structure and dynamics of inner magnetosphere and their effects on radiation belt electrons
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Structure and Dynamics of Inner Structure and Dynamics of Inner
Magnetosphere Magnetosphere
and Their Effects on Radiation Belt and Their Effects on Radiation Belt
ElectronsElectrons
Chia-Lin Huang Boston University, MA, USA
CISM Seminar, March 24th, 2008
Special thanks: Harlan Spence, Mary Hudson, John Lyon, Jeff Hughes, Howard Singer, Scot Elkington, and many more
APL
2
Goals of my ResearchGoals of my Research
To understand the physics describing the structure and dynamics of field configurations in the inner magnetosphere
To assess the performance of global magnetospheric models under various conditions
To quantify the response of global magnetic and electric fields to solar wind variations, and ultimately their effects on radial transport of radiation belt electrons.
3
Motivation: Radiation BeltsMotivation: Radiation Belts
Discovery of Van Allen radiation belts – Explorer 1, 1958
Trapped protons & electrons, spatial distribution (2-7 RE),
energy (~MeV)
outer belt slot region inner belt
J. Goldstein
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Dynamical Radiation Belt Dynamical Radiation Belt ElectronsElectrons
Why study radiation belt electrons? Because they are
physically interesting
Radiation damage to spacecraft and human activity in space
Goal: describe and predict how radiation belts evolves in time at a given point in spaceGreen [2002]
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Solar Wind and MagnetosphereSolar Wind and Magnetosphere
Average picture of solar wind and magnetosphere (magnetic field, regions, inner mag. plasmas)
Variations of Psw, IMF Bz causes magnetospheric dynamics
Ring Current
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Magnetic StormsMagnetic Storms Most intense solar
wind-magnetosphere coupling
IMF Bz southward, strong electric field in the tail
Formation of ring current and its effect to field configurations
Dst measures ring current development Storm sudden commencement (SSC),
main phase, and recovery phase Duration: days
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Magnetospheric PulsationsMagnetospheric Pulsations Ultra-low-frequency (ULF) MHD waves
Frequency and time scale: 2-7 mHz, 1-10 minutes Field fluctuation magnitude
First observed in 19th century Waves standing along the magnetic field lines connect to
ionospheres [Dungey, 1954]
Morphology and generation mechanisms are not fully understood
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Global Magnetospheric ModelsGlobal Magnetospheric Models Provide global B and E fields needed for radiation belt study Data-based: Tsyganenko models
Parameterized, quansi-static state of average magnetic field configurations
Physics-based: Global MHD code Self-consistent, time dependent, realistic magnetosphere
Importance and applications, validation of the global models
Em
pir
ical m
odel
Glo
bal M
HD
sim
ula
tion
LFM MHD codeTsyganenko model
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Charged Particle Motion in Charged Particle Motion in MagnetosphereMagnetosphere
Gyro, bounce and drift motions Gyro ~millisecond, bounce ~ 0.1-1 second, drift ~1-10 minutes
Adiabatic invariants and L-shell
To change particle energy, must violate one or more invariants Sudden changes of field configurations Small but periodic variation of field configurations
BdS
dspJ
B
W
||
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Why is it so Hard? What Would Why is it so Hard? What Would Help?Help?
Proposed physical processes Acceleration: large- and small-scale recirculations, heating by
Whistler waves, radial diffusion by ULF waves, cusp source, substorm injection, sudden impulse of solar wind pressure and etc.
Loss: pitch angle diffusion, Coulomb collision, and Magnetopause shadowing.
Transport
Difficulties to differentiate the mechanisms: Lack of Measurements Lack of an accurate magnetic and electric field model Converting particle flux to distribution function is tricky Need better understanding of wave-particle interactions Computational resource
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The Rest of the TalkThe Rest of the Talk
Magnetospheric field dynamics: data & models Large-scale: Magnetic storms Small-scale: ULF wave fields
Effects of field dynamics on radiation belt electrons Create wave field simulations Quantify electron radial transport in the wave fields
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Lyon-Fedder-Mobbary Code Lyon-Fedder-Mobbary Code Lyon et al. [2004]
Uses the ideal MHD equations to model the interaction between the solar wind, magnetosphere, and ionosphere Simulation domain and grid 2D electrostatic ionosphere Solar wind inputs
Field configurations and wave field validations by comparing w/ GOES data
LFM grid in equatorial plane
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Data/Model Case StudyData/Model Case Study 24-26 September 1998 major storm event (Dst minimum -213 nT) LFM inputs: solar wind and IMF data Geosynchronous orbit
Sep98 event: solar wind data and Dst
Compare LFM and GOES B-field at GEO orbit
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Statistical Data/Model Statistical Data/Model ComparisonsComparisons
9 magnetic storms; 2-month non-storm interval LFM field lines are
consistently under-stretched, especially during storm-time, on the nightside
Predict reasonable non-storm time field
Improvements of LFM Increase grid
resolution Add ring current
Field residual B = BMHD – BGOES
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Statistical comparison of Statistical comparison of Tsyganenko models and GOES Tsyganenko models and GOES
datadata 52 major magnetic storm from 1996 to 2004 TS05 has the best performance in all local time and storm levels
Under-estimate
Perfect prediction
Over-estimate
Field residual B = BGOES – BTmodel
T96 T02 TS05
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Consequence of field model Consequence of field model errorserrors
Inaccurate B-field model could alter the results of related studies Example: radial profiles of phase space density of radiation belt electrons
Discrepancies between Tsyganenko models using same inputs Model field lines traced from GOES-8’s position (left) Pitch angles at GOES-8’s position and at magnetic equator (right)
~15% error between T96 and TS05
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ULF Waves in ULF Waves in MagnetosphereMagnetosphere
Wave sources: shear flow, variation in the solar wind pressure, IMF Bz, and instability etc.
Previous studies: integrated wave power, wave occurrence Next, calculate wave power as function of frequency using GOES data;
wave field prediction of LFM and T model.
NASA
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Power Spectral Density (PSD)Power Spectral Density (PSD)
Calculate PSD using 3-hour GOES B-field data
Procedures: 1. Take out sudden field
change
2. De-trend w/ polynomial fit
3. De-spike w/ 3 standard deviations
4. High pass filter (0.5 mHz)
5. FFT to obtain PSD [nT2/Hz]
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GOES B-field PSDs in FACGOES B-field PSDs in FAC 9 years of GOES data (G-8, G-9 and G-10
satellites) Field-aligned coordinates Separate into 3-hour intervals (8 local time sectors) Calculate PSDs Median PSD in each frequency bin
Noon
Midnight
DawnDusk
Compressional Azimuthal Radial
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Sorting GOES BSorting GOES Bbb PSD by SW Vx PSD by SW Vx
PSD
B [n
T2/H
z]
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Sorting GOES BSorting GOES Bbb PSD by IMF Bz PSD by IMF Bz
PSD
B [n
T2/H
z]
Bz
sout
hwar
d
Bz
nort
hwar
d
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ULF Waves in LFM codeULF Waves in LFM codeDirect comparisons of ULF waves during Feb-Apr 1996 in field-
aligned coord.
PSD
B [n
T2/H
z]
Local Time
LF
M o
utp
ut
GO
ES
da
ta
Bb compressional
Bn radial
Bφ
azimuthal
Much better than expected!
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Dst and Kp effects on ULF wave Dst and Kp effects on ULF wave powerpower
High Kp intervalKp ≥ 4
Low Kp intervalKp < 4
High Dst interval Low Dst interval Dst ≤ -40 nT Dst > -40 nT
ULF wave power has higher dependence on Kp than Dst
Even though LFM does not reproduce perfect ring current, it predicts reasonable field perturbations
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ULF wave prediction of Tsyganenko ULF wave prediction of Tsyganenko modelmodel
TS
05 m
od
el
L
FM
co
de
G
OE
S d
ata
Underestimates the wave power at geosynchronous orbit
Field fluctuations are results of an external driver
Lack of the internal physical processes
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Summary of Model Summary of Model PerformancePerformance
Use LFM’s wave fields during non-storm time to study ULF wave effects on radiation belt electrons
Such conditions exist during high speed solar wind streams intervals.
OX
OLFM MHD code
XO
OTsyganenko model
ULF wave fieldStorm config.
Non-stormModel
OX
OLFM MHD code
XO
OTsyganenko model
ULF wave fieldStorm config.
Non-stormModel
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ULF Wave Effects on RB ULF Wave Effects on RB Electrons Electrons
Strong correlation between ULF wave power and radiation belt electron flux [Rostoker et al., 1998]
Drift resonant theory [Hudson et al., 1999 and Elkington et al., 1999]
ULF waves can effectively accelerate relativistic electrons
Quantitative description of wave-particle interaction
Rostoker et al. [1998]Elkington et al. [2003]
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Particle Diffusion in Particle Diffusion in MagnetosphereMagnetosphere
Diffusion theory: time evolution of a distribution of particles whose trajectories are disturbed by innumerable small, random changes.
Pitch angle diffusion (loss): violate 1st or 2nd invariant
Radial diffusion (transport and acceleration): violate 3rd invariant
fLLL
DLt
fLL
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1 1
2
2
day
LDLL
(Radial diffusion coefficient)(Radial diffusion equation)
, where
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Radial Diffusion Coefficient, Radial Diffusion Coefficient, DDLLLL
Large deviations in previous studies
Possible shortcomings Over simplified theoretical
assumptions
Lack of accurate magnetic field model and wave field map
Insufficient measurement
M. Walt’s suggestion: follow RB particles in realistic magnetospheric configurations
Walt [1994]
Experimental (solid) and theoretical (dashed) DLL values
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When Does LFM Predict Waves When Does LFM Predict Waves Well?Well?
GOES and LFM PSDs sorted by solar wind Vx bins
LFM does better during moderate activities
Create ULF wave activities by driving the LFM code with synthetic solar wind pressure input
X O
O O
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Solar Wind Pressure Solar Wind Pressure Variation Variation
Histograms of solar wind dynamic pressure from 9 years of Wind data for Vx = 400, 500, and 600 km/s bins
Make time-series pressure variations proportional to solar wind Vx
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Synthetic Solar Wind Pressure Synthetic Solar Wind Pressure (Vx)(Vx)
LFM inputs: Constant Vx; variation in number density. Northward IMF Bz (+2 nT), to isolate pressure driven waves.
Idealized LFM Vx simulations using high time and spatial resolutions
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Idealized Vx SimulationsIdealized Vx Simulations
GOES statistical study (9 years data) as function of Vx (“mostly” northward IMF)
Drive LFM to produce “real” ULF waves with solar wind dynamic pressure variations as function of Vx (“purely” northward IMF)
LFM
Vx r
uns
G
OE
S d
ata
Vx = 400 Vx = 500 Vx=600
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Eφ Wave Power Spatial Eφ Wave Power Spatial Distributions Distributions
Wave power increases as Vx (Pd variations) increases Wave amplitude is higher at larger radial distance (wave source)
])/[()( 26
5.0
mmVdffPSDpowerWavemHz
mHz
E
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Radiation Belt SimulationsRadiation Belt Simulations Test particle code [Elkington et al., 2004]
Satisfy 1st adiabatic invariant Guiding center approximation 90o pitch angle electron Push particles using LFM magnetic and electric
fields
Simulate particles in LFM Vx = 400 and 600 km/s runs
Particle initial conditions Fixed μ = 1800 MeV/G Radial: 4 to 8 RE
1o azimuthal direction ~15000 particles /run
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Rate of Electron Radial Transport Rate of Electron Radial Transport (D(DLLLL))
Convert particle location to L* [Roederer, 1970]
Calculate our radial diffusion coefficient, DLL(Vx) 2
2LDLL
DLL increases with L
DLL
increases with Vx
ER
kL 0* 2
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Compare DCompare DLLLL Values I Values I The major differences
between previous studies and this work Amplitude of wave field IMF Bz Magnetic field model Particle energy Calculating method Theoretical assumption
Differences make it impossible for a fair comparison
Highlight: Selesnick et al. [1997]
B ~10 nT
B ~1 nT
B ~2 nT
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Compare DCompare DLLLL Values II Values II
DLL ~ dB2 [Schulz and Lanzerotti, 1974]
After scaling for wave power Compare to Selesnick et al.
[1997] again
Match well with Vx=600 km/s interval (L-dependent)
Average Vx of Selesnick et al. [2007] and IMF Bz effect
This suggests that radial diffusion is well-simulated, can differentiate from other physical processes
DLL(Vx, Bz, Pdyn, Kp etc.)
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SummarySummary TS05 best predicts GEO magnetic fields in all conditions
LFM has good predictions of quiet time fields, but not for storm time
ULF wave structures and amplitudes at GEO sorted by selected parameters
ULF wave field predictions: LFM is very good, but not TS05
Radial diffusion coefficient derived from MHD/Particle code
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Conclusions and AchievementsConclusions and Achievements
Most comprehensive, independent study of state-of-the-art empirical magnetic field models
Most quantitative investigation of global MHD simulations in the inner magnetosphere
Most comprehensive observational ULF wave fields at geosynchronous orbit dedicated to outer zone electron study
First exploration on ULF wave field performance of global magnetospheric models
First DLL calculation by following relativistic electrons in realistic, self-consistent field configurations and wave fields of an MHD code
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