THREE-DIMENSIONAL ANISOTROPIC THREE-DIMENSIONAL ANISOTROPIC TRANSPORT OF SOLAR ENERGETIC TRANSPORT OF SOLAR ENERGETIC PARTICLES IN THE INNER PARTICLES IN THE INNER HELIOSPHEREHELIOSPHERE

CRISM-2011, Montpellier, 27 June – 1 July, 2011

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Collaborators: W. Dröge, B. Klecker, G.A. Kovaltsov

Y.KartavykhUniversity of Würzburg (Germany),Ioffe Physical-Technical Institute (Russia)

Solar cosmic rays = Solar Solar cosmic rays = Solar Energetic ParticlesEnergetic Particles

Generated in solar explosive Generated in solar explosive processesprocesses

Short time scale in comparison Short time scale in comparison with time scales typical for GCRwith time scales typical for GCR

Anisotropic fluxes at ~ 1 AUAnisotropic fluxes at ~ 1 AU

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are there more than one accelerationprocesses, stages, phases?

are interacting and escaping particlesfrom the same population?

gamma-ray imaging of solar flares

reconstruction of event geometry

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focus here onparticles from impulsive events

avoids complicationsdue to CMEs and interplanetary shocks

energetic particles in the Heliosphere

realistic transport models required to reconstruct particleproperties at the Sun from spacecraft observations:

acceleration time scales, energy and charge spectra, relation to electromagnetic emission close to the Sun(radio, X-ray, gamma-ray)

44

Because of anisotropy in SEP events one should consider pitch-angle diffusion

5 Dec 1997 107 keV electrons Wind 3DP PI: R.P.Lin

Pitch-angle distributions for the 2003, March, 17 event

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Variation of peak intensities Im with connection angle Connection plot and electron time profiles for the flare event of 1979 January 15.

Early Multi-Spacecraft Observations of Impulsive Solar EventsWibberenz & Cane (2006)

electrons in the MeV range can be detected more than 80 degrees from the flare longitude

evidence for lateral transport

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DROPOUTS CUTOFFS STEPS

Mazur et al. (2000) ACE ULEIS 1 May 2000 Wind 3DP 4 Nov 1997

• no velocitiy dispersion• time variations correspond to spatial gradients perpendicular to B which are convected past the spacecraft

goal: find a suitable phenomenological description which can be used as starting point for comparison with theory

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SOLAR PARTICLE PROPAGATION

COMBINATION OF:

AZIMUTHAL TRANSPORT CLOSETO THE SUN (CORONAL DIFFUSION)

TRANSPORT PARALLEL TO BPITCH ANGLE SCATTERING, FOCUSING,ADIABATIC LOSSES

POSSIBLE DIFFUSION ACROSS THEAVERAGE MAGNETIC FIELD

considered here only particles from impulsive eventsavoids complications due to CMEs and shocks

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In our model we solve stochastic differential equations

( ) 2 ( )Bdr t dte dW s dt BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB BBB

dtD

LtdWDtd

)1(2

)(2)( 2

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Results of the model: - SEP‘ time profiles - spatial distributions - pitch-angle distributions (therefore, anisotropy, too)

sin)(),,(

0),,(

),,(

2

0

2

0

r

RRr

uBrB

rB

r

RBrB

SW

r

Parker field

1010

Way of 4 MeV proton, with and without perpendicular diffusion.

=0.01 , =0.3 / cos AU

cos=1/(1+2sin2r2/Usw2)0.5 1111

Droege et al, 2010

Protons,

4 MeV

3.5-4.5 hrs

1212

Droege et al, 2010

1313

107 keV electrons

0.75-1.25 h

1414

Droege et al, 2010

Protons,

4 MeV,

23.5-24.5 hrs

1515Droege et al, 2010

1616Droege et al, 2010

No perpdiff, one-dimensional or homogen.

Perpdiff, no corotation

Corotation, no perpdiff, perpdiff, 4 degr. flank

1717Droege et al, 2010

1818

1919

Electron intensities in the energy range 65-105 keV at 1 AU, without perpendicular diffusion, and for two values of α. Angular distances of SC to the source are given on the legends.

2020

Anisotropies of electrons. Upper panel: location of SC on the magnetic line connected to the flare, α=0.01. Middle panel: angle of observations 30 degrees, α=0.01. Lower panel: angle of observations 30 degrees, α=0.1. In all cases

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Comparison of protons intensities, observed from different longitudes, at a radial distance 0.31 AU (see legend) in case of multiple injection from the point-like source.

Comparison of protons intensities, observed from different longitudes, at a radial distance 1 AU (see legend) in case of multiple injection from the point-like source.

2222

2010, January 17 event

From N.Dresing 2323

2424

2010, August, 18 event

From R.Gόmes-Herrero 2525

Time profiles from point-like source

2626

18 August, 2010

C O N C L U S I O N S

- Propagation of charged particles in a magnetic field strong in comparison with superposed irregularities should be considered in a pitch-angle diffusion approximation

- The observed sharp intensities variations (cutoffs and drop-outs) can be explained by a very weak diffusion in a perpendicular to the large scale magnetic filed direction

- The existing multispacecraft observations can serve as a tool to determine the characteristics of interplanetary space

- Time profiles, together with directional properties of SEP events strongly depend on the angular distance and distance along the magnetic field line from the source.

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