Transcript Structure and Dynamics of Inner Magnetosphere and Their Effects on Radiation Belt Electrons APL Chia-Lin Huang Boston University, MA, USA CISM Seminar, March 24th,

Structure and Dynamics of Inner Magnetosphere
and Their Effects on Radiation Belt Electrons
APL
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
Goals 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.
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Motivation: 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 Electrons
 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 space
Green [2002]
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Solar Wind and Magnetosphere
Ring Current

Average picture of solar wind and magnetosphere (magnetic field, regions,
inner mag. plasmas)

Variations of Psw, IMF Bz causes magnetospheric dynamics
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Magnetic 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 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 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
Global MHD simulation
Importance and applications, validation of the global models
Empirical model

Tsyganenko model
LFM MHD code
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Charged Particle Motion in Magnetosphere
 Gyro, bounce and drift motions
 Gyro ~millisecond, bounce ~ 0.1-1 second, drift ~1-10 minutes
 Adiabatic invariants and L-shell
W

B
J   p|| ds
   BdS
 To change particle energy, must violate one or more invariants
 Sudden changes of field configurations
 Small but periodic variation of field configurations
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Why is it so Hard? What Would 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 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 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
LFM grid in equatorial plane
 Field configurations and
wave field validations by
comparing w/ GOES
data
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Data/Model Case Study



24-26 September 1998 major storm event (Dst minimum -213 nT)
LFM inputs: solar wind and IMF data
Geosynchronous orbit

Compare LFM and GOES B-field at
GEO orbit
Sep98 event: solar wind data and Dst
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Statistical Data/Model Comparisons
 9 magnetic storms; 2month non-storm interval
Field residual B = BMHD – BGOES
 LFM field lines are
consistently understretched, especially
during storm-time, on
the nightside
 Predict reasonable nonstorm time field
 Improvements of LFM
 Increase grid resolution
 Add ring current
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Statistical comparison of
Tsyganenko models and GOES data


52 major magnetic storm from 1996 to 2004
TS05 has the best performance in all local time and storm levels
Field residual B = BGOES – BTmodel
Under-estimate
T96
T02
TS05
Perfect prediction
Over-estimate
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Consequence of field model errors

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 Magnetosphere
NASA

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.
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Power Spectral Density (PSD)

Calculate PSD using 3hour 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 FAC

Noon
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)
Dawn
Dusk
 Calculate PSDs
 Median PSD in each frequency bin
Compressional
Azimuthal
Midnight
Radial
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PSDB [nT2/Hz]
Sorting GOES Bb PSD by SW Vx
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Bz southward
PSDB [nT2/Hz]
Bz northward
Sorting GOES Bb PSD by IMF Bz
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ULF Waves in LFM code
Direct comparisons of ULF waves during Feb-Apr 1996 in field-aligned coord.
GOES data
Bb
compressional
Bn
radial
PSDB [nT2/Hz]
LFM output
Bφ
azimuthal
Local Time
Much
better than
expected!
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Dst and Kp effects on ULF wave power
High Dst interval
Dst ≤ -40 nT
Low Dst interval
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
High Kp interval
Kp ≥ 4
Low Kp interval
Kp < 4
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TS05 model
LFM code
GOES data
ULF wave prediction of Tsyganenko model

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 Performance
Model
Tsyganenko model
LFM MHD code
Storm config.
Non-storm
O
O
X
O
ULF wave field
X
O
 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.
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ULF Wave Effects on RB 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
Elkington et al. [2003]
Rostoker et al. [1998]
 Quantitative description of wave-particle interaction
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Particle Diffusion in Magnetosphere
 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
f
 
1  2 

D
L f 
LL
2

t L 
L L

 
(Radial diffusion equation)
, where DLL 
 L2
2
day 
1
(Radial diffusion coefficient)
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Radial Diffusion Coefficient, DLL
 Large deviations in previous studies
 Possible shortcomings
Experimental (solid) and
theoretical (dashed) DLL values
Walt [1994]
 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
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When Does LFM Predict Waves 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 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 (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 Simulations
LFM Vx runs
GOES data
Vx = 400
Vx = 500
Vx=600
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)
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Eφ Wave Power Spatial Distributions
6 mHz
Wave power 
 PSDE ( f ) df
[(m V / m) 2 ]
0.5 mHz

Wave power increases as Vx (Pd variations) increases

Wave amplitude is higher at larger radial distance (wave source)
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Radiation 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 (DLL)
 Convert particle location to L* [Roederer, 1970] L*  
2 k0
RE 
 Calculate our radial diffusion coefficient, DLL(Vx) DLL 
 L2
2
DLL
increases
with Vx
DLL increases with L
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Compare DLL Values I

The major differences
between previous studies
and this work
B ~10 nT
 Amplitude of wave field
 IMF Bz
 Magnetic field model
 Particle energy
 Calculating method
 Theoretical assumption


Differences make it
impossible for a fair
comparison
B ~2 nT
B ~1 nT
Highlight: Selesnick et al.
[1997]
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Compare DLL 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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Summary
 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 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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