Magnetic Field - Ionosphere Modeling the Space Environment Manuel Ruiz Delgado

European Masters in Aeronautics and Space ´ E.T.S.I. Aeronauticos ´ Universidad Politecnica de Madrid April 2008

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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 Magnetic Field - Ionosphere– p. 2/37

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

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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:

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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.

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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:

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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.

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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)

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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 ¯ lm : Schmidt functions (Normalized Normalized P¯lm , g¯lm , h Legendre associtated functions) and coefficients Earth parameters from WGS-84

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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 Magnetic Field - Ionosphere– p. 19/37

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◦

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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 Magnetic Field - Ionosphere– p. 22/37

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.

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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.

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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

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South Atlantic Anomaly

Courtesy ESA

Courtesy Nasa

Because of dipole tilt and offset, magnetic field weaker over Brazil → Radiation Belt closer, higher radiation levels.

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Plasmasphere and Userful Orbits HEO

GEO MEO

Image courtesy NASA/Modified by Manuel Ruiz

LEO

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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

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Model Application ESA ECSS-E-ST-10-04A recommendations: Ionosphere, for altitudes 60< h 50 deg and 80-2000 km Plasmasfere, for h >2000 k (appr. L=1,3 at equator), and 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

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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

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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

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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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