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\title{\huge Spatially dependent turbulence and particle diffusion in an interplanetary magnetic flux rope}
\author[Krittinatham et al.]{\underline{Watcharawuth\ Krittinatham}$^1$, David\ Ruffolo$^{2,3}$, John W. Bieber$^4$}
\institute[NARIT]{$^1$National Astronomical Research Institute of Thailand, Chiang Mai, 50200, Thailand, e-mail: watcharawuth@narit.or.th \\
$^2$Department of Physics, Faculty of Science, Mahidol University and $^3$ Thailand Center of Excellence in Physics, CHE, Ministry of Education, Bangkok, 10400, Thailand \\
$^4$ Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, 19716, USA}
%\date[Aug. 31 , 2007]{Aug. 31 , 2007}
% abbreviations
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
\begin{frame}{}
\vspace{-2.5cm}
\begin{columns}
\begin{column}{.54\linewidth}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{block}{1.Introduction}
%\item The high energy particles originating outside the solar system called galactic cosmic rays (GCRs) strike the Earth’s %atmosphere from all directions and create the secondary GCRs that can be detected by ground-base detector e.g. neutron monitor
\vspace{-2.0cm}
\begin{columns}
\begin{column}{0.63\textwidth}
\begin{itemize}
\item Interplanetary Coronal Mass Ejections (ICMEs) are large-scale plasma bubbles and magnetic field structures expelled from the Sun into space.
\item Some ICMEs have large and smooth rotation of magnetic field lines, implying an “interplanetary magnetic flux rope (IMFR).”
\item When an IMFR sweeps past Earth, it deflects away some Galactic Cosmic Rays (GCRs) that would otherwise strike our planet from all directions, then the GCRs have a lower density inside the IMFR and the ground-based detectors experience the sudden drops in the signal called “Forbush Decreases (FDs).
\item \textcolor{blue!99.0}{We consider how GCRs fill the flux rope until the signal comes close to its ambient level.}
\end{itemize}
\end{column}

\begin{column}{0.22\textwidth}
\vspace{-1.0cm}
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{Fig02_2stepsFD.eps}
%\caption{\footnotesize 1. Forbush Decrease in July 1982 detected by Deep River, Mt.Wellington, and Kerguelen neutron monitors  to end of Forbush Decrease (from Cane $[1]$).}
\label{fig:Fig02_2stepsFD}
\end{figure}
\end{column}

\begin{column}{0.15\textwidth}
{\newline \footnotesize [\emph{left}] \textcolor{blue!99.0}{Figure 1}: Forbush Decrease and recovery to ambient intensity in July 1982 detected by Deep River, Mt.Wellington, and Kerguelen neutron monitors (from Cane [1]).}
\end{column}

\end{columns}
\end{block}

\begin{block}{2.Systematic physical processes of GCR transport}
\vspace{-2.5cm}
\begin{columns}

\begin{column}{0.46\textwidth}
\begin{itemize}
\item Parallel to the mean magnetic field: streaming and focusing, conserving the first adiabatic invariant.
\item Perpendicular to the mean magnetic field: gradient drift ($v_g$) and curvature drift ($v_c$).
\item The equation of the motion of the guiding center is $ d\mathbf{r}/dt = \mu v \mathbf{\hat{b}} + \mathbf{v}_g + \mathbf{v}_c$ where the pitch angle cosine is $\mu = \mathbf{p} \cdot \mathbf{B} / |\mathbf{p}||\mathbf{B}|$ and $\mathbf{p}$ is the particle’s momentum.
\item An analytic IMFR model developed by [2] in quasi-toroidal coordinates ($r,\phi,\theta$) relative to a circle of radius $R$, which is the axis of flux rope. A flux surface is defined by $r = a \cos(\phi/2)$, where $a$ is the radius of the flux surface at the apex of the rope ($\phi = 0$) (see Fig. 2).
\item Examples of some trapped-particle trajectories (Fig. 3a) in terms of $\mu$, and the distance from the Sun along the loop $Z = R(\pi-\phi)$, for varying initial $\mu_0$ at the apex. These trajectories exhibit magnetic mirroring.
\item The drift velocity across the flux rope surface, $v_n  = (v_g + v_c)\hat{n}$, where $\hat{n}$ is the outward normal to the surface, yields an inflow rate (Fig.3b) and outflow rate (Fig.3c) averaged over the flux rope surface (averaged over $\theta$) as a function of $\mu$ and $Z$. The drifts across the flux rope boundary are predominantly inward along one leg of the loop and predominantly outward along the other.
\item During a Forbush decrease, this should contribute a unidirectional anisotropy and net flow of GCRs. The flow direction is determined by the poloidal field direction [2].
\end{itemize}
\end{column}
%\begin{equation}
%\mathbf{v}_g = \frac{\gamma m_0 (1-\mu^2)v^2}{2q} \left[ \frac{\mathbf{B} \times \nabla B}{B^3} \right].
%\end{equation}
%\begin{equation}
%\mathbf{v}_c = -\frac{\gamma m_0 \mu^2 v^2}{2 q B^2} \mathbf{B} \times \left[ \frac{\nabla B \times (\nabla %\times %\mathbf{B} ) }{B^2} - \frac{\nabla B}{B} \right].
%\end{equation}

\begin{column}{0.54\textwidth}

\begin{columns}
\begin{column}{0.62\textwidth}
\vspace{-1.5cm}
\begin{figure}
\centering
\includegraphics[width=0.70\textwidth]{Fig01_Orientation.eps}
%\caption{\footnotesize 3.Global analytic magnetic flux rope model developed by $[2]$.}
\label{fig:Fig01_Orientation}
\end{figure}
{\footnotesize [\emph{left}] \textcolor{blue!99.0}{Figure 2}: Global, analytic magnetic flux rope model $[2]$.}
\end{column}

\begin{column}{0.38\textwidth}
\vspace{-1.5cm}
\begin{figure}
\centering
\includegraphics[width=0.9\textwidth]{f6.eps}
%\caption{\footnotesize 4.(a) Particle trajectories in terms of $\mu$, and $Z$ (b) In?ow rate and (c) out?ow rate averaged over the surface of the ?ux rope(averaged over $\theta$) as a function of $\mu$ and Z in unit  AU km s$^{?1}$ .}
\label{fig:resultsdriftgcrs}
\end{figure}
\end{column}
\end{columns}
\vspace{0.5cm}
{\footnotesize [\emph{right}] \textcolor{blue!99.0}{Figure 3}: (a) Particle trajectories in terms of $\mu$, and $Z$ (b) Inflow rate and (c) outflow rate averaged over the surface of the flux rope(averaged over $\theta$) as a function of $\mu$ and $Z$ in units of AU km s$^{-1}$.}
\end{column}
\end{columns}
\end{block}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{block}{3.Stochastic processes and spatial dependence of turbulence}
\vspace{-2.5cm}
\begin{columns}
\begin{column}{0.75\textwidth}
\begin{itemize}
\item Magnetic turbulence described by the $2D$+Slab model of [3]: $\mathbf{B} = B_m \hat{z} + \mathbf{b}(x,y,z) = B_m \hat{z} + \mathbf{b}_{2D}(x,y) + \mathbf{b}_{SL}(z)$, where $B_m \hat{z}$ is the mean magnetic field, and $\mathbf{b}_{2D}(x,y)$ and $\mathbf{b}_{SL}(z)$ are transverse fluctuation fields.
\item Field Line Random Walk (FLRW): Particles diffuse because they undergo no parallel scattering and are tied to a field line, which undergoes a random walk.
\item The Non-Linear Guiding Center (NLGC)theory is based on the \textcolor{blue!99.0}{FLRW, parallel diffusion along the mean field}, and \textcolor{blue!99.0}{diffusion of guiding center} [4,5].
\item Pitch angle scattering: particles scattered by parallel force $\mathbf{F}_{||} = q \mathbf{v}_{\perp} \times \mathbf{b}$, which randomly changes the pitch angle.
\item Assumption: flux rope originally had uniform turbulence, but during expansion and stretching of the ICME, at relative speeds faster than the Alfv\’en speed, turbulence properties became non-uniform.
\item Assumption: 2D correlation length $l_{2D}$, expands as a perpendicular length scale proportional to the flux rope radius: $l_{2D} = l_{2D,Apex}\cos(\phi/2)$.
\item Assumption: Slab correlation length, $l_{SL}$, is stretched along with the loop like the field line winding: $l_{SL} = l_{SL,Apex} / \cos(\phi/2)$.
%\begin{equation}
%D_{\perp} = \frac{D_{SL} + \sqrt{D_{SL}^2 + 4D_{2D}^2} }{2},
%\end{equation}
%where $D_{\perp}$, $D_{SL}$, and $D_{2D}$ are FLRW perpendicular, 2D and slab diffusion coefficients. \\
%\begin{figure}[h]
%        \centering
%        \includegraphics[width=0.5\textwidth]{FigCh03_FluctuationField.eps}
%            \caption{\tiny Illustration of (a) the field line fluctuation of winding magnetic field line in a magnetic flux rope and the particle motion gyrate around fluctuated field line and (b) the magnetic field line random walk perpendicular displacements $\Delta x$ and $\Delta y$}
%            \label{fig:FigCh03_FluctuationField}
%        \end{figure}
\item Assumption: Spatial dependence of turbulent energy density $b^2$ is related to local expansion/stretching of the volume, giving $\mathbf{b} = \mathbf{b}_{Apex} / \sqrt{\cos(\phi/2)}$.
\end{itemize}
\end{column}

\begin{column}{0.25\textwidth}
\begin{figure}
\centering
\includegraphics[width=0.80\textwidth]{FigCh03_NLGC.eps}
%\caption{\footnotesize 2.The basis of NLGC theory.}
\label{fig:FigCh03_NLGC}
\end{figure}
{\footnotesize \textcolor{blue!99.0}{Figure 4}: The basis of NLGC theory.}
\end{column}
\end{columns}
\end{block}

\end{column}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{column}{.42\linewidth}
\begin{block}{4.Results}
\begin{itemize}
\item We use an energy ratio $E_{SL}/E_{2D} = 10.0/90.0$, $\langle b_{SL}^2 \rangle/ \langle b_{2D}^2 \rangle = 0.18$, $b^2/B_m^2 = 0.05$, $l_{2D,Apex} = 0.006$ AU, and $l_{SL,Apex} = 0.003$ AU.
\item The particles’ perpendicular mean free path and diffusion coefficients calculated from the NLGC theory compared with the results from the FLRW theory are shown in Fig.5.
\item We simulate GCR motion by initially placing the guiding centers of protons of 1 GeV kinetic energy at flux rope surface. Then we trace the trajectories due to systematic and stochastic processes. as mentioned before. The results are shown in Figs. 6 and 7 by plotting the positions of particle guiding centers in a cross-section of the flux rope ($a-\theta$ space), integrating over the entire rope (integrate over $\phi$) as a function of time.
\end{itemize}
\vspace{-2.25cm}
\begin{columns}
\begin{column}{0.33\textwidth}
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{Fig_compare_lambda_vary_phi.eps}
%\caption{\footnotesize 5. a) Comparison of parallel diffusion mean free path calculated from NLGC theory at various flux surface $a = 0.0$, $0.05$, and $0.10$ AU. b) Show the perpendicular mean free path calculated from NLGC theory (solid lines) and FLRW theory (dashed lines) comparison at various $a$, and c) comparison of perpendicular diffusion coefficients.}
\label{fig:FigCh03_NLGC}
\end{figure}
\end{column}

\begin{column}{0.33\textwidth}
%\begin{figure}
%      \centering
%      \includegraphics[width=1.0\textwidth]{Fig_compare_lambda_vary_theta.eps}
%      \caption{a) Comparison of parallel diffusion mean free path calculated from NLGC theory at various flux surface $a = 0.0$, $0.05$, and $0.10$ AU. b) Show the perpendicular mean free path calculated from NLGC theory (solid lines) and FLRW theory (dashed lines) comparison at various $a$, and c) comparison of perpendicular diffusion coefficients.}
%      \label{fig:FigCh03_NLGC}
%      \end{figure}
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{Results_DriftOnly.eps}
%\caption{\footnotesize 6. The position of guiding center in cross-section of flux rope as the results of simulation with systematic process (drifts and first adiabatic invariant) only.}
\label{fig:driftonly}
\end{figure}
\end{column}

\begin{column}{0.33\textwidth}
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{Results_Drift_Diffusion.eps}
%\caption{\footnotesize 7. Same as Fig.6 but adding stochastic process in the simulation.}
\label{fig:driftdiff}
\end{figure}
\end{column}
\end{columns}
{\footnotesize [\emph{left}] \textcolor{blue!99.0}{Figure 5}: (a) Comparison of parallel diffusion mean free path calculated from quasilinear theory at various flux surfaces $a = 0.0$, $0.05$, and $0.10$ AU. (b) Perpendicular mean free paths calculated from FLRW (solid lines) and NLGC theory (dashed lines). Because the difference is not great, and FLRW is much faster to compute, we employ this theory in the simulations.} \newline
{\footnotesize[\emph{center}] \textcolor{blue!99.0}{Figure 6}: The position of guiding centers in integrated cross-section of flux rope at various times from a simulation with systematic processes only (streaming, focusing, and drifts).} \newline
{\footnotesize [\emph{right}] \textcolor{blue!99.0}{Figure 7}: Same as Fig.6 but adding stochastic processes to the simulation.}
\end{block}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{block}{5.Conclusions}
\begin{itemize}
\item The drifts alone cannot transport the GCRs into the inner portion of the rope.
\item The drifts alone do not are not sufficient to fill the flux rope with GCRs to come close to an ambient level over a time scale of several hours.
\item In a weak turbulence environment such as that inside a magnetic cloud, the particles’ perpendicular mean free path and perpendicular diffusion coefficient can be similar for FLRW \& NLGC theories (see also [5]).
\item The perpendicular mean free path at the center of the IMFR is short, and becomes longer away from the flux rope axis.
\item The parallel mean free path is very long in the loop leg regions, and then shorter at the flux rope’s apex.
\item The perpendicular mean free path is short at the loop leg regions, and then longer at the flux rope’s apex.
\item When adding stochastic processes such as perpendicular diffusion and pitch angle scattering, the particle is able to travel into the center region of an IMFR.
\end{itemize}
\end{block}
\vspace{-2.0cm}
\begin{columns}
\begin{column}{0.60\textwidth}
\begin{block}{6.References}
%\begin{enumerate}
{\small
[1] H. V. Cane 2000, \emph{J. Geophys. Res.}, 98,3509  \newline
[2] W. Krittinatham, D. Ruffolo 2009, \emph{Astrophys. J.}, 704, 831 \newline
[3] W. H. Matthaeus \etal 1995, \emph{Phys. Rev. Lett.}, 75, 2136 \newline
[4] W. H. Matthaeus \etal 2003, \emph{Astrophys. J.},  590, L53 \newline
[5] D. Ruffolo \etal 2008, \emph{Astrophys. J.}, 686, 1231
}
%\end{enumerate}
\end{block}
\end{column}

\begin{column}{0.36\textwidth}
\begin{block}{Acknowledgements}
This work is partially supported by the Thailand Research Fund and NASA grant NNX07AH73G.
\end{block}
\end{column}
\end{columns}
%\bibliographystyle{alpha}
%\bibliography{poster.bib}
%\begin{thebibliography}{}
%\bibitem[Burlaga et al (1990)]{BurlagaEA90} Burlaga, L.F., Lepping, R.P.,\&  Jones, J.A. 1990, \emph{Physics of Magnetic Flux Rope}, (Washington, DC.), 373
%\bibitem[Cane (2000)]{Cane00} Cane, H.V. 2000, \emph{Space Sci. Rev.}, 93, 55
%\bibitem[Droge (2000)]{Droge00} Dr\”{o}ge, W., 2000, \emph{Astrophys. J.}, 537, 1073
%\bibitem[Earl (1994)]{Earl94} Earl, J.A. 1994, \emph{Astrophys. J.}, 425, 331
%\bibitem[Krittinatham \& Ruffolo (2009)]{KrittinathamRuffolo09} Krittinatham, W., \& Ruffolo, D. 2009, \emph{Astrophysical J.}, 704, 831
%\bibitem[Matthaeus et al (2007)]{MatthaeusEA07} Matthaeus, W.H., Bieber, J.W., Ruffolo, D., Chuychai, P., \& Minnie, J. 2007, \emph{Astrophys. J.}, 667, 956
%\bibitem[Matthaeus et al (2003)]{MatthaeusEA03} Matthaeus, W.H., Qin, G., Bieber, J.W., \& Zank, G. 2003, \emph{Astrophys. J.}, 590, L53
%\bibitem[Matthaeus et al (1995)]{MatthaeusEA95} Matthaeus, W.H., Gray, P.C., Pontius, D.H., \& Bieber, J.W. 1995, \emph{Phys. Rev. Lett.}, 75, 2136
%\bibitem[Meyer et al (1956)]{MeyerEA56} Meyer, P., Parker, E.N., \& Simpson, J.A. 1956, \emph{Phys. Rev.}, 104(3), 768
%\bibitem[Russell \& Mulligan (2002)]{RussellMulligan02} Russell, C.T., Mulligan, T. 2002, \emph{Planet. \& Space Sci.}, 50, 527
%\end{thebibliography}
\end{column}
\end{columns}
\end{frame}

\end{document}

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ข้อดีคือไฟล์ขนาด Double A Zero นี่ถ้าทำด้วย Power Point จะสร้างไม่ได้เนื่องจากลิมิตของโปรแกรม  ถ้าจะทำด้วย Illustrator Class โปรแกรมอย่าง Inkscape หรือ Adobe Illustrator ก็จะ “เปลือง Ram” มากครับ ดีไม่ดีนี่ Laptop ช้าๆ อาจจะทำไม่ได้เลยด้วยซ้ำ ดังนั้นการเขียนด้วย LaTeX จึงเป็นทางออกที่ดีที่สุดเนื่องจากเป็นการทำงานใน text mode ธรรมดาเท่านั้น  แต่ต้องใช้ “จินตนาการ” หรือ คอมไพล์ code ในสมองเอาเองว่ามันจะออกมาเป็นอย่างไร   แล้วคอมพิวเตอร์จะทำงานหนักอีกทีตอน compile file LaTeX เป็น  dvi, ps หรือ pdf file ครับ

นี่คือไฟล์ที่คอมไพล์เสร็จแล้ว (>_<)>

Spatially dependent turbulence and particle diffusion in an interplanetary magnetic flux rope SH33B-1837

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