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- Nov 27, 2015, 11:33:04 AM (9 years ago)
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- papers/2015_FrUa
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papers/2015_FrUa/models/FrenchUkrainianW2015Nov/FrUkrWshp_SPR_MalovytsNov2015.aux
r300 r301 1 1 \relax 2 2 \citation{SPRSmithPurcell} 3 \citation{ FreeElLaser}3 \citation{NIMA_SP_2014} 4 4 \citation{compsprKarlovetsPotylitsyn} 5 5 \citation{sprpwKarlovetsPotylitsyn} … … 7 7 \citation{sprpwKarlovetsPotylitsyn} 8 8 \citation{trVerzilov} 9 \citation{sprpwKarlovetsPotylitsyn} 10 \citation{sprpwKarlovetsPotylitsyn} 9 11 \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}} 10 12 \newlabel{eq:diff_length}{{1}{1}} 11 \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Disposition of the grating, detector, bunch and radiation. Flat grating.\relax }}{1}}12 \providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}13 \newlabel{fig:geom1}{{1}{1}}14 \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Disposition of the grating, detector and bunch. Grating with inclined strips\relax }}{1}}15 \newlabel{fig:geom2}{{2}{1}}16 13 \@writefile{toc}{\contentsline {section}{\numberline {2}Models}{1}} 17 14 \citation{sprpwKarlovetsPotylitsyn} 18 \citation{sprpwKarlovetsPotylitsyn} 19 \citation{sprpwKarlovetsPotylitsyn} 15 \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Disposition of the grating, detector, bunch and radiation. Flat grating.\relax }}{2}} 16 \providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}} 17 \newlabel{fig:geom1}{{1}{2}} 18 \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Disposition of the grating, detector and bunch. Grating with inclined strips\relax }}{2}} 19 \newlabel{fig:geom2}{{2}{2}} 20 20 \newlabel{eq:balzing_modifier}{{2}{2}} 21 21 \@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Simplifications of BDR}{2}} … … 24 24 \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.1.1}Far zone}{2}} 25 25 \newlabel{eq:far_crit}{{5}{2}} 26 \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.1.2}Short grating strips}{ 2}}27 \newlabel{eq:short_crit}{{6}{ 2}}26 \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.1.2}Short grating strips}{3}} 27 \newlabel{eq:short_crit}{{6}{3}} 28 28 \@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Experimental parameters}{3}} 29 29 \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Comparison of the SC, RDR and BDR}{3}} 30 \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Phi distribution for SPESO(left) and E 203 d=1,5mm(right)\relax }}{3}} 31 \newlabel{fig:Phi1}{{3}{3}} 32 \bibstyle{phaip} 33 \bibdata{bibliography} 34 \bibcite{SPRSmithPurcell}{1} 30 \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Phi distribution for SPESO(left) and E 203 d=1,5mm(right)\relax }}{4}} 31 \newlabel{fig:Phi1}{{3}{4}} 35 32 \@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Phi Distribution for E 203 d=250$\mu $m(left) and E 203 d=50$\mu $m(right)\relax }}{4}} 36 33 \newlabel{fig:Phi2}{{4}{4}} 37 34 \@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Phi Distribution for E 203 d=50$\mu $m M=30mm(left) and M=120mm(right)\relax }}{4}} 38 35 \newlabel{fig:Phi3}{{5}{4}} 39 \@writefile{toc}{\contentsline {section}{\numberline {3}Interference}{4}} 40 \bibcite{FreeElLaser}{2} 41 \bibcite{compsprKarlovetsPotylitsyn}{3} 42 \bibcite{sprpwKarlovetsPotylitsyn}{4} 43 \bibcite{trVerzilov}{5} 36 \bibstyle{phaip} 37 \bibdata{bibliography} 38 \@writefile{toc}{\contentsline {section}{\numberline {3}Interference}{5}} 44 39 \@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Dependance of the intensity from R\relax }}{5}} 45 40 \newlabel{fig:IntensR}{{6}{5}} … … 49 44 \newlabel{fig:Colormap}{{8}{5}} 50 45 \@writefile{toc}{\contentsline {section}{\numberline {4}Summary}{5}} 46 \bibcite{SPRSmithPurcell}{1} 47 \bibcite{NIMA_SP_2014}{2} 48 \bibcite{compsprKarlovetsPotylitsyn}{3} 49 \bibcite{sprpwKarlovetsPotylitsyn}{4} 50 \bibcite{trVerzilov}{5} -
papers/2015_FrUa/models/FrenchUkrainianW2015Nov/FrUkrWshp_SPR_MalovytsNov2015.bbl
r300 r301 5 5 \newblock Phys. Rev. {\bf 92}, 1069 (1953). 6 6 7 \bibitem{FreeElLaser} 8 V.~Kumar and K.-J. Kim, 9 \newblock Phys. Rev. E {\bf 73}, 026501 (2006). 7 \bibitem{NIMA_SP_2014} 8 H.~Andrews et~al., 9 \newblock Nuclear Instruments and Methods in Physics Research Section A: 10 Accelerators, Spectrometers, Detectors and Associated Equipment {\bf 740}, 11 212 (2014), 12 \newblock Proceedings of the first European Advanced Accelerator Concepts 13 Workshop 2013. 10 14 11 15 \bibitem{compsprKarlovetsPotylitsyn} -
papers/2015_FrUa/models/FrenchUkrainianW2015Nov/FrUkrWshp_SPR_MalovytsNov2015.blg
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papers/2015_FrUa/models/FrenchUkrainianW2015Nov/FrUkrWshp_SPR_MalovytsNov2015.log
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papers/2015_FrUa/models/FrenchUkrainianW2015Nov/FrUkrWshp_SPR_MalovytsNov2015.tex
r300 r301 16 16 \begin{document} 17 17 \title{Comparison of Smith-Purcell radiation models} 18 \author{Maksym Malovytsia }18 \author{Maksym Malovytsia$^{1,2}$, Nicolas Delerue$^{2}$\\$^{1}$ Kharkiv University\\ $^{2}$ LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France. } 19 19 \renewcommand{\today}{2015} 20 20 \maketitle 21 \begin{abstract} 22 Smith-Purcell radiation is used in several applications including the measurement of the longitudinal profile of electron bunches. A correct reconstruction of such profile requires a good understanding of the underlaying model. We have compared the two leading models of Smith-Purcell radiation and shown that they are in good agreement. We have also studied the interference effects that modulate the signal in the near-field zone. 23 \end{abstract} 24 21 25 \section{Introduction} 22 \par Smith-Purcell (SP) radiation \cite{SPRSmithPurcell} has been discovered sixty years ago. This phenomena occurs, when charged particles pass near periodical conductive grating. Wavelength of produced radiation could be determinedby a simple equation:26 \par Smith-Purcell (SP) radiation \cite{SPRSmithPurcell} has been discovered sixty years ago. This phenomena occurs, when charged particles pass near periodical conductive grating. The wavelength of the radiation produced is given by a simple equation: 23 27 \begin{equation}\label{eq:diff_length} 24 28 \lambda=\frac{d}{n}\left(\frac{1}{\beta}-cos{\theta}\right) 25 29 \end{equation} 26 \textit{Where $ \lambda $ - length of the radiation, $ d $ - period of the grating, $ n $ - order of radiation and $ \theta $ -polar observation angle (see Fig. \ref{fig:geom1})} 27 28 There are several ideas based on SP radiation, such as compact free electron laser \cite{FreeElLaser} and non-invasive bunch profile measurement methods [insert citation]. 29 30 Several models \cite{compsprKarlovetsPotylitsyn} of SP radiation intensity distribution were proposed. Though there are experiment [insert citation] for each of these models, that agrees with theory, it has been pointed out in \cite{sprpwKarlovetsPotylitsyn} that there should be interference effects that affects predicted intensities. 30 Where $ \lambda $ is the wavelength of the radiation, $ d $ is the period of the grating, $ n $ is the order of the radiation and $ \theta $ is the polar observation angle (see Fig. \ref{fig:geom1}). 31 32 There are several ideas of applications based on SP radiation, including non-invasive bunch profile measurement methods \cite{NIMA_SP_2014}. 33 34 Several models \cite{compsprKarlovetsPotylitsyn} of SP radiation intensity distribution were proposed. Though there are experiment for each of these models, that agrees with these theory a comparison of these models is important to discriminate them experimentally. 35 36 It has also been shown in \cite{sprpwKarlovetsPotylitsyn} that the predicted intensities should be affected by interference effects. 31 37 32 38 \begin{figure}[!htb] … … 52 58 \section{Models} 53 59 54 Surface Current (SC) and Resonant Diffraction Radiation (RDR) models presented in \cite{compsprKarlovetsPotylitsyn} as a semi-analytical equations, which could be easily calculated, so they are likely to be used in the SP radiation simulations. But those expressions are achieved with assumptions thatdetector is infinitely far from the source of radiation and grating strips have infinite length.55 56 Karlovets and Poptylitsyn in their work \cite{sprpwKarlovetsPotylitsyn} proposed more basic model of SP radiation. The idea was to use Backward~Diffraction~Radiation~(BDR), described in \cite{trVerzilov}, and calculate intensity on the detector point as interference of the waves from each point of the grating. Using this approach automatically includes grating sizes and source-detector distance. The problem of using this method is long computation time, as the equations for intensity of SP radiation are expressed through double integrals.60 The Surface Current (SC) and Resonant Diffraction Radiation (RDR) models are presented in \cite{compsprKarlovetsPotylitsyn} as a semi-analytical equations, which could be easily calculated, so they are easy to use in the SP radiation simulations. However those expressions are achieved with the assumption that the detector is infinitely far from the source of radiation and grating strips have infinite length. 61 62 Karlovets and Poptylitsyn in their work \cite{sprpwKarlovetsPotylitsyn} proposed a basic model of SP radiation. The idea was to use Backward~Diffraction~Radiation~(BDR), described in \cite{trVerzilov}, and calculate the intensity on the detector point as interference of the waves from each point of the grating. Using this approach automatically includes grating sizes and source-detector distance. The problem of using this method is long computation time, as the equations for intensity of SP radiation are expressed through double integrals. 57 63 58 64 It is also must be mentioned that, unlike SC and RDR models, BDR model proposed in \cite{sprpwKarlovetsPotylitsyn} does not include blaze angle $\theta_0$ (see Fig. \ref{fig:geom2}). It could be easily done, by changing every term of the Eq.~8 in \cite{sprpwKarlovetsPotylitsyn}, that represents beam-grating separation, by variable that depends on the position over the grating. For example: … … 102 108 \end{split} 103 109 \end{equation} 110 104 111 \subsubsection{Far zone} 105 Far zone is reference to the range of distances between the source and the detector at which interference effects are not visible, alternatively it could be said, that it is distances at which we see our grating as single point of radiation. Criterion of far zone isobtained by Karlovets and Potylitsyn in \cite{sprpwKarlovetsPotylitsyn}:112 The far zone is the range of distances between the source and the detector at which interference effects are not visible, alternatively it could be said, that it is distances at which we see our grating as single point of radiation. Criterion for the far zone has been obtained by Karlovets and Potylitsyn in \cite{sprpwKarlovetsPotylitsyn}: 106 113 \begin{equation}\label{eq:far_crit} 107 114 R_0 \gg N^2 d (1+\cos{\theta}) … … 110 117 Using this approximations it is easy to transform Eq.~(\ref{eq:full_model}) into two separated single integrals, which will significantly decrease computation time. 111 118 \subsubsection{Short grating strips} 112 It could happen, that our's detector is closer than given far zone criterion Eq.~(\ref{eq:far_crit}). In that case smaller parameter could be used such as strip width "a". It is simple to calculate criterion for this case, it will be:119 When the detector is closer that the far zone limit different assumption are possible if the following condition is met: 113 120 \begin{equation}\label{eq:short_crit} 114 121 R_0 \gg \frac{d}{4(1-\cos{\theta})} … … 117 124 118 125 \subsection{Experimental parameters} 119 As initial data for simulation it was decided to use real experiments, as it would be possible to compare theory with experiment later. The experiments are SPESO at Soleil synchrotron and E203 at SLAC. For convenience the initial parameters are presented in the table below.126 As parameters for our simulations it was decided to use real experiments, as it would be possible to compare theory with experiment later. The experiments are SPESO at Soleil Synchrotron and E-203 at SLAC. For convenience the initial parameters are presented in the table below. 120 127 \begin{center} 121 128 \begin{tabular}{|l|c|c|c|c|} 122 129 \hline 123 130 % after \\: \hline or \cline{col1-col2} \cline{col3-col4} ... 124 Parameter/Experiment & SPESO & E 203 & E 203 & E203 \\ \hline131 Parameter/Experiment & SPESO & E-203 & E-203 & E-203 \\ \hline 125 132 $\gamma$ & 200 & 40000 & 40000 & 40000 \\ 126 133 $d, \mu m$ & 10000 & 1500 & 250 & 50 \\ … … 167 174 \end{figure} 168 175 176 As one can see on Fig.~\ref{fig:Phi2} and Fig.~\ref{fig:Phi3} the RDR and SC models produce the same angular distribute and the signal intensity are comparable (within experimental uncertainties). It would there fore be difficult to discriminate experimentally between these models. 177 169 178 \section{Interference} 170 In far zone models intensity is inverse proportional to the square of distance between source and observer. Picture changes when observer go closer to the source and use full model for BDR. As can be seen at the Fig. \ref{fig:IntensR} Intensity per solid angle is constant at big distances and begins to oscillate at small distances. This means that interference at near source distances depends not only on the angles, but on distance also. And as shown on the \ref{fig:IntensR} interference effect isconsiderable.179 In far zone models the signal intensity is inversely proportional to the square of the distance between the source and the detector. This changes when is closer closer to the source and one must then use the full model for BDR. As can be seen on Fig. \ref{fig:IntensR} the intensity per solid angle is constant at big distances and begins to oscillate at small distances. This means that the interference at near source distances depends not only on the angles, but on the distance also. And as shown on the \ref{fig:IntensR} the interference effect can be considerable. 171 180 172 181 \begin{figure}[!htb] … … 183 192 \end{figure} 184 193 185 It is important to know if we should consider interference effects in our calculations or no , for this we have criterion for determining if we are in the far zone or not is \ref{eq:far_crit}. For easier understanding it could be visualized as curve in the two dimensional plotFig. \ref{fig:FarPlot}, where ZY plane is $X_T$$Z_T$ on Fig. \ref{fig:geom1}.194 It is important to know if we should consider interference effects in our calculations or not, for this we have criterion for determining if we are in the far zone or not is Eq. \ref{eq:far_crit}. For easier understanding it could be visualized as curve in the two dimensional plot shown on Fig. \ref{fig:FarPlot}, where ZY plane is $X_T$$Z_T$ on Fig. \ref{fig:geom1}. 186 195 \begin{figure}[!htb] 187 196 \minipage{0.49\textwidth} … … 196 205 \end{figure} 197 206 \section{Summary} 207 We have studied two important effect that can change the intensity of the Smith-Purcell Radiation and could thus affect its usability as a longitudinal profile monitor. 208 We have compared the two leading models under experimental conditions and shown that it would not be possible to discriminate them experimentally. We have also shown that interferences in the near field zone have a significant effect and must be taken into account to estimate the correct intensity of SPR. 198 209 199 210 \bibliographystyle{phaip} -
papers/2015_FrUa/models/FrenchUkrainianW2015Nov/bibliography.bib
r300 r301 263 263 doi = {10.1103/PhysRevE.73.026501}, 264 264 url = {http://link.aps.org/doi/10.1103/PhysRevE.73.026501} 265 } 265 } 266 267 @article{NIMA_SP_2014, 268 Author = {H.L. Andrews and F. Bakkali Taheri and J. Barros and R. Bartolini and L. Cassinari and C. Clarke and S. Le Corre and N. Delerue and G. Doucas and N. Fuster-Martinez and I. Konoplev and M. Labat and C. Perry and A. Reichold and S. Stevenson and M. Vieille Grosjean}, 269 Date-Added = {2014-10-10 01:03:36 +0000}, 270 Date-Modified = {2014-10-10 01:03:52 +0000}, 271 Doi = {http://dx.doi.org/10.1016/j.nima.2013.11.090}, 272 Issn = {0168-9002}, 273 Journal = {Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment}, 274 Keywords = {Synchrotron \{SOLEIL\}}, 275 Note = {Proceedings of the first European Advanced Accelerator Concepts Workshop 2013}, 276 Number = {0}, 277 Pages = {212 - 215}, 278 Title = {Longitudinal profile monitors using Coherent Smith--Purcell radiation}, 279 Url = {http://www.sciencedirect.com/science/article/pii/S0168900213016550}, 280 Volume = {740}, 281 Year = {2014}, 282 Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0168900213016550}, 283 Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.nima.2013.11.090}} 284 285
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