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16 // _________________________________________________________________
19 // <h2> AliTPCBoundaryVoltError class </h2>
20 // This class calculates the space point distortions due to residual voltage errors on
21 // the main boundaries of the TPC. For example, the inner vessel of the TPC is shifted
22 // by a certain amount, whereas the ROCs on the A side and the C side follow this mechanical
23 // shift (at the inner vessel) in z direction. This example can be named "conical deformation"
24 // of the TPC field cage (see example below).
26 // The boundary conditions can be set via two arrays (A and C side) which contain the
27 // residual voltage setting modeling a possible shift or an inhomogeneity on the TPC field
28 // cage. In order to avoid that the user splits the Central Electrode (CE), the settings for
29 // the C side is taken from the array on the A side (points: A.6 and A.7). The region betweem
30 // the points is interpolated linearly onto the boundaries.
32 // The class uses the PoissonRelaxation2D (see AliTPCCorrection) to calculate the resulting
33 // electrical field inhomogeneities in the (r,z)-plane. Then, the Langevin-integral formalism
34 // is used to calculate the space point distortions. <br>
35 // Note: This class assumes a homogeneous magnetic field.
37 // One has two possibilities when calculating the $dz$ distortions. The resulting distortions
38 // are purely due to the change of the drift velocity (along with the change of the drift field)
39 // when the SetROCDisplacement is FALSE. This emulates for example a Gating-Grid Voltage offset
40 // without moving the ROCs. When the flag is set to TRUE, the ROCs are assumed to be misaligned
41 // and the corresponding offset in z is added.
44 // Begin_Macro(source)
46 // gROOT->SetStyle("Plain"); gStyle->SetPalette(1);
47 // TCanvas *c2 = new TCanvas("cAliTPCBoundaryVoltError","cAliTPCBoundaryVoltError",500,300);
48 // AliTPCBoundaryVoltError bve;
49 // Float_t val = 40;// [Volt]; 40V corresponds to 1mm
50 // /* IFC shift, CE follows, ROC follows by factor half */
51 // Float_t boundA[8] = { val, val, val,0,0,0,0,val}; // voltages A-side
52 // Float_t boundC[6] = {-val,-val,-val,0,0,0}; // voltages C-side
53 // bve.SetBoundariesA(boundA);
54 // bve.SetBoundariesC(boundC);
55 // bve.SetOmegaTauT1T2(-0.32,1,1);
56 // bve.SetROCDisplacement(kTRUE); // include the chamber offset in z when calculating the dz distortions
57 // bve.CreateHistoDRinZR(0)->Draw("surf2");
64 // Date: 01/06/2010 <br>
65 // Authors: Jim Thomas, Stefan Rossegger
67 // _________________________________________________________________
71 #include "TGeoGlobalMagField.h"
72 #include "AliTPCcalibDB.h"
73 #include "AliTPCParam.h"
78 #include "AliTPCROC.h"
79 #include "AliTPCBoundaryVoltError.h"
81 ClassImp(AliTPCBoundaryVoltError)
83 AliTPCBoundaryVoltError::AliTPCBoundaryVoltError()
84 : AliTPCCorrection("BoundaryVoltError","Boundary Voltage Error"),
86 fROCdisplacement(kTRUE),
90 // default constructor
92 for (Int_t i=0; i<8; i++){
94 if (i<6) fBoundariesC[i]= 0;
98 AliTPCBoundaryVoltError::~AliTPCBoundaryVoltError() {
100 // default destructor
106 void AliTPCBoundaryVoltError::Init() {
108 // Initialization funtion
111 AliMagF* magF= (AliMagF*)TGeoGlobalMagField::Instance()->GetField();
112 if (!magF) AliError("Magneticd field - not initialized");
113 Double_t bzField = magF->SolenoidField()/10.; //field in T
114 AliTPCParam *param= AliTPCcalibDB::Instance()->GetParameters();
115 if (!param) AliError("Parameters - not initialized");
116 Double_t vdrift = param->GetDriftV()/1000000.; // [cm/us] // From dataBase: to be updated: per second (ideally)
117 Double_t ezField = 400; // [V/cm] // to be updated: never (hopefully)
118 Double_t wt = -10.0 * (bzField*10) * vdrift / ezField ;
119 // Correction Terms for effective omegaTau; obtained by a laser calibration run
120 SetOmegaTauT1T2(wt,fT1,fT2);
122 InitBoundaryVoltErrorDistortion();
125 void AliTPCBoundaryVoltError::Update(const TTimeStamp &/*timeStamp*/) {
129 AliMagF* magF= (AliMagF*)TGeoGlobalMagField::Instance()->GetField();
130 if (!magF) AliError("Magneticd field - not initialized");
131 Double_t bzField = magF->SolenoidField()/10.; //field in T
132 AliTPCParam *param= AliTPCcalibDB::Instance()->GetParameters();
133 if (!param) AliError("Parameters - not initialized");
134 Double_t vdrift = param->GetDriftV()/1000000.; // [cm/us] // From dataBase: to be updated: per second (ideally)
135 Double_t ezField = 400; // [V/cm] // to be updated: never (hopefully)
136 Double_t wt = -10.0 * (bzField*10) * vdrift / ezField ;
137 // Correction Terms for effective omegaTau; obtained by a laser calibration run
138 SetOmegaTauT1T2(wt,fT1,fT2);
144 void AliTPCBoundaryVoltError::GetCorrection(const Float_t x[],const Short_t roc,Float_t dx[]) {
146 // Calculates the correction due e.g. residual voltage errors on the TPC boundaries
150 AliInfo("Lookup table was not initialized! Perform the inizialisation now ...");
151 InitBoundaryVoltErrorDistortion();
154 Int_t order = 1 ; // FIXME: hardcoded? Linear interpolation = 1, Quadratic = 2
155 // note that the poisson solution was linearly mirroed on this grid!
156 Double_t intEr, intEphi, intdEz ;
160 r = TMath::Sqrt( x[0]*x[0] + x[1]*x[1] ) ;
161 phi = TMath::ATan2(x[1],x[0]) ;
162 if ( phi < 0 ) phi += TMath::TwoPi() ; // Table uses phi from 0 to 2*Pi
163 z = x[2] ; // Create temporary copy of x[2]
165 if ( (roc%36) < 18 ) {
166 sign = 1; // (TPC A side)
168 sign = -1; // (TPC C side)
171 if ( sign==1 && z < fgkZOffSet ) z = fgkZOffSet; // Protect against discontinuity at CE
172 if ( sign==-1 && z > -fgkZOffSet ) z = -fgkZOffSet; // Protect against discontinuity at CE
175 intEphi = 0.0; // Efield is symmetric in phi - 2D calculation
177 if ( (sign==1 && z<0) || (sign==-1 && z>0) ) // just a consistency check
178 AliError("ROC number does not correspond to z coordinate! Calculation of distortions is most likely wrong!");
180 // Get the E field integral
181 Interpolate2DEdistortion( order, r, z, fLookUpErOverEz, intEr );
182 // Get DeltaEz field integral
183 Interpolate2DEdistortion( order, r, z, fLookUpDeltaEz, intdEz );
185 // Calculate distorted position
187 phi = phi + ( fC0*intEphi - fC1*intEr ) / r;
188 r = r + ( fC0*intEr + fC1*intEphi );
191 // Calculate correction in cartesian coordinates
192 dx[0] = r * TMath::Cos(phi) - x[0];
193 dx[1] = r * TMath::Sin(phi) - x[1];
194 dx[2] = intdEz; // z distortion - (internally scaled with driftvelocity dependency
195 // on the Ez field plus the actual ROC misalignment (if set TRUE)
200 void AliTPCBoundaryVoltError::InitBoundaryVoltErrorDistortion() {
202 // Initialization of the Lookup table which contains the solutions of the
203 // Dirichlet boundary problem
206 const Float_t gridSizeR = (fgkOFCRadius-fgkIFCRadius) / (kRows-1) ;
207 const Float_t gridSizeZ = fgkTPCZ0 / (kColumns-1) ;
209 TMatrixD voltArrayA(kRows,kColumns), voltArrayC(kRows,kColumns); // boundary vectors
210 TMatrixD chargeDensity(kRows,kColumns); // dummy charge
211 TMatrixD arrayErOverEzA(kRows,kColumns), arrayErOverEzC(kRows,kColumns); // solution
212 TMatrixD arrayDeltaEzA(kRows,kColumns), arrayDeltaEzC(kRows,kColumns); // solution
214 Double_t rList[kRows], zedList[kColumns] ;
216 // Fill arrays with initial conditions. V on the boundary and ChargeDensity in the volume.
217 for ( Int_t j = 0 ; j < kColumns ; j++ ) {
218 Double_t zed = j*gridSizeZ ;
220 for ( Int_t i = 0 ; i < kRows ; i++ ) {
221 Double_t radius = fgkIFCRadius + i*gridSizeR ;
223 voltArrayA(i,j) = 0; // Initialize voltArrayA to zero
224 voltArrayC(i,j) = 0; // Initialize voltArrayC to zero
225 chargeDensity(i,j) = 0; // Initialize ChargeDensity to zero - not used in this class
230 // check if boundary values are the same for the C side (for later, saving some calculation time)
232 Int_t symmetry = -1; // assume that A and C side are identical (but anti-symmetric!) // e.g conical deformation
235 // check if boundaries are different (regardless the sign)
236 for (Int_t i=0; i<8; i++) {
237 if (TMath::Abs(TMath::Abs(fBoundariesA[i]) - TMath::Abs(fBoundariesC[i])) > 1e-5)
239 sVec[i] = (Int_t)( TMath::Sign((Float_t)1.,fBoundariesA[i]) * TMath::Sign((Float_t)1.,fBoundariesC[i]));
241 if (symmetry==-1) { // still the same values?
242 // check the kind of symmetry , if even ...
243 if (sVec[0]==1 && sVec[1]==1 && sVec[2]==1 && sVec[3]==1 && sVec[4]==1 && sVec[5]==1 && sVec[6]==1 && sVec[7]==1 )
245 else if (sVec[0]==-1 && sVec[1]==-1 && sVec[2]==-1 && sVec[3]==-1 && sVec[4]==-1 && sVec[5]==-1 && sVec[6]==-1 && sVec[7]==-1 )
248 symmetry = 0; // some of the values differ in the sign -> neither symmetric nor antisymmetric
253 // Solve the electrosatic problem in 2D
255 // Fill the complete Boundary vectors
256 // Start at IFC at CE and work anti-clockwise through IFC, ROC, OFC, and CE (clockwise for C side)
257 for ( Int_t j = 0 ; j < kColumns ; j++ ) {
258 Double_t zed = j*gridSizeZ ;
259 for ( Int_t i = 0 ; i < kRows ; i++ ) {
260 Double_t radius = fgkIFCRadius + i*gridSizeR ;
262 // A side boundary vectors
263 if ( i == 0 ) voltArrayA(i,j) += zed *((fBoundariesA[1]-fBoundariesA[0])/((kColumns-1)*gridSizeZ))
264 + fBoundariesA[0] ; // IFC
265 if ( j == kColumns-1 ) voltArrayA(i,j) += (radius-fgkIFCRadius)*((fBoundariesA[3]-fBoundariesA[2])/((kRows-1)*gridSizeR))
266 + fBoundariesA[2] ; // ROC
267 if ( i == kRows-1 ) voltArrayA(i,j) += zed *((fBoundariesA[4]-fBoundariesA[5])/((kColumns-1)*gridSizeZ))
268 + fBoundariesA[5] ; // OFC
269 if ( j == 0 ) voltArrayA(i,j) += (radius-fgkIFCRadius)*((fBoundariesA[6]-fBoundariesA[7])/((kRows-1)*gridSizeR))
270 + fBoundariesA[7] ; // CE
273 // C side boundary vectors
274 if ( i == 0 ) voltArrayC(i,j) += zed *((fBoundariesC[1]-fBoundariesC[0])/((kColumns-1)*gridSizeZ))
275 + fBoundariesC[0] ; // IFC
276 if ( j == kColumns-1 ) voltArrayC(i,j) += (radius-fgkIFCRadius)*((fBoundariesC[3]-fBoundariesC[2])/((kRows-1)*gridSizeR))
277 + fBoundariesC[2] ; // ROC
278 if ( i == kRows-1 ) voltArrayC(i,j) += zed *((fBoundariesC[4]-fBoundariesC[5])/((kColumns-1)*gridSizeZ))
279 + fBoundariesC[5] ; // OFC
280 if ( j == 0 ) voltArrayC(i,j) += (radius-fgkIFCRadius)*((fBoundariesC[6]-fBoundariesC[7])/((kRows-1)*gridSizeR))
281 + fBoundariesC[7] ; // CE
287 voltArrayA(0,0) *= 0.5 ; // Use average boundary condition at corner
288 voltArrayA(kRows-1,0) *= 0.5 ; // Use average boundary condition at corner
289 voltArrayA(0,kColumns-1) *= 0.5 ; // Use average boundary condition at corner
290 voltArrayA(kRows-1,kColumns-1)*= 0.5 ; // Use average boundary condition at corner
293 voltArrayC(0,0) *= 0.5 ; // Use average boundary condition at corner
294 voltArrayC(kRows-1,0) *= 0.5 ; // Use average boundary condition at corner
295 voltArrayC(0,kColumns-1) *= 0.5 ; // Use average boundary condition at corner
296 voltArrayC(kRows-1,kColumns-1)*= 0.5 ; // Use average boundary condition at corner
300 // always solve the problem on the A side
301 PoissonRelaxation2D( voltArrayA, chargeDensity, arrayErOverEzA, arrayDeltaEzA,
302 kRows, kColumns, kIterations, fROCdisplacement ) ;
304 if (symmetry!=0) { // A and C side are the same ("anti-symmetric" or "symmetric")
305 for ( Int_t j = 0 ; j < kColumns ; j++ ) {
306 for ( Int_t i = 0 ; i < kRows ; i++ ) {
307 arrayErOverEzC(i,j) = symmetry*arrayErOverEzA(i,j);
308 arrayDeltaEzC(i,j) = -symmetry*arrayDeltaEzA(i,j);
311 } else if (symmetry==0) { // A and C side are different - Solve the problem on the C side too
312 PoissonRelaxation2D( voltArrayC, chargeDensity, arrayErOverEzC, arrayDeltaEzC,
313 kRows, kColumns, kIterations, fROCdisplacement ) ;
314 for ( Int_t j = 0 ; j < kColumns ; j++ ) {
315 for ( Int_t i = 0 ; i < kRows ; i++ ) {
316 arrayDeltaEzC(i,j) = -arrayDeltaEzC(i,j); // negative z coordinate!
321 // Interpolate results onto standard grid for Electric Fields
322 Int_t ilow=0, jlow=0 ;
326 for ( Int_t i = 0 ; i < kNZ ; ++i ) {
327 z = TMath::Abs( fgkZList[i] ) ;
328 for ( Int_t j = 0 ; j < kNR ; ++j ) {
329 // Linear interpolation !!
331 Search( kRows, rList, r, ilow ) ; // Note switch - R in rows and Z in columns
332 Search( kColumns, zedList, z, jlow ) ;
333 if ( ilow < 0 ) ilow = 0 ; // check if out of range
334 if ( jlow < 0 ) jlow = 0 ;
335 if ( ilow + 1 >= kRows - 1 ) ilow = kRows - 2 ;
336 if ( jlow + 1 >= kColumns - 1 ) jlow = kColumns - 2 ;
338 if (fgkZList[i]>0) { // A side solution
339 saveEr[0] = arrayErOverEzA(ilow,jlow) +
340 (arrayErOverEzA(ilow,jlow+1)-arrayErOverEzA(ilow,jlow))*(z-zedList[jlow])/gridSizeZ ;
341 saveEr[1] = arrayErOverEzA(ilow+1,jlow) +
342 (arrayErOverEzA(ilow+1,jlow+1)-arrayErOverEzA(ilow+1,jlow))*(z-zedList[jlow])/gridSizeZ ;
343 saveEz[0] = arrayDeltaEzA(ilow,jlow) +
344 (arrayDeltaEzA(ilow,jlow+1)-arrayDeltaEzA(ilow,jlow))*(z-zedList[jlow])/gridSizeZ ;
345 saveEz[1] = arrayDeltaEzA(ilow+1,jlow) +
346 (arrayDeltaEzA(ilow+1,jlow+1)-arrayDeltaEzA(ilow+1,jlow))*(z-zedList[jlow])/gridSizeZ ;
348 } else if (fgkZList[i]<0) { // C side solution
349 saveEr[0] = arrayErOverEzC(ilow,jlow) +
350 (arrayErOverEzC(ilow,jlow+1)-arrayErOverEzC(ilow,jlow))*(z-zedList[jlow])/gridSizeZ ;
351 saveEr[1] = arrayErOverEzC(ilow+1,jlow) +
352 (arrayErOverEzC(ilow+1,jlow+1)-arrayErOverEzC(ilow+1,jlow))*(z-zedList[jlow])/gridSizeZ ;
353 saveEz[0] = arrayDeltaEzC(ilow,jlow) +
354 (arrayDeltaEzC(ilow,jlow+1)-arrayDeltaEzC(ilow,jlow))*(z-zedList[jlow])/gridSizeZ ;
355 saveEz[1] = arrayDeltaEzC(ilow+1,jlow) +
356 (arrayDeltaEzC(ilow+1,jlow+1)-arrayDeltaEzC(ilow+1,jlow))*(z-zedList[jlow])/gridSizeZ ;
359 AliWarning("Field calculation at z=0 (CE) is not allowed!");
360 saveEr[0]=0; saveEr[1]=0;
361 saveEz[0]=0; saveEz[1]=0;
363 fLookUpErOverEz[i][j] = saveEr[0] + (saveEr[1]-saveEr[0])*(r-rList[ilow])/gridSizeR ;
364 fLookUpDeltaEz[i][j] = saveEz[0] + (saveEz[1]-saveEz[0])*(r-rList[ilow])/gridSizeR ;
370 chargeDensity.Clear();
371 arrayErOverEzA.Clear();
372 arrayErOverEzC.Clear();
373 arrayDeltaEzA.Clear();
374 arrayDeltaEzC.Clear();
380 void AliTPCBoundaryVoltError::Print(const Option_t* option) const {
382 // Print function to check the settings of the boundary vectors
383 // option=="a" prints the C0 and C1 coefficents for calibration purposes
386 TString opt = option; opt.ToLower();
387 printf("%s\n",GetTitle());
388 printf(" - Voltage settings (on the TPC boundaries) - linearly interpolated\n");
389 printf(" : A-side (anti-clockwise)\n");
390 printf(" (0,1):\t IFC (CE) : %3.1f V \t IFC (ROC): %3.1f V \n",fBoundariesA[0],fBoundariesA[1]);
391 printf(" (2,3):\t ROC (IFC): %3.1f V \t ROC (OFC): %3.1f V \n",fBoundariesA[2],fBoundariesA[3]);
392 printf(" (4,5):\t OFC (ROC): %3.1f V \t OFC (CE) : %3.1f V \n",fBoundariesA[4],fBoundariesA[5]);
393 printf(" (6,7):\t CE (OFC): %3.1f V \t CE (IFC): %3.1f V \n",fBoundariesA[6],fBoundariesA[7]);
394 printf(" : C-side (clockwise)\n");
395 printf(" (0,1):\t IFC (CE) : %3.1f V \t IFC (ROC): %3.1f V \n",fBoundariesC[0],fBoundariesC[1]);
396 printf(" (2,3):\t ROC (IFC): %3.1f V \t ROC (OFC): %3.1f V \n",fBoundariesC[2],fBoundariesC[3]);
397 printf(" (4,5):\t OFC (ROC): %3.1f V \t OFC (CE) : %3.1f V \n",fBoundariesC[4],fBoundariesC[5]);
398 printf(" (6,7):\t CE (OFC): %3.1f V \t CE (IFC): %3.1f V \n",fBoundariesC[6],fBoundariesC[7]);
400 // Check wether the settings of the Central Electrode agree (on the A and C side)
401 // Note: they have to be antisymmetric!
402 if (( TMath::Abs(fBoundariesA[6]+fBoundariesC[6])>1e-5) || ( TMath::Abs(fBoundariesA[7]+fBoundariesC[7])>1e-5 ) ){
403 AliWarning("Boundary parameters for the Central Electrode (CE) are not anti-symmetric! HOW DID YOU MANAGE THAT?");
404 AliWarning("Congratulations, you just splitted the Central Electrode of the TPC!");
405 AliWarning("Non-physical settings of the boundary parameter at the Central Electrode");
408 if (opt.Contains("a")) { // Print all details
409 printf(" - T1: %1.4f, T2: %1.4f \n",fT1,fT2);
410 printf(" - C1: %1.4f, C0: %1.4f \n",fC1,fC0);
414 AliError("Lookup table was not initialized! You should do InitBoundaryVoltErrorDistortion() ...");
419 void AliTPCBoundaryVoltError::SetBoundariesA(Float_t boundariesA[8]){
421 // set voltage errors on the TPC boundaries - A side
423 // Start at IFC at the Central electrode and work anti-clockwise (clockwise for C side) through
424 // IFC, ROC, OFC, and CE. The boundary conditions are currently defined to be a linear
425 // interpolation between pairs of numbers in the Boundary (e.g. fBoundariesA) vector.
426 // The first pair of numbers represent the beginning and end of the Inner Field cage, etc.
427 // The unit of the error potential vector is [Volt], whereas 1mm shift of the IFC would
428 // correspond to ~ 40 V
430 // Note: The setting for the CE will be passed to the C side!
432 for (Int_t i=0; i<8; i++) {
433 fBoundariesA[i]= boundariesA[i];
434 if (i>5) fBoundariesC[i]= -boundariesA[i]; // setting for the CE is passed to C side
438 void AliTPCBoundaryVoltError::SetBoundariesC(Float_t boundariesC[6]){
440 // set voltage errors on the TPC boundaries - C side
442 // Start at IFC at the Central electrode and work clockwise (for C side) through
443 // IFC, ROC and OFC. The boundary conditions are currently defined to be a linear
444 // interpolation between pairs of numbers in the Boundary (e.g. fBoundariesC) vector.
445 // The first pair of numbers represent the beginning and end of the Inner Field cage, etc.
446 // The unit of the error potential vector is [Volt], whereas 1mm shift of the IFC would
447 // correspond to ~ 40 V
449 // Note: The setting for the CE will be taken from the A side (pos 6 and 7)!
451 for (Int_t i=0; i<6; i++) {
452 fBoundariesC[i]= boundariesC[i];