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

航天,航天器,航天器环境,空间辐射

AdvancesinSpaceResearch36(2005)

2003–2011

/locate/asr

Modelsofsolarenergeticparticle uxes:Themainrequirements

andthedevelopmentprospects

N.V.Kuznetsov,R.A.Nymmik*,M.I.Panasyuk

SkobeltsynInstituteofNuclearPhysics,MoscowStateUniversity,VorobjovyGory,Moscow119992,Russia

Received19October2002;receivedinrevisedform5May2003;accepted27September2004

Abstract

Themodelsofsolarenergeticparticles(SEP)areintendedforcalculatingtheproton uencesandpeak uxes,whichareexpectedtooccurforagivenperiodatanyknownorpredictedsolaractivitylevelandtoexceedtheircalculatedsizeswithinagivenprob-ability.AnySEPmodelshouldre ecttheobjectivereality,includingtheregularfeaturesinherenttotheparticles.Therequirementsareformulated,whichhavetobemetbythepresent-daymodelsaimedatpredictingtheSEP uxesinthespacecrafttrajectoriesasaccuratelyaspossible.Particularattentionispaidtoanalyzingthefactorsthatcausethemostfrequentde cienciesofthepresent-daysolarenergeticparticle uxmodels.

Ó2005COSPAR.PublishedbyElsevierLtd.Allrightsreserved.

Keywords:Solarenergeticparticles;SEP uxmodels;Modelrequirements;Modeldevelopmentprospects

1.Introduction

Thesolarenergeticparticle(SEP)models,likeanymodelthatdescribesthenaturalphenomenon,shouldre ecttheobjectivereality,includingtheregularfea-turesinherenttothereality.Themodelsmustbedevel-oped,ifpossible,intermsoftheconceptsandbehavioralfeaturesthatareclosetothephysicalessenceofamod-elednaturalphenomenon.

Thisprerequisiteimpliesthat: sincetheSEP uxoccurrenceintheEarthÕsorbitisassociatedwithaparticulareventofparticlegenera-tionandejectioninthesolarchromosphere,eachoftheoccurrences(calledaSEPevent)mustberegardedasresultingfromacertainsingleeventthatoriginatesontheSun;

*

Correspondingauthor.Tel.:+7959328861;fax:+7959395034.E-mailaddress:nymmik@sinp.msu.ru(R.A.Nymmik).

sincetheSEPeventoccurrenceprobabilitydependsonsolaractivity,themodelsmustpredicttheSEP uxesasdependentonanysolaractivitylevel.ThedependenceofSEPeventoccurrencefrequencyonsolaractivityisasmoothcontinuousfunction;theexperimentaldataindicateneitherathresholde ect,noranabruptjumplikevariation,noraplateau;

sincetheSEPdistributionfunctionbelongstotherangeofthedistributionfunctionsofothersolarimpulseevents(theradio(Fitzerreiteretal.,1976),X-ray(Crosbyetal.,1993),andgamma-ray(Luetal.,1993) ares),whichhavebeenproperlystudiedandarepower-lawfunctions,itisquiteobvioustoassumethattheSEPdistributionisalsodescribedbyapower-lawfunction.Becauseofthelimitedsolarenergetics,thepower-lawdistributionfunctionscan-notextenduptoin nityasthesolarimpulseevent(includingSEPevents)sizeincreases,butmustsu eraturno ,whichisjustobservedactually(Luetal.,1993;Xapsosetal.,1998,1999;Nymmik,1999a);

0273-1177/$30Ó2005COSPAR.PublishedbyElsevierLtd.Allrightsreserved.doi:10.1016/j.asr.2004.09.021

航天,航天器,航天器环境,空间辐射

2004N.V.Kuznetsovetal./AdvancesinSpaceResearch36(2005)2003–2011

sincetheSEPimpactisafunctionoftheparticleenergy(theenergytransfertomatterandthecross-sectionsforinelasticinteractionsareenergy-depen-dent),theparticle ux,asamodeloutput,mustbeknownforanyenergy,i.e.,wemustdeterminethecontinuousdi erentialSEPenergyspectrathatsuitanyfurtheron-lineanalysis;

sincemanyoftheradiatione ectsdependontheheavyparticle ux,theSEPmodelsmustincludenotonlyprotons,butalsoallsolarheavyions;

sincethesolarheavyion uxesarerelativelysmall(likethehigh-energyproton uxes),anysu cientlycomprehensiveSEPmodelcannotbedevelopedbas-ingonlyonthemeasuredion uxdistributionbecauseofthescantystatistics,butshouldbebasedonthefoundfeaturesoftheSEPion uxes,theenergydependenceoftherelativeparticlecompositionincluded(see,forinstance,Nymmik,1998,1999b); sincethedatabasesofSEP uxesmeasuredbysepa-rateinstrumentsaredi erentenough,thusindicatingsigni cantsystematicandmethodologicalerrorsoftheSEPmeasurements(MottlandNymmik,2003a),anySEPmodelcannotbedevelopedwithoutcheckingonthefullreliabilityoftheinputexperimentaldata.Atthesametime,theoutputofthemodelsmustper-mititson-lineusagetocalculatetheimpactofchargedparticle uxesonmaterials,equipment,andbiologicalobjects.

Mostofthepresent-daySEPmodelsfailtomeettheaboverequirements.Weshallattempttodrawattentiontothedi erencesintheconceptsandtodi erentwaysofdesigningtheSEPmodels.

Theapproach(Feynmanetal.,1993,2002;Xapsosetal.,1998,1999)usedmostextensivelyelsewhereistosimulatethemeasuredsolarproton uencesbasingontheSEPdatabasesthatdisregardthedistortionsfromthemeasurementdataobtainedwithdi erentinstru-ments(MottlandNymmik,2003a)andfromthethresh-olde ects(KurtandNymmik,1997)andalsomakeuseofthephysicallyincorrectSEPeventconcept(seethispa-perbelow).Wewillshowthattheapproachislittlepromisingbecauseitislimitedtodescribingthoseparti-clespecies(protons)andthoseparticleenergies(<100MeV)thatcanonlybemeasuredwithinthestatis-ticalaccuracythatwouldbehighenoughtosu cethesimulation.

Anotherapproach(Nymmik,1998,1999b)istosim-ulateanaturalphenomenonbasingonthebehavioralfeaturesinherenttosingleSEPevents(accordingtotheSEPdatabasesbyBazilevskayaetal.,1986,1990andSladkovaetal.,1998)andtoSEP uxesandinclud-ingtheexperimentaldatasetdistortionsintroducedbythethresholde ectsandbythemeasurementmethods.Theapproachhasmadeitpossibletodevelopthemodel(Nymmik,1998,1999b),whichcoverstheparticlespe-

cies(16Z628)andenergies(10MeV6E610GeV)thatcannotbedeterminedinanywayreliablybecauseoftheirinsu cientstatisticalsupport.

2.Thesep uxesinquietsunyears

Mostofthepresent-daymodelsdisregardtheSEP uxesinthequietSunyears(4yearof11-yearcycle)anddescribetheSEP uxesintheactiveSunyears(7yearsof11-yearcycle)only(Feynmanetal.,1990b,1993,2002;Xapsosetal.,1998,1999).Thisapproachdoesnotseemtobesu cientlyaccuratebecauseofthefollowing.

Ifthemodelsareappliedtoperiodsthatareclosetothe7-yearactiveSunperiod,theinaccuracyarisingfromusingthesameSEPeventoccurrencefrequencyforsuchsolarcyclesas19and20doesnotexceed35%.Incasethemodelsareappliedseparatelytoeachofseven1-yearactiveSunperiods,whensolaractivitymayvarybyafactorofupto5fromyeartoyear(theWolfnumbersvaryfrom40to200)andthemeanSEPeventoccur-rencefrequencyvariesaccordingly(Nymmik,1999c),theinaccuraciesintheparticle uxmodelestimationscanalsoreachfactor5ontheaverage.

Meanwhile,thequestionarisesastowhetherthequietSunSEP uxescanbedisregarded.

WeshallshowwhatarethemeasuredSEP uencesofthequietSunperiods(Nymmik,2001)ascomparedwiththeSEP uxesduringsolarmaximum.Forthatpurpose,wedeterminedthesmoothedsunspotnumbersÆWæonthecommencementdayofeachSEPeventandsepa-ratedtheeventsthatoccurredatÆWæ<40,i.e.,duringquietSunperiods.Since1965,22eventswithP30MeVproton uences(U30)inexcessof106pro-tons/cm2havebeenrecordedinquietsunperiods.Ofthem,18eventswererecordedbefore1985(Feynmanetal.,1990b)and4eventsof1994–1997werefoundbyourIMP-8database(INTERNET:IMP-8)analysis.TheseSEPeventsareasfollows(theyearsandthedaysofayearoftheSEPeventcommencementsareindi-cated):1965(36),1973(210,250,307),1974(159,184,254,309),1975(232),1976(83,121,235),1977(203,251),1985(21,114,185,198),1994(51),1995(293),1997(308,310).

Table1

Thetotal(upper3lines)andmean-annual(lower3lines)proton uencesmeasuredduringtimeT(months)atdi erentsolaractivitylevelsin1965–1997WperiodW640;period1W640;period21456W6155RUEP107.82·1081.24·1098.6109

RUEP301.36·1084.0·1081.63·109RUEP60–1.3·1083.89·108T

101

85

24

ÆUEP10æ8.9·1071.74·1084.3·109ÆUEP30æ1.6·1075.68·1078.6·108ÆUEP60æ

–

1.84·107

1.95·108

航天,航天器,航天器环境,空间辐射

N.V.Kuznetsovetal./AdvancesinSpaceResearch36(2005)2003–20112005

Forthepurposesoftheanalysis,thisdatasetshouldbedividedintotwogroups:

1.1965–1977period,whentheP10andP30MeVpro-tons uxesonlyweremeasuredand

2.1985–1997period,whentheP60MeVprotons uxeswerealsomeasured.Thetotal(summarizedwithrespecttoallevents)par-ticle uencedataarepresentedinTable1.ThetotalperiodsT(inmonths)ofproton uencemeasurementsinquietSuntimearealsopresented.

Forcomparison,themeanannualproton uencedataontheSEPeventsthatoccurredwhenthesunspotnumberwas1456ÆWæ6155arepresentedaccordingtothesamedatabasefor1965–1997.

UsingtheTable1data,themean-annualproton u-encesforenergiesP10,P30,andP60MeVwerecalcu-latedandaredisplayedinFig.1.ForthesecondquietSunperioddataandforthe1456ÆWæ6155data,itispossibletoextrapolatetheenergyspectrumtohighenergiesinconformitywiththepropositionthattheen-ergyspectraoftheP30MeVSEPsarepower-lawfunc-tionsofprotonrigidity(Nymmik,1993,1995;Mottletal.,2001;MottlandNymmik,2003b).Forthe rstquietSunperiod,wehaveextrapolatedtheenergyspec-trumtothehigh-energyrangeusingthesameindexoftherigidityspectrum(cp=4.14)asforthesecondquietSunperiod.

Fig.1showsalsothemodel-calculated(Nymmiketal.,1996)annualintegralenergyspectraofgalacticcosmicrayprotonsduringthesametwosolaractivityperiods.ItisseenthatduringthequietSunperiod,itisonlythe10MeVannualintegralsolarenergeticpro-ton uencesthatexceedtheannualgalacticproton u-ence.Duringhighsolaractivity,therecordedsolar

energeticproton uencesexceedthegalacticproton u-encesevenat>60MeV.

Itisthedi erentialenergyspectraoftheparticlesthatdeterminenotonlythespaceradiationenvironmentbutalsotheradiatione ectsinducedbyparticle uxes.Fig.2showsthedi erentialenergyspectrathatcorre-spondtotheintegralenergyspectradisplayedinFig.1.SincethegalacticandSEPeventprotonenergyspec-traareofdi erentforms,thesituationchangesdrasti-cally.Fig.2showsthatthemeanannualSEPeventproton uencesmeasuredintheEarthÕsorbitduringthequietSunperiodsexceedthemodel-calculatedgalac-ticcosmicray uencesunlesstheprotonenergiesreach100MeV,andthe10MeVsolarenergeticproton u-encesareupto3–4ordersashighasthegalacticparticle uences.Duringhighsolaractivity,themeasuredmeanannualSEPeventproton uencesbecomeequaltothecalculatedgalacticcosmicrayproton uencesat400MeV.

Fromtheaboveanalysis,itfollowsthattheSEPeventproton uencescountmuchduringallthesolaractivityperiods,thequietsunincluded.Therefore,iftheSEPeventsduringlowsolaractivityaredisregarded,aninaccuracyofuptoafeworderswilloccurindeter-miningtheparticle uxesininterplanetaryspace.

OuranalysishasdemonstratedthatthechoiceoflowsolaractivityperiodsforinterplanetarymissionsdoesnotexcludetheSEP-inducedhazard.Moreover,thereex-istsasigni cantprobabilityduringlowsolaractivityfortheSEPparticle uencestoexceedU30P1.9108pro-tons/cm2,whichisjustthe6November1997occurrence.Therefore,giventhemodelsthatdescribetheSEP uxesforactiveSunperiodsonly(Feynmanetal.,1993,2002;Xapsosetal.,1998,1999;Tylkaetal.,1997),wecannotdeterminetheradiationhazardforallpossiblespacemissionperiods.

Intheaboveanalysis,weproceededfromourunder-standing(basedonthestatisticalanalysisofexperimen-taldata)thatthemeanSEPeventoccurrence

frequency

Fig.2.Thedi erentialenergyspectraofannualproton uences.Thecurvesarethedi erentialspectracalculatedfromintegralspectradisplayedinFig.1.ThenotationforthecurvesisthesameasinFig.1.

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

航天,航天器,航天器环境,空间辐射

ofgalacticprotonscalculatedintermsofthemodel(Nymmiketal.,1996)forsolarminimum(sunspotnum-berW=10)andsolarmaximum(W=150).TheSEPeventselectionthresholdusedintheJPL-1991model(Feynmanetal.,1993)isshowntoo.

FromFig.3itfollowsthatamong10SEPeventswiththepeak uxdetectionthresholdFadoptedintheJPL-91model(FP1proton/(cm2ssr)),themodelmakesuseofaslittleassixeventsatEP30MeV,foureventsatEP60MeV,andtwoeventsatEP100MeV.Itcanbeseenfromthisexamplethat,inthecaseofthesmall uencesizesoftheselectedevents,theselectionmethodappliedwillleadtoarti cialeliminationoftheevents,whichhavealowpeak ux,i.e.,thetime-extendedevents(gradualevents)areeliminated.

Asaresult,thedistributionfunctionswerecalculatedforallof104Monte-Carlo-simulatedSEPeventsandalsoseparatelyforeachofthethreesetsofevents,inwhichthepeakproton uxeswereaboveoneofthethreethresholdlevelsshowninFig.3.

ThecalculationresultsareshowninFig.4(thedi er-entialdistributions)andFig.5(theintegraldistribu-tions).Itisseenthattheinitialpower-lawfunctioninEq.(1)isdistortedbyeachofthethreethresholdsandcanconditionallybedescribedtobelognormal.

Fromtheabovedata,itisseenthattheeventdetec-tionthresholdsdistortthedistributionfortheU306107protons/cm2 uences.Itisobviousthat,iftheresultantdistributionsareapproximatedbyalog-normalfunctions,themean uencesizelogarithmandthestandarddeviationofthedistributionsprovetobearti cial(butarenotthecharacteristicsofthetrue

SEPeventdistribution,whichisapowerlaw),andtode-pendontheeventdetectionandselectionthresholds.3.3.Distortionofthemeanlogarithmic uencesizebyincreasingparticleenergy

Thedistortionoftherealdistributionfunction,whichispower-law,leadsunavoidablytodistortionofthemeasuredSEP uxparametersre ectedinthemodelrepresentationatE>30MeV.

Forthesamen=104Monte-Carlo-calculatedU30P106SEPeventsobtainedintermsofthedistribu-tionEq.(1),wecalculatedthemeanlog uencesÆUlogæ

PnlogðUhUi¼10

iÞ

i¼1

ð4Þ

forthedistributionsofproton uenceswithenergies

exceedingagivenlevel,whicharebothundistortedanddistortedbythreeselectionthresholdsmentionedabove.

ThecalculationresultsareshowninFig.6.Itisseenthat,asenergyincreases,themeanlog uencesareover-estimatedarti ciallyduetoeliminationofanever-increasingnumberofeventswithsmall-sizepeak uxesfromthedataset.Hence,iftheJPL-91selectioncriterionisusedatprotonenergiesP60,themeanlog uencesareoverestimatedbyfactor5.5,whichisfullycon rmedbytheJPL-1991modelparametervalueÆU60æ=8·106protons/cm2,insteadofÆU60æ=1.4·106protons/cm2calculatedbyus(seeFig.6).IfwewanttousethesamemethodsasusedinJPL-91inthecaseofP100MeVprotons,thesystematicerrorwouldreachfactor10.Iftheselectionthresholdisdecreasedtothethresholdsde nedbytheintegralgalacticprotonspec-trum,thedistortiondecreasessomewhat.Nevertheless,thefundamentalobstaclesstillprecludeusageofthelog-normaldistributionmethodindescribingthehigh-energyparticle uencesinthe

space.

航天,航天器,航天器环境,空间辐射

3.4.ThemodelsforthemeasuredandnaturalSEP uxes.Theiceberge ect

Fromtheabove,itfollowsthatthemethodsforrecordingandanalyzingtheSEP uxesmayintroducesu cientdistortionsintotheexperimentaldatasetand,hence,intothedescriptiveexperimentaldatamodels.ThedistortionsarevalidforalltheSEPmodelsbasedonthecumulative uencedistributionmethod(Feyn-manetal.,1990a,b,1993,2002;Tylkaetal.,1997).ThisisduetothecharacteristicfeaturesoftheprobabilisticnatureoftheSEPevents,namely,duetothe uctuationsoftheSEPeventsizeandduration(causedbydispersionoftheeventpeak uxsizesfortheeventswiththesame uencesize),aswellasthe uctuationsoftheenergyspectrumrigidity.RandomdispersionoftheSEPchar-acteristics,whencombinedwiththegalacticbackground(whichvariesoversolaractivitycycle)orwiththearti -ciallyintroducedselectioncriteria,leadstoselectionofafractionoftheeventswithcertaincharacteristics.

Thus,thelognormaldistributionofmedium-energy(<40MeV)particles,thoughitaccountsforthecontri-butionofrelativelylargeeventstotheradiationenviron-ment,stilldisregardsthenear-orunderthresholdevents,whichcanmakeasubstantialcontributiontotheparticle uxesofthesaidenergies(comparedwithgalacticparticles)inthespaceduringshort-termspacemissions,orduringlowsolaractivity.

Thecaseisevenworsefor>40MeVparticle uxes.Ifthelognormaldistributionisusedtodescribetheparti-cles,thecharacteristicsofthedistributiongetdistorted,sotheparticle uxmodelsbasedonthisapproachover-estimatethe uxes.Sincealltheprocessesofinelasticinteractionsofprotonsandnucleiwithmatteroccurat>30MeV/(nucleon),themodelsdevelopedbasingon

thelognormaldistributionapproachprovetobeinade-quateandcannotbeused(withoutadditionalcommentsandlimitation)todescribesecondaryradiatione ectsinducedbySEPeventsandtocalculatedosesbehindP1g/cm2shieldings.

Allthee ectsillustratedbytheproton uxexamplesshouldbeinherenttoevenalargerextenttorecordingheavy-particle uxesandtodevelopingthemodelsforthembecausethevariationsoftheparticleenergyspec-trumcharacteristicsareaccompaniedbyvariationsinthecompositionoftheeventparticles.Inthecaseofheavyparticles,obviously,theSEPeventsenrichedwithheavyparticlesarerecorded rstofall,whichshouldleadtoanevenstronger(ascomparedwiththeprotoncase)overestimationoftheir uxesbythemodelsbasedontherecordsofthethreshold-exceedingSEPparticle uxes.

TheSEP uxesaresomewhatsimilartoaniceberginthatasigni cantfractionofthe uxesareunobservablebecauseofthegalacticbackground(seeFig.3,SEP uxesbelowgalacticbackground),justastheunderwa-terpartofanicebergcannotbeobservedvisually.Like-wise,justasitisimpossibletohaveanideaoftheicebergpropertiesbasingondescriptionofitsabove-waterpartonly,anyobjectiveSEP uencemodelcanhardlybeconstructedusingthefractionoftheSEP uxesobservedabovethegalacticbackground.3.5.TheSEPeventdistributionfunction

Themeasurementprocedureswereshownabovetodistortthesmall-sizeSEPeventdistributionfunction.Now,weshalldiscusstheroleofthefunctionintheSEPmodelsintermsoftheimpactonanobjectiveap-praisalofradiationenvironment.

Thedistributionfunctionformde nesthefollowingtwoaspectsofestimatingandpredictingtheradiationhazard.

Inthecaseofsmall-size(U3<106protons/cm2)eventsrecordedintheEarthÕsorbit,twocompetingviewsofthedistributionfunctionformleadtoverydif-ferentconclusions.

Ifthefunctionforsmall-sizeeventsisabranchoflog-normaldistribution,whilethenumberofeventsde-creaseswithdecreasingtheeventsizeintheEarthÕsorbit,thenthesizeoftheeventswillincreasewhenmov-ingfromtheEarthtotheSun,whereasthenumberoftheeventswillremainconstant.

If,astheeventsizedecreases,thedistributionfunc-tionis(andremains)apower-lawfunctionwithacon-stantspectralindex,then,whenmovingtotheSun,theoccurrencefrequencyoftherecordedgiven-sizeeventswillincrease.Duringhighsolaractivity,there-fore,thesmall-sizeeventswillfolloweachotheraftersosmalltimeintervalsthattheSEP uxeswillconstitutethequasi-stablebackgroundoflow-energy(<10

MeV)

航天,航天器,航天器环境,空间辐射

N.V.Kuznetsovetal./AdvancesinSpaceResearch36(2005)2003–20112009

particles,whichisobservedtobethelow-energy(<10–20MeV)componentofinterplanetarymedium.

Giventheabovetwoviewsofthesmall-sizeSEPeventdistributionfunction,webelievethepower-lawfunctiontobetruebecause,asshownabove,thelognor-malfunctionarisesonlyfromthepersistentdistortionofthenaturalentitiesbythethresholde ectsofeventdetectionandselectionand,therefore,isofnophysicalmeaning.

Intermsofradiationhazard,thelargesizeSEPeventdistributionfunctionismostimportant.

Therecentcommonpracticewastoestimatethehigh-estpossibleparticle uxbythe uxsizesoftheSEPeventsrecordedearlier.Formanyyears,forinstance,eitherthe uxesofthe20August1972event(CREME,Adamsetal.,1981)orthemultiplesizesofthelatter(King,1974)weretakentobethehighestpossible uxes.AftertheSEPeventsof1989,usewassometimesmadeoftheirhigh-energyparticle uxes(CREME-96,Tylkaetal.,1997).Obviously,suchanapproachsigni estheabsenceofanyscienti callygroundedviewsoftheoccurrenceprobabilityoftheextremelylargeSEP uxes.Theproblemsofthehighestparticle uxesproduciblebytheSuncanbesolvedusingtheformofthelarge-sizeSEPeventdistributionfunction.Atpresent,threefunda-mentallydi erentversionsofthedistributionfunctionhavebeenproposedtodescribetheextremelylargeSEPevents.Thesearetheright-handbranchoflognor-malfunction(Feynmanetal.,1990b,1993),exponentialturno ofpower-lawfunction(Eq.(1)andNymmik,1999a,c),andtheextremevaluescalculatedbythemax-imumentropyprinciple(Xapsosetal.,1999).Inthe rsttwomodels,thehighestpossibleSEP uxsizeisdeter-minedinnowayexplicitly.Inthethirdmodel,thestrictlyprescribedvaluesareused(U30=1.32·1010cmÀ2),whichcanbefurtherspeci edasfreshexperimentaldataareaccumulated.

3.6.Otherremarksontheprospectsofperfectingthesepmodels

Weshallbrie ydiscusssomeotherweakaspectsthathamperthedevelopmentofanycredibleandreliableSEP uxmodel.

3.7.TheSEPeventconceptinengineeringandinphysicsTheSEPeventistreatedbymostresearchersintermsoftheformalde nitionofaneventtobe‘‘thetotal u-enceoccurringoverseriesofdaysduringwhichthepro-ton uence(orlocalpeak ux)exceededtheselectedthreshold’’(Feynmanetal.,1993).

Itshouldbenotedthattheabovede nitionisoftheengineeringnatureandisfarfromde ningtheSEPeventintermsofitsphysicalmeaning.Thisisreadilyunderstandable,consideringthattheSEP

eventstraileachother,sothe uxesoftheeventsgetoverlappedduringhighsolaractivity,inparticular.Thefollowingtwoexamplesarerelevanthere.TheSEPeventsof19,22,and24October1989aretakenbyphysiciststobethreeevents.Intermsoftheengi-neering,theyaretreatedtobeasingleevent.Anotherexampleistheengineeringeventthatcommencedon24April1981andlastedfor30days(Feynmanetal.,1990b),whichistakenbyBazilevskayaetal.(1990)ly,singlephysicaleventsaretreatedduringlowsolaractivityandthese-quencesofphysicaleventsduringhighsolaractivity.TheengineeringapproachtotheSEPeventconceptcanreadilybeshowntochange(distort)theeventdis-tributionfunctionandthedependenceoftheeventoccurrencefrequencyonsolaractivity.

So,theusageoftheengineeringSEPeventconceptinsteadofthephysicaloneexplainswhytheauthorsofthepapers(Feynmanetal.,1990a,2002)cannot ndthedependence(proportionality)oftheSEPeventsoccurrencefrequencyonsolaractivity,asshownbyNymmik(1999c),whobasedhisanalysisonthephysicalconceptsoftheSEPeventsfollowingthecatalogs(Baz-ilevskayaetal.,1986,1990;Sladkovaetal.,1998).Thedisregardofthisdependenceisoneoftheindirectargu-mentsfordisregardingtheSEPphenomenonforquietSunperiodinmostoftheSEPmodels.

ItiseasytounderstandanddemonstratethattheuseoftheengineeringSEPeventconceptinsteadofthephysicaloneincasetheSEPeventdistributionisapower-lawfunctionleadstochangingthespectralindexandtodistortingtheturno characteristicsinthehigh- uencerangeofthisfunction.

3.8.Theparticle uxdatabasesandtheSEPeventenergyspectra

ReliabilityoftheavailableSEP uxdatabasesisamongtheweakpointsofthemodeling.

Thepresent-daydatabasesareoftwolevels.The rstlevelincludestheinputdataandconsistsofcontinuoussequencesofthedataonparticle uxesininterplanetaryspace.ThedirectSEP uxdata(on uencesorpeak uxes)constitutethecatalogsthatarethesecond-leveldatabases.

Havingbeenanalyzed,the rst-leveldatabasesprovedtoincludethestatistical,instrumental,andmeth-odologicalerrors.Theinstrumentalerrorsincludetheerrorsthatdistortthereadingsofthecharged-particledetectors.Despitethefactthattheexperimentersre-movedthedistorteddatafromthedatabases,separateerrorsstillremain.Therefore,theautomateddatapro-cessingisdi culttomakeafterwards.Ontheotherhand,theerrorsmayincludethecontrollableand

航天,航天器,航天器环境,空间辐射

2010N.V.Kuznetsovetal./AdvancesinSpaceResearch36(2005)2003–2011

uncontrollablesensitivityvariationsoftheinstrumentchannels.

Themethodologicalmeasurementerrorsareverydangerousandcaptiousandarisemainlyfromtheaddedparticlecountsinthedetectorsthatmeasurethehighest-energyparticle uxes.Asaresult,themeasuredSEPeventprotonenergyspectrabecomespuriouslyri-gid.Themagnitudeoftheresultantdistortionsisdis-cussedin(MottlandNymmik,2003a).

Besidetheengineeringprinciplesofeventdetermina-tion,theSEPeventcataloguessu ermainlyfromtheuncertaintiesthatarisewhencalculatingtheintegralpar-ticle uxesfromthemeasureddi erential uxes.Theuncertaintiesareproducedbydi erentapproximationsthatmustbeusedtogooverfromthe uxesmeasuredbydi erentialchannelsofinstrumentstotheintegralSEP uxes.Di erentauthorsmakeuseofdi erenttech-niques,sothereliabilityoftheresultantdatabasesandtheirassociatemodelsisdi culttodetermine.4.Themodeloutputrequirements

Theimperativerequirementofthelatestcomputa-tionalmethodsisthattheSEPmodeloutputshouldbedescribedintermsofdi erentialSEPenergyspectra,permittingtheradiatione ectstobecalculatedas

EF¼CZEmax

rðEÞ

dF

dE;ð5ÞEmindEwherer(E)designatestheenergydependenceoftheef-fect(theenergylossincluded).

5.Discussion

Ourviewsonthepresent-daysituationwithcon-structingSEP uxmodelshavebeenstatedabove.Bas-ingonthemodelrequirements,whichwebelievetobequiteobvious,westrivedtoexposesomeofthemaindrawbacksoftherecentmodelsandto ndoutthewaysofeliminatingthem.

The rststepmustbetodenythemechanicalexperi-mentaldatadescription,whichisregardingthedetectionthresholde ectsandthedistortionsthatarisewhenmea-suringtheSEP uxesduetothegalacticbackgroundandbecauseofthearti cialeventselectioncriteria.

Anattemptwasmadeabovetosingleoutthedistor-tionsoftheSEP uxcharacteristics(theeventdistribu-tionfunction,nparticular)thatarisefromdisregardingthedetectionthresholde ects.Obviously,theparame-tersoflognormaleventdistributions,whichariseessen-tiallyfromdistortionoftheinputpower-lawdistributionfunctions,arenottheparametersoftheSEPdistributions,whilethevaluesoftheparameterseitherre ectthearbitraryselectioncriteriaintroduced

bydi erentauthors,ordependonthegalacticback-groundde nedbythevaryingsolaractivity.Ithasbe-comeclearthatallthreeparametersusedtodescribe

theSEP uxesintermsofthecumulative uencedistri-butions,namely,themeanofthelognormaldistribu-tion,thestandarddeviation,andtheaveragedSEPeventoccurrencefrequency(see,forexample,Feynmanetal.,1993),arearbitraryandessentiallyirrelevanttothenaturalphenomenonproper.Allthreeparametersvary,givendi erentenergythresholdusedtodeterminethecumulativeSEPevent uencedistribution.

WeclaimthatanySEP uxmodelshouldbedevel-opedbasingontheknownregularfeaturesandonthefeaturestobefoundbystudyingtheSEP uxesandtheirrelationshipstosolaractivityandtoothersolar areactivitydisplays.

Toreachthesaidlevelofdevelopingthemodels,wemust

rejecttheengineeringideaofeventandgoovertophys-icaldeterminationofSEPeventtobeaparticle uxgeneratedinasingleeventofaccelerationand/orejec-tionofaSEP uxfromthesolarchromosphere;

makeuseofthemethodsandvaluesthatwouldbeadequatetothevariationrateofthegeneralsolaractivitylevel;themean-yearlycharacteristicsofsolaractivityandSEP uxesarenottobeusedintheanal-ysisbecausetheyaretooroughandcamou agethetruecharacterofthespectraldependencesinherenttothestudiedphenomenon;

rejectsuchvisualsemi-quantitativesolaractivityparametersastheyearscountedfromsolarmaximumorminimum;instead,wemustusetherealsolaractiv-itycharacteristics(sunspotnumbers,radioemissionintensity,etc.).

However,theseproposalswouldbebutpalliativeun-lesswefullyrevisealltheSEPeventdatabasesbecausetheyhavebeencompiledmainlyintermsofthe‘‘engi-neering’’determinationoftheeventswithoutdetermin-ingthereliabilityandmethodologicalerrorsforthevariousinstruments ownondi erentspacecraft,whosereadingsareusedtodeterminetheSEPeventsandtheirphysicalparameters.

ItistheaboveprinciplesthatunderlieourdevelopingtheSEP uxmodel,whoseintermediateversionispre-sentedin(Nymmik,1999a).Themodelisbeingspeci edcontinuallyastheprinciplesandthefoundrelevantreg-ularfeaturesofSEPeventsareusedmoreandmoreextensively.

6.Conclusion

Wehavereportedourviewsofthepresent-daystatusofmodelingSEP uxesandoutlinedthewaysofover-

航天,航天器,航天器环境,空间辐射

N.V.Kuznetsovetal./AdvancesinSpaceResearch36(2005)2003–20112011

comingtheexplicitmethodologicalcrisis,whichgener-atedsomefalseideasoftheSEP uxesandtheiroccur-rencefeatures.Thus,weinviteourcolleaguestopaydueattentiontotheSEP uxmodelconstructiontechniques,whichwehaveusedformanyyearsandwhichdi erfun-damentallyfromthewidelyusedmethodsand,there-fore,havenotyetbeenrecognizedatlarge.

Acknowledgment

ThisworkhasbeensupportedpartlybytheGrantINTAS-00-629.

References

Adams,J.,Silberberg,R.,Chao,C.H.Cosmicraye ectson

microelectronics,PartI:Thenear-earthparticle–environment,NRLMemorandumReport4506,25August1981.

Bazilevskaya,G.A.,Vashenyuk,E.V.,Ishkov,V.N.,etal..in:

Logachov,Yu.I.(Ed.),Catalogofenergyspectraofsolarprotonevents1970–1979.IZMIRAN,Moscow,1986.

Bazilevskaya,G.A.,Vashenyuk,E.V.,Ishkov,V.N.etal.Solarproton

events.Catalogue1980–1986,in:Logatshov,Yu.I.(Ed.),SovietGeophysicalCommittee,AcademyofSciencesoftheUSSR,Moscow,1990.

Crosby,N.,Aschwanden,M.,Dennis,B.Frequencydistributionsand

correlationsofsolarX-ray areparameters.SolarPhysics143,275–299,1993.

Feynman,J.,Armstrong,T.P.,Dao-Gibner,L.,Silberman,S.Solar

protoneventsduringsolarcycles19,20,and21.SolarPhysics126,385–400,1990a.

Feynman,J.,Armstrong,T.P.,Dao-Gibner,L.,Silberman,S.New

interplanetaryproton uencemodel.JournalofSpacecraft27,403–410,1990b.

Feynman,J.,Spitale,G.,Wang,J.,Gabriel,S.Interplanetaryproton

uencemodel:JPL1991.JGR98(A8),13281–13294,1993.

Feynman,J.,Ruzmaikin,A.,Derdichevsky,V.THEJPLproton

uencemodel:anupdate.JournalofAtmosphericandSolar-TerrestrialPhysics64(16),1679–1686,2002.

Fitzerreiter,R.,Fainberg,J.,Bundy,R.Directivityoflowfrequency

solartypeIIIradiobursts.SolarPhysics46,465–473,1976.

King,J.H.Solarproton uencesfor1977–1983.SpaceMissions,

SpacecraftandRockets11(6),401,1974.

Victoriya,Kurt,Nymmik,R.A.Distributionofsolarcosmicrayevents

overproton uences.SpaceResearch35(6),559–569,1997.

Lu,E.T.,Hamilton,R.J.,McTiernan,J.M.,Bromund,K.R.Solar

Flaresandvalancesindrivendissipativesystems.ApJ412,841–852,1993.

Mottl,D.A.,Nymmik,R.A.,Sladkova,A.I.Spectraofsolarenergetic

protonsderivedfromstatisticalanalysisofexperimentaldataonalargesetofevents,in:Proceedingsofthe27thICRC,vol.8,3185–3188,2001.

Mottl,D.A.,Nymmik,R.A.Errorsintheparticle uxmeasurement

datarelevanttosolarenergeticparticlespectra.AdvancesinSpaceResearch32(11),2349–2353,2003a.

Mottl,D.A.,Nymmik,R.A.Energyspectraofsolarenergetic

particles:realitiesandmisconceptions.IzvestiyaAN,ser,phys.67(4),462–464,2003b.

Nymmik,R.A.Averagedenergyspectraofpeak uxand uence

valuesinsolarcosmicrayevents,in:Proceedingsofthe23rdICRC,Calgary,vol.3,29–32,1993.

Nymmik,R.A.Behavioralfeaturesofenergyspectraofparticle

uencesandpeak uxesinsolarcosmicrays,in:Proceedingsofthe24thICRC,Roma,vol.4,66–69,1995.

Nymmik,R.A.Radiationenvironmentinducedbycosmicrayparticle

uxesintheInternationalSpaceStationOrbitaccordingtoRecentGalacticandSolarCosmicRayModels.AdvancesinSpaceResearch21(12),1689–1698,1998.

Nymmik,R.A.SEPeventdistributionfunctionasinferredfrom

spacebornemeasurementsandlunarrockisotopicdata,in:Proceedingsofthe26thICRC,vol.6,268–271,1999a.

Nymmik,R.A.Probabilisticmodelfor uencesandpeak uxesof

solarenergeticparticles.RadiationMeasurement30,296–298,1999b.

Nymmik,R.A.Relationshipsamongsolaractivity,SEPoccurrence

frequency,andsolarenergeticparticleeventdistributionfunction,in:Proceedingsofthe26thICRC,vol.6,280–183,1999c.

Nymmik,R.A.Themaincharacteristicsofthesolarenergeticparticle

eventsrelevanttothesolaractivity,in:Proceedingsofthe27thICRC,vol.8,3197–3200,2001.

Nymmik,R.A.,Panasyuk,M.I.,Suslov,A.A.Galacticcosmicray ux

simulationandprediction.AdvancesinSpaceResearch17(2),19–30,1996.

Sladkova,A.I.,Bazilevskaya,G.A.,Ishkov,V.N.,etal..in:Logatc-hov,Yu.I.(Ed.),CatalogueofSolarProtonEvents,1987–1996.MoscowUniversity,1998.

Tylka,A.J.,Adams,J.H.,Boberg,P.R.,etal.CREME96:arevision

ofthecosmicraye ectsonmicro-electronicscode.IEEETrans-actionsonNuclearScience44(6),2150–2160,1997.

Xapsos,M.A.,Summers,G.P.,Burke,E.A.Probabilitymodelfor

peak uxesofsolarprotonevents.IEEETransactionsonNuclearScience45(6),2948–2953,1998.

Xapsos,M.A.,Summers,G.P.,Barth,J.L.,Stassinopulos,E.G.,

Burke,E.A.Probabilitymodelforcumulativeprotonevent uences,RADEC99,SessionA-25,1999.

本文来源：https://www.bwwdw.com/article/ti3j.html