Development of a Statistical Dynamic Radiation Belt Model

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Development of a Statistical Dynamic Development of a Statistical Dynamic Radiation Belt ModelRadiation Belt Model

[email protected]

Center for Space Radiations (CSR)

UCL, Louvain-La-Neuve, Belgium

S. Benck, L. Mazzino, V. Pierrard, S. Benck, L. Mazzino, V. Pierrard, M. Cyamukungu, J. CabreraM. Cyamukungu, J. Cabrera

ESWW5, Brussels, Belgium, 17-21 November 2008

mailto:[email protected]

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McIlwain in 1966 identifies 5 « Processes acting upon outer zone electrons »

Process 1: Rapid non adiabatic accelerationProcess 2: Persistent decayProcess 3: Radial DiffusionProcess 4: Adiabatic AccelerationProcess 5: Rapid Loss

(From McIlwain, 1996 AGU)

Measured radiation dose (black) compared to the static model prediction (red) based on flux averages (see Glossy brochure of the SREM from Contraves-PSI)

Steady state GS pobabilities Flux variations ConclusionDecay timesIntroduction

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st = Steady state flux measured

n = The expected flux variation following a storm (average)

res = Diff. between. flux before storm and steady state flux

T = Decay time of flux for a given position and energy

= Time elapsed from the storm min. Dst_prev (or drop-

out min) to 0 (Maximum flux)

N = Number of bins in Dst range

S = Solar par. that indicates phase within the solar cycle

Type = Type of storm: CME, CIR, Mix

F(Dst_prev) = Flux var. induced by prev. storm of min Dstprev

Dst prev = The min. value reached by Dst in the prev. storm

.

.

.

)_(0 prevDSTresst F 1

/01 )( T

stst e

2/

12 )( Tstst e

nTstnstn e

/

1 )(

)(0

)(),,,(

N

k

DststypeDstnDstn kprevk FP L. Mazzino, et al (2008)

T

flux = steady state background + geomagnetic activity dependent value


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Introduction GS pobabilities Flux variations ConclusionDecay times

~100 days

st

nTstnstn e

/

1 )(

Steady state

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st as a function of L (B>0.3 G)

st as a function of longitude, latitude and altitude

Introduction GS pobabilities Flux variations ConclusionDecay timesSteady state

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Black dots correspond to Dst minimum of the GS. The number of storms is outlined for each of the solar cycles (orange). Solar maximum and minimum activity are delineated (green and blue lines respectively, dates indicated), corresponding to solar cycles 19 (incomplete), 20, 21, 22 and 23. Sunspot number is plotted on the black curve with superimposed smoothed curve in red.

Introduction Steady state Flux variations ConclusionDecay times

)(0

)(),,,(

N

k

DststypeDstnDstn kprevk FP

GS probabilities

50 years of Dst and sunspot number data, including ~1200 storms have been analyzed

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Probability of having a GS of a given Dstk after a previous GS of any magnitude, for the declining phase .

Probability of two successive GS with a given time interval, for the declining phase of the different solar cycles Poisson distribution

Introduction Steady state GS pobabilities Flux variations ConclusionDecay times

Nice agreement with: Tsubouchi and Omura, Long-term occurrence probabilities of intense geomagnetic storm events, Space Weather, 2007

8(Picture: Courtesy of CNES)

http://smsc.cnes.fr/DEMETER/(Picture: Courtesy of CONAE)

http://www.conae.gov.ar/sac-c/

DEMETER/IDP SAC-C/ICARE

Electron fluxes data: Two LEO Satellites, Ee= 200 keV – 1.2 MeV

Orbit at 710 km 98.23 deg. Incl.

Orbit at 702 km 98.2 deg. Incl.

Introduction Steady state GS pobabilities ConclusionDecay times

nTstnstn e

/

1 )(

)(0

)(),,,(

N

k

DststypeDstnDstn kprevk FP

F and as a function of GS type

Flux variations

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Flux enhancement (F) and Time interval between storm and flux max ()


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TYPE 1 (mainly CME)


TYPE 2 (mainly CIR)

Kataoka and Miyoshi, “Flux enhancement of radiation belt electrons during geomagnetic storms driven by coronal mass ejections and corotating interaction regions.” Space weather, 2006

Storm type definition

short Bz/t, ’’peak’’, t ~3-4h long Bz/t, ’’inconsistent’’, t >7h

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The time interval between magnetic storm and flux maximum () seems to be linear for the classified isolated storms, but random for all other storms. Need more parameters

TYPE 1(yellow), TYPE 2 (red)


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Resultant flux enhancement F as a function of storm severity, corresponding to isolated TYPE 1 (yellow), TYPE 2 (red), and mixed non isolated storms (blue)

Introduction RABEM Model Dat Dat and parameters and parameters Results SummaryIntroduction Steady state GS pobabilities Flux variations ConclusionDecay times

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L-parameter

slop

e

TYPE 1sl

ope

L-parameter

TYPE 2


At low L the flux enhancement increases steeper with Dstmin (slope > 0) for lower energies

At high L the flux enhancement decreases steeper with Dstmin (slope < 0) for lower energies.

For all L values, the flux enhancement increases steeper with Dstmin (slope > 0) for lower energies

For all energies the slope decreases with L

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Decay time constant (loss timescales) of electron fluxes (T)


Condition of measurement: The time resolution is 12 h The maximum flux after storm must

occur 3 days before the defined end of the storm

DEMETER/IDP – SACC/ICARE comparison

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A pattern that is often observed during individual storms: At low L, the decay time decreases with increasing energy, while at high L this pattern is inversed.

Meredith et al, “Energetic outer zone electron loss timescales during low geomagnetic activity.” JGR (2006)

3<L<5, T(Ehigh) > T (Elow), for <15°

Decay time of electron fluxes (T) as a function of position and energy

Lyons et al, “Pitch-angle diffusion of radiation belt electrons within the plasmasphere.” JGR (1972) T=min at around L =3Re (theory)

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Meredith et al, “Evidence for acceleration of outer zone electrons to relativistic energies by whistler mode chorus.” Annales Geophysicae (2002)

(Benck et al, Study of correlations between waves and particle fluxes measured on board the DEMETER satellite, Advances in Space research (2008)

Cases where the electron flux increases continuously

(wave activity) ?

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Identified Parameters

Steady statest

Storm occurence and related probabilities

Dstprev, Dstk (1224 storms!)

t (time interval between two storms)

Solar Cycle parameter (SSN)

Flux variations during storm time

Type of storm (presently 2 types)

(elapsed time between storm max (Dstmin) and maximum flux)

Maximum Flux and Flux enhancement F

T (Decay time)

Solar parameters data: Courtesy of GSFC Space Physics Data Facility http://omniweb.gsfc.nasa.gov/index.html

SAMPEX DATA: Courtesy of SAMPEX Data Center http://www.srl.caltech.edu/sampex/DataCenter/ SAC-C Data: Courtesy of CNES/DCT/AQ/EC Section, ONERA/DESP and CONAE Sunspot Number Data: Courtesy of Solar Influences Data Analysis Center – SIDC, Belgium

Introduction Steady state GS pobabilities Flux variations Decay times Conclusion

L. Mazzino et al, Development of a statistical dynamic radiation belt model: Analysis of storm time particle flux variations, ESA Ionizing Radiation Detection and Data Exploitation Workshop proceedings, 2008

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Example of geomagnetic storm

Storm Sudden commencement

Main phase

Strength of storm:Minimum Dst reached

Recovery phase

Introduction RABEM Model Data and parameters Results Summary

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steady state background i.e. mapping of quiet time fluxes

Statistical dynamic radiation belt model

Geomagnetic storm (GS) prediction (Dst<-50 nT) - Occurrence probability

Flux variation associated to GS, as a function of energy, position and type of storm

Flux decay time as a function of energy, position, ...

+


L. Mazzino et al, Development of a statistical dynamic radiation belt model: Analysis of storm time particle flux variations, ESA Ionizing Radiation Detection and Data Exploitation Workshop proceedings, 2008

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Dst data (black) with filtered data (red): The second graph shows the filter detail, and the fourth shows a closed up of the event, with actual amplitude of the storm in green.

Butterworth filter:z = cutoff frequency n

z

filter *211

(Dst Data: Courtesy of World Data Center for Geomagnetism, Kyoto)

Dst

Introduction RABEM Model Data and parameters Results Summary Additional

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Correlation between number of storms per month for different phases in a solar cycle with the Sunspot Maximum corresponding to that cycle.


Sunspot Number Maxima

(smoothed)

Solar cycle #20: 109

Solar Cycle #21: 159



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Histogram of Dstk vs. Dstprev

number of bins = 100

Introducton RABEM Model Data and parameters Results Summary

Probability of having a storm with intensity Dstk considering that the previous one was of intensity Dstprev

All Dstmin given in absolute value


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Introduction RABEM Model Data and parameters Result Summary

For few events the time interval between storms is greater than 100 days, and the time interval between those storms can be used to find the steady state.

All Dstmin given in absolute value

Histogram of Dstk vs. time interval, number of

bins = 100

Nice agreement with: Tsubouchi and Omura, Long-term occurrence probabilities of intense geomagnetic storm events, Space Weather, 2007


Probability of having a storm with intensity Dstk considering a given time interval elapsed since the previous storm

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Sunspot number maximum is a good parameter to represent solar cycle activity vs. total number of storms.

The total number of storms per month in a cycle correlates directly to the severity of the solar cycle: For solar cycles with higher SSN maxima, SC 21 and SC 22,the total number of storms is higher than for SC 20 and SC 23 with lower maxima

Solar Parameter (S): Sun Spot Number

Sunspot Number Maxima

(smoothed)

Solar cycle #20: 109





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Histogram of smoothed Sunspot number vs. Time interval between storms (number of bins = 25 time resolution = 10 days)

The distribution of time interval between storms for all 1204 storms in the last 50 years seems to be Poisson-distributed.


Probability of having a certain time interval between storms considering the sunspot number

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Difference of time interval distribution function depending on phase and severity of solar cycle activity


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DEMETER Fluxes


Geomagnetic storm: particle flux enhancement

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(SAC-C Data: Courtesy of CNES/DCT/AQ/EC Section, ONERA/DESP and CONAE)


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FLUX ENHANCEMENT DUE TO GEOMAGNETIC STOMS

SAC-C

Introduction RABEM Model Data Data and parameters and parameters Results Summary

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Resultant flux enhancement difference as a function of storm severity, corresponding to

isolated CME’s (yellow), CIR’s (red), and mixed non isolated storms (blue)

Resultant maximum flux as a function of storm severity, corresponding to isolated CME’s

(yellow), CIR’s (red), and mixed non isolated storms (blue)


Results: Fluxes

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(SAC-C Data: Courtesy of CNES/DCT/AQ/EC Section, ONERA/DESP and CONAE)

TYPE 1(yellow), TYPE 2 (red)

3333


TYPE 2

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Decay time of electron fluxes (T) independent of Dst

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• In a dipole:

We need a reference invariable with time

Hess (1968)

McIlwain (1961-1966)

• Magnetic Coordinates:

Illustration from: http://en.wikipedia.org/wiki/L-shell

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CIR’s: Corotating Interaction Regions

Hundhausen, 1972Akasofu and Hakamada, 1983

MHD simulation of (1) high speed streams which cause the development of CIR structure and (2) the propagation of

transient shocks which also modify the CIR structure (bottom two panels particularly)

Schematic illustration of a fast streaminteracting with a slow stream

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CME’s: Coronal Mass Ejection

Space Weather Laboratory, George Madison University

Schematic of a coronal mass ejection in the form of a magnetic cloud with a shock.

Cravens, 1997

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Development of a Statistical Dynamic Radiation Belt Model