern regions that constitute most of the
magnetotail. Stretches very far (≃200 ER). Low denstity. Plasma is
eventually swept into solar wind.
Magnetic Field - Ionosphere– p. 26/37
Magnetosphere Models
Empirical or semi-empirical: Tsyganenko 1996
Geomagnetic field (IGRF10) + Solar wind + Magnetic Storms
Fortran code available: http://geo.phys.spbu.ru/
~tsyganenko/modeling.html
Good for average values as a function of solar activity
Analytical: Paraboloid Model of Alexeev et al., 2001
ESA recommended, ISO draft standard. Fortran code:
http://www.magnetosphere.ru/iso/index.html
Magneto-hydrodynamic: none yet ready, improving
Some empirical models already predict instant field variations, such
as substorm conditions: Tsyganenko 2001 and 04; not recommended
because it is difficult go give accurate inputs in an enginneering
environment.
Magnetic Field - Ionosphere– p. 27/37
Ionospheric Plasma
Image courtesy NOAA
Plasma: ionized gas, made up of
ions(+) and free electrons
Plasma
Gas
Liquid
Solid
Energy
Cause of Plasma: Absorption of
UV/EUV/X-ray by the atmosphere.
At 60 km, most has been filtered:
heating → plasma
Magnetic Field - Ionosphere– p. 28/37
Plasmasphere
Plasmashpere: at higher levels, ionospheric plasma is trapped by the
rotating geomagnetic lines within the plasmapause.
Image courtesy of Windows to the Universe, http://www.windows.ucar.edu/
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Trapped Radiation Belts
Charged particles in the Plasmasphere
move with
Fast gyration about magnetic field
lines (Larmor radius)
Slower bouncing from one point
close to Earth North to the mirror
point South and back.
Slow drift along magnetic longitude
Particles are stably trapped in radiation
belts
Energies reach up to hundreds of MeV
for protons and tens of MeV for electrons.
Electron flux density from AE-8 model output with E>1 MeV.
Images courtesy SPENVIS
Magnetic Field - Ionosphere– p. 30/37
South Atlantic Anomaly
Courtesy ESA
Courtesy Nasa
Because of dipole tilt and offset, magnetic
field weaker over Brazil → Radiation Belt
closer, higher radiation levels.
Magnetic Field - Ionosphere– p. 31/37
Plasmasphere and Userful Orbits
HEO
GEO
MEO
Image courtesy NASA/Modified by Manuel Ruiz
LEO
Magnetic Field - Ionosphere– p. 32/37
Plasma Environment
Shielding: Charged objects in a plasma environment are surrounded
by a cloud of opposite sign ions/elctrons, shielding it from other
charges.
Debye length: The electric potential of a charge q in a plasma
atenuates as
q
U=
e−r/λD
4πǫ0 r
The Debye length λD is the distance at which the electric field of a
charge drops to 1/e of the void value.
Charging: selected parts of a spacecraft can accumulate charges
from the plasma environment. Can be absolute, the whole spacecraft
has a bias relative to environment; or differential between parts of
the craft, which can lead to arcing
Magnetic Field - Ionosphere– p. 33/37
Model Application
ESA ECSS-E-ST-10-04A recommendations:
Ionosphere, for altitudes 60< h <2000 km
Auroral charging environment, for i > 50 deg and 80-2000 km
Plasmasfere, for h >2000 k (appr. L=1,3 at equator), and L <7
Outer Magnetosphere for all L >3, within the magnetopause
(includes GEO)
Magnetosheath, between magnetopause and bow shock
Solar wind, outside of the magnetopause and bow shock
Magnetotail and distant magnetosheath, within the bow shock and
more than 30 RE in anti-Sunward direction
Planetary plasma environment, when applicable to the planet, as
above
L: L-Shell, distance in Earth radii to the field line magnetic equator crossing
Magnetic Field - Ionosphere– p. 34/37
Ionospheric Models
ESA ECSS-E-ST-10-04A recommendations:
The International Reference Ionosphere IRI-95 will be used
(updated models available: IRI-07)
User inputs: geographic or geomagnetic coordinates: latitude and
longitude; date; local or universal time; altitude range
Other inputs: model comes with periodically updated data files
for solar and geomagnetic indices: sunspot numbers Rz12, IG12,
F10,7 and ap
For future dates, the projected standard solar cycle values shall
be used
Fortran code and on-line interface available
USAF MIL-STD-1809 for the auroral zone
Charging: NASA’s NASCAP or NASCAP-GEO routines
Magnetic Field - Ionosphere– p. 35/37
Application: Electrodynamic Tether
A bare conductor moving in the
ionosphere collect electrons
Bare tethers (several km long) can get
thousands of volts EMF.
An electric current can be closed
through the Geomagnetic field lines.
Conductor moving in a magnetic field
→ Lorenz force: motor/brake
Connect an electric load: generator
Debris eliminator, ISS orbit raising, Jupiter exploration
Images courtesy NASA
Magnetic Field - Ionosphere– p. 36/37
Application: Tether System Simulation
Computations needed at each integration step:
Compute GCRS to ITRF rotation matrix: integration in inertial axes, most models
in Earth-fixed axes. Usually, only the daily rotation part.
Gravitational field. For long tethers, at several points to compute torque
Find Sun vector for SRP and 3rd body, Moon vector for 3rd body
Call IRI for electron density; keep the value of magnetic field that is used
internally. For long tethers, at several points
Apply charging model (e.g., OLM) for the EMF and current in the tether
With this and magnetic field, compute Lorenz force
Call atmospheric density model to compute air drag. In some IRI versions, this
value can be taken from the IRI intermediate computations.
Add all perturbation forces and torques to give integration step
Note that those models are very computation-intensive.
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