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Advances in Space Research 43 (2009) 735–738

The method for predicting solar proton events

V.M. Dvornikov *, M.V. Kravtsova, A.A. Lukovnikova, V.E. Sdobnov

Institute of Solar-Terrestrial Physics SB RAS, Irkutsk P.O. Box 291, Lermontov Street, 126a, 664033 Irkutsk, Russia

Received 23 February 2008; received in revised form 13 May 2008; accepted 8 October 2008

Abstract

Dynamic processes in the interplanetary space have been investigated using time variations in time parameters of the cosmic-ray rigid-ity spectrum. Change of heliosphere electromagnetic characteristics has been found out to precede sporadic phenomena on the Sun. Inparticular, it is shown that sporadic phenomena are followed by generation of local polarization electric fields, decrease of the magnetic-field strength in small-scale heliospheric structures, and increase of the potential difference between the pole and the plane of the ecliptic.These features allow prediction of solar proton events in advance (from several hours to several tens of hours) with a high degree ofconfirmation.� 2008 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Solar proton events; Solar proton prediction; Heliospheric electromagnetic characteristics; Solar magnetic fields

1. Introduction

Predicting of solar proton events (SPEs) is associatedwith various complicated circumstances, the most impor-tant of which is the absence of theoretically proved algo-rithms for solving the given problem. Thus we can notdetermine necessary and sufficient predictors for identifica-tion of pre-flare situation on the Sun. However, if thisproblem had been solved, difficulties would have arisen inpredicting flux localization of accelerated particles in theinterplanetary space, and in predicting their arrival at theEarth. There are some organizations engaged in a short-term prediction of solar flares. The leading among themis the Prognosis Centre that is a division of the Space Envi-ronment Centre and is under the joint guidance of theNational Oceanic and Atmospheric Administration(NOAA) and the US air forces. Prognosis methods usedare based on data about structure and dynamics of mag-netic fields and active photospheric and chromospheric for-mations. These formations can be defined from directmagnetic-field measurements in the photosphere or from

0273-1177/$34.00 � 2008 COSPAR. Published by Elsevier Ltd. All rights rese

doi:10.1016/j.asr.2008.10.028

* Corresponding author.E-mail address: dvornikov@iszf.irk.ru (V.M. Dvornikov).

indirect methods with the use of Sun images in chromo-spheric and coronal spectral lines made by ground-basedand satellite instruments.

There is a prognosis method for low-energy protonfluxes from behaviour of high-energy particle intensity atthe initial increase stage (at SCR ground level enhancement(GLE), Dorman et al., 2004) and of high-energy electrons(http://physorg.com/news122143679.html) with predictionadvance time of about 1 h. The first method is suitable onlyfor the GLE registration, as registration frequency of GLEis less than that of high-energy SCR.

We can solve SPE prediction problem with an accept-able advance time and confirmation degree, only if the flareenergy accumulation is the result of dynamics of currentsystems localized in the solar corona and stretched up tosome distances in the heliosphere. In this case an attemptto find SPE predictors using the heliosphere diagnosticsfrom cosmic-ray (CR) effects is worthwhile. Such diagnos-tics is performed in the interplanetary magnetic-field (IMF)lines that now connect the Earth with correspondingregions on the Sun. Articles Volodichev et al. (1985) andDvornikov et al. (1984, 1988) prove the existence of suchsituations. The purpose of this article is to realize such apossibility.

rved.

736 V.M. Dvornikov et al. / Advances in Space Research 43 (2009) 735–738

2. Data and method

We used mid-hour observation data of proton intensitywithin energy ranges of 4–9, 9–15, 15–40, 40–80, 80–165,165–500 MeV registered at the satellite GOES-10 (http://spidr.ngdc.gov/spidr/index.html) for analysis. We alsoused data on intensity variations of various-rigidity CRobtained by the spectrographic global survey (SGS)method (Dvornikov and Sdobnov, 1997) from ground-based measurements at the world network of neutron mon-itors (38 stations).

The expression from Volodichev et al. (1985) was usedfor description of the CR rigidity spectrum over a wideenergy range.

JðRÞ ¼ Aðe2 � e2

0Þðeþ DeÞ2 � e2

0

" #3=2

� eþ Dee

2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðeþ DeÞ2 � e2

0

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðe2 � e2

0Þp

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðe2 � e2

0Þp

24

35�c

; ð1Þ

where e is the total particle energy; e0 is the rest energy, A

and c are spectral indices of galactic spectrum; De are par-ticle energy variations in the heliosphere electromagneticfields specified by the expression:

DeðRÞ ¼ De0 þ De1½1� f ðR; bþ R0Þ�þ De2½1� f ðR; bþ R0Þ�f ðR;R0Þ

þ ½eð1� ea=2Þ þ e�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffibðe2 � e2

0Þ þ e20

q�f ðR;R0Þ: ð2Þ

The expression (1) was derived from the Liouville theo-rem on the assumption that the energy range observed hasno solar particle source (SCR). The expression (2) wasderived from the general solution of particle motion equa-tion in the drift approximation (Dvornikov et al., 2005a)on the assumption that polarization and vortex electricalfields might be generated in the heliosphere along with aninduced electric field. Generation of polarization electricalfields may result from distribution of beam particles, accel-erated on the Sun, in inhomogeneous magnetic fieldsbecause of protons and electrons drifting in opposite direc-tions. This may lead to charge separation and potential dif-ference between beam boundaries along magnetic drifttrajectories, if spatial inhomogeneity of accelerated parti-cles is observed. This fact in its turn results in generationof polarization electrical field increasing with time andpolarization drift of plasma background particles of thesolar wind, solar coronas and galactic cosmic rays alongthis field. Thus we observe particle acceleration of the solarcorona and interplanetary medium with their Larmor radiiless than the across size of the given beam. Appearance ofdepolarizing longitudinal currents leads to current systemformation, generation of magnetic field and vortex electri-cal field, which accelerates particles due to the betatronicmechanism, etc. L. Lindberg’s Alfven (1981) laboratoryexperiments proved generation of such fields.

Spectrum parameters De1, De2, a, b, and R0 present thefollowing heliosphere characteristics: R0 is the parameterdescribing the structural formation scale in the heliospherewith non-stationary electromagnetic fields; De1 determinesCR energy variations caused by gradient and centrifugalparticle drifts in the spiral interplanetary magnetic field(IMF) in the direction opposite to the induced electric field,and it is proportional to the IMF intensity; De2 defines suchvariations in the fields of coronal mass ejections (CME)and is proportional to the magnetic-field intensity inCME and to the solar wind (SW) velocity (Dvornikovand Sdobnov, 2002). The parameter b equals B/B0, whereB0 is the background field intensity, and B is the time-var-iable IMF intensity; the parameter describes influence ofnon-stationary magnetic fields on the CR spectrum (withmagnetic rigidity of particles R 6 R0); the parametera = Epl

2/B2 characterizes influence of polarization electricfields Epl. Quasi-step functions f(R,R0), f(R,b + R0) areintroduced to lend importance to this or that mechanismof particle energy variations over energy ranges[0.108, R0], [R0,R0 + b] and [R0 + b, 1] GV, where b = 5GV. These functions tend to 1 at R < R0 or R < b + R0

and to 0 at R > R0 or R > b + R0. Expression for thequasi-step function, its parameters and the constant De0

including the residual modulation for low-energy particleshave been found empirically in Dvornikov et al. (2005b).

Thus we can monitor heliosphere electromagneticcharacteristics and their dynamics via the determinationof differential CR rigidity spectrum parameters with theuse of the Eq. (1) solution in view of (2) according to mea-suring data on particle intensity in given energy ranges pereach observation hour. Monitoring of the interplanetarymedium during the period of October–November 2003and in 2004 was carried out with this method.

3. Analysis of results

Triangles in three upper panels of Fig. 1 demonstrateobservation data on proton intensities within energyranges 4–9 MeV (0.108 GV), 9–15 MeV (0.223 GV) and5 GV; solid curves present calculation results made withthe use of model spectrum and obtained values of itsparameters. Dst-index values are presented in the fourthpanel. Mid-hour values of rigidity spectrum parametersDe1, a, b, and R0 are presented in four lower panels.These parameters have been determined during the per-iod under study.

Comparison of temporal variations of CR rigidityspectrum parameters with temporal intensity profiles oflow-energy CR (the first two panels of Fig. 1) implies thatchanges in heliosphere electromagnetic characteristicsoccur on the day before solar proton events. In particular,generation of local polarization electric fields (increase ofthe parameter a) takes place several hours or tens of hoursbefore SPE. During this period, we also observe decrease inthe magnetic-field strength in small-scale structures of the

0.108 GV102

100

10-2

10-4

0.223 GV

10-4

102

100

10-2

5 GV

1.10-5

8.10-6

6.10-6

4.10-6

prot

ons

(cm

2 s

sr Ì

V)-1

-400

-200

0

Dst

, nT

0

1

2

3

R0,

GV

0.4

0.8

1.2

1, G

eV

5 10 15 20 25 30 5 10 15 20 25 30 October November

2003

0.16

0.2

0.24

00.5

11.5

22.5

Δ εα

β

Fig. 1. Temporal profiles of the CR intensity at R = 0.108, 0.223 and 5 GV (solid line marks calculation, triangles mark observation data), Dst-index andparameters of the CR rigidity spectrum R0, De1, a, b in October–November 2003. Moments of SPE predictors’ appearance are marked by vertical lines inthe upper panel.

V.M. Dvornikov et al. / Advances in Space Research 43 (2009) 735–738 737

heliosphere (decrease of the parameter b), and increase inthe large-scale spiral IMF strength (parameter De1).

This fact permits us to predict SPE using monitoring ofheliosphere electromagnetic characteristics (in the real-timeregime) through effects in cosmic rays.

We used these three factors for SPE predicting with2-month data sampling in October–November 2003. Thesefactors were hourly analyzed; if they were indicating pre-flare situation during 5 h, prognostic index was assigned1, otherwise it was 0. Vertical lines in the upper panel ofFig. 1 demonstrate moments when the prognostic indexwas 1, i.e. the factors (predictors for given events) were

realized. Similar information for 2004 is presented inFig. 2; it demonstrates a high degree of confirmation(about 90%) for the method developed.

4. Conclusion

Diagnostics of electromagnetic conditions in the inter-planetary medium using CR effects allows the predictionof solar proton events in advance (from several hours toseveral tens of hours) with a high degree of confirmation.It proves the modulation model adequacy and validity of

0 8 16 24 32 40 48 56 64 72 80 88

88 96 104 112 120 128 136 144 152 160 168 176 184

180 188 196 204 212 220 228 236 244 252 260 268 276

272 280 288 296 304 312 320 328 336 344 352 360 368

364 372 380 388 396 404 412 420 428 436 444 452

456 464 472 480 488 496 504 512 520 528 536 544

544 552 560 568 576 584 592 600 608 616 624 632 640

636 644 652 660 668 676 684 692 700 708 716 724 732

10-4

10-2

100

10-4

10-2

100

10-4

10-2

100

102

10-4

10-2

100

102

10-4

10-2

100

102

10-4

10-2

100

102

10-4

10-2

100

102

10-3

prot

ons

/(cm

2 s s

r M

V)

2004 - 2005

Fig. 2. Time profile of the CR intensity within the energy range 4–9 MeV in 2004–2005. Moments of SPE predictors’ appearance are shown by dottedvertical lines.

738 V.M. Dvornikov et al. / Advances in Space Research 43 (2009) 735–738

the obtained information on dynamic processes in theheliosphere.

Acknowledgements

This work is supported by the complex integrationproject SB RAS-2006 No 3.10 and the RAS Presidiumprogram ‘‘Neutrino physics” in the frames of the project‘‘Research into modulation effects of cosmic rays withground-based and stratospheric monitoring”.

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