Changeset 548 in ETALON for papers/2016_IPAC/2016_IPAC_Malovytsia_ModelComparison/MOPMB004.tex
- Timestamp:
- Apr 25, 2016, 7:48:28 PM (8 years ago)
- File:
-
- 1 edited
Legend:
- Unmodified
- Added
- Removed
-
papers/2016_IPAC/2016_IPAC_Malovytsia_ModelComparison/MOPMB004.tex
r500 r548 3 3 %boxit, 4 4 %titlepage, % separate title page 5 refpage % separate references5 %refpage % separate references 6 6 ]{jacow} 7 7 … … 68 68 \title{Comparison of the Smith-Purcell radiation yield for different models} 69 69 70 \author{N. Delerue\textsuperscript{1}, M.S.Malovytsia\textsuperscript{1,2}\\70 \author{N.~Delerue\textsuperscript{1}, M.~S.~Malovytsia\textsuperscript{1,2}\\ 71 71 \textsuperscript{1}Laboratoire de l'Accélérateur Linéaire, Université Paris-Sud, Orsay, France\\ 72 72 \textsuperscript{2}Kharkiv National University, Kharkov, Ukraine} … … 83 83 and shown that they are in agreement 84 84 within the experimental errors. 85 To have a better agreement86 between predictions and experimental measurements87 we also report on the interference effects88 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. 89 89 \end{abstract} 90 90 … … 100 100 To measure reliably the length of such short bunches with destroying them several approaches are possible: 101 101 \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), 105 105 uses a grating to induce the emission of radiation. It 106 106 has the advantage of dispersing the radiation at the point of emission and therefore being more immune to background noise. It is described below. … … 156 156 157 157 \item The Surface Current (SC) 158 model~\cite{ SCDoucas98}, that explains SPR through the currents that are being induced158 model~\cite{gfw}, that explains SPR through the currents that are being induced 159 159 on the surface of the grating by a charge passing nearby. This theory has proven to be 160 160 in a good agreement with experiments for energies from a few MeV to 28.5 GeV~\cite{p010, p019, p043, p026}. … … 172 172 $R^2$ is a grating efficiency parameter, that depends on the radiation angle and blaze angle. 173 173 174 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. 174 175 175 176 \item The Resonant Diffraction Radiation (RDR) model, … … 189 190 190 191 \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. 192 193 The expression for the intensity of this model is given in the~\cite{p041}. 193 194 … … 234 235 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. 235 236 236 Although authors of the~\cite{p041} chose geometry of a plain strips237 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}). 238 239 \end{itemize} 239 240 … … 256 257 $ n $ & 1 & mm & The order of the radiation\\ \hline 257 258 $ \theta_0 $ & 30& degree & The blaze angle \\ \hline 258 $ Const $ & 2 .5& mm$^{-2}$ & The normalization constant for the RRR model \\ \hline259 $ Const $ & 22.4 & mm$^{-2}$ & The normalization constant for the RRR model \\ \hline 259 260 \end{tabular} 260 261 \caption{Parameters for the simulation of the SPESO experiment} … … 263 264 264 265 265 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} 282 281 \begin{figure}[!ht] 283 282 \centering 284 \includegraphics[width=0. 45\textwidth]{MOPMB004f4.png}283 \includegraphics[width=0.5\textwidth]{MOPMB004f2.png} 285 284 \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} 286 285 \label{fig:SPESO_theta_RDR_SC_RRR} 287 286 \end{figure} 288 \begin{figure}[!ht]289 \centering290 \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} 294 293 295 294 %======================================================================================================= … … 308 307 % More detailed explanations are presented in the~\cite{p019}. 309 308 310 \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-detector315 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 the317 interference effects.318 \end{enumerate}319 The criterion for far/pre-wave zones separation were calculated in \cite{p041}. The condition for the far320 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 \centering328 \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} 332 331 333 332 334 333 \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. 336 335 337 336 % 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. … … 342 341 %---------------------------------------------------------------------------------------- 343 342 \begin{thebibliography}{99} % Use for 10-99 references 344 345 \bibitem{FELEvt}, 346 P.~Evtushenko \emph{et al.}, 347 ``Bunch length measurements at JLAB FEL'', 348 in \textit{Proc. FEL 2006}, 349 BESSY, Berlin, Germany, Aug.--Sept. 2006, 350 paper THPPH064, pp. 736--739.\\ 351 352 \bibitem{PLASMABerry06} 353 F.-J.~Decker \emph{et al.}, 354 ``Multi-GeV Plasma Wakefield Accelera-tion Experiments'', 355 In: \textit{E-167 Proposal}, 2005, 356 \url{https://www.slac.stanford.edu/grp/rd/epac/Proposal/E167.pdf} 357 \\ 358 359 \bibitem{EOBerden2004} 360 G.~Berden \emph{et al.}, 361 ``Electro-Optic Technique with Improved Time Resolution for Real-Time, Non destructive, Single-Shot Measurements of Femtosecond Electron Bunch Profiles'', 362 \emph{Phys. Rev. Lett.}, vol. 93, 363 p. 114802., Sept. 2004. \\ 364 343 \bibitem{Fitch99} 344 M. J. Fitch \emph{et al.}, 345 ``PICOSECOND ELECTRON BUNCH LENGTH MEASUREMENT BY ELECTRO-OPTIC DETECTION OF THE WAKEFIELD'', 346 in \textit{Proc. PAC’99}, 347 New York, USA, March-Apr.~1999, 348 paper~WEA134, pp.~2181-- 2183.\\ 365 349 \bibitem{EOLimSteff09} 366 B.~Steffen et al., 367 ``Electro-optic time profile monitors for femtosecond electron bunches at the soft x-ray free-electron laser FLASH'', 368 \emph{Phys. Rev. ST Accel. Beams}, vol. 12, 369 p. 032802., Mar. 2009, \\ 370 371 \bibitem{CTRMurokh98} 372 A.~Murokh \emph{et al.}, 373 ``Bunch length measurement of picosecond electron beams from a photoinjector using coherent transition radiation'', 374 \emph{Nucl. Instrum. Methods Phys. Res. Sect. A}, vol. 410, no. 3, 375 pp. 452-–460, 1998 \\ 376 377 350 B.~Steffen et al., 351 ``Electro-optic time profile monitors for femtosecond electron bunches at the soft x-ray free-electron laser FLASH'', 352 \emph{Phys. Rev. ST Accel. Beams}, vol. 12, 353 p. 032802., Mar. 2009, \\ 354 \bibitem{Lai94} 355 R.~Lai, U.~Happek and A.~J.~Sievers, 356 ``Measurement of the longitudinal asymmetry of a charged particle bunch from the coherent synchrotron or transition radiation spectrum'', 357 \emph{Phys. Rev. E}, vol. 50, 358 pp. R4294--R4297, Dec. 1994.\\ 378 359 \bibitem{SP53} 379 S.~J.~Smith and E.~M.~Purcell., 380 ``Visible Light from Localized Surface Charges Moving across a Grating'', 381 \emph{Phys. Rev.}, vol. 92, 382 pp. 1069-–1069., 1953. \\ 383 360 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. \\ 364 \bibitem{Nguyen97} 365 D.~C.~Nguyen, 366 ``Electron Bunch Length Diagnostic With Coherent Smith-Purcell Radiation'', 367 in \emph{Proc. PAC'97}, 368 Vancouver, B.C., Canada, May 1997, 369 paper 97CH36167, pp. 1990--1992. 384 370 \bibitem{p020} 385 J.~H.~Brownell and G.~Doucas., 386 ``Role of the grating profile in Smith-Purcell radiation at high energies'', 387 \emph{Phys. Rev. ST Accel. Beams}, vol. 8, 388 p. 091301., Sept. 2005. \\ 389 371 J.~H.~Brownell and G.~Doucas., 372 ``Role of the grating profile in Smith-Purcell radiation at high energies'', 373 \emph{Phys. Rev. ST Accel. Beams}, vol. 8, 374 p. 091301., Sept. 2005. \\ 390 375 \bibitem{p043} 391 G.~Doucas \emph{et al.}, 392 ``Longitudinal electron bunch profile diagnostics at 45 MeV using coherent Smith-Purcell radiation'', 393 \emph{Phys. Rev. ST Accel. Beams}, vol. 9, 394 p. 092801., Sept. 2006. \\ 395 376 G.~Doucas \emph{et al.}, 377 ``Longitudinal electron bunch profile diagnostics at 45 MeV using coherent Smith-Purcell radiation'', 378 \emph{Phys. Rev. ST Accel. Beams}, vol. 9, 379 p. 092801., Sept. 2006. \\ 396 380 \bibitem{p026} 397 V.~Blackmore \emph{et al.}, 398 ``First measurements of the longitudinal bunch profile of a 28.5 GeV beam using coherent Smith-Purcell radiation'', 399 \emph{Phys. Rev. ST Accel. Beams}, vol. 12, 400 p. 032803., Mar. 2009. \\ 401 381 V.~Blackmore \emph{et al.}, 382 ``First measurements of the longitudinal bunch profile of a 28.5 GeV beam using coherent Smith-Purcell radiation'', 383 \emph{Phys. Rev. ST Accel. Beams}, vol. 12, 384 p. 032803., Mar. 2009. \\ 402 385 \bibitem{p019} 403 G.~Doucas \emph{et al.}, 404 ``Determination of longitudinal bunch shape by means of coherent Smith-Purcell radiation'', 405 \emph{Phys. Rev. ST Accel. Beams}, vol. 5, 406 p. 072802., July 2002. \\ 407 408 386 G.~Doucas \emph{et al.}, 387 ``Determination of longitudinal bunch shape by means of coherent Smith-Purcell radiation'', 388 \emph{Phys. Rev. ST Accel. Beams}, vol. 5, 389 p. 072802., July 2002. \\ 390 \bibitem{p039} 391 V.~Blackmore \emph{et al.}, 392 ``First observation of coherent Smith-Purcell radiation in the highly relativistic regime.'' 393 \emph{Nucl. Instrum. Methods Phys. Res., Sect. B}, vol. 266, no. 17, 394 pp. 3803--3810, 2008. \\ 395 \bibitem{gfw} 396 J.~H.~Brownell, J.~Walsh, G.~Doucas, 397 ``Spontaneous Smith-Purcell radiation described through induced surface currents'', 398 \emph{Phys. Rev. E} vol. 57, 399 pp. 1075--1080, Jan. 1998.\\ 409 400 \bibitem{p010} 410 G.~Doucas \emph{et al.}, 411 ``First observation of Smith-Purcell radiation from relativistic electrons'', 412 \emph{Phys. Rev. Lett.}, vol. 69, 413 pp. 1761--1764, Sept. 1992. \\ 414 415 \bibitem{SCDoucas98} 416 J.~H.~Brownell, J.~Walsh and G.~Doucas., 417 ``Spontaneous Smith-Purcell radiation described through induced surface currents'', 418 \emph{Phys. Rev. E}, vol. 57, 419 pp. 1075–-1080., Jan. 1998. \\ 420 421 \bibitem{SPExpWoods95} 422 K.~J.~Woods \emph{et al.}, 423 ``Forward Directed Smith-Purcell Radiation from Relativistic Electrons'', 424 \emph{Phys. Rev. Lett.}, vol. 74, 425 pp. 1761–1764., Sept. 1992. \\ 401 G.~Doucas \emph{et al.}, 402 ``First observation of Smith-Purcell radiation from relativistic electrons'', 403 \emph{Phys. Rev. Lett.}, vol. 69, 404 pp. 1761--1764, Sept. 1992. \\ 405 \bibitem{p021} 406 D.~V.~Karlovets and A.~P.~Potylitsyn. 407 ``Comparison of Smith-Purcell radiation models and criteria for their verification'', 408 \emph{Phys. Rev. ST Accel. Beams}, vol. 9, 409 p. 080701, Aug. 2006. \\ 410 \bibitem{Mikaelian72} 411 M.~L.~Ter-Mikaelian., 412 \emph{High Energy Electromagnetic Processes in Condensed Media}. 413 New York, USA: 414 John Wiley and Sons Inc, 1972. \\ 415 \bibitem{Haeberl94} 416 O.~Haeberl\'e \emph{et al.}, 417 ``Calculations of Smith-Purcell radiation generated by electrons of 1\char21{}100 MeV'', 418 \emph{Phys. Rev. E}, vol. 49, 419 pp. 3340--3352, Apr. 1994. \\ 420 \bibitem{p041} 421 D.~V.~Karlovets and A.~P.~Potylitsyn., 422 ``Smith-Purcell radiation in the ``pre-wave'' zone”, 423 \emph{JETP Letters}, vol. 84, no. 9, 424 pp. 489-–493, 2006. \\ 425 \bibitem{SPESO} 426 N.~Delerue \emph{et al.}, 427 `First Measurements of Coherent Smith-Purcell Radiation in the SOLEIL Linac'', 428 paper MOPMB002, these proceedings.\\ 429 \bibitem{p046} 430 N.~Delerue \emph{et al.}, 431 ``Electron Bunch Profile Diagnostics in the Few fs Regime using Coherent Smith-Purcell Radiation'', 432 in \textit{Proc. IPAC’11}, 433 San Sebastian, Spain, Sept. 2011, 434 paper MOP057, pp. 567--569.\\ 435 426 436 427 \bibitem{p021} 428 D.~V.~Karlovets and A.~P.~Potylitsyn. 429 ``Comparison of Smith-Purcell radiation models and criteria for their verification'', 430 \emph{Phys. Rev. ST Accel. Beams}, vol. 9, 431 p. 080701, Aug. 2006. \\ 432 433 \bibitem{Mikaelian72} 434 M.~L.~Ter-Mikaelian., 435 \emph{High Energy Electromagnetic Processes in Condensed Media}. 436 New York, USA: 437 John Wiley and Sons Inc, 1972. \\ 438 439 \bibitem{p041} 440 D.~V.~Karlovets and A.~P.~Potylitsyn., 441 ``Smith-Purcell radiation in the ``pre-wave'' zone”, 442 \emph{JETP Letters}, vol. 84, no. 9, 443 pp. 489-–493, 2006. \\ 444 445 \bibitem{p013} 446 V.~A~Verzilov., 447 ``Transition radiation in the pre-wave zone'', 448 \emph{Physics Letters A}, vol. 273, no. 1-2, 449 pp. 135–140, 2000. \\ 450 451 \bibitem{p039} 452 V.~Blackmore \emph{et al.}, 453 ``First observation of coherent Smith-Purcell radiation in the highly relativistic regime.'' 454 \emph{Nucl. Instrum. Methods Phys. Res., Sect. B}, vol. 266, no. 17, 455 pp. 3803--3810, 2008. \\ 456 457 \bibitem{p046} 458 N.~Delerue \emph{et al.}, 459 ``Electron Bunch Profile Diagnostics in the Few fs Regime using Coherent Smith-Purcell Radiation'', 460 in \textit{Proc. IPAC’11}, 461 San Sebastian, Spain, Sept. 2011, 462 paper MOP057, pp. 567--569.\\ 463 464 \bibitem{SPESO} 465 N.Delerue et al., MOPMB002, ''First Measurements of Coherent Smith-Purcell Radiation in the SOLEIL Linac'', these proceedings. 437 % \bibitem{FELEvt}, 438 % P.~Evtushenko \emph{et al.}, 439 % ``Bunch length measurements at JLAB FEL'', 440 % in \textit{Proc. FEL 2006}, 441 % BESSY, Berlin, Germany, Aug.--Sept. 2006, 442 % paper THPPH064, pp. 736--739.\\ 443 % \bibitem{PLASMABerry06} 444 % F.-J.~Decker \emph{et al.}, 445 % ``Multi-GeV Plasma Wakefield Accelera-tion Experiments'', 446 % In: \textit{E-167 Proposal}, 2005, 447 % \url{https://www.slac.stanford.edu/grp/rd/epac/Proposal/E167.pdf}\\ 448 % \bibitem{EOBerden2004} 449 % G.~Berden \emph{et al.}, 450 % ``Electro-Optic Technique with Improved Time Resolution for Real-Time, Non destructive, Single-Shot Measurements of Femtosecond Electron Bunch Profiles'', 451 % \emph{Phys. Rev. Lett.}, vol. 93, 452 % p. 114802., Sept. 2004. \\ 453 % \bibitem{CTRMurokh98} 454 % A.~Murokh \emph{et al.}, 455 % ``Bunch length measurement of picosecond electron beams from a photoinjector using coherent transition radiation'', 456 % \emph{Nucl. Instrum. Methods Phys. Res. Sect. A}, vol. 410, no. 3, 457 % pp. 452-–460, 1998 \\ 458 % 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. \\ 464 % \bibitem{SPExpWoods95} 465 % K.~J.~Woods \emph{et al.}, 466 % ``Forward Directed Smith-Purcell Radiation from Relativistic Electrons'', 467 % \emph{Phys. Rev. Lett.}, vol. 74, 468 % pp. 1761–1764., Sept. 1992. \\ 469 % \bibitem{p013} 470 % V.~A~Verzilov., 471 % ``Transition radiation in the pre-wave zone'', 472 % \emph{Physics Letters A}, vol. 273, no. 1-2, 473 % pp. 135–140, 2000. \\ 474 % 475 476 466 477 467 478 \end{thebibliography}
Note: See TracChangeset
for help on using the changeset viewer.