Changeset 562 in ETALON


Ignore:
Timestamp:
Apr 27, 2016, 3:38:26 PM (8 years ago)
Author:
malovyts
Message:

Added second figure of the results, Changed text accordingly

Location:
papers/2016_IPAC/2016_IPAC_Malovytsia_ModelComparison
Files:
1 deleted
4 edited

Legend:

Unmodified
Added
Removed

  • papers/2016_IPAC/2016_IPAC_Malovytsia_ModelComparison/MOPMB004.tex

    r556 r562  
    3636\usepackage{multirow}
    3737\usepackage{ragged2e}
     38\usepackage{subcaption}
     39\usepackage{array}
    3840
    3941%\usepackage{biblatex}
    … …  
    6466%\usepackage{eso-pic}
    6567%\AddToShipoutPictureFG*{\AtTextLowerLeft{\textcolor{red}{COPYRIGHTSPACE}}}
    66 
    6768\begin{document}
    6869        \title{Comparison of the Smith-Purcell radiation yield for different models}
    6970
    7071        \author{N.~Delerue\textsuperscript{1}\thanks{delerue@lal.in2p3.fr}, M.~S.~Malovytsia\textsuperscript{1,2}\\
    71                 \textsuperscript{1}Laboratoire de l'Acc\'el\'erateur Lin\'eaire, Universit\'e Paris-Sud, Orsay, France\\
     72                \textsuperscript{1}LAL, CNRS/IN2P3, Universit\'e Paris-Saclay, Univ. Paris-Sud, Orsay, France\\
    7273                \textsuperscript{2}Kharkiv National University, Kharkov, Ukraine}
    7374
    7475        \maketitle
     76
    7577        \begin{abstract}
    7678                Smith-Purcell radiation is used in several applications
    … …  
    102104          \item Electro-Optic (EO) sampling~\cite{Fitch99} uses a non linear crystal in which the bunch wakefield will induce optical changes. It requires a femtosecond laser. Its limitations due to material properties are discussed in~\cite{EOLimSteff09}.
    103105          \item Coherent Transition Radiation (CTR)~\cite{Lai94} uses the radiation emitted when the beam crosses a thin foil. In some cases it may be difficult to discriminate the signal from CTR for other sources of radiation (e.g.: synchrotron radiation) generated further upstream.
    104          \item Coherent Smith-Purcell Radiation~\cite{SP53,Nguyen97} (CSPR),
     106         \item Coherent Smith-Purcell Radiation~\cite{Nguyen97} (CSPR),
    105107           uses a grating to induce the emission of radiation. It
    106108           has the advantage of dispersing the radiation at the point of emission and therefore being more immune to background noise. It is described below.
    … …  
    201203                        \end{array}
    202204                        \right)
    203                         = Const\frac{e}{\gamma\lambda}
     205                        = C_1\frac{e}{\gamma\lambda}
    204206                        \displaystyle\int\limits_{-M/2}^{M/2}dX_T
    205207                        \displaystyle\int\limits_{-L/2}^{L/2}dZ_T\left(
    … …  
    227229        \begin{equation}
    228230        \begin{split}
    229         I&=Const^2\left( (E_x^D)^2 + (E_z^D)^2\right)
     231        I&=C_1'\left( (E_x^D)^2 + (E_z^D)^2\right)
    230232        \end{split}
    231233        \end{equation} 
    … …  
    241243
    242244         \section{Simulation of SEY for different models}
    243          The parameters of the SPESO experiment~\cite{SPESO} were used in the simulation (see table~\ref{tab:SPESO}). The constant of the RRR model was calculated from the assumption, that the intensities of the SC and RRR models are equal at $\theta=90^\circ$.
     245         The parameters of the SPESO at SOLEIL synchrotron and E203 at FACET at SLAC experiments~{\cite{SPESO,p046}} were used in the simulation (see table~\ref{tab:SPESO_E203}). The constant of the RRR model was calculated from the assumption, that the intensities of the SC and RRR models are equal at $\theta=90^\circ$.
    244246
    245247        \begin{table}[!ht]
    246248                \centering
    247          \begin{tabular}{|l|l|l|p{3.5cm}|}
    248                 \hline
    249                 Name & Value & Units & Description\\ \hline
    250                 $\gamma$ & 200 & 1 & Lorentz factor (E=100~MeV)\\ \hline
    251                 $ d $ & 10 & mm & The grating period\\ \hline
    252                 $ a $ & 7.5 & mm & The width of one strip\\ \hline
    253                 $ R_0 $ & 310 & mm & The distance between detector and grating\\ \hline
    254                 $ L $ & 90 & mm & The length of the grating\\ \hline
    255                 $ M $ & 20 & mm & The width of the grating\\ \hline
    256                 $ h $ & 5 & mm & The beam-grating separation\\ \hline
    257                 $ n $ & 1 & mm & The order of the radiation\\ \hline
    258                 $ \theta_0 $ & 30& degree & The blaze angle \\ \hline
    259                 $ Const $ & 22.4 & mm$^{-2}$ & The normalization constant for the RRR model \\ \hline
    260          \end{tabular}
    261         \caption{Parameters for the simulation of the SPESO experiment}
    262         \label{tab:SPESO}
     249                \caption{The simulation parameters}
     250                \label{tab:SPESO_E203}
     251                \small
     252                \begin{tabular}{|m{6mm}|m{8mm}|m{7mm}|m{6mm}|m{30mm}|}
     253                        \hline
     254                        Symb.           & SPESO & E203  & Units & Description\\ \hline
     255                        $\gamma$        & 200   & 4$\times$10\textsuperscript{4}        & 1             & The Lorentz factor (E=100~MeV)        \\ \hline
     256                        $ d $           & 10    & 0.25  & mm            & The grating period                    \\ \hline
     257                        $ a $           & 7.5   & 0.187 & mm            & The width of one strip                \\ \hline
     258                        $ R_0 $         & 310   & 220   & mm            & The distance between detector and grating\\ \hline
     259                        $ L $           & 90    & 40    & mm            & The length of the grating             \\ \hline
     260                        $ M $           & 20    & 20    & mm            & The width of the grating              \\ \hline
     261                        $ h $           & 5             & 1             & mm            & The beam-grating separation   \\ \hline
     262                        %$ n $          & 1             & 1             & 1                     & The order of the radiation    \\ \hline
     263                        $ \theta_0 $& 30        & 30    & deg           & The blaze angle                               \\ \hline
     264                        $ C_1' $        & 400   & 6395  & mm\textsuperscript{-3} & The normalization constant for the RRR model \\
     265                        \hline
     266                \end{tabular}
     267                \normalsize
    263268        \end{table}
    264 
    265          
     269         \begin{figure}[!ht]
     270                        \centering
     271                 \begin{subfigure}[t]{0.5\textwidth}
     272                        \includegraphics[width=\textwidth]{MOPMB004f2.png}
     273                        \caption{SPESO experiment}
     274                        \label{fig:SPESO_RDR_SC_RRR}
     275                 \end{subfigure}
     276                 \begin{subfigure}[t]{0.5\textwidth}
     277                        \includegraphics[width=\textwidth]{MOPMB004f3.png}
     278                        \caption{E203 experiment}
     279                        \label{fig:E203_RDR_SC_RRR}
     280                 \end{subfigure}
     281                        \caption{Calculated curves for the RDR (solid blue line), RRR (green line with circle marker), SC (blue dashed line) and GFW (purple line with square marker) models and their ratios.}
     282                        \label{fig:theta_RDR_SC_RRR}
     283         \end{figure}
     284%        \begin{figure}[!ht]
     285%                       \centering
     286%                       \includegraphics[width=0.5\textwidth]{MOPMB004f3.png}
     287%                       \caption{Calculated curves for the RDR, RRR, SC and GFW models. Top plot is the calculated data, bottom plot is the ratio between models}
     288%                       \label{fig:E203_theta_RDR_SC_RRR}
     289%        \end{figure}
     290                 
    266291         Taking into account an angular aperture of the detectors of 10$^\circ$, for each value of $\theta$ the intensity was integrated in $\phi$ over the range ${-5^\circ<\phi<5^\circ}$, in theta over the range ${\theta_i-5^\circ<\theta<\theta_i+5^\circ}$, where $\theta_i$ is the measurement angle. The calculation were done for ${40^\circ~<~\theta_i~<~140^\circ}$, with the step of $10^\circ$.
    267292         
    268          The figure~\ref{fig:SPESO_theta_RDR_SC_RRR} shows the comparison of the RDR, SC, RRR in the far zone, and GFW models, and their ratio. It is seen that for the RDR, SC and RRR models the difference is not greater than the factor of 2, which is within experimental errors. The GFW model gives intensity 10 times bigger, than the RDR and SC models, which could be explained by the fact, that in GFW calculations authors take into account the width of the grating, and the grating efficiency parameter is calculated numerically, for the case of N grating facets.
     293         The figures~\ref{fig:SPESO_RDR_SC_RRR},~\ref{fig:E203_RDR_SC_RRR} show the comparison of the RDR, SC, RRR in the far zone, and GFW models, and their ratio. It is seen that for the RDR, SC and RRR models the difference is not greater than the factor of 2, which is within experimental errors. The GFW model gives intensity 10 times bigger, than the RDR and SC models, which could be explained by the fact, that in GFW calculations authors take into account the width of the grating, and the grating efficiency parameter is calculated numerically, for the case of N grating facets.
    269294         
    270295%        The figure~\ref{fig:SPESO_theta_RDR_SC_RRR} additionally has curve of the RRR model in the far-zone, normalized at $\theta=90^\circ$, and below the main plot is the ratio of the RRR and SC model, the ratio is not bigger than one order and have oscillations similar to the sine.
    … …  
    279304%                       \label{fig:SPESO_theta_RDR_SC}
    280305%        \end{figure}
    281          \begin{figure}[!ht]
    282                 \centering
    283                 \includegraphics[width=0.5\textwidth]{MOPMB004f2.png}
    284                 \caption{Calculated curves for the RDR~(solid blue line), RRR~(solid green line with dots) and SC~(dashed blue line) models. Top plot is the calculated data, bottom plot is the ratio between SC and RRR models}
    285                 \label{fig:SPESO_theta_RDR_SC_RRR}
    286          \end{figure}
     306
    287307%        \begin{figure}[!ht]
    288308%               \centering
    … …  
    332352         
    333353         \section{Conclusions}
    334         The SEY of the several leading models of the SPR were compared. The simulation shows that the SC and RDR models are in agreement within experimental errors. The RRR model is also close to the RDR and SC, but more detailed explanation on the constant required. The calculations were also done for the E203 experiment~\cite{p046} at FACET at SLAC, and the  conclusions were similar.
     354        The SEY of the several leading models of the SPR were compared. The simulation shows that the SC and RDR models are in agreement within experimental errors. The RRR model is also close to the RDR and SC, but more detailed explanation on the constant required. The consideration of the grating width in the GFW simulation gives the intensity 10 times bigger. The ratios between the models are not changing with the parameters~(except the observation angle), which means that it is possible to introduce a parameter-independent model correction factor.
     355        % The calculations were also done for the E203 experiment~\cite{p046} at FACET at SLAC, and the  conclusions were similar.
    335356       
    336357%       While analysing the results of the SPR experiments, one should be aware of the pre-wave zone correction, that could be calculated using two approaches (RRR model and osillators approximation), that are giving close result.
    … …  
    343364        \bibitem{Fitch99}
    344365                M. J. Fitch     \emph{et al.},
    345                 ``PICOSECOND ELECTRON BUNCH LENGTH MEASUREMENT BY       ELECTRO-OPTIC DETECTION OF THE WAKEFIELD'',
     366                ``Picosecond electron bunch length measurement by electro-optic detection of the wakefield'',
    346367                in \textit{Proc. PAC’99},
    347368                New York, USA, March-Apr.~1999,
    … …  
    357378                \emph{Phys. Rev. E}, vol. 50,
    358379                pp. R4294--R4297, Dec. 1994.\\
    359         \bibitem{SP53}
    360                 S.~J.~Smith and E.~M.~Purcell.,
    361                 ``Visible Light from Localized  Surface Charges Moving across a Grating'',
    362                 \emph{Phys. Rev.}, vol. 92,
    363                 pp. 1069-–1069.,        1953. \\       
     380%       \bibitem{SP53}
     381%               S.~J.~Smith and E.~M.~Purcell.,
     382%               ``Visible Light from Localized  Surface Charges Moving across a Grating'',
     383%               \emph{Phys. Rev.}, vol. 92,
     384%               pp. 1069-–1069.,        1953. \\       
    364385        \bibitem{Nguyen97}
    365386                D.~C.~Nguyen,
    … …  
    396417                J.~H.~Brownell, J.~Walsh, G.~Doucas,
    397418                ``Spontaneous Smith-Purcell radiation described through induced surface currents'',
    398                 \emph{Phys. Rev. E} vol. 57,
    399                 pp. 1075--1080,  Jan. 1998.\\
     419                \emph{Phys. Rev. E} vol.~57,
     420                pp.~1075--1080,  Jan.~1998.\\
    400421        \bibitem{p010}
    401422                G.~Doucas \emph{et al.},
    402423                ``First observation of Smith-Purcell radiation from     relativistic electrons'',
    403                 \emph{Phys. Rev. Lett.}, vol. 69,
    404                 pp. 1761--1764, Sept. 1992. \\ 
     424                \emph{Phys. Rev. Lett.}, vol.~69,
     425                pp.~1761--1764, Sept.~1992. \\ 
    405426        \bibitem{p021}
    406427                D.~V.~Karlovets and A.~P.~Potylitsyn.
    … …  
    457478%               pp. 452-–460, 1998 \\
    458479%
    459 %       \bibitem{SCDoucas98}
    460 %               J.~H.~Brownell, J.~Walsh and G.~Doucas.,
    461 %               ``Spontaneous Smith-Purcell radiation described through induced surface currents'',
    462 %               \emph{Phys. Rev. E}, vol. 57,
    463 %               pp. 1075–-1080., Jan. 1998. \\
    464480%       \bibitem{SPExpWoods95}
    465481%               K.~J.~Woods \emph{et al.},
Note: See TracChangeset for help on using the changeset viewer.