Changeset 578 in ETALON

Timestamp:

Apr 28, 2016, 4:20:18 PM (8 years ago)

Author:

delerue

Message:

Comparison paper updated

Location:

papers/2016_IPAC/2016_IPAC_Malovytsia_ModelComparison

Files:

• MOPMB004.pdf (modified) (previous)
• MOPMB004.tex (modified) (4 diffs)

papers/2016_IPAC/2016_IPAC_Malovytsia_ModelComparison/MOPMB004.tex

@@ -193 +193 @@
         \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
          as a sum of the virtual plain waves~\cite{Mikaelian72,Haeberl94}, that will become real after scattering on the grating. 
-         The expression for the intensity of this model is given in the~\cite{p041}.
+         The expression for the intensity of this model is given in reference~\cite{p041}.
         
                         \begin{equation}\label{eq:BDR}
@@ -235 +235 @@
 of the second order, $\chi$ equals $1$ on the grating and $0$ in the gap, $\mathcal{R}(X_T,Z_T,\theta,\phi)$ is the grating-detector distance.
 
- 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.
+ In reference~\cite{p041}, by assuming the distances from the grating to be infinite, the authors also derived the far-zone approximation of the RRR model.
  
 %       Although authors of the~\cite{p041} chose geometry of a plain strips
@@ -291 +291 @@
          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 $10^\circ$. 
          
-         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.
+         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 a 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.
          
 %        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.
@@ -352 +352 @@
          
          \section{Conclusions}
-        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 is required.  More detailed consideration of the grating profile and width in the GFW simulation gives the intensity 10 times bigger. The ratios between the models are not changing much with the parameters~(except the observation angle), which means that it is possible to introduce a parameter-independent model correction factor.
+        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 is required.  More detailed consideration of the grating profile and width in the GFW simulation gives the intensity 10 times bigger. The ratios between the models are not changing much with the parameters~(except for the observation angle). This work will allow us to estimate the error due to theoretical uncertainty when SPR is used for longitudinal profile reconstruction.
         % The calculations were also done for the E203 experiment~\cite{p046} at FACET at SLAC, and the  conclusions were similar.