Simulations of Lateral Transport and Dropout Structure of Energetic Particles from Impulsive Solar Flares Paisan Tooprakai1, Achara Seripienlert2, David Ruffolo2, Piyanate Chuychai3, and William H. Matthaeus4 1Chulalongkorn U., Thailand 2Mahidol U., Thailand 3Burapha U., Thailand 4U. Delaware, USA ก่อนอื่น คงต้องขออนุญาตพูดในภาษาอังกฤษครับ เพราะมีผู้ฟังบางท่านที่ไม่ค่อยถนัดกับภาษาไทยครับ

Observations from Advanced Composition Explorer (ACE) [Mazur et al Observations from Advanced Composition Explorer (ACE) [Mazur et al. 2000, Gosling et al. 2004, Chollet & Giacalone 2008] a) Energy of H-Fe ions (in units of MeV nucleon-1) vs. arrival time at 1 AU for the impulsive flare event of 1999 January 9. b) H-Fe counts vs. time in smoothed, ~14 minute bins. Observations from ACE showed SEP flux near Earth repeatedly disappearing and reappearing non-dispersively: “DROPOUTS” Usually interpreted as indicating a filamentary distribution of SEPs and little diffusion across these boundaries … … due to filamentary magnetic connectivity to a narrow source region at/near Sun date 1/9/1999 1/10/1999 1/ 11/1999 [Mazur et al. 2000]

Not diffusive during initial transport. A new view of lateral transport of field lines and particles: Not diffusive during initial transport. Filamentary magnetic connectivity from a narrow source region naturally arises from turbulence model. “core” of SEP with dropouts “halo” of low SEP density over wide lateral region [Ruffolo, Matthaeus, & Chuychai 2003; details of the process have been worked out by Chuychai et al. (2005, 2007), Tooprakai et al. (2007), Seripienlert et al. (2010)] October 11, 2006 @ STT32 3

The Maltese cross (of space physics) [Matthaeus et al. 1990] Correlation function of solar wind turbulence parallel and perpendicular to the magnetic field. Consistent with theoretical expectation of Shebalin et al. (1983). [Not to be confused with anisotropy in B direction.]

The 2D+slab Model of Magnetic Turbulence This model provides a useful description of magnetic fluctuations in the solar wind (e.g., Bieber et al. 1994, 1996)

Two components of turbulence [Ph.D. thesis of Achara Seripienlert, based on drawings by W. Dröge]

Topology of 2D turbulence leads to dropouts Two component model: slab turbulence 2D turbulence [Bieber et al. 1994] For 2D component: O-point  local maxima or minima in a(x,y) X-point  saddle points of a(x,y) Contour plot of potential function a(x,y)

Topology of 2D turbulence leads to dropouts Two component model: slab turbulence 2D turbulence Dropouts can be explained by filamentary magnetic connection due to Temporary topological trapping near O-points [Ruffolo et al. 2003] Suppressed diffusive escape [Chuychai et al. 2005, 2007] Contour plot of potential function a(x,y)

2D fields along angular coordinates in spherical geometry [Tooprakai et al. 2016] Spherical harmonic expansion 2D Fast Fourier Transform 2D MHD: Develop coherent structures

Recent results in spherical geometry Spatial distribution of magnetic field lines from narrow solar injection (impulsive solar flare) Dropout pattern becomes more complex farther from Sun [see also Servidio et al. 2014] Total spread is ~25o at 1 AU [consistent with Reames 1990, ApJS] Recent results in spherical geometry

For 1 MeV and 1 GeV, the initial large-scale spatial pattern is similar. At 1 MeV, pattern persists for long s = vt. At 1 GeV, after s = 4 AU (i.e., about 35 min. after the first particle arrival) the spatial pattern is much smoother. Still not diffusive! Particles remain within outer trapping boundary. Recent results for full proton orbit calculation in spherical geometry (so focusing occurs) as a function of energy and distance traveled s=vt. 1 MeV 1 GeV

What should Solar Probe Plus and Solar Orbiter see? (0.25 AU from Sun) Expect pulse of SEPs according to injected time profile, then delay as wait for backscattered particles [Earl 1976]. Many locations miss the pulse due to dropout pattern, see backscatter. Backscattered particles at long s = vt are initially close to same field line pattern, later spread within outer envelope. Again, the lateral transport is never diffusive! Solar Orbiter may corotate with Sun at perihelion: No dropouts Solar Probe Plus could observe non-dispersive dropout features X and γ imaging: Valuable data on magnetic connectivity. s=0.25-0.29 AU s=1.2-2.4 AU s=2.4-6 AU s=6-9 AU s=9-12 AU For details, see Tooprakai et al. (2016)

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