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, 2007

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.

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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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Highly Structured and Dynamical Highly Structured and Dynamical Relativistic ElectronsRelativistic Electrons

Relativistic electron events: magnetic storms, high speed solar wind stream and quiet intervals

Reeves et al. [2007]

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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.

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