Changeset 548 in ETALON


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Timestamp:
Apr 25, 2016, 7:48:28 PM (8 years ago)
Author:
malovyts
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Edited links: numbering and checked their priority to others
Added GFW line to the plot

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

    r500 r548  
    33               %boxit,
    44               %titlepage,   % separate title page
    5                refpage      % separate references
     5               %refpage      % separate references
    66              ]{jacow}
    77
    … …  
    6868        \title{Comparison of the Smith-Purcell radiation yield for different models}
    6969
    70         \author{N. Delerue\textsuperscript{1}, M.S. Malovytsia\textsuperscript{1,2}\\
     70        \author{N.~Delerue\textsuperscript{1}, M.~S.~Malovytsia\textsuperscript{1,2}\\
    7171                \textsuperscript{1}Laboratoire de l'Accélérateur Linéaire, Université Paris-Sud, Orsay, France\\
    7272                \textsuperscript{2}Kharkiv National University, Kharkov, Ukraine}
    … …  
    8383                and shown that they are in agreement
    8484                within the experimental errors.
    85                 To have a better agreement
    86                 between predictions and experimental measurements
    87                 we also report on the interference effects
    88                 that modulate the signal in the near-field zone.
     85                %To have a better agreement
     86                %between predictions and experimental measurements
     87                %we also report on the interference effects
     88                %that modulate the signal in the near-field zone.
    8989        \end{abstract}
    9090       
    … …  
    100100To measure reliably the length of such short bunches with destroying them several approaches are possible:
    101101         \begin{itemize}
    102           \item Electro-Optic (EO) sampling~\cite{EOBerden2004} 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}.
    103           \item Coherent Transition Radiation (CTR)~\cite{CTRMurokh98} 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,sp020} (CSPR),
     102          \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}.
     103          \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),
    105105           uses a grating to induce the emission of radiation. It
    106106           has the advantage of dispersing the radiation at the point of emission and therefore being more immune to background noise. It is described below.
    … …  
    156156               
    157157        \item The Surface Current (SC)
    158          model~\cite{SCDoucas98}, that explains SPR through the currents that are being induced
     158         model~\cite{gfw}, that explains SPR through the currents that are being induced
    159159         on the surface of the grating by a charge passing nearby. This theory has proven to be
    160160         in a good agreement with experiments for energies from a few MeV to 28.5 GeV~\cite{p010, p019, p043, p026}.
    … …  
    172172         $R^2$ is a grating efficiency parameter, that depends on the radiation angle and blaze angle.
    173173         
     174         Further in the paper, the results obtained with the expression for $R^2$ taken from~\cite{p021} will be called SC, and from the~\cite{gfw} will be referred to as GFW.
    174175       
    175176        \item The Resonant Diffraction Radiation (RDR) model,
    … …  
    189190       
    190191        \item The model so-called Resonant Reflection Radiation (RRR) model based on the fact that a field of a moving charged particle could be described
    191          as a sum of the virtual plain waves~\cite{Mikaelian72} XXX Can you cite also Haberle here? XXX , that will become real after scattering on the grating.
     192         as a sum of the virtual plain waves~\cite{Mikaelian72,Haeberl94}, that will become real after scattering on the grating.
    192193         The expression for the intensity of this model is given in the~\cite{p041}.
    193194       
    … …  
    234235 In the~\cite{p041}, by assuming the distances from the grating to be infinite, authors also derived the far-zone approximation of the RRR model.
    235236 
    236         Although authors of the~\cite{p041} chose geometry of a plain strips
    237          it could be easily changed into the geometry discussed in this paper (Fig.~\ref{fig:geom1}).
     237%       Although authors of the~\cite{p041} chose geometry of a plain strips
     238%        it could be easily changed into the geometry discussed in this paper (Fig.~\ref{fig:geom1}).
    238239        \end{itemize}
    239240
    … …  
    256257                $ n $ & 1 & mm & The order of the radiation\\ \hline
    257258                $ \theta_0 $ & 30& degree & The blaze angle \\ \hline
    258                 $ Const $ & 2.5 & mm$^{-2}$ & The normalization constant for the RRR model \\ \hline
     259                $ Const $ & 22.4 & mm$^{-2}$ & The normalization constant for the RRR model \\ \hline
    259260         \end{tabular}
    260261        \caption{Parameters for the simulation of the SPESO experiment}
    … …  
    263264
    264265         
    265          Taking into account an angular aperture of the detectors of XXXX CHECK XXXX 5$^\circ$, for each value of $\theta$ the intensity was integrated in $\phi$ over the range $-5^\circ<\phi<5^\circ$ XXX THETA OR PHI - OVER wWHICH RANGE DID YOU INTEGRATE IN THETA? XXX. The calculation were done for $40^\circ~<~\theta~<~140^\circ$, with the step of $10^\circ$.
    266          
    267          The results of the simulation are presented on figures~\ref{fig:SPESO_theta_RDR_SC},~\ref{fig:SPESO_theta_RDR_SC_RRR},~\ref{fig:far_correction}.
    268          
    269          The figure~\ref{fig:SPESO_theta_RDR_SC} shows the comparison of the RDR and SC models, and their ratio, it is seen that the difference between those models is not greater than the factor of 2, which is within experimental errors.
    270          
    271          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.
    272          
    273          The figure~\ref{fig:far_correction} shows the correction factor, i.e. the ratio between the intensity of the SPR in the pre-wave zone and in the far-zone. The solid red line was made by calculating the ratio between RRR model and RRR model in the pre-wave zone.
    274          The blue dashed line is the correction factor calculated by considering the strips of the grating as oscillators, and then calculating interference in the pre-wave zone. Their difference is within 10\%, so it could be said that they are in agreement.
    275          
    276         \begin{figure}[!ht]     
    277                         \centering
    278                         \includegraphics[width=0.45\textwidth]{MOPMB004f3.png}
    279                         \caption{Calculated curves for the RDR~(solid blue line) and SC~(dashed blue line) models. Top plot is the calculated data, bottom plot is the ratio between SC and RDR models}
    280                         \label{fig:SPESO_theta_RDR_SC}
    281          \end{figure}
     266         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 $10^\circ$.
     267         
     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.
     269         
     270%        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.
     271         
     272%        The figure~\ref{fig:far_correction} shows the correction factor, i.e. the ratio between the intensity of the SPR in the pre-wave zone and in the far-zone. The solid red line was made by calculating the ratio between RRR model and RRR model in the pre-wave zone.
     273%        The blue dashed line is the correction factor calculated by considering the strips of the grating as oscillators, and then calculating interference in the pre-wave zone. Their difference is within 10\%, so it could be said that they are in agreement.
     274         
     275%       \begin{figure}[!ht]     
     276%                       \centering
     277%                       \includegraphics[width=0.45\textwidth]{MOPMB004f3.png}
     278%                       \caption{Calculated curves for the RDR~(solid blue line) and SC~(dashed blue line) models. Top plot is the calculated data, bottom plot is the ratio between SC and RDR models}
     279%                       \label{fig:SPESO_theta_RDR_SC}
     280%        \end{figure}
    282281         \begin{figure}[!ht]
    283282                \centering
    284                 \includegraphics[width=0.45\textwidth]{MOPMB004f4.png}
     283                \includegraphics[width=0.5\textwidth]{MOPMB004f2.png}
    285284                \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}
    286285                \label{fig:SPESO_theta_RDR_SC_RRR}
    287286         \end{figure}
    288          \begin{figure}[!ht]
    289                 \centering
    290                 \includegraphics[width=0.45\textwidth]{MOPMB004f5.png}
    291                 \caption{The correction factor from the RRR~(solid red line) model and from the SC~(dashed blue line) model}
    292                 \label{fig:far_correction}
    293           \end{figure} 
     287%        \begin{figure}[!ht]
     288%               \centering
     289%               \includegraphics[width=0.45\textwidth]{MOPMB004f5.png}
     290%               \caption{The correction factor from the RRR~(solid red line) model and from the SC~(dashed blue line) model}
     291%               \label{fig:far_correction}
     292%         \end{figure} 
    294293
    295294%=======================================================================================================
    … …  
    308307%        More detailed explanations are presented in the~\cite{p019}.
    309308         
    310         \section{Near-field zone effect}
    311                 In every radiative phenomenon it is possible to identify the three zones~\cite{p013}:
    312                 \begin{enumerate}
    313                 \item The wave-zone~--- at distances comparable to the wavelength,
    314                 \item The far-zone~--- for the large distances at which the grating could be considered a single-point oscillator. In this zone intensity per solid angle is independent from the grating-detector
    315                 separation.
    316                 \item The pre-wave zone~--- between the first two zones, where the grating sizes should be taken into account. Here, intensity per solid angle is dependant on the grating-detector separation due to the
    317                 interference effects.
    318                 \end{enumerate}
    319                 The criterion for far/pre-wave zones separation were calculated in  \cite{p041}. The condition for the far
    320                 zone is:
    321                  \begin{equation}
    322                  \mathcal{R} \gg \frac{1}{n}dN^2(1+\cos{\theta}).
    323                  \end{equation}
    324                 For $N=800$ and $d=$\SI{0.05}{mm} at $\theta=90^\circ$, the far zone should be considered starting \SI{30}{m} which is much greater than available distances at the experiments, for other angles the far zone criterion is presented on the Fig.~\ref{fig:zones}, the (0,~0) coordinate correspond to the position of the grating.
    325                
    326         \begin{figure}[!ht]
    327                 \centering
    328                 \includegraphics[width=0.4\textwidth]{MOPMB004f2.png}
    329                 \caption{Visualisation of the far/pre-wave zones}
    330                 \label{fig:zones}
    331          \end{figure}
     309%       \section{Near-field zone effect}
     310%               In every radiative phenomenon it is possible to identify the three zones~\cite{p013}:
     311%               \begin{enumerate}
     312%               \item The wave-zone~--- at distances comparable to the wavelength,
     313%               \item The far-zone~--- for the large distances at which the grating could be considered a single-point oscillator. In this zone intensity per solid angle is independent from the grating-detector
     314%               separation.
     315%               \item The pre-wave zone~--- between the first two zones, where the grating sizes should be taken into account. Here, intensity per solid angle is dependant on the grating-detector separation due to the
     316%               interference effects.
     317%               \end{enumerate}
     318%               The criterion for far/pre-wave zones separation were calculated in  \cite{p041}. The condition for the far
     319%               zone is:
     320%                \begin{equation}
     321%                \mathcal{R} \gg \frac{1}{n}dN^2(1+\cos{\theta}).
     322%                \end{equation}
     323%               For $N=800$ and $d=$\SI{0.05}{mm} at $\theta=90^\circ$, the far zone should be considered starting \SI{30}{m} which is much greater than available distances at the experiments, for other angles the far zone criterion is presented on the Fig.~\ref{fig:zones}, the (0,~0) coordinate correspond to the position of the grating.
     324%               
     325%       \begin{figure}[!ht]
     326%               \centering
     327%               \includegraphics[width=0.4\textwidth]{MOPMB004f2.png}
     328%               \caption{Visualisation of the far/pre-wave zones}
     329%               \label{fig:zones}
     330%        \end{figure}
    332331               
    333332         
    334333         \section{Conclusions}
    335         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 .
     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.
    336335       
    337336%       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.
    … …  
    342341        %----------------------------------------------------------------------------------------
    343342\begin{thebibliography}{99} % Use for 10-99 references
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    460         in \textit{Proc. IPAC’11},
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     457%               pp. 452-–460, 1998 \\
     458%
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     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. \\
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     465%               K.~J.~Woods \emph{et al.},
     466%               ``Forward Directed Smith-Purcell Radiation from Relativistic Electrons'',
     467%               \emph{Phys. Rev. Lett.}, vol. 74,
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     474%
     475       
     476
    466477
    467478\end{thebibliography}
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