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1 Development of a Statistical Dynamic Radiation Belt Model benck@spaceradiations.be Center for Space Radiations (CSR) UCL, Louvain-La-Neuve, Belgium S. Benck, L. Mazzino, V. Pierrard, M. Cyamukungu, J. Cabrera ESWW5, Brussels, Belgium, 17-21 November 2008

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2 McIlwain in 1966 identifies 5 « Processes acting upon outer zone electrons » Process 1: Rapid non adiabatic acceleration Process 2: Persistent decay Process 3: Radial Diffusion Process 4: Adiabatic Acceleration Process 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 stateGS pobabilitiesFlux variationsConclusionDecay timesIntroduction

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3 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 Dst prev Dst prev = The min. value reached by Dst in the prev. storm...... L. Mazzino, et al (2008) T flux = steady state background + geomagnetic activity dependent value Steady stateGS pobabilitiesFlux variationsConclusionDecay timesIntroduction

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4 GS pobabilitiesFlux variationsConclusionDecay times ~100 days st Steady state

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5 st as a function of L (B>0.3 G) st as a function of longitude, latitude and altitude IntroductionGS pobabilitiesFlux variationsConclusionDecay timesSteady state

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6 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. IntroductionSteady stateFlux variationsConclusionDecay timesGS probabilities 50 years of Dst and sunspot number data, including ~1200 storms have been analyzed

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7 Probability of having a GS of a given Dst k 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 IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times Nice agreement with: Tsubouchi and Omura, Long- term occurrence probabilities of intense geomagnetic storm events, Space Weather, 2007

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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, E e = 200 keV – 1.2 MeV Orbit at 710 km 98.23 deg. Incl. Orbit at 702 km 98.2 deg. Incl. IntroductionSteady stateGS pobabilitiesConclusionDecay times F and as a function of GS type Flux variations

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9 Flux enhancement ( F) and Time interval between storm and flux max ( ) IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times

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10 TYPE 1 (mainly CME) IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times 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 ~3-4hlong Bz/ t, inconsistent, t >7h

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11 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) IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times

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12 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) IntroductionRABEM Model Dat and parameters ResultsSummary IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times

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13 L-parameter slope TYPE 1 slope L-parameter TYPE 2 IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times At low L the flux enhancement increases steeper with Dst min (slope > 0) for lower energies At high L the flux enhancement decreases steeper with Dst min (slope < 0) for lower energies. For all L values, the flux enhancement increases steeper with Dst min (slope > 0) for lower energies For all energies the slope decreases with L

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14 Decay time constant (loss timescales) of electron fluxes (T) IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times 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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15 IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times 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 T (E low ), 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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16 IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times 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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17 Identified Parameters Steady state st Storm occurence and related probabilities Dst prev, Dst k (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 (Dst min ) 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 IntroductionSteady stateGS pobabilitiesFlux variationsDecay timesConclusion 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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19 Example of geomagnetic storm Storm Sudden commencement Main phase Strength of storm: Minimum Dst reached Recovery phase IntroductionRABEM ModelData and parametersResultsSummary

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20 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,... + Steady stateGS pobabilitiesFlux variationsConclusionDecay timesIntroduction 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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21 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 (Dst Data: Courtesy of World Data Center for Geomagnetism, Kyoto) Dst IntroductionRABEM ModelData and parametersResultsSummaryAdditional

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22 Correlation between number of storms per month for different phases in a solar cycle with the Sunspot Maximum corresponding to that cycle. IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times Sunspot Number Maxima (smoothed) Solar cycle #20: 109 Solar Cycle #21: 159 Solar Cycle #22: 157 Solar Cycle #23: 121

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23 Histogram of Dst k vs. Dst prev number of bins = 100 IntroductonRABEM ModelData and parametersResultsSummary Probability of having a storm with intensity Dst k considering that the previous one was of intensity Dst prev All Dst min given in absolute value IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times

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24 IntroductionRABEM ModelData and parametersResultSummary 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 Dst min given in absolute value Histogram of Dst k 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 IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times Probability of having a storm with intensity Dst k considering a given time interval elapsed since the previous storm

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25 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 Solar Cycle #21: 159 Solar Cycle #22: 157 Solar Cycle #23: 121 IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times

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26 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. IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times Probability of having a certain time interval between storms considering the sunspot number

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27 Difference of time interval distribution function depending on phase and severity of solar cycle activity IntroductionRABEM ModelData and parametersResultsSummaryAdditional

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28 DEMETER Fluxes IntroductionRABEM ModelData and parametersResultsSummaryAdditional Geomagnetic storm: particle flux enhancement

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

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30 FLUX ENHANCEMENT DUE TO GEOMAGNETIC STOMS SAC-C IntroductionRABEM Model Data and parameters ResultsSummary

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31 Resultant flux enhancement difference as a function of storm severity, corresponding to isolated CMEs (yellow), CIRs (red), and mixed non isolated storms (blue) Resultant maximum flux as a function of storm severity, corresponding to isolated CMEs (yellow), CIRs (red), and mixed non isolated storms (blue) IntroductionRABEM ModelData and parametersResultsSummaryAdditional Results: Fluxes

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32 IntroductionRABEM ModelData and parametersResultsSummaryAdditional (SAC-C Data: Courtesy of CNES/DCT/AQ/EC Section, ONERA/DESP and CONAE) TYPE 1(yellow), TYPE 2 (red)

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33 IntroductionRABEM ModelData and parametersResultsSummaryAdditional TYPE 2

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34 IntroductionSteady stateGS pobabilitiesFlux variationsConclusionDecay times Decay time of electron fluxes (T) independent of Dst

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35 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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36 CIRs: Corotating Interaction Regions Hundhausen, 1972 Akasofu 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 stream interacting with a slow stream

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37 CMEs: 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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