Models of solar energetic particle fluxes- the main requirem(7)

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