tcv diagnostics semestrial report study of magnetic ﬂux ... · centre de recherches en physique...

CENTRE DE RECHERCHES EN PHYSIQUE DES PLASMAS (CRPP)Association EURATOM - Confederation suisse

TCV Diagnostics

Semestrial report

Study of magnetic flux shaped basefunctions for tomography

Christian Schlatter(1)

CRPP EPFLPPB

CH-1015 Lausanne

June, 2002

Made with LATEX2ε

(1) TP IV in physics, [email protected]

Contents

1 Introduction 1

2 Magnetic FLUx shaped TOmography (FLUTO) 22.1 General description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Compatibility with Matlab 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Problems and modifications of FLUTO 43.1 The pixel overlapping problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2 Pixel truncation at cross section border . . . . . . . . . . . . . . . . . . . . . . . 5

4 Testing and application of FLUTO 74.1 The PSI value selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2 Single time frame reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.3 The influence of deleted channels . . . . . . . . . . . . . . . . . . . . . . . . . . 104.4 Location of magnetic axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 Conclusion 13

A User configuration flags 15A.1 Flags in fluto.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15A.2 Flags in flutorec.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

A.2.1 Separatrix basefunction system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

A.2.2 Central base function system . . . . . . . . . . . . . . . . . . . . . . . . 17A.2.3 Wall base function system . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Centre de recherches en physique des plasmas (CRPP) i Christian Schlatter

List of Figures

1.1 GUI extension for BTOMO by Zoletnik and Kalvin. Magnetic fluxshaped expansions for tomography using bolometry. . . . . . . . . . . . . . . . . 1

3.1 TCV shot # 17831 : Separatrix base function superposition bug. Thesurface in orange represents 100 % coverage of the cross section. The two jaggedpeak in red are due to a bad arrangement of the base pixel. . . . . . . . . . . . . 4

3.2 TCV shot # 17831 : Separatrix, center and wall base function super-position bug. Emissions from the wall are getting amplified almost up to thedouble in respect to the rest of the cross section. . . . . . . . . . . . . . . . . . . 5

3.3 TCV shot # 17831 : Corrected separatrix, center and wall base func-tion superposition. All regions of the cross section have now uniform weight. . 6

3.4 Reshaping of hexagonal base area. Red points are base points. The greenpoint outside the vessel is replaced by two new, here drawn in blue. . . . . . . . 6

3.5 Pixel at the upper border of the vessel. The outline is formed of eight basepoints and the height of the pixel is constrained to zero everywhere on the baseshape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.1 LCFS and designation of neighboring regions. 1 : scrape-off layer; 2 :divertor; 3 : inside LCFS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.2 Separatrix base function. PSI value configuration in region 1 : + 0.1, 2 : -0.1, 3 : - 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8



4.5 Separatrix base function. PSI value configuration in region 1 : + 0.1, 2 : -0.1, 3 : - 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.6 Shot # 17831 @ 0.2 s. PSI value configuration in region 1 : + 0.9, 2 : - 0.12,3 : - 0.2. The red closed line represents the LCFS. . . . . . . . . . . . . . . . . . 9

4.7 Shot # 17831 @ 0.5 s. PSI value configuration in region 1 : + 0.9, 2 : - 0.12,3 : - 0.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.8 Shot # 17831 @ 1.2 s. PSI value configuration in region 1 : + 0.9, 2 : - 0.12,3 : - 0.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.9 Shot # 19780. Reconstruction of pixel 144 using all 64 bolometer channels.The figure on the left shows the initial source distribution. The figure on theright shows the reconstructed sources. The yellow closed line is the LCFS. Thegreen chords represents the viewing lines of the available bolometry detectors. . 11

4.10 Shot # 19780. Reconstruction of pixel 29 without disabled channels. Theresult is delocalized. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Centre de recherches en physique des plasmas (CRPP) ii Christian Schlatter

LIST OF FIGURES iii

4.11 Shot # 19780. Reconstruction of pixel 29 using all 64 bolometer channels. . . 114.12 Shot # 16197. Reconstruction of a radiating LCFS using all 64 bolometer

channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.13 Shot # 16197. Reconstruction of a radiating LCFS without disabled channels. 12

5.1 Shot # 16197. Superposition of the whole center base function set. . . . . . . 135.2 Shot # 16197. Superposition of the whole wall base function set. . . . . . . . . 13

Centre de recherches en physique des plasmas (CRPP) Christian Schlatter

Chapter 1

Introduction

Ten years ago Zoletnik and Kalvin wrotetheir basic article about tomography usingarbitrary expansions [1]. Several algorithmsfor Soft X-Ray and bolometry using thistechnique have been developed, but due totheir heavy computational overhead(1) theyhave never been really employed.

Figure 1.1: GUI extension for BTOMO byZoletnik and Kalvin. Magnetic fluxshaped expansions for tomography us-ing bolometry.

This TP IV aimed to test the existingsolution for bolometry and to adapt it foreasier use, i.e to control the code with lessparameters(2) and to check for possibilitieshow to make the algorithm faster.

(1) the reconstruction of one single time framewith FLUTO takes about twenty minutes onHAL.

(2) for example the detection of the stable mag-netic configuration regime, the determinationof the position of the magnetic configuration,the optimal PSI settings etc.

Contrary to all expectations Zoletniks andKalvins algorithm didn’t work on Matlab 6.1and therefore a large amount of time wasnecessary to make it compatible (see section2.2). Today a working solution exist, so thata few tests were performed.

The next chapter gives an overview aboutmagnetic flux shaped pixels used in tomog-raphy, the existing implementations and thenew package FLUTO, which has a commandline interface and is now able to run underMatlab 6.1.

Chapter three deals with problems thatcame across when the integration for Matlab6.1 was established, namely the pixel over-lapping problem (which is fixed now) andthe pixel truncation at the border of thevessel.

One chapter further some results from spe-cific tests are presented. The PSI value se-lection shows the effect on how the pixels arescaled in flux values around the LCFS. Toensure the integrity of FLUTO, single timeframes of given shots has been processed andcompared to inversions obtained with otherpackages. A section try to analyze the im-pact of disabled data acquisition channels onthe reconstructed image. A last test checksfor reliability of the magnetic configurationprovided by LIUQE.

Centre de recherches en physique des plasmas (CRPP) 1 Christian Schlatter

Chapter 2

Magnetic FLUx shaped TOmography(FLUTO)

2.1 General description

Surfaces with constant magnetic flux confinethe plasma and therefore the emissivityalong these surfaces is nearly constant.Hence it would be desirable to have a set ofpixels whose shape is given by the magneticconfiguration of the plasma. In comparisonwith completely rectangular grid the numberof necessary pixels is smaller to get similarresults - this will reduce the effort to calcu-late the tomographic inversion. Further, thechoice of pixels covering almost the wholecross-section of the tokamak permits thereconstruction of localized sources.

A description of a method using arbitraryexpansions (given by magnetic flux shapedbase functions for example) for tomographycan be found in [1].

Kalvin and Zoletnik developed some kind ofa plug-in(1) for the bolometry tomographypackage BTOMO [2] (see figure 1.1) forCRPP which is described in [3]. In factit is a release for bolometry of the olderextension of the TCVXTI package forsoft-X-ray tomography [4].

Since the availability of this diagnostictool it has been hardly used during dailyroutine on TCV. In particular a thoroughcomparison with existing reconstructiontechniques was pending.

(1) HAL: \home\zoletnik\matlab\btomo final.

To make testing easier, a GUI-less packagecalled FLUTO (magnetic FLUx shapedTOmography) has been created. It is basedessentially on the mentioned BTOMOpackage with Zoletniks and Kalvins fluxgrid tomography extension. The creationof the base function system and the tomo-graphic inversion is identical to Zoletniksand Kalvins engine.

Before running the package on given shots,the user should check the configuration flagsas described in appendix A. The call ofFLUTO follows the philosophy introducedwithin FABCAT [5], i.e:

- fluto(shot):treats the specified plasma shot and de-livers the reconstruction at the LIUQEtimes.

- fluto(shot, tmin, tmax):loads and treats each time frame locatedbetween tmin and tmax [s] only.

In its present form, FLUTO shows theresult of the inversion in an special releaseof the BTOMOGRAPHICS window(BTOMO package), which makes theanalysis of the shot as simple as possible.

Instead of writing directly to the MDS+tree,results are stored to disk in shotxxxxx sub-folders, where xxxxx stands for the treatedshot number.


2.2 Compatibility with Matlab 6.1 3

2.2 Compatibility with

Matlab 6.1

Zoletnik and Kalvin developed their exten-sion to BTOMO on Matlab Release 5.3. Theuse under Matlab 6.1 (which is available atCRPP since testing began) caused severalerror and warning messages, preventinga successful execution of the code. Thelocalization of the incompatibility with thenew release of Matlab was not an easyjob and so a lot of time was necessary tounderstand how the algorithm works indetails and which Matlab built-in functionsare used. This effort didn’t only reveal theorigin of these problems but also uncoveredsome bugs in the existing code, which arediscussed in the following chapter.

Zoletnik and Kalvin use the delaunay.m

function for the triangularization of themagnetic flux surfaces [6]. It turned outthat they integrated the Matlab 5.3 functiongriddata.m into their package (namedas btgriddata.m) which was not properlyworking with the Matlab 6.1 functions it wasinvoking. In fact Mathworks implementeda new triangularization algorithm based onthe higher dimensional convex hull program(Qhull) [7]. To prevent collisions withother older Matlab functions in Matlabssearch path, the full triangularization andinterpolation function set has been copied tothe local FLUTO folder(2).

There still was a persisting error message(3)

appearing every time delaunay.m calledthe compiled library file tsrchmax.mexrs6,responsible for the selection of the nearestneighboring triangles to a given point. Thisfile was not available in source code formatand therefore a fault analysis could not beperformed. Mathworks Technical Supportfinally declared that this is related to trunca-

(2) delaunay.m, griddata.m, qhullmx.m,tsearch.m, qhullmx.mexrs6,tsrchmx.mexrs6.

(3) Warning : one or more points did not con-verge!

tion errors and can be ignored... Such kindof misleading messages are now disabled byusing the warnings off command.

The data loading (from MDS) and pre-processing (calibration and smoothing) hasbeen completely replaced by the solutionused in the FABCAT package. That waythe same choice of methods for channeldeletion and data calibration is availableas in FABCAT. The fragmented solutionof Zoletnik and Kalvin did calibration atseveral places, even inside the inversionroutine regulo 2d flux.m.

Several command styles which weren’tsupported any longer by Matlab 6.1 havebeen modified(4).

Further modifications and added features aredescribed in the following sections.

(4) for example the fuzz parameter fordelaunay.m is obsolete now.


Chapter 3

Problems and modifications of FLUTO

3.1 The pixel overlapping

problem

In quest of the error leading to the failureof the inversion the creation of the basefunction system has been analyzed. It hasbeen found that the superposition of thebase functions shows a bad overlapping.

A pixel is given by six base points forminga hexagone at level zero height and a singlesummit point with height one. The sumover all these pixels should give a uniformsurface at level one. Figure 3.1 shows athree dimensional representation of the sep-aratrix base function, i.e. the base functionsystem around the Last Closed Flux Surface(LCFS).

It can clearly be seen that there are at leasttwo regions (in red) where the superpositiongives too high levels. This means thatemissions originating from these regionswould be amplified in the solution, due to anelevated weight of the base function system.For the separatrix a predominance up to 400% has been observed for other shots!

Another problem causes the interferencebetween the three base function systemsthemselves. There are some shots wherethe LCFS is quite near to the border of thecross section and therefore the separatrixbase functions overlap with the wall basefunctions, as this can be seen on figure 3.2,where the wall and center pixel have beenadded relative to figure 3.1.

Figure 3.1: TCV shot # 17831 : Separatrixbase function superposition bug.The surface in orange represents 100 %coverage of the cross section. The twojagged peak in red are due to a bad ar-rangement of the base pixel.


3.2 Pixel truncation at cross section border 5

Figure 3.2: TCV shot # 17831 : Separatrix,center and wall base function su-perposition bug. Emissions from thewall are getting amplified almost up tothe double in respect to the rest of thecross section.

The appearance of overweighed pixels insidea single base function system is not easy tounderstand. A checking of Zoletniks andKalvins code didn’t lead to understanding,there must be further documentation to seewhat they are doing. A reason may be thepixel truncation at the cross section borderas described in the next section.

The overlapping between the different basefunction systems may be redressed by choos-ing limiting PSI flux values (see appendixA and section 4.1) closer to the LCFS toisolate them spatially. But this would limitthe scope of the covering of the cross sectionnot only where the base systems approach,leading to uncovered zones in the crosssection.

In the release at issue the pixels are con-tinuously superposed at creation of the basefunction systems and any overlapping withalready created pixels is subtracted from therecent one. This has been implemented forall three base function systems(1). Duringcreation of the base function systems its con-struction is drawn on screen. Figure 3.3shows the results with the modified code forseparatrix, center and wall base functions.This type of figures can easily be obtainedby using the tool basetest.m available in theFLUTO package.

3.2 Pixel truncation at

cross section border

For pixels at the border of the cross sectionof TCV one or more of the base points canoccasionally be located outside the vessel.In general the shape of the pixels basepoints form a hexagone. If a base pointlies outside the vessel, this one is replacedby two new base points, determined by theintersections of the vessels limiting curve

(1) see modified sections in make function sep.m(separatrix), make base function cent.m(center) and make base function wall.m(wall base function).


3.2 Pixel truncation at cross section border 6

Figure 3.3: TCV shot # 17831 : Correctedseparatrix, center and wall basefunction superposition. All regionsof the cross section have now uniformweight.

and the line relying the deleted base pointwith his neighbors, see figure 3.4.

This procedure is obviously necessary be-cause emissions can only come from insidethe vessel ! Nevertheless Zoletnik and Kalvindo linear interpolation through the trianglecomprised from these two new base pointsto the top point. There should rather beinterpolation first with the base point lyingoutside and restriction of the whole pixel tothe new base points afterwards, so that theweight at the periphery doesn’t decrease tozero. This fact is shown in figure 3.5 whereone counts eight base points. This pixel islocated at the upper frontier of TCV crosssection.

The fact that the discussed pixel overlappingproblem occurs only at the outer pixel of theseparatrix base function system may be re-lated to the manner how pixels are treatedthere.

new

base

points

replaced

basepoint

border of vessel

Figure 3.4: Reshaping of hexagonal base area.Red points are base points. The greenpoint outside the vessel is replaced bytwo new, here drawn in blue.

0 10 20 30 40 50 60 70 800

5

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Figure 3.5: Pixel at the upper border of thevessel. The outline is formed of eightbase points and the height of the pixelis constrained to zero everywhere onthe base shape.


Chapter 4

Testing and application of FLUTO

4.1 The PSI value selec-

tion

The creation of the separatrix base functionsystem can essentially be configured throughthe three PSI value settings(1).

The magnetic flux surface constituting theLCFS has the magnetic flux value zeroassigned. See figure 4.1 for the numbering ofthe adjacent regions.

3

12

Figure 4.1: LCFS and designation of neigh-boring regions. 1 : scrape-off layer;2 : divertor; 3 : inside LCFS.

(1) gf para.reg1 val (region 1), gf para.reg2 val(region 2) and gf para.reg3 val (region 3) influtorec.m

The settings steer how close (the closer thesettings are to zero) the separatrix basefunction pixels are arranged around LCFS.

In region 1 the value must be positive,in region 2 and 3 negative(2). For regionthree there is some kind of an automaticdetermination(3) of the settings value, whichin general works well, so that the centraland separatrix base function systems fittogether. In rare cases there was an onlypartially covered (weight < 100 %) ring in-side LCFS due to malfunction of this feature.

Figures 4.2 to 4.5 shows results for severalconfigurations of these limiting flux settings.The automatic setting for region 3 value hasbeen disabled for these tests.

(2) Attention : The indications in Zoletniks andKalvins documentation [3] are wrong !

(3) flutrec.m, line 161


4.1 The PSI value selection 8

Figure 4.2: Separatrix base function. PSI valueconfiguration in region 1 : + 0.1, 2 : -0.1, 3 : - 0.1.



Figure 4.5: Separatrix base function. PSI valueconfiguration in region 1 : + 0.1, 2 : -0.1, 3 : - 1.0


4.2 Single time frame reconstruction 9

For most of the analyzed shots the divertorregion is so narrow that its associated PSIvalue doesn’t have much implications (youmay compare figure 4.4 to 4.2).

For the center region an expansion of theseparatrix base function decreases the extentof the center base function. This may onlybe interesting when choosing different pixeldimensions for these two base function sets.

The choice of the region 1 value is importantif emissions appear far from the separatrix: there may be large zones which will notbe covered by any of the base functionsand therefore will be inaccessible for theinversion.

When enlarging the separatrix coverage oneshould also increase the resolution, i.e. thenumber of intermediate poloidal flux val-ues(4), so that localized sources still can betraced.

(4) gf para.reg1 nu, region 1 contour number

4.2 Single time frame re-

construction

After several modifications of the originalcode some reconstructions of real shots havebeen performed.Especially the question arose, if there is nowsome difference to Zoletniks and Kalvinsresults. You may compare figures 4.6 to4.8 to those given in [3](5), where the basefunction system has been calculated forevery fifth time frame.

However, the following figures use the mag-netic configuration established only for thesingle time frame they represent. Furtherthe spatial configuration (resolution andlimitation of separatrix base function) ofZoletniks and Kalvins images are unknown.

Please note that this type of images heavilydepend on color scaling.

Despite these facts the qualitative coinci-dence is quite good.

Figure 4.6: Shot # 17831 @ 0.2 s. PSI valueconfiguration in region 1 : + 0.9, 2 :- 0.12, 3 : - 0.2. The red closed linerepresents the LCFS.

(5) figure 21 on page 17.


4.3 The influence of deleted channels 10

Figure 4.7: Shot # 17831 @ 0.5 s. PSI valueconfiguration in region 1 : + 0.9, 2 : -0.12, 3 : - 0.2

Figure 4.8: Shot # 17831 @ 1.2 s. PSI valueconfiguration in region 1 : + 0.9, 2 : -0.12, 3 : - 0.2

4.3 The influence of

deleted channels

For some shots the inversion didn’t suc-ceed when the regularization was executedwith the radiation intensity constrained topositive values only(6). All these shots hadin common, that an elevated number ofchannels were not taken into consideration.

To test the code for sensibility to disabledchannels a base function system for such ashot has been calculated. To each pixel animaginary radiation intensity equal to itsweight has been assigned. Pixel per pixel,the fictive line integrated radiation collectedby each bolometer has been determinedfollowed by a reconstruction of the ”filled”pixel. This has been done in respect to dis-abled channels as well as when all channelswere activated. Figure 4.9 shows a fictive ra-diation source located on the wall (left partof the figure). Even with all 64 bolometerchannels enabled this zone is intercepted bynone of the central viewing lines. The result(right part of the figure) is quite astonishing: The radiation is assigned to the twonarrow zones which are not seen by anyof the cameras. Finally, the reconstructedtotal radiated power is almost 5 times higher.

Figure 4.10 shows a radiating outer pixelof the separatrix without the disabledchannels(7). The radiation is thereforeonly collected by the uppermost lateralpinhole camera. The result is a smearedreconstruction, where radiation is supposedto come from domains exclusively seen bythis camera.

(6) configuration flag gf para.meth in flutorec.m(7) 12 channels, namely number 3, 6 - 8, 31 and

58 - 64 were disabled.


4.3 The influence of deleted channels 11

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Figure 4.9: Shot # 19780. Reconstruction ofpixel 144 using all 64 bolometer chan-nels. The figure on the left shows theinitial source distribution. The figureon the right shows the reconstructedsources. The yellow closed line is theLCFS. The green chords represents theviewing lines of the available bolometrydetectors.

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Figure 4.10: Shot # 19780. Reconstruction ofpixel 29 without disabled channels.The result is delocalized.

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Figure 4.11: Shot # 19780. Reconstruction ofpixel 29 using all 64 bolometer chan-nels.

Enabling all 64 bolometer channels, thereconstructed radiation is much betterlocalized (see figure 4.11).

An interesting test is represented by thefigures 4.12 and 4.13. Radiating sourceshave been placed on the pixels lying on theseparatrix. With disabled channels(8) thering oriented to the center of the tokamakis only coated by the lateral channels whichsee first the exterior part of the separatrix.Hence the radiation is attributed to thisouter region only - the inner separatrix sharestays empty (figure 4.13). This is not thecase when all channels were activated (4.12).

For large source distributions or multiple dis-tribution centers it is important that mainlythe top and bottom channels can be used.

(8) 7 of 8 top (1 - 4, 6 - 8) and bottom channels(57 - 63) were out.


4.4 Location of magnetic axis 12

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Figure 4.13: Shot # 16197. Reconstruction ofa radiating LCFS without disabledchannels.

4.4 Location of magnetic

axis

Problems with position of the magneticconfiguration as provided by LIUQE hasbeen discovered recently using Soft X-Raytomography measurements. Soft X-Raygave higher or lower location of the magneticaxis. This could be verified using magneticflux shaped base functions with bolometry,since the quality of the reconstructed imageshould be better when correct magnetic po-sition are used. FLUTO has been extendedto modify the whole magnetic configurationby moving the flux surfaces vertically(9).

Table 4.1 gives the smooting parameterκ for the regularization functional(10) forseveral vertical shifts of LIUQE’s magneticconfiguration.

shot # time [s] ∆ z [cm] κ

16197 1 0 1.027·1026

16197 1 + 2 9.25·1025

16197 1 - 2 9.58·1025

19303 0.9 0 8.26·1026

19303 0.9 - 1.5 7.87·1026

Table 4.1: Magnetic flux surface postion andsmooting parameter κ. The bold linesare the corrections suggested by Soft X-Ray measurements.

A higher κ means a smoother reconstruc-tion. The expectations from SXR measure-ments have not been confirmed. But addi-tional tests should also verify that there isno misalignment in radial direction, so that asimultaneous displacement in horizontal andvertical direction would maybe give higher κ.

(9) see parameter vert shift in flutorec.m (line45).

(10) it is the Lagrange multiplier for the solutionof the PN = LS problem as described in [1].


Chapter 5

Conclusion

With FLUTO a working solution usingmagnetic flux shaped expansions is ready torun on CRPP’s server. A first range of testshave already been carried out.

Further tests will be necessary to prove thereliability of flux shaped pixel tomography.Position measurement tests of the magneticsurfaces may be a candidate.

At this stage, the code is not very versatileand quite slow. The added code to preventwrong superposition of the pixels doesn’tcost lot of computation time. Any challengeto make the whole package faster shouldstart with improving the creation of the basefunction system, since this task takes about90 % of the necessary time of the whole inver-sion process. The present implementation isquite arcane, first step would be a better un-derstanding of how this task is done actually.

Improvements of the versatility of the codeshould aim to reduce the number of settingsto choose be the user. All parameters shouldbe moved to the main program fluto.m.The very next step should be the imple-mentation of the stable regime detectionof the magnetic configuration, i.e. whichtime frame is chosen to calculate the basefunction system and on which time intervalit can be used to get good results.

I would like to thank Jan Mlynar who -despite his stay at JET - was ready to acceptme as TP IV student.

Christian Schlatter, Prilly, june 2002

Figure 5.1: Shot # 16197. Superposition of thewhole center base function set.

Figure 5.2: Shot # 16197. Superposition of thewhole wall base function set.


References

[1] Sandor Zoletnik and Sandor Kalvin; A method for tomography using arbitraryexpansions, Rev. Sci. Instrum. volume 64, part 5, Budapest 1993.

[2] Iwan Jerjen and Jan Mlynar; BTOMO: The Software Package used for theBolometry on TCV Tokamak, CRPP EPFL Lausanne, INT 197/99.

[3] Sandor Kalvin and Sandor Zoletnik; Tomographic Reconstruction of RadiationIntensity Profiles from Bolometric Measurements on the TCV Tokamak,CAT-Science Bt. for CRPP EPFL Lausanne 2000, INT.

[4] Sandor Kalvin and Sandor Zoletnik; Extension of the TCVXTI software package,CAT-Science Bt. for CRPP EPFL Lausanne 1999, INT.

[5] Christian Schlatter and Jan Mlynar; Fast-Algorithm Bolometric ComputerAided Tomography (FABCAT); CRPP EPFL Lausanne 2002, INT 205/02.

[6] David E. Watson; Contouring: A Guide to the Analysis and Display of SpatialData, Tarrytown 1992.

[7] Higher dimensional convex hull program (Qhull); The National Science and Tech-nology Research Center for Computation and Visualization of Geometric Structures,University of Minnesota, see http://www.geom.umn.edu/locate/qhull/ for documenta-tion.


Appendix A

User configuration flags

In the header of the main program filefluto.m and in the inversion routineflutorec.m several flags are specified to con-trol the behavior of the package. When expe-riencing problems with the execution of thepackage the first thing to check are these con-figuration flags and try to run them using thedefault settings. The settings in fluto.m arealmost the same as in fabcat.m of the FAB-CAT package.

A.1 Flags in fluto.m

- f camSpecifies which pinhole cameras shouldbe used. Each camera gathers eightbolometers looking through the samepinhole of the section.Default setting = [1 1 1 1 1 1 1 1],i.e. all eight cameras are activated.

- chantestThe package can itself try to identifybad channels. The following values areadmitted :0: no automatic testing for bad chan-nels.1: Testing using Christian Deschenaux’smethod (backfiltering).2: Testing using Arno Refke’s method(consistency check).3: Testing using both methods.Default setting = 2.

- smoothmodeSpecifies the method by which the rawbolometry signals are treated and cali-brated.0: no data treatment is done.1: Processing using Bernard Joye’smethod (polynomial fitting).2: Processing using Christian De-schenaux’s method (backfiltering).Default setting = 2.

- delchanuserAllows the specification of channel num-bers which will be ignored by the re-construction. Maybe useful if singlebolometers are defective.Default setting = [], i.e. no channelexcluded.

- runsigmaProvides the global multiplication fac-tor for the error bars. The constantsunity is in percent. The variance σi willstill be divided by the individual chan-nel etendue.Default setting = 3.

- lambda initProvides the initial λ for the regulariza-tion routine, i.e. the balance betweenfitting and smoothing.Default setting = 0.1.

- chitarTarget χ2, i.e. the reconstruction triesto obtain this final χ2

target.Default setting = 1, i.e. a reconstruc-tion image having maximum variance σi.


A.2 Flags in flutorec.m 16

- errchiSupreme difference between the time av-eraged final χ2 and the target χ2

target (seeflag chitar) which qualifies the shot stillas a good one. This parameter was cho-sen arbitrary.Default setting = 0.05.

A.2 Flags in flutorec.m

- gf para.frame valFrame value providing the flux shapeto calculate the base function system inSINGLE PSI MODE. Set it to 1 if a sin-gle time frame is calculated or choose atime frame where the magnetic configu-ration is stable.

- vert shiftPermits to shift the magnetic flux sur-faces vertically. The offset is given in[cm]. Positive offset moves the magneticconfiguration up. This is useful for LI-UQE testing purposes.

- gf para.sigmaSIGMA error bars.Default setting = 0.03

- gf para.methControl flag if the radiation should keptpositive. Either 1 (no constrain) or 2(only positive radiation intensity).Default setting = 2.

- gf para.rmethodInversion method. Either 1 (single PSImethod, i.e. one single base functionsystem is calculated) or 2 (multiple PSImethod, i.e. for each time frame a newbase function system is calculated).Default setting = 1.

- gf para.calc radIf set to 1 then the total radiation in-tensity and radiation fractions in variousregions is calculated.Default setting = 1.

- use graphicIf set to 1 then several graphics showingthe creation of the base function systemsare printed on screen.Default setting = 0.

A.2.1 Separatrix basefunction system

- gf para.use sbEnables (1) / disables (0) the separatrixbase function set.Default setting = 1.

- gf para.crp spCross point spacing [cm]. This is thespacing of the base points along the fluxcontours.Default setting = 7.

- gf para.reg1 valRegion 1 PSI value, must be positive.The flux has level zero on the separa-trix. The closer you choose the values tozero the narrower the belts are groupedaround the separatrix.Default setting = 0.9.

- gf para.reg1 nuRegion 1 contour number. This is thenumber of flux contours to use in this re-gion. Attention : this includes the sep-aratrix LCFS so this setting has to begreater than 1.Default setting = 10.

- gf para.reg2 valRegion 2 PSI value, must be negative.Default setting = -0.12.

- gf para.reg2 nuRegion 2 contour number.Default setting = 6.

- gf para.reg3 valRegion 3 PSI value, must be nega-tive. This setting gets adjusted auto-matically.Default setting = -0.2.


A.2 Flags in flutorec.m 17

- gf para.reg3 nuRegion 3 contour number.Default setting = 6.

A.2.2 Central base functionsystem

- gf para.use ceEnables (1) / disables (0) the center basefunction set.Default setting = 1.

- gf para.cent nrNumber of radial zones for center basefunction.Default setting = 3.

- gf para.cent ntNumber of poloidal zones for center basefunction.Default setting = 4.

- gf para.cent methRadial base function determinationmethod, either 1 (harmonic) or 2 (grid).Default setting = 2.

- gf para.cent psiRadial base function placement method,either 1 (equally spaced in averaged ra-dius) or 2 (equally spaced in flux value).Default setting = 2.

A.2.3 Wall base functionsystem

gf para.use waEnables (1) / disables (0) the wall basefunction set.Default setting = 1.

- gf para.wall wtWidth (away from the wall) of the pixelsfor the wall base function [cm].Default setting = 5.

- gf para.wall ntNumber of pixels for the wall base func-tion.Default setting = 50.


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