deletions | additions       diff --git a/Abstract.tex b/Abstract.tex  index e96cde0..6aba4c4 100644  --- a/Abstract.tex  +++ b/Abstract.tex 
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\begin{abstract}  Various MHD (magnetohydrodynamic) equilibrium tools, some of which being recently developed or considerably updated, are used on the COMPASS tokamak at IPP Prague. MHD equilibrium is a fundamental property of the tokamak plasma, whose knowledge is required for many diagnostics and modelling tools. Proper benchmarking and validation of equilibrium tools is thus key for interpreting and planning tokamak experiments. We present here benchmarks and comparisons to experimental data of the EFIT++ reconstruction code [L.C. Appel et al., EPS 2006, P2.184], the free-boundary equilibrium code FREEBIE [J.-F. Artaud, S.H. Kim, EPS 2012, P4.023], and a rapid plasma boundary reconstruction code VacTH [B. Faugeras et al., PPCF 2014, accepted]. 114010].  We demonstrate that FREEBIE can calculate the equilibrium and corresponding poloidal field (PF) coils currents consistently with EFIT++ reconstructions from experimental data. Both EFIT++ and VacTH can reconstruct equilibria generated by FREEBIE from synthetic, optionally noisy diagnostic data. Hence, VacTH is suitable for real-time control. Optimum reconstruction parameters are estimated. \end{abstract}  diff --git a/Conclusions.tex b/Conclusions.tex  index 56800c8..a3a6c40 100644  --- a/Conclusions.tex  +++ b/Conclusions.tex 
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\label{sec:conclusions}  Two new codes---FREEBIE and VacTH---have been successfully set up on COMPASS, which enabled to perform an extensive cross-benchmarking and validation of free-boundary equilibrium tools. We show that FREEBIE can predict equilibria that are consistent with EFIT++ reconstructions from experimental data. FREEBIE model equilibria, either with linear $p'$ and $FF'$ profiles or with pressure profiles from Thomson scattering diagnostic, then served to assess the credibility of EFIT++ reconstructions.   We show that magnetic reconstruction Magnetic  EFIT++ reconstruction  with linear $p'$ and $FF'$ features a relatively good accuracy of 1 -- 2 cm in the plasma shapereconstruction  but introduces systematic errors both in the shape and in internal plasma parameters, such as $W$, $l_{\mathrm i}$, $\beta_{\mathrm p}$ or $q_0$. The reconstruction properties can be significantly improved by using quadratic $p'$ for elongated elliptical  and divertor plasmas, which removes the systematic error and also improves the LCFS reconstruction. EFIT++ converges in 100~\% cases in this regime. Optimum parameters for VacTH have been estimated. In particular, the optimum number of harmonics is 4 otherwise VacTH fails to converge in many cases, even without any input error. 16 flux loops and only 8 magnetic probes  must be used as VacTH input. With less flux loops or more magnetic probes the code performs significantly worse. We conclude that VacTH is a promising tool pertinent for a real-time feedback control of the plasma shape. shape, although its robustness and accuracy should be improved.  % section conclusions (end)  diff --git a/Introduction.tex b/Introduction.tex  index 7cbfbe1..d731382 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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\label{sec:introduction}  We report here on validation and verification of tokamak equilibrium tools used for the COMPASS tokamak \cite{compass2006}. We particularly focus on fundamental global plasma parameters and the shapes of magnetic flux surfaces, which are crucial in diagnostics interpretation and other analyses.   EFIT++ \cite{efitpp2006} is used for routine equilibrium reconstruction on COMPASS. FREEBIE \cite{freebie2012} is a recent free-boundary equilibrium code; FREEBIE enables predictive equilibrium calculation consistent with the poloidal field (PF) components of the tokamak. In this study, FREEBIE is used in the so-called inverse mode, which predicts PF coils currents from a give given  plasma boundary and profiles. The third code employed in this study is VacTH \cite{vacthref}, which provides a fast reconstruction of the plasma boundary from magnetic measurements using a toroidal harmonics basis. In order to verify and validate the aforementioned tools, we analyse EFIT++ and VacTH reconstructions of equilibria constructed with FREEBIE. Synthetic diagnostics (e.g., magnetic probes or flux loops) with optional artificial errors provide inputs for the reconstructions.   diff --git a/JUrban_SOFT2014.pdf b/JUrban_SOFT2014.pdf  index 44bf19e..a6c9ac0 100644  Binary files a/JUrban_SOFT2014.pdf and b/JUrban_SOFT2014.pdf differ diff --git a/Procedure.tex b/Procedure.tex  index eecbf41..def27fc 100644  --- a/Procedure.tex  +++ b/Procedure.tex 
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In the second step, FREEBIE inputs $I_\mathrm{p}$, $p'\left( {\bar \psi } \right)$ and $FF'\left( {\bar \psi } \right)$ profiles, the plasma boundary coordinates and an initial guess for the PF coils currents. Here, $p$ is the plasma pressure, $F = RB_\phi$ and $\bar\psi$ is the normalized poloidal magnetic flux ($\bar\psi = 0$ on the magnetic axis and $\bar\psi = 1$ on the plasma boundary). $p'$ comes either from the EFIT++ reconstruction or from Thomson scattering pressure profile $p_\mathrm{TS} = 1.3 n_\mathrm{e} p_\mathrm{e}$. FREEBIE then seeks a solution to the Grad-Shafranov equation, including the PF coils currents, which minimizes the given plasma shape constraint. (This regime is called the inverse mode.)  It should be noted here that to set up a free-boundary equilibrium code, a rather complete machine description is necessary (in particular, the PF coils geometry and circuits, limiter, vessel and other passive PF elements and magnetic diagnostics configuration). We adopted the description that was already available for EFIT++ and transformed it to ITM CPO's (Integrated Tokamak Modelling Consistent Physical Objects) Objects \cite{Manduchi2008})  structures, which are subsequently either used directly in FREEBIE or converted to VacTH specific input format. FREEBIE can naturally output arbitrary synthetic diagnostics. We use here additional 24 poloidally and 24 radially oriented partial Rogowski coils (which are actually mounted on COMPASS) and an artificial set of 16 flux loops located at the same positions as the basic magnetic probes. Hereafter, the number of magnetic probes and flux loops are denoted $n_\mathrm{mp}$ and $n_\mathrm{fl}$. $n_\mathrm{mp}=16$, $n_\mathrm{fl}=4$ refers the basic set of magnetic measurements, $n_\mathrm{mp}=64$ refers to a set of all presently mounted partial Rogowski coils on COMPASS and $n_\mathrm{fl}=16$ implies artificial flux loops positioned at the same locations as the basic magnetic probes.  In FREEBIE inputs can be modified in  the optional third step, an artificial random noise is added to the calculated values of $I_\mathrm{p}$, magnetic probes and flux loops. step.  Inparticular, for a given noise level $\epsilon$, $\tilde X = \left( {1 + U\left( { - \epsilon, \epsilon} \right)^\mathrm{T}} \right)X$, where $X$ is a row vector of the synthetic diagnostics data and $U\left( { - \epsilon, \epsilon} \right)$ is a random vector of  the same shape as $X$ with a uniform distribution on $\left( { - \epsilon, \epsilon} \right)$. following analysis, we particularly use realistic pressure profiles, estimated by Thomson scattering diagnostics.  The final fourth step consists of reconstructing the equilibria form synthetic FREEBIE data using EFIT++ and VacTH. An artificial random noise is added to the calculated values of $I_\mathrm{p}$, magnetic probes and flux loops. In particular, for a given noise level $\epsilon$, $\tilde X = \left( {1 + U\left( { - \epsilon, \epsilon} \right)^\mathrm{T}} \right)X$, where $X$ is a row vector of the synthetic diagnostics data and $U\left( { - \epsilon, \epsilon} \right)$ is a random vector of the same shape as $X$ with a uniform distribution on $\left( { - \epsilon, \epsilon} \right)$.  The reconstructions are then compared to the original equilibrium, focusing on global parameters and geometry. Scans are performed over noise levels ($\epsilon$) and selected code parameters: $p'$ and $FF'$ polynomial degrees in EFIT++ ($n_{p'}$, $n_{FF'}$) and the number of harmonics ($n_P$, $n_Q$) in VacTH. The following quantities are used for the comparison. \begin{table}[!h]  \begin{tabular}{ll}  $R_{\mathrm ax}$, $Z_{\mathrm ax}$ & $R,Z$ coordinates of the magnetic axis \\  diff --git a/RZstats.pdf b/RZstats.pdf  index 255c8e0..09afedf 100644  Binary files a/RZstats.pdf and b/RZstats.pdf differ diff --git a/Results.tex b/Results.tex  index 4c8faac..228559d 100644  --- a/Results.tex  +++ b/Results.tex 
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\begin{figure*}[!htb]  \centering %\begin{center}  \hfill{}  \includegraphics[width=18cm]{example_6962.pdf} \includegraphics[width=17.5cm]{example_6962.pdf}  \hfill{}  %\end{center}  \caption{EFIT++ reconstructed pressure profiles and contours of $\bar\psi=\left(0.5,1\right)$ and VacTH LCFS from FREEBIE data, shot 6962 with Thomson scattering pressure profiles. EFIT++ parameters: $n_\mathrm{mp} = 16$, $n_\mathrm{fl} = 4$, $n_{FF'} = 1$. VacTH parameters: $n_\mathrm{mp} = 8$, $n_\mathrm{fl} = 16$, $n_P = n_Q = 4$. 3~\% random input data noise is used in the case of VacTH and EFIT++ with $n_{p'} = 2$, zero noise otherwise.} 
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\end{figure*}  We have selected five time slices from COMPAS shots 4275 and 6962 (i.e. 10 cases in total) for the analysis. These cases include circular, elongated elliptical (limited)  and diverted plasmas with different currents. \subsection{Example cases} 
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\begin{figure*}[!htb]  \centering %\begin{center}  \hfill{}  \includegraphics[width=18cm]{RZstats.pdf} \includegraphics[width=17.5cm]{RZstats.pdf}  \hfill{}  %\end{center}  \caption{Absolute errors in LCFS extents for convergent cases. EFIT++ results in the first row, VacTH in the second row. S1 denotes linear $p'$ and $FF'$ in EFIT++ as well as FREEBIE, s2 denotes TS pressure profiles in FREEBIE and $n_{p'} = n_{FF'} = 1$ in EFIT++, s3 denotes TS pressure profiles in FREEBIE and $n_{p'} = 2$ in EFIT++. Full lines show the means. VacTH parameters are $n_P=n_Q=4$, ``8 mp, 16 fl'' denotes $n_\mathrm{mp}=8$, $n_\mathrm{fl}=16$. Input error is calculated as an average of $I_{\rm{p}}$, magnetic probes and flux loops values. %  Zero input error data are scattered for a better visibility.} visibility.  }  \label{fig:RZstats}  \end{figure*}  \begin{figure*}[!htb]  \centering %\begin{center}  \hfill{}  \includegraphics[width=18cm]{kinetic_stats_opt.pdf} \includegraphics[width=17.5cm]{kinetic_stats_opt.pdf}  \hfill{}  %\end{center}  \caption{Internal plasma parameters relative errors for EFIT++ reconstructions using $n_{p'}=n_{FF'}=1$ in the top row and more optimized $n_{p'}$ in the bottom row. Zero input error data are scattered for a better visibility.} 
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\subsection{Statistical analysis} % (fold)  \label{sub:statistical_analysis}  In order to get a global overview of EFIT++ and VacTH reconstruction properties on COMPASS, we perform a scan over major code parameters and signal noise levels. In particular, $n_{p',FF'} = 1,2 $, $(n_\mathrm{mp}, n_\mathrm{fl}) = (16, 4), (64, 4), (8, 16)$, $\epsilon = 0, 0.02, 0.04, 0.06$, $n_{P,Q} = 4, 5, 6$. The same cases as above (time slices of shots 4275 and 6962) are used as target equilibria. For shot 6962, equilibria with TS pressure profiles and with linear $p'$ and $FF'$. $FF'$ are used.  This means there is 15 different target equilibria in total. Absolute errors of the reconstructed LCFS extents for convergent cases from the scan are shown in Fig. \ref{fig:RZstats}. We can observer observe  that the LCFS reconstructed with EFIT++ for target linear $p'$ and $FF'$ profiles (selection 1) are within 1~cm errors. There are, however, cases with up to 3 cm errors in $Z_{\rm{min}}$ for the more realistic TS pressure profiles (selection 2) if $n_{p'}=1$ is used. This error can be reduced by using $n_{p'}=2$. Input errors do not pose major difficulties for EFIT++. VacTH is performing reasonably well for its most favourable diagnostic set of 8 magnetic probes and 16 flux loops and $n_P = n_Q = 4$. With a higher number of harmonics or with less flux loops, VacTH becomes unreliable and yields significant errors. Unfortunately, only 4 flux loops are currently available on COMPASS. In fact, it is easier for VacTH to fit magnetic probes than flux loops  An additional optimization of the fitting weights or algorithm is probably needed. The current behaviour might be quite anti-intuitive as VacTH performs significantly worse with 16 flux loops and 16 or 64 magnetic probes in comparison to 16 flux loops and only 8 magnetic probes.   EFIT++ internal plasma parameters reconstruction results are shown in Fig. \ref{fig:kinetic_stats}. It shows that purely magnetic reconstruction with $n_{p'}=n_{FF'}=1$ introduces (except for $I_{\rm{p}}$) a systematic error for realistic pressure profiles, i.e. for plasmas that do not have the same profile parametrization.   It is known that magnetic reconstruction with EFIT is difficult for small circular plasmas (without additional constraints, particularly the stored energy) \cite{efit1985}.  This suggests that using $n_{p'}=1$ for circular plasmas and $n_{p'}=2$ for elongated elliptical  and diverted plasmas might lead to better results. This is demonstrated in the bottom row of Fig. \ref{fig:kinetic_stats}. Reconstructions with such optimized parameters do not suffer from the systematic error; however, they generally increase the error bars for target equilibria with linear $p'$ and $FF'$, especially for $q_0$. It is also notable that $\delta l_{\rm{i}} \cong 0.1$ for all $n_{p'}=n_{FF'}=1$ reconstructions.  \begin{figure}  diff --git a/bibliography/biblio.bib b/bibliography/biblio.bib  index 57a57fb..d2fd7d6 100644  --- a/bibliography/biblio.bib  +++ b/bibliography/biblio.bib 
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Pages = {P2.184},  Year = {2006} }  %% hal-00862399, version 2  %% http://hal.archives-ouvertes.fr/hal-00862399  @article{vacthref,  hal_id = {hal-00862399},  url = {http://hal.archives-ouvertes.fr/hal-00862399},  title = {{2D interpolation and extrapolation of discrete magnetic measurements with toroidal harmonics for equilibrium reconstruction in a Tokamak}},  author = {Faugeras, Blaise and Blum, Jacques and Boulbe, C{\'e}dric and Moreau, Philippe and Nardon, Eric},  abstract = {{We present a method based on the use of toroidal harmonics and on a modelization of the poloidal field coils and divertor coils for the 2D interpolation and extrapolation of discrete magnetic measurements in a Tokamak. The method is generic and can be used to provide Cauchy boundary conditions needed as input by a fixed domain equilibrium reconstruction code like Equinox. It can also be used to extrapolate the magnetic measurements in order to compute the plasma boundary itself. The proposed method and algorithm are detailed in the paper and results from numerous numerical experiments are presented. The method is foreseen to be used in the real time plasma control loop on the WEST Tokamak.}},  language = {English},  affiliation = {Laboratoire Jean Alexandre Dieudonn{\'e} - JAD , CASTOR - INRIA Sophia Antipolis , Institut de Recherche sur la Fusion par confinement Magn{\'e}tique (ex DRFC) - IRFM},  pages = {accepted},  journal = {Plasma Physics and Controlled Fusion},  audience = {international },  year = {2014},  pdf = {http://hal.archives-ouvertes.fr/hal-00862399/PDF/vacth.pdf},  }  @article{vacthref,  Author = {Faugeras, B. and Blum, J. and Boulbe, C. and Moreau, P. and Nardon, E.},  Title = {{2D} interpolation and extrapolation of discrete magnetic measurements with toroidal harmonics for equilibrium reconstruction in a tokamak},  Journal = {Plasma Physics and Controlled Fusion},  Volume = {56},  Number = {11},  Pages = {114010},  Abstract = {We present a method based on the use of toroidal harmonics and on a modelization of the poloidal field coils and divertor coils for the 2D interpolation and extrapolation of discrete magnetic measurements in a tokamak. The method is generic and can be used to provide the Cauchy boundary conditions needed as input by a fixed domain equilibrium reconstruction code like Equinox (Blum et al 2012 J. Comput. Phys. 231 960-80). It can also be used to extrapolate the magnetic measurements in order to compute the plasma boundary itself. The proposed method and algorithm are detailed in this paper and results from numerous numerical experiments are presented. The method is foreseen to be used in the real-time plasma control loop on the WEST tokamak (Bucalossi et al 2011 Fusion Eng. Des. 86 684-8).},  Keywords = {tokamak  plasma equilibrium  plasma boundary  toroidal harmonics  magnetic measurements  inverse problem  real-time  current-density  tore-supra  plasma  identification  expansion  shape  diagnostics  code  flux},  Year = {2014} }  @article{ 
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Year = {1985} }  @article{  Manduchi2008,  Author = {Manduchi, G. and Iannone, F. and Imbeaux, F. and Huysmans, G. and Lister, J. B. and Guillerminet, B. and Strand, P. and Eriksson, L. G. and Romanelli, M. and Programme, ITM TF Work},  Title = {A universal access layer for the integrated Tokamak Modelling Task Force},  Journal = {Fusion Engineering and Design},  Volume = {83},  Number = {2-3},  Pages = {462-466},  Abstract = {The Integrated Tokamak Modelling (ITM) Task Force aims at providing a suite of codes for preparing and analyzing future ITER discharges. In the framework of the ITM, the universal access layer (UAL) provides the capability of storing and retrieving data involved in simulation. The underlying data structure is hierarchical and the granularity in data access is given by the definition of a set of consistent physical objects (CPOs). To describe the data structure of the overall ITM database, the XML schema description (XSD) has been used. Originally intended to describe the structure of XML documents, XSD is used here to provide an unambiguous way of describing how data are structured, regardless of the actual implementation of the underlying database.  The MDSplus-based UAL implementation is currently under test and other prototypes for investigating alternative data storage systems are foreseen. (C) 2007 Elsevier B.V. All rights reserved.},  Keywords = {data structures  xml  database systems},  Year = {2008} }  diff --git a/figures/RZstats.pdf b/figures/RZstats.pdf  index 255c8e0..09afedf 100644  Binary files a/figures/RZstats.pdf and b/figures/RZstats.pdf differ diff --git a/review1/comments.txt b/review1/comments.txt  new file mode 100644  index 0000000..5debc62  --- /dev/null  +++ b/review1/comments.txt 
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Reviewers' comments:  Dear author, first of all let us apologise for the long delay. We had significant difficulties in finding referees which were ready to accept our requests for reviews.  In the particular case of your paper, after having invited several referees we could only get one report. The report includes enough analysis and detail so that we can trust it and after reading the paper myself I have taken the decision to go ahead with a single referee.  Best regards  Joaquin Sanchez  Guest editor  Reviewer #2: The manuscript is well organized and written in general. I found some misprints and other small inconsistencies to check for the final version. I have also some comments.  Misprints.  1. Introduction.   now: … which predicts PF coils currents from a give plasma boundary and profiles.  to be: … which predicts PF coils currents from a given plasma boundary and profiles.  3.2 Statistical analysis  now: For shot 6962, equilibria with TS pressure profiles and with linear p' and FF'.  to be: For shot 6962, equilibria with TS pressure profiles and with linear p' and FF' is used.  3.2 Statistical analysis  now: We can observer that the…  to be: We can observe that the…  Inconsistencies.  2. Verification and validation procedure.  When defining verification and validation procedure you specify 4 steps. Then you expain them, but in explanation you change order:  Procedure definition:  4. Reconstruct FREEBIE equilibria using EFIT++ and VacTH with various parameters and artificial input noise.  Later in text:  In the optional third step, an artificial random noise is added to the calculated values of Ip, magnetic probes and flux loops.  3. Results.  You introduce different shapes as circular elongated and diverted. Then in 3.1 you are using term 'eliptical' several times, that can refer to both elongated and diverted plasmas. Could you specify which plasmas you refer to in each case.  Comments.  1. When talking about ITM CPOs, I think you need reference to explain what is it. It could be for example:  G. Manduchi et al, Fusion Eng. Design 83 (2008) 462  2. Annotation to Fig.2. Last sentence is not clear for me, what do you mean? Have you artificially scattered zero error data? Could you explain this?  3. Fig.2. I propose to change color for case s3 from purple to (for example) green to distinguish results (it is hard to do now).  4. Conclusions. When you are saying that VacTH is a promising tool for a real-feedback control, on what reasoning are you relying? In the text it is shown that VacTH is able to reconstruct plasma surface with 'reasonable' accuracy. I think in order to conclude about it's applicability for real-time control it should be verified against another real-time tools. My conclusion from the results shown is that further improvements in the code are needed to make it more robust (that is required for real-time feedback control).  diff --git a/review1/response.txt b/review1/response.txt  new file mode 100644  index 0000000..507e99b  --- /dev/null  +++ b/review1/response.txt 
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Dear editors, dear referee,  thank you for your valuable comments concerning our manuscript. We have addressed all of them and corrected the text accordingly. Please find detailed answers below.  Best regards,  Jakub Urban  > Reviewer #2: The manuscript is well organized and written in general. I found some misprints and other small inconsistencies to check for the final version. I have also some comments.  > Misprints.  > 1. Introduction.   > now: … which predicts PF coils currents from a give plasma boundary and profiles.  > to be: … which predicts PF coils currents from a given plasma boundary and profiles.  > 3.2 Statistical analysis  > now: For shot 6962, equilibria with TS pressure profiles and with linear p' and FF'.  > to be: For shot 6962, equilibria with TS pressure profiles and with linear p' and FF' is used.  > 3.2 Statistical analysis  > now: We can observer that the…  > to be: We can observe that the…  All the misprints have been corrected.  > Inconsistencies.  >   > 2. Verification and validation procedure.  > When defining verification and validation procedure you specify 4 steps. Then you expain them, but in explanation you change order:  > Procedure definition:  > 4. Reconstruct FREEBIE equilibria using EFIT++ and VacTH with various parameters and artificial input noise.  > Later in text:  > In the optional third step, an artificial random noise is added to the calculated values of Ip, magnetic probes and flux loops.  We have changed the text of chapter 2:  " ...  FREEBIE inputs can be modified in the optional third step. In the following analysis, we particularly use realistic pressure profiles, estimated by Thomson scattering diagnostics.  The final fourth step consists of reconstructing the equilibria form synthetic FREEBIE data using EFIT++ and VacTH. An artificial random noise is added to the calculated values of $I_\mathrm{p}$, magnetic probes and flux loops. In particular, for a given noise level $\epsilon$, $\tilde X = \left( {1 + U\left( { - \epsilon, \epsilon} \right)^\mathrm{T}} \right)X$, where $X$ is a row vector of the synthetic diagnostics data and $U\left( { - \epsilon, \epsilon} \right)$ is a random vector of the same shape as $X$ with a uniform distribution on $\left( { - \epsilon, \epsilon} \right)$. The reconstructions are then compared to the original equilibrium, focusing on global parameters and geometry. Scans are performed over noise levels ($\epsilon$) and selected code parameters: $p'$ and $FF'$ polynomial degrees in EFIT++ ($n_{p'}$, $n_{FF'}$) and the number of harmonics ($n_P$, $n_Q$) in VacTH. The following quantities are used for the comparison.  ... "  > 3. Results.  > You introduce different shapes as circular elongated and diverted. Then in 3.1 you are using term 'eliptical' several times, that can refer to both elongated and diverted plasmas. Could you specify which plasmas you refer to in each case.  We now use 'elliptical' throughout the paper when referring to elongated, limited plasmas. In the beginning of chapter 3, we now explicitly say: "These cases include circular, elliptical (limited) and diverted plasmas with different currents." We believe that this avoids any confusion since diverted plasmas are always designated explicitly.    > Comments.  >   > 1. When talking about ITM CPOs, I think you need reference to explain what is it. It could be for example:  > G. Manduchi et al, Fusion Eng. Design 83 (2008) 462  The reference has been added.  > 2. Annotation to Fig.2. Last sentence is not clear for me, what do you mean? Have you artificially scattered zero error data? Could you explain this?  We simply scattered the x position of the data points with zero input error in order to suppress their overlap. We have removed this sentence from the caption as it should be clear enough that the error of these data points is zero. Based on your comment, the sentence was a bit confusing.    > 3. Fig.2. I propose to change color for case s3 from purple to (for example) green to distinguish results (it is hard to do now).  The colour has been changed.  > 4. Conclusions. When you are saying that VacTH is a promising tool for a real-feedback control, on what reasoning are you relying? In the text it is shown that VacTH is able to reconstruct plasma surface with 'reasonable' accuracy. I think in order to conclude about it's applicability for real-time control it should be verified against another real-time tools. My conclusion from the results shown is that further improvements in the code are needed to make it more robust (that is required for real-time feedback control).  The conclusion we draw in the paper is that VacTH is promising for real-time shape control. In out opinion, the accuracy of VacTH shape reconstruction shall be reasonable for real time plasma position/shape control. However, we agree that the robustness (and the accuracy as well) should be improved. There are actually new results for VacTH parameters optimizations. We do not think that VacTH must necessarily be compared to other real-time shape reconstruction tools providing that it shows enough accuracy, robustness and speed required by a particular feed-back algorithm. Since such an algorithm does not exist yet on COMPASS, we do not have absolute measures.  We have extended the last sentence of the conclusions: "We conclude that VacTH is a promising tool pertinent for a real-time feedback control of the plasma shape, although its robustness and accuracy should be improved."