1. Multi-spacecraft observations of solar energetic electron events during the rising phase of solar cycle 24 W. Droege 1, R. Gomez-Herrero 2, J. Kartavykh 1, A. Klassen 2, N. Dresing B. Klecker 3, B. Heber 2, L. Sun 1, R. Mueller-Mellin 2 1 Universität Würzburg, D-97074 Würzburg, Germany 2 Universität Kiel, D-24098 Kiel, Germany 3 Max-Planck-Institut für extraterrestrische Physik, Garching, Germany 32nd International Cosmic Ray Conference, Bejing, China, 11 – 18 August 2011 motivation: detailed modeling of multi-spacecraft observations which are becoming available (STEREO / ACE / Wind) reconstruction of parallel and perpendicular diffusion coefficients, injection time history, longitudinal and latitudinal distribution, energy spectra of the particles -- focus on electrons from impulsive events testing of current theories which relate properties of magnetic fluctuations in the solar wind to both parallel and perpendicular diffusion

2. Instrumentation ACE / EPAM / LEFS60 spin axis towards Sun 8 sectors electrons: 45 – 312 keV Gold et al. 1998, SSR 86, 541 STEREO / IMPACT / SEPT 3-axis stabilized 4 viewing directions electrons: 30 – 400 keV protons: 60 keV – 7 MeV Müller-Mellin et al. 2008, SSR 136, 363

3. ACE / STEREO observations of May 2007 solar particle events magnetic field structure on STEREO-B distorted by magnetic cloud ( Liu et al. 2008) particle source: AR 10956 ~ W 06 19 May 2007 ~ W 60 23 May 2007

4. propagation conditions in the solar wind and particle profiles on ACE and STEREO were strongly influenced by a magnetic cloud which was released during the May 19 solar event and passed near-Earth space during May 22 Liu et al., 2008

5. omni-directional intensity I and anisotropy A which are necessary for a modeling of the particle event have to be reconstructed from observed pitch-angle distributions pitch-angle distributions were fitted by 3rd-order polynomials or exponentials in  of the form for ACE both polynomial and exponential fits gave reasonable results in case of sufficient pitch-angle coverage for STEREO polynomial fits usually gave better results in case of sufficient pitch-angle coverage in case of insufficient pitch-angle coverage the intensity was determined as the sector average and the anisotropy was set to zero

6. http://sd-www.jhuapl.edu/ACE/EPAM http://solarscience.msfc.nasa.gov/predict.shtml http://neutronm.bartol.udel.edu/ rather low solar activity until ~ 2009 !

7. modeling of electron event observed simultaneously on STEREO-A, STEREO-B, and ACE / Wind on 7 February 2010 STEREO-A STEREO-B ACE STBACESTA -15.9° 52.7° 116.8° N21 E11 M 6.4 02:20-02:39

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

9. transport equation for solar energetic particles with large anisotropies (Skilling 1975, Ruffolo 1995, Isenberg 1997, Zhang et al. 2009) stochastic differential equation solver: convection, adiabatic deceleration and drift taken into account by transformations between (Kocharov et al, 1998, Dröge et al 2010): 1) Heliocentric Inertial system 2) co-rotating system 3) co-moving system

10. upper curve: random walk of quasi-particle along field line without perpendicular diffuison lower curve: same as before, but now with perpendicular diffusion no co-rotation anisotropic 3-dimensional transport - results (Dröge et al 2010) impulsive injection of 4 MeV protons on single field line  = 0.01  

11. transport modeling of STEREO-A/B and ACE electron observations on 7 Feb 2010: in a first step only time-dependent injection close to Sun and parallel tranport considered red curves assumption of coronal transport and propagation parallel to IMF only does not explain observations  also perpendicular diffusion required ! WAVES data by M. Kaiser GSFC/CDAWeb

12. CONCLUSIONS   modeling of 3D transport is important for reconstruction of time history and longitudinal and latitudinal distribution of injection energy and charge spectra  provides test for theories which relate properties of magnetic fluctuations in the solar wind to both parallel and perpendicular diffusion  tools for modeling anisotropic 3D transport are being developed  evidence for significant perpendicular transport,  ~ 10 -2   combined ACE / Wind / STEREO observations of solar particles will provide new insight into lateral transport in the corona and in the interplanetary medium more results: May 2009 events Dresing et al. Poster 0918 18 Aug 2010 event Gomez-Herrero et al. Poster 0947