Structure and Dynamics of Inner Magnetosphere Structure and Dynamics of Inner Magnetosphere and Their Effects on Radiation Belt Electronsand Their Effects on Radiation Belt Electrons

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, 1958Trapped protons & electrons, spatial distribution (2-7 RE), energy (~MeV)

outer belt slot region inner belt

J. Goldstein

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Dynamical Radiation Belt ElectronsDynamical 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 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 StormsMost 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 developmentStorm sudden commencement (SSC), main phase, and recovery phaseDuration: days

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Magnetospheric PulsationsMagnetospheric PulsationsUltra-low-frequency (ULF) MHD waves

Frequency and time scale: 2-7 mHz, 1-10 minutes

Field fluctuation magnitude

First observed in 19th centuryWaves 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 ModelsProvide global B and E fields needed for radiation belt study

Data-based: Tsyganenko modelsParameterized, quansi-static state of average magnetic field configurations

Physics-based: Global MHD codeSelf-consistent, time dependent, realistic magnetosphere

Importance and applications, validation of the global models

Empi

rical

mod

el

Glo

bal M

HD

sim

ulat

ion

LFM MHD codeTsyganenko model

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Charged Particle Motion in MagnetosphereCharged Particle Motion in Magnetosphere

Gyro, bounce and drift motionsGyro ~millisecond, bounce ~ 0.1-1 second, drift ~1-10 minutes

Adiabatic invariants and L-shell

To change particle energy, must violate one or more invariantsSudden changes of field configurations

Small but periodic variation of field configurations

∫∫

=Φ

=

= ⊥

BdS

dspJB

W

||

μ

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Why is it so Hard? What Would Help?Why is it so Hard? What Would Help?

Proposed physical processesAcceleration: 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 MeasurementsLack of an accurate magnetic and electric field model Converting particle flux to distribution function is trickyNeed better understanding of wave-particle interactionsComputational resource

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The Rest of the TalkThe Rest of the Talk

Magnetospheric field dynamics: data & modelsLarge-scale: Magnetic stormsSmall-scale: ULF wave fields

Effects of field dynamics on radiation belt electronsCreate wave field simulationsQuantify electron radial transport in the wave fields

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LyonLyon--FedderFedder--Mobbary Code 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 Study24-26 September 1998 major storm event (Dst minimum -213 nT)LFM inputs: solar wind and IMF dataGeosynchronous orbit

Sep98 event: solar wind data and Dst

Compare LFM and GOES B-field at GEO orbit

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Statistical Data/Model ComparisonsStatistical Data/Model Comparisons

9 magnetic storms; 2-month non-storm interval

LFM field lines are consistently under-stretched, especially during storm-time, on the nightsidePredict reasonable non-storm time field

Improvements of LFMIncrease grid resolution Add ring current

Field residual ΔB = BMHD – BGOES

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Statistical comparison of Statistical comparison of Tsyganenko models and GOES dataTsyganenko models and GOES data

52 major magnetic storm from 1996 to 2004TS05 has the best performance in all local time and storm levels

Under-estimate

Perfect prediction

Over-estimate

T96 T02 TS05

Field residual ΔB = BGOES – BTmodel

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Consequence of field model errorsConsequence of field model errorsInaccurate 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 inputsModel 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 MagnetosphereULF Waves in Magnetosphere

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

change2. De-trend w/ polynomial

fit3. De-spike w/ 3 standard

deviations4. High pass filter (0.5 mHz)5. FFT to obtain PSD

[nT2/Hz]

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GOES BGOES B--field field PSDsPSDs in FACin FAC9 years of GOES data (G-8, G-9 and G-10 satellites)

Field-aligned coordinatesSeparate into 3-hour intervals (8 local time sectors)Calculate PSDsMedian PSD in each frequency bin

Noon

Midnight

DawnDusk

Compressional Azimuthal Radial

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Sorting GOES BSorting GOES Bbb PSD by SW PSD by SW VxVx

PSD

B [n

T2/H

z]

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Sorting GOES BSorting GOES Bbb PSD by IMF PSD by IMF BzBz

PSD

B [n

T2/H

z]

Bz

sout

hwar

d

B

zno

rthw

ard

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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

LFM

out

put

GO

ES d

ata

Bbcompressional

Bnradial

Bφazimuthal

Much better than expected!

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DstDst and and KpKp effects on ULF wave powereffects on ULF wave power

High Kp intervalKp ≥ 4

Low Kp intervalKp < 4

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 Dst interval Low Dst intervalDst ≤ -40 nT Dst > -40 nT

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ULF wave prediction of Tsyganenko modelULF wave prediction of Tsyganenko modelTS

05 m

odel

LFM

cod

e

GO

ES 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 PerformanceSummary of Model Performance

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 Electrons 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

Quantitative description of wave-particle interaction

Rostoker et al. [1998]Elkington et al. [2003]

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Particle Diffusion in MagnetosphereParticle 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

( )⎥⎦⎤

⎢⎣⎡

∂∂

∂∂

=∂∂ fL

LLD

Ltf

LL2

2

1 [ ]12

2−

Δ= day

LDLL τ

(Radial diffusion coefficient)(Radial diffusion equation)

, where

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Radial Diffusion Coefficient, DRadial Diffusion Coefficient, DLLLL

Large deviations in previous studies

Possible shortcomingsOver 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 Well?When Does LFM Predict Waves Well?

GOES and LFM PSDssorted by solar wind Vxbins

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 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 (Synthetic Solar Wind Pressure (VxVx))

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 Idealized VxVx SimulationsSimulations

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

runs

G

OES

dat

a

Vx = 400 Vx = 500 Vx=600

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EφEφ Wave Power Spatial Distributions Wave Power Spatial Distributions

Wave power increases as Vx (Pd variations) increases

Wave amplitude is higher at larger radial distance (wave source)

])/[()( 26

5.0

mmVdffPSDpowerWavemHz

mHzE∫=ϕ

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Radiation Belt SimulationsRadiation Belt SimulationsTest particle code [Elkington et al., 2004]

Satisfy 1st adiabatic invariantGuiding center approximation90o pitch angle electron Push particles using LFM magnetic and electric fields

Simulate particles inLFM Vx = 400 and 600 km/s runs

Particle initial conditionsFixed μ = 1800 MeV/GRadial: 4 to 8 RE

1o azimuthal direction~15000 particles /run

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Rate of Electron Radial Transport (Rate of Electron Radial Transport (DDLLLL))

Convert particle location to L* [Roederer, 1970]

Calculate our radial diffusion coefficient, DLL(Vx) τ2

2LDLL

Δ=

DLL increases with L

DLLincreases with Vx

Φ−=

ERkL 0* 2π

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Compare DCompare DLLLL Values IValues IThe major differences between previous studies and this work

Amplitude of wave fieldIMF BzMagnetic field modelParticle energyCalculating methodTheoretical assumption

Differences make it impossible for a fair comparison

Highlight: Selesnick et al.[1997]

ΔB ~10 nT

ΔB ~1 nT

ΔB ~2 nT

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Compare DCompare DLLLL Values IIValues IIDLL ~ dB2 [Schulz and Lanzerotti, 1974]

After scaling for wave powerCompare 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, ΔPdyn, Kp etc.)

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SummarySummaryTS05 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 theinner 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