Models of solar energetic particle fluxes- the main requirements and development prospects(4)

航天,航天器,航天器环境,空间辐射

isproportionaltosolaractivity(Wolfnumbers)(Nym-mik,1999b,c)andthat,whennormalizedtosolaractiv-ity,theeventsizedistributionfunctionisinvariantofsolaractivity(Nymmik,1999a,c).Theunderstandingimpliesthatneitherdi erencesinsolarcyclesnorre-movaloftheSEPoccurrencemomentfromsolarmaxi-mumorminimumcana ectreliablyboththeSEPeventoccurrencefrequencyandtheSEPeventsize(Nymmik,1999b).

3.Whatnaturegivesusandwhatwegetfrommeasurements3.1.Analysismethod

First,letthedi erencebedemonstratedbetweentheSEP uencecharacteristicsandtheirmeasuredcounter-partsthatarisefromthelimitationsofSEP uxmea-surementsagainstthegalacticbackground.Itisimportanttoemphasizethatthedistortionsintheparti-cle uencemodelcharacteristicsarisewhenthedatabaseisselectedbypeak uxsizes.

Withthispurpose,theprocessofrecordingasetofSEPeventsshouldbesimulatedmathematically.Thein-putSEPeventdistributionofP30MeVproton uencesistakentobeapower-lawfunction,whoseformhasbeendeterminedin(Nymmik,1999c)forSEPevents:

dN1.41

dUdT¼Const

UÀ3030Áexp

U;ð1Þ

Uc

whereUc=4Æ109protons/cm2describestheturno ofthefunctionsathigh uencesizes.

Conformingtothefunction(1),weusedtheMonte-CarlotechniquetoinfertherandomsizesoftheSEPeventproton uences.

Theeventcharacteristic,whichindicateswhetheraneventcanberecorded,isthepeakSEP uxFanditsex-cessoverthegalacticcosmicraybackground,ratherthantheevent uence.Theeventswithidentical uencesizesU30canhavebothlarge(theimpulsiveevents)andsmall(thegradualevents)peak uxsizes.Theexperi-mentaldataanalysis(Nymmik,1995)hasshownthatthespectralcoe cientCFofthepeakproton uxesisdistributedarounditsmeanvalue

hC¼0.008Á U30

Fiprotons=ðcm2106

srsMeVÞð2Þwiththemeansquaredeviationoflog-normaldistribu-tionr1gCF¼0.45.TheenergyspectraofP30MeVpro-tonsarebestdescribedbythepower-lawfunctionofparticlemomentum(orrigidityinthecaseofprotons)(seeMottletal.,2001;MottlandNymmik,2003b,forexample):

dF p Àc

dE

dE¼CFp;ð3Þ0whereb¼p=qp

¼p b

EðEþ2mc2Þ

isprotonmomentum;p2þðmc2Þ2

isrelativevelocity;p0=239MV(E=30MeV).

Thespectralindicesofthepower-lawspectrumforseparateeventswereproposedandwerecalculatedtoberandomanddistributedaroundmeanvalueÆcæ=5.8(lgÆcæ=0.76)withmeansquaredeviationoflognormaldistribution,r1gr=0.17.

Theabove-presentedformulaepermitustocalculatethe uencesandpeak uxesofprotonsforanyrandomSEPeventofrandomsizeU30andrandomspectralindexc.

Comparingthepeak uxesofdi erent-energypro-tonsfromdi erentSEPeventswiththegalacticcosmicray uxes,wecandeterminewhethertheSEPeventpar-ticlescanbeseparatedfromthegalacticbackgroundandwhetheragiveneventcanbeeliminatedfromtheanalysisbecauseitisinconsistentwiththeselectioncriterion.

3.2.Distortionofthedistributionfunction

Accordingtothedistribution(1),wegenerated104randomSEPeventswithU30P106.

EachofthecalculatedSEPeventdi erentialpeak uxenergyspectra(3)wasintegratedandcomparedwiththreethresholdvaluesasshowninFig.3forthe rst10eventsgenerated.Fig.3showstheintegralen-ergyspectraofpeakproton uxesfor10randomSEPeventswithsizeU30P106protons/cm2calculatedbytheMonte-Carlotechniqueintermsofthedistribution(2).The gureshowsalsotheintegralenergy

spectra

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