Inverse Prbles fr Great Slar Energetic Particle Event: Mnitring by Netwrk Statins and Frecasting L.I. Dran, Israel Csic Ray and Space Weather Center and Eili Segre Observatry, Tel Aviv University, Technin and Israel Space Agency, Israel Csic Ray Departent, Pushkv Institute f Terrestrial Magnetis, Insphere and Radi Wave Prpagatin (IZMIRAN, Russian Acadey f Sciences, Russia e-ail: lid@physics.technin.ac.il Received: 6 Nveber 008 ; Accepted: 8 Deceber 008 Abstract. It is well knwn that energy spectru f slar energetic particles (SEP, bserved by grund-based neutrn nitrs (NM and un telescpes (in the high energy regin; the transfer t the space fr the grund bservatins is ade by the ethd f cupling functins and by detectrs n satellites and space-prbes (in sall energy regin, is significantly changed with tie (usually fr very hard at the beginning f event t very sft at the end f event. The bserved spectru f SEP and its change with tie are deterined by three ain paraeters: energy spectru in surce, tie f ejectin and prpagatin de. In the past we cnsidered the first step fr frecasting f radiatin hazard - the siple istrpic de f SEP prpagatin in the interplanetary space. It was shwn that n the basis f bservatinal data at several ents f tie there culd be slved the inverse prble and deterined energy spectru in surce, tie f ejectin and diffusin cefficient in dependence n energy and distance fr the Sun. Here we cnsider the inverse prble fr the cplicated case, naely, the de f anistrpic diffusin and kinetic apprach. We shw that in this case the inverse prble can als be slved, but there is need in neutrn nitr data at least fr several lcatins n the Earth. We shw that in this case the slutin f inverse prble starts t wrk well sufficiently earlier than slutin fr istrpic diffusin, but after 0-5 inutes bth slutins give abut the sae results. It is iprtant that btained results and reality f used del can be cntrlled by independent data n SEP energy spectru in ther ents f tie (is nt used at slving f inverse prble. On the basis f btained results ne can estiate the ttal release energy in the SEP event and radiatin envirnent in the inner helisphere, the agnetsphere and atsphere f the Earth during SEP event. 008 BBSCS RN SWS. All rights reserved. Keywrds: slar energetic particles; csic rays; neutrn nitr; inverse prble; frecasting. Intrductin Fr frecasting f great slar energetic particle (SEP events we need t slve step by step fllwing prbles: I. On each csic ray (CR statins ust wrk prgra autatically deterining the start f SEP event. This prgra wrks any years cntinuusly fr neutrn nitr (NM n Mt. Hern. The descriptin f algriths and calculatins f prbability f false and issed alerts n the start f SEP in dependence n aplitude f CR increase are carried ut in Sectins -4. II. After deterining f the start f SEP event, ust begin t wrk prgra deterining the spectru f SEP ut f the Earth s agnetsphere fr each ent f tie by using ethd f cupling functins (fr algriths, see: Sectin 5; ethd was described in details in Chapter f bk []. III. The next step is uch re cplicated: n the basis f btained data n SEP energy spectru in the frae f siple del f istrpic diffusin t deterine paraeters f prpagatin, surce functin and start f acceleratin and ejectin f slar CR int interplanetary space. This del wrked well nly after ne-tw scatterings f SEP in space when the SEP distributin becae abut istrpic, i.e. after abut 5-0 in after ejectins f SEP fr slar crna. In this case fr frecasting f ttal radiatin hazard ay be used nly ne r few NM (see: Sectins 6-8. IV. T extraplate btained SEP spectru fr high energies (few GeV n the basis f NM bservatins t sall energies (hundreds MeV it is als necessary t use thrugh Internet available ne-inute data btained n-line n satellites (see: Sectin 9. V. Fr earlier warning f radiatin hazard fr great SEP events it is necessary t use re cplicated de f prpagatin which describes well the earliest stages f prpagatin based n kinetic equatin and anistrpic diffusin appraches (see: Sectins 0-5. 9
L.I.Dran. Inverse prbles fr great SEP event: nitring by netwrk statins and frecasting. The ethd f autatically search f the start f great SEP event Let us cnsider the prble f autatic searching fr the start f great SEP event. The deterinatin f increasing flux is ade by cparisn with intensity averaged fr 0 t 6 inutes befre the present Z-th ne-inute data. Fr each Z inute data, the prgra SEP-Search--in starts, which fr bth independent channels A and B and fr each Z-th inute, deterines the values k Z 60 ( I ln( 60 AZ I σ D ln A Z k Z 0 Ak, ( k Z 60 ( I ln( 60 BZ I σ D ln B Z k Z 0 Bk, ( where I Ak and I Bk are ne-inute ttal intensities in the sectins f neutrn super- nitr A and B. If siultaneusly DA.5, Z DB.5, ( Z the prgra SEP-Search--in repeats the calculatin fr the next Z+-th inute and if Eq. is satisfied again, the nset f great SEP is established and the prgra SEP-Research/Spectru starts. In Fig. shws the picture fr ur Internet site, upgraded each inute.. The prbability f false alars Because the prbability functin Φ (.5 0. 9876, then the prbability f an accidental increase with aplitude re than.5σ in ne channel will be ( Φ(.5 0.006 in, that eans ne in 6. in (in ne day we expect 8.9 accidental increases in ne channel. The prbability f accidental increases siultaneusly in bth channels will be 5 (( Φ(.5.845 0 in that eans ne in 6007 in 8 days. The prbability that the increases f.5σ will be accidental in bth channels in tw successive inutes is equal t 4 9 (( Φ(.5.478 0 in that eans ne in 6.76 0 8 in 86 years. If this false alar (ne in abut 00 years is sent, it is nt dangerus, because the first alar is preliinary and can be cancelled if in the third successive inute there is n increase in bth channels bigger than.5σ (it is nt excluded that in the third inute there will be als an accidental increase, but the prbability f this false alar is negligible: 6 4 (( Φ(.5 5.685 0 in that eans ne in 7.4 0 years. It shuld be nted that the false alar can be sent als in the case f slar neutrn event (which really is nt dangerus fr electrnics in spacecrafts r fr astrnaut s health, but this event usually is very shrt (nly few inutes and this alar will be autatically canceled in the successive inute after the end f a slar neutrn event. EXAMPLE OF INTERNET PRESENTATION OF REAL TIME DATA FROM ESO (ISRAEL Fig.. The picture fr Internet site f Israel Csic Ray and Space Weather Center, upgraded each inute. 0
4. The prbability f issed triggers The prbability f issed triggers very strngly depends n the aplitude f the increase. Let us suppse that, fr exaple, we have a real increase f 7σ (that fr ESO crrespnds t an increase f abut 9.8 %. The trigger will be issed if in any f bth channels and in any f bth successive inutes if as a result f statistical fluctuatins the increase f intensity is less than.5σ. Fr this, the statistical fluctuatin ust be negative with aplitude re than 4.5σ. The prbability f this negative fluctuatin in ne channel in ne inute is equal t ( ( 4.5.9 0 6 Φ in, and the prbability f issed trigger fr tw successive inutes f bservatin siultaneusly in tw channels is 4 ties larger: 5.6 0. It eans that issed trigger is expected nly ne per abut 70000 events. 5. On-line deterining f the SEP spectru The bserved CR variatin δ I ( Rc, t ΔI ( Rc, t I ( Rc f se cpnent can be described in the first apprxiatin by functin F ( R,γ c : ( R t b( t F ( R γ ( t δ I,, (4 c c where tt,,,, 4, 5, 6, 7, 8 fr neutrn nitr data (but can dente als the data btained by un telescpes at different zenith angles and data fr satellites, and k k + k F R a k a R R + γ (5, γ exp exp a R ( ( c ( ( c ( dr is the knwn functin. Let us cpare data fr tw cpnents and n. Accrding t Eq.(4 we btain ( R t δi ( R, t Ψ ( R γ δ I c, n c n c,, (6 where n ( R γ F ( R, γ F ( R, γ Ψ (7 c, c n c are calculated by using Eq.(5. Cparisn f experiental results with functin Ψ n ( R,γ c accrding t Eq.(6 gives the value f γ ( t, and then fr Eq.(4 the value f the paraeter b ( t. 6. On-line deterinatin siultaneusly tie f ejectin, diffusin cefficient and SEP spectru in surce We suppse that the tie variatin f SEP flux and energy spectru can be described in the first apprxiatin by the slutin f istrpic diffusin fr the pinting instantaneus surce described by functin Q( R, r, t N ( R δ ( r δ ( t. In this case the expected SEP rigidity spectru n the distance r fr the Sun at the tie t after ejectin will be N ( R, r, t N ( R K( R t π exp (8 where ( R Rc [ ( ] r 4K( R t N is the rigidity spectru f ttal nuber f SEP in the surce, t is the tie relative t the tie f ejectin and K( R is the diffusin cefficient in the interplanetary space in the perid f SEP event. Let us suppse that the tie f ejectin T, diffusin cefficient e K ( R, and the surce spectru N ( R are unknwn. In this case fr deterining n-line siultaneusly tie f ejectin T e, diffusin cefficient K( R and SEP spectru in surce N ( R we need infratin n bserved SEP spectru at least in three ents f tie T, T and T (all ties T are in UT scale. In this case fr ties after SEP ejectin fr the Sun int slar wind we will have: t T Te x, t T T + x, t T T + x (9 where T -T and T -T are knwn values and x is unknwn value what we need t deterine at the first. Fr three equatins f type Eq. (8, but fr ties t, t and t we btain T T x ( T T + x T T x ( T T + x ( R b( T ln ( x ( T T + x R [ ( T ( T ] b( T γ 4K γ r ( R b( T ln ( x ( T T + x R [ ( T ( T ] b( T γ 4K γ r After dividing Eq. (0 and Eq. ( we btain [( T T Ψ ( T ] ( Ψ (0 ( x ( where T Ψ T T T T b ln b b ln b ( T ( x ( T T + x ( ( ( Rγ T γ T T ( T ( x ( T T + x R ( T ( T ( T γ γ ( Eq. ( can be slved by the iteratin ethd: as the first apprxiatin, we can use x T Te 500 sec which is a iniu tie f relativistic particles prpagatin fr the Sun t the Earth s rbit. Then by Eq. ( we deterine Ψ ( x and by Eq. ( deterine the secnd apprxiatin x, and s n. After slving Eq. ( and deterining the tie f ejectin, we easily cpute diffusin cefficient fr Eq. (0 r Eq. (: K ( R ln b ln b r ( T T 4x( T T + x b( T ( x ( T T + x R ( T γ ( T b( T r ( T T 4x( T T + x ( T ( ( ( ( x T T + x Rγ T γ T ( T γ (4
L.I.Dran. Inverse prbles fr great SEP event: nitring by netwrk statins and frecasting After deterining the tie f ejectin and diffusin cefficient, it is very easy t deterine the SEP spectru in surce: ( ( ( / N / R t R π b t γ D ( R ( K( R t exp( r /( 4K( R t (5 ( ( / π/ b t R γ t D ( R ( K( R t exp( r /( 4K( R t / ( ( / π b t R γ t D ( R ( K( R t exp( r /( 4K( R t 7. The inverse prble fr the case when the diffusin cefficient depends fr the distance t the Sun (istrpic diffusin Let us suppse that the diffusin cefficient K ( R, r K ( ( β R r r. In this case (see the well-knwn bk f Parker, 96 β ( ( β ( ( ( β β β N R r K Rt r r (6 n( R, r, t ( ( ( exp 4+ β β Γ( ( β β ( β K ( R t t, t t, If we knw n, n, n at ents f tie, the R will be final slutins fr β, ( R N K, and ( t ( ( ( t t ( ( ( ( ln ln ln ln( ( t t t β t t t t n n n n t t t t ( t t K ( ( r t t R N ( t t, (7 r ( β ln( t t ( β ln( n n n ( β ln( t t ( β ln( n (8 ( ( ( 4+ β ( β β ( ( ( β Γ ( ( ( β R n β β r K R t exp r ( β K ( R t k k (9 In the last Eq. (9 index k, r. 8. SEP frecasting by using nly NM data By using f the SEP event first few inutes f NM data we can deterine by Eq. (7 (9 effective paraeters β, K ( R, and N ( R, crrespnding t the rigidity abut 7 0 GV, and then by Eq.(6 we deterine the frecasting curve f expected SEP flux behavir fr ttal neutrn intensity. We cpare this curve with tie variatin f bserved ttal neutrn intensity. Really we use data fr re than three ents f tie by fitting btained results in cparisn with experiental data t reach the inial residual (see Fig., which cntains 8 panels fr tie ents t 0 in up t t 0 in after 0.00 UT f 9 Septeber, 989. Fr Fig. it can be seen that using nly the first few inutes f NM data (t 0 in is nt enugh: the btained curve frecasts t lw intensity. Fr t 5 in the frecast shws little bigger intensity, but it als is nt enugh. Only fr t 0 in (5 inutes after beginning and later, up t t 40 in (5 inutes after beginning we btain alst stable frecast with gd agreeent with bserved CR intensity (with accuracy f abut ± 0 %. 9. Frecasting by using bth NM and satellite data All described abve results, based n NM n-line data, reflect the situatin in SEP behavir in the high energy (re than few GeV regin. Fr extraplatin f these results t the lw energy interval (dangerus fr space-prbes and satellites, we use satellite n-line data available thrugh the Internet. The prble is hw t extraplate the SEP energy spectru fr high NM energies t very lw energies detected in GOES satellite. The ain idea f this extraplatin is as fllwing: the surce functin, tie f ejectin and diffusin cefficient in bth energy ranges are the sae. The surce functin relative t tie and space is δ functin, and relative t energy is pwer functin with an energy- Fig.. Calculatin n line paraeters β, K ( R, and ( R N and frecasting f ttal neutrn intensity (tie t is in inutes after 0.00 UT f Septeber 9, 989; curves frecasting, circles bserved ttal neutrn intensity.
Fig.. Predicted SEP integral fluxes fr Ek E 0. GeV, Ek E GeV, Ek E GeV. The frecasted integral flux fr Ek E 0. GeV we cpare with bserved fluxes fr E k 00MeV n GOES satellite. The rdinate is lg 0 f SEP integral flux (in c - sec - sr -, and the abscissa is tie in inutes fr 0.00 UT f Septeber 9, 989. dependent index γ ( γ + ln( Ek Ek E exp( γ N k E k : ax ( γ + ln( Ek Ek ( R, T ( T T R e γ with axiu at δ. (0 In Fig. there are shwn results based n the NM and satellite data f frecasting f expected SEP fluxes als in sall energy intervals and cparisn with bservatin satellite data. Fr Fig. it can be seen that by using n-line data fr grund NM in the high-energy range and fr satellites in the lw-energy range during the first 0-40 inutes after the start f the SEP event, it is pssible t predict the expected SEP integral fluxes fr different energies up t a few days ahead. 0. The case f kinetic and anistrpic diffusin appraches: the atter f prble Fr cnsideratin f istrpic diffusin in Sectins 6-8 we can see that in this case the del starts t wrk well nly after abut 5-0 inutes fr the real start f event. It eans that the used abve del f istrpic diffusin cannt adequately describe the slar CR prpagatin at the beginning f event. T ake re exact and earlier frecast it is iprtant t use als data f these beginning inutes. As we entined in Abstract, fr this we need t use the apprach f anistrpic diffusin and kinetic apprach. These appraches were cnsidered in details in Chapter f bk []. Here we will cnsider principles f slving this very iprtant fr practice and very cplicated inverse prble n the basis f synchrnically wrking netwrk f neutrn nitrs with ne-inute real data cllecting. Our research will be based ainly n theretical wrks [-6]. Accrding t [5], in the theretical cnsideratin the regular IMF is taken t be hgeneus. Nevertheless, the fratin f an initial angle distributin f particles int narrw strea alng the regular IMF [7] wed t the agnetic fcusing f frce-lines near the Sun is included (see: belw. Thus, evlutin f the particle distributin functin f τ, fllws fr the kinetic equatin written in the drift apprxiatin, in which the particle scattering n stable agnetic inhgeneities is suppsed t be istrpic [4]: ν τ f f f fd s ( + y + δ ( y δ ( τ ϕ( v where y and τ are the crdinate alng regular IMF and the tie, respectively (in the diensinless units y zν s v, τ ν st ; ν s is the cllisin frequency f particles with the agnetic cluds; z is the crdinate alng the IMF, csθ, θ is the particle pitch-angle. The right-hand side f Eq. ( describes an instantaneus injectin f CR particles with an initial angular distributin ϕ ( aδ ( Δ + ( ( where (,. The value f the cnstant a, which depends n a axial value directin f and a width Δ, can be fund fr the nralizatin cnditin,, and it is equal t ϕ( d
L.I.Dran. Inverse prbles fr great SEP event: nitring by netwrk statins and frecasting a + arctan + arctan Δ Δ ( Owing t the fcusing effect in the IMF entined, and Δ have values equal t and 0.0, respectively (see nuerical estiatins by [].. Pitch-angle respnse functin fr neutrn nitrs In [5] there is used the pitch-angle respnse functin fr neutrn nitrs ψ( which is siilar t ϕ ( in which has t be replaced by ( is the pitch-angle f an asypttic NM directin related t the regular IMF directin. The value f crrespnds t the angle f a axial sensitivity f detectr, the paraeter Δ characterizes a width f directinal diagra f the neutrn nitrs.. Tie-finite injectin Accrding t [5], an intensity enhanceent f the registered by neutrn nitrs slar energetic particles arises suddenly at τ y fr a δ-like particle injectin, and a width f the ipulse peak cnnected with arriving f the first particles is very shrt. Usually ne needs t suppse, based n the descriptin f easured tepral prfiles f past slar prtn events, that the injectin f high energy particles int the interplanetary ediu has a finite duratin, which is caused ainly by the prpagatin f accelerated particles in the slar crna [7, 8]. The injectin f accelerated particles fr the surce int the IMF during a finite tie can be represented by the fllwing tie injectin functin: χ ( τ ν τ exp( ν τ, (4 where the diensinless quantity ν is an unique paraeter, which characterizes the ean duratin f the injectin as well as the instant f axiu at τ ν. It was assued that τ is easured in the diensinless quantity τ tν s vt Λ, where Λ is the particle ean path. It is als reasnable t suppse that the duratin f the eissin by that particle surce f the lwer energy particles is lnger, s the quantity ν will be dependent n the particle rigidity. Building all these weight functins abve int the cnsideratin, a detectr will register τ τ dξ dχ( τ ξ f ξ, ψ ( 0 G. (5. Three parts f resulting slutin The slutin G τ, described by Eq. (5, has been btained in [] using the ethd f the direct and inverse Furier Laplace transfr and it cnsists f three ters: G d τ G τ + G τ G τ us s + s. (6 The first cpnent describes a cntributin f the unscattered particles which expnentially decreases with tie τ: Gus τ τ ν sν exp( ν τ dξ y y (7 ( τ ξ ϕ ψ exp( ξ( ν v ξ ξ ξ 0 A cntributin f the scattered particles can be divided Gs, als expnentially decreasing with tie, and anther int tw parts. One is the nn-diffusive ter τ Gs d, has a leading eaning in the diffusive liit f τ >>. Naely, the nn-diffusive ter is ter, τ Gs τ where Ψ y τ ν ( sν exp ν τ d 8πv 0 y τ τ, η ηψ τ, η [ S( τ S( y ] + dηψ τ, η [ S( y η S( y ] exp( yλ( η ( η + Δ ( η ( + Δ (8 (9 exp ( ( ( A S ξ S ξ; y, τ, η {( βb + βb cs( π ( y ξη + ( βb βb sin( π ( y ξη }, A + ( πη (0 In Eqs. (9 and (0 the fllwing deninatins are used: A Λ b A ( ( ( πη πη πηa ν ηλ η, β τ ξ A+, β ( τ ξ + A + ( πη A + ( πη ( η ln( η ln( + η, b π( ΔaΠ ( η + ΔaΠ ( η, Π ( η Π ( η π Δ Δ a a, Π ( η ( η + Δ ( α + a Λ( η, [ ln( Δ + ( + ln( Δ + ( ]. a α 4 ( The last (diffusive nn-vanishing ter in Eq.(6 has a sense nly fr y < τ: ( s τκ ( ( y τ τ ν + yκ y, Φ y, k e e [ + ( τ y( ν + κ ] { } π d ν ν dk G s πv 4 k π where κ k ct k, and Φ B k ( B B Γ Γ cs( ky + ( B Γ + Γ B sin( ky D D cs k, ( ( ( k Δ a ( + Δ k tan k + ( Δ + Δ α tan k Δ a k tan k + (4 4
Γ ( k [( + Δ α ( + Δ tan k Δ a k tan k + ( Δ α ] tan k ( k [ ( + Δ tan k] 4 tan k (5 D +. (6 The expressins fr siilar quantities B, Γ, D, Π, a, α fllw fr the abve described expressins by substituting,, Δ Δ. and Fedrv et al. [5] nte that bth ters ( y,τ G us G s τ vanish in the diffusive liit wed t the reaining factr f exp ( ν τ ; s nly G d s τ gives the ain cntributin in this liit. 4. Expected tepral prfiles fr neutrn nitrs and cparisn with bservatins Accrding t [5], the ain peculiarity f the slar CR events is cnnected t se neutrn nitrs (Hbart HO, Mt. Wellingtn WE, Lnicky Stit LS having the narrw peak f the anistrpic strea f the first fast particles; ther neutrn nitrs (Oulu OU, Apatity AP, Thule TH, Durha DU, Mt. Washingtn WA shw a diffusive tail with a wide axiu at a later tie, r, shw bth the first narrw peak with a secnd diffusin axiu (Suth Ple SP. Fr exaple, se selected NM data fr the 4 May 990 are denstrated in Fig. 4. The tie (in in is easured fr the nset f particle injectin taken as 0.50 UT f May 4 990. Cparisn f the NM data with the theretical predictin based n the kinetic equatin slutin requires a chice f a nralizing NM statin and cnsequent rigidity-dependent re-calculatin f input paraeters entering int the theretical prfile calculatin. The NM statin HO was chsen t be that statin because it allws t deterine the starting paraeters at its ean rigidity R (HO. GV. This value as well as the thers have been calculated by 5 assuptin f a particle rigidity spectru rughly R in the initial phase. Fr ther NMs there were taken the fllwing calculated values f the ean rigidity: R WE. GV, R. GV, LS R.0 GV, OU R.0 GV, DU R WA.8 GV, and R SP 0.8 GV. The ean rigidity R was btained fr trajectry cputatins fr R < 0 GV with a step f 0.0 GV by a technique wed t [9]. Each allwed trajectry was assigned by the weight crrespnding t the slar prtn spectra 5 R and the cupling functin accrding t [0, ]. The geagnetic field del fr trajectry calculatins included the IGRF plus the Tsyganenk 89 del [] fr Kp > 5. The asypttic directins fr NMs have been btained by nuerical integratin f particle tin in the geagnetic field (by the ethd described in [9]; see in details in the Chapter f bk [] fr the given epch at :00 hurs, and then they were averaged ver bth the rigidity-dependent respnse functin f NM and the particle rigidity spectru. Fr each allwed trajectry the pitch-angle was assigned and the ean value as well as dispersin Δ were btained fr the histgra f the expected pitch-angle distributin (fr the cputatins there are used vertically incident particles. This siplificatin is used because: (a the cntributin t NM cunt rate is in the geetric apprach inversely prprtinal t csine f zenith angle, (b the ain liitatin fr the trajectry cputatins is the agnetic field del (Sart et al., 000, (c these cputed results [9] can be cpared with the vertical cutff rigidities btained by ther ethds [4]. Fig. 4. Tw grups f NM recrds f the event n 4 May 990. Left - the narrw peak f the anistrpic strea f the first fast particles (HO Hbart, WE Mt.Wellingtn, LS Lnicky Stit; right - shw a diffusive tail with a wide axiu at a later tie (OU Oulu, DU Durha, WA Mt.Washingtn [5]. 5
L.I.Dran. Inverse prbles fr great SEP event: nitring by netwrk statins and frecasting, Δ and ean R fr each NM. On the rdinate axis there is shwn expected intensity relative t HO in axiu [5]. Fig. 5. Theretical predictin f tepral prfiles fr the selected NMs using calculated paraeters The ean transprt path Λ in IMF is suppsed t be independent n rigidity fr the cnsidered interval f NM sensitivity rigidity. Eleentary calculatin shws that ( 0.8 t ( Λ z 0. 8 ( yt ν (7 where z and y z/λ is the distance f the detectr (the Earth fr the surce (the Sun and the diensinless ne, respectively. Therefre the fit f the theretical curve t experiental data f HO deterines ν ν ( t fr given y HO. The best fit gives t.4 in fr y HO 0.6. Values f ν fr the ther NMs are calculated assuing the rigidity dependence f β t R using the given value y. The spectru index HO β characterizes shape f a lw energy particle delay in the crna. Fedrv et al. [5] have used the value β. Fr cparisn f theretical dependences with the experiental data the dependence f galactic CR intensity n particle rigidity als has been taken int γ g cnsideratin. Let this dependence be I g R, where γ g is galactic CR spectru index, and the slar CR rigidity dependence at the instant f its injectin int IMF is γ I R s s. All theretical curves are standardized t a axiu relative t the ean rigidity f HO, i.e., the curve HO has the value in axiu. The ultipliers γ ( R s γ g HO R i (where i OU, WE, WA, etc. which take int accunt the rigidity spectra f galactic CR and SCR, ust be used in calculatin f the rigidity dependence f the i - th NM. The values f the axia f the theretical curves f the i - th NM are cnditined by the difference f Δ γ γ s γ g. The experiental recrds f tepral prfiles can be divided rughly int tw grups, ne f NMs which in the initial phase (abut the first hur after the particle nset have asypttic directin near the regular IMF directin (Fig. 4, left panel, and the thers whse asypttic directin differs fr it (Fig. 4, right panel. The theretically predicted tepral prfiles fr the selected NMs in the del described abve are denstrated in Fig. 5, left and right panels, respectively, using the calculated asypttic directin fr each NM statin. This calculatin shws that HO and WE have very siilar characteristics, is 0.9 and 0.86, respectively, with Δ 0.6. Statin LS has 0.4, Δ 0.4. In the secnd grup f NM s, OU, DU, and WA have 0.94, 0.9, 0.85 and Δ 0.06, 0., 0., respectively. Nte that Oulu and Apatity give abslutely the sae theretical curves resulting fr their siilar characteristics and very siilar tepral prfiles f the event. The last tw NMs (DU and WA experienced sall increases at hurs after nset, as the thery predicts (see Fig. 4 (right panel, wing t saller and larger Δ and larger ean R. 5. Cnclusins and six steps f frecasting Fr realizatin f the first step f frecasting we need ne inute real-tie data fr alst all NMs f the wrld netwrk. On the each NM there ust wrk autatically the prgra fr the search f the start SEP events as it was described in Sectins -. This search will help t deterine which NM fr abut 50 f ttal nuber perated in the wrld netwrk shws the narrw peak f the anistrpic strea f the first arrived slar CR (NM f the -st type and which shws a diffusive tail with a wide axiu at a later tie (NM f the -nd type. In the secnd step we deterine rigidity spectru f arrived slar CR γ I R s s by using separately NM f the -st type and -nd type by using ethd f cupling functins as it was described in Sectin 4 (fr details, see: Chapter in []. In the third step we need t deterine fr different NMs the ean R, and Δ characterizing this event. By using these paraeters and experiental data n NM tie prfiles in the beginning tie we cane deterine paraeters f slar CR nnscattering and diffusive prpagatin, described in Sectin (the furth step. On the basis f deterined paraeters f slar CR nn-scattering and diffusive 6
prpagatin we then deterine expected CR fluxes and pitch-angle distributin fr ttal event in interplanetary space in dependence n tie after ejectin (the fifth step. In the sixth step by using again ethd f cupling functins we can deterine expected radiatin dze which will be btained during this event inside space prbes in interplanetary space, satellites in the agnetsphere, aircrafts at different altitudes and cutff rigidities, fr peple and technlgies n the grund. REFERENCES [] L.I.Dran, Csic Rays in the Earth s Atsphere and Undergrund, Kluwer Acadeic Publ., Drdrecht/Bstn/Lndn, 004. 855 pages. [] L.I.Dran, Csic Ray Interactins, Prpagatin, and Acceleratin in Space Plasas, Springer, Netherlands, 006. 847 pages. [] Yu.I.Fedrv, M.Stehlik Descriptin f Anistrpic Particle Pulse Transprt Based n the Kinetic Equatin, Astrphys. Space Sci., 997, v. 5, n., pp. 55-7. [4] Yu.I.Fedrv, B.A.Shakhv, M.Stehlik Nn-Diffusive Transprt f Csic Rays in Hgeneus. Regular Magnetic Fields, Astrn. Astrphys., 995, v.0, n., pp. 6-64. [5] Yu.I.Fedrv, M.Stehlik, K.Kudela, J.Kassvicva Nn- Diffusive Particle Pulse Transprt: Applicatin t an Anistrpic Slar GLE, Slar Phys., 00, v. 08, n., pp. 5-4. [6] L.I.Dran, B.A.Shakhv, M.Stehlik The Secnd Order Pitch- Angle Apprxiatin fr the Csic Ray Fkker-Planck kinetic equatins, in: Prceedings f the 8 th Internatinal Csic Ray Cnference, Tsukuba, Japan, 00, v. 6, pp. 55-58. [7] M.Lue, M.Nieinen, J.J.Trsti, E.Vainikka, J.Peltnen Interplanetary Prpagatin f Relativistic Slar Prtns, Slar Phys., 986, v. 07, n., pp. 8-94. [8] L.P.Brvkv, L.L.Lazutin, O.I.Shuilv, E.V.Vashenyuk Injectin Characteristics f Energetic Particles n the Sun during GLE, in: Prceedings f the 0 th Internatinal Csic Ray Cnference, Mscw, Russia, 987, v., pp. 4-7. [9] J.Kassvicva, K.Kudela On the Cputatins f Csic Ray Trajectries in the Geagnetic Field", Preprint IEP SAS, Ksice, 998, pp. -. [0] L.I.Dran, Experiental and Theretical Principles f Csic Ray Astrphysics, Physatgiz, Mscw, 975. [] P.I.Y.Velinv, G.Nestrv, L.I.Dran, Csic Ray Effects n the Insphere and n the Radiwaves Prpagatin, Publ. Huse f Bulg. Acad. Sci., Sfia, 974, pages. [] N.A.Tsyganenk. A Magnetspheric Magnetic Field Mdel with a Warped Tail Current Sheet, Planet. Space Sci., 989, v. 7, n., pp. 5-0. [] L.I.Dran, Csic Rays in Magnetspheres f the Earth and ther Planets", Springer, Netherlands, 009, 770 pages. [4] M.A.Shea, D.F.Sart, Vertical Cutff Rigidities fr Csic ray Statins since 955, in: Prceedings f the 7 th Internatinal Csic Ray Cnference, Haburg, Gerany, 00, v., pp. 406-4066. 7