THREE-DIMENSIONAL ANISOTROPIC TRANSPORT OF SOLAR ENERGETIC PARTICLES IN THE INNER HELIOSPHERE CRISM- 2011, Montpellier, 27 June – 1 July, Collaborators: W. Dröge, B. Klecker, G.A. Kovaltsov Y.Kartavykh University of Würzburg (Germany), Ioffe Physical-Technical Institute (Russia)

Solar cosmic rays = Solar Energetic Particles Generated in solar explosive processes Generated in solar explosive processes Short time scale in comparison with time scales typical for GCR Short time scale in comparison with time scales typical for GCR Anisotropic fluxes at ~ 1 AU Anisotropic fluxes at ~ 1 AU 2

are there more than one acceleration processes, stages, phases? are interacting and escaping particles from the same population? gamma-ray imaging of solar flares reconstruction of event geometry 3

focus here on particles from impulsive events avoids complications due to CMEs and interplanetary shocks energetic particles in the Heliosphere realistic transport models required to reconstruct particle properties 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) 4

Because of anisotropy in SEP events one should consider pitch-angle diffusion 5 Dec keV electrons Wind 3DP PI: R.P.Lin Pitch-angle distributions for the 2003, March, 17 event 5

Variation of peak intensities I m with connection angleConnection plot and electron time profiles for the flare event of 1979 January 15. Early Multi-Spacecraft Observations of Impulsive Solar Events Wibberenz & Cane (2006) electrons in the MeV range can be detected more than 80 degrees from the flare longitude evidence for lateral transport 6

DROPOUTSCUTOFFSSTEPS Mazur et al. (2000)ACE ULEIS 1 May 2000Wind 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 7

SOLAR PARTICLE PROPAGATION COMBINATION OF: AZIMUTHAL TRANSPORT CLOSE TO THE SUN (CORONAL DIFFUSION) TRANSPORT PARALLEL TO B PITCH ANGLE SCATTERING, FOCUSING, ADIABATIC LOSSES POSSIBLE DIFFUSION ACROSS THE AVERAGE MAGNETIC FIELD considered here only particles from impulsive events avoids complications due to CMEs and shocks 8

In our model we solve stochastic differential equations 9 Results of the model: - SEP‘ time profiles - spatial distributions - pitch-angle distributions (therefore, anisotropy, too)

Parker field 10

Way of 4 MeV proton, with and without perpendicular diffusion.  =0.01 ,  =0.3 / cos  AU cos  =1/(1+  2 sin 2  r 2 /U sw 2 ) Droege et al, 2010

Protons, 4 MeV hrs 12 Droege et al, 2010

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107 keV electrons h 14 Droege et al, 2010

Protons, 4 MeV, hrs 15 Droege et al, 2010

16 Droege et al, 2010

No perpdiff, one- dimensional or homogen. Perpdiff, no corotation Corotation, no perpdiff, perpdiff, 4 degr. flank 17 Droege et al, 2010

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Electron intensities in the energy range 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. 20

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 21

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. 22

2010, January 17 event From N.Dresing 23

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2010, August, 18 event From R.Gόmes-Herrero 25

Time profiles from point-like source 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. 27