1 /**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
17 // This implementation AliTPCExB is using an "exact" calculation of the ExB
18 // effect. That is, it uses the drift ODE to calculate the distortion
19 // without any further assumption.
20 // Due to the numerical integration of the ODE, there are some numerical
21 // uncertencies involed.
25 #include "TTreeStream.h"
27 #include "AliTPCExBExact.h"
29 ClassImp(AliTPCExBExact)
31 const Double_t AliTPCExBExact::fgkEM=1.602176487e-19/9.10938215e-31;
32 const Double_t AliTPCExBExact::fgkDriftField=-40.e3;
34 AliTPCExBExact::AliTPCExBExact()
38 fkNX(0),fkNY(0),fkNZ(0),
39 fkXMin(-250.),fkXMax(250.),fkYMin(-250.),fkYMax(250.),
40 fkZMin(-250.),fkZMax(250.),
41 fkNLook(0),fkLook(0) {
47 AliTPCExBExact::AliTPCExBExact(const AliMagF *bField,
48 Double_t driftVelocity,
49 Int_t nx,Int_t ny,Int_t nz,Int_t n)
50 : fDriftVelocity(driftVelocity),
52 fkField(bField),fkN(n),
53 fkNX(nx),fkNY(ny),fkNZ(nz),
54 fkXMin(-250.),fkXMax(250.),fkYMin(-250.),fkYMax(250.),
55 fkZMin(-250.),fkZMax(250.),
56 fkNLook(0),fkLook(0) {
58 // The constructor. One has to supply a magnetic field and an (initial)
59 // drift velocity. Since some kind of lookuptable is created the
60 // number of its meshpoints can be supplied.
61 // n sets the number of integration steps to be used when integrating
62 // over the full drift length.
68 AliTPCExBExact::AliTPCExBExact(const AliFieldMap *bFieldMap,
69 Double_t driftVelocity,Int_t n)
70 : fDriftVelocity(driftVelocity),
71 fkMap(bFieldMap),fkField(0),fkN(n),
72 fkNX(0),fkNY(0),fkNZ(0),
73 fkXMin(-250.),fkXMax(250.),fkYMin(-250.),fkYMax(250.),
74 fkZMin(-250.),fkZMax(250.),
75 fkNLook(0),fkLook(0) {
77 // The constructor. One has to supply a field map and an (initial)
79 // n sets the number of integration steps to be used when integrating
80 // over the full drift length.
83 fkXMin=bFieldMap->Xmin()
84 -TMath::Ceil( (bFieldMap->Xmin()+250.0)/bFieldMap->DelX())
86 fkXMax=bFieldMap->Xmax()
87 -TMath::Floor((bFieldMap->Xmax()-250.0)/bFieldMap->DelX())
89 fkYMin=bFieldMap->Ymin()
90 -TMath::Ceil( (bFieldMap->Ymin()+250.0)/bFieldMap->DelY())
92 fkYMax=bFieldMap->Ymax()
93 -TMath::Floor((bFieldMap->Ymax()-250.0)/bFieldMap->DelY())
95 fkZMax=bFieldMap->Zmax()
96 -TMath::Floor((bFieldMap->Zmax()-250.0)/bFieldMap->DelZ())
98 fkZMax=TMath::Max(0.,fkZMax); // I really hope that this is unnecessary!
100 fkNX=static_cast<Int_t>((fkXMax-fkXMin)/bFieldMap->DelX()+1.1);
101 fkNY=static_cast<Int_t>((fkYMax-fkYMin)/bFieldMap->DelY()+1.1);
102 fkNZ=static_cast<Int_t>((fkZMax-fkZMin)/bFieldMap->DelZ()+1.1);
108 AliTPCExBExact::~AliTPCExBExact() {
110 // destruct the poor object.
115 void AliTPCExBExact::Correct(const Double_t *position, Double_t *corrected) {
117 // correct for the distortion
119 Double_t x=(position[0]-fkXMin)/(fkXMax-fkXMin)*(fkNX-1);
120 Int_t xi1=static_cast<Int_t>(x);
121 xi1=TMath::Max(TMath::Min(xi1,fkNX-2),0);
124 Double_t dx1=(xi2-x);
126 Double_t y=(position[1]-fkYMin)/(fkYMax-fkYMin)*(fkNY-1);
127 Int_t yi1=static_cast<Int_t>(y);
128 yi1=TMath::Max(TMath::Min(yi1,fkNY-2),0);
131 Double_t dy1=(yi2-y);
133 Double_t z=position[2]/fkZMax*(fkNZ-1);
142 Int_t zi1=static_cast<Int_t>(z);
143 zi1=TMath::Max(TMath::Min(zi1,fkNZ-2),0);
146 Double_t dz1=(zi2-z);
148 for (int i=0;i<3;++i)
150 =fkLook[(((xi1*fkNY+yi1)*fkNZ+zi1)*2+side)*3+i]*dx1*dy1*dz1
151 +fkLook[(((xi1*fkNY+yi1)*fkNZ+zi2)*2+side)*3+i]*dx1*dy1*dz
152 +fkLook[(((xi1*fkNY+yi2)*fkNZ+zi1)*2+side)*3+i]*dx1*dy *dz1
153 +fkLook[(((xi1*fkNY+yi2)*fkNZ+zi2)*2+side)*3+i]*dx1*dy *dz
154 +fkLook[(((xi2*fkNY+yi2)*fkNZ+zi1)*2+side)*3+i]*dx *dy *dz1
155 +fkLook[(((xi2*fkNY+yi2)*fkNZ+zi2)*2+side)*3+i]*dx *dy *dz
156 +fkLook[(((xi2*fkNY+yi1)*fkNZ+zi1)*2+side)*3+i]*dx *dy1*dz1
157 +fkLook[(((xi2*fkNY+yi1)*fkNZ+zi2)*2+side)*3+i]*dx *dy1*dz ;
158 // corrected[2]=position[2];
162 void AliTPCExBExact::TestThisBeautifulObject(const AliFieldMap *bFieldMap,
163 const char* fileName) {
165 // Have a look at the common part "TestThisBeautifulObjectGeneric".
169 TestThisBeautifulObjectGeneric(fileName);
173 void AliTPCExBExact::TestThisBeautifulObject(const AliMagF *bField,
174 const char* fileName) {
176 // Have a look at the common part "TestThisBeautifulObjectGeneric".
180 TestThisBeautifulObjectGeneric(fileName);
183 void AliTPCExBExact::TestThisBeautifulObjectGeneric(const char* fileName) {
185 // Well, as the name sais... it tests the object.
187 TTreeSRedirector ts(fileName);
189 for (x[0]=-250.;x[0]<=250.;x[0]+=10.)
190 for (x[1]=-250.;x[1]<=250.;x[1]+=10.)
191 for (x[2]=-250.;x[2]<=250.;x[2]+=10.) {
195 CalculateDistortion(x,dnl);
196 Double_t r=TMath::Sqrt(x[0]*x[0]+x[1]*x[1]);
197 Double_t rd=TMath::Sqrt(d[0]*d[0]+d[1]*d[1]);
199 Double_t phi=TMath::ATan2(x[0],x[1]);
200 Double_t phid=TMath::ATan2(d[0],d[1]);
201 Double_t dphi=phi-phid;
202 if (dphi<0.) dphi+=TMath::TwoPi();
203 if (dphi>TMath::Pi()) dphi=TMath::TwoPi()-dphi;
204 Double_t drphi=r*dphi;
205 Double_t dx=x[0]-d[0];
206 Double_t dy=x[1]-d[1];
207 Double_t dz=x[2]-d[2];
208 Double_t dnlx=x[0]-dnl[0];
209 Double_t dnly=x[1]-dnl[1];
210 Double_t dnlz=x[2]-dnl[2];
234 void AliTPCExBExact::CreateLookupTable() {
236 // Helper function to fill the lookup table.
238 fkNLook=fkNX*fkNY*fkNZ*2*3;
239 fkLook=new Double_t[fkNLook];
241 for (int i=0;i<fkNX;++i) {
242 x[0]=fkXMin+(fkXMax-fkXMin)/(fkNX-1)*i;
243 for (int j=0;j<fkNY;++j) {
244 x[1]=fkYMin+(fkYMax-fkYMin)/(fkNY-1)*j;
245 for (int k=0;k<fkNZ;++k) {
246 x[2]=1.*fkZMax/(fkNZ-1)*k;
247 x[2]=TMath::Max((Double_t)0.0001,x[2]); //ugly
248 CalculateDistortion(x,&fkLook[(((i*fkNY+j)*fkNZ+k)*2+1)*3]);
250 CalculateDistortion(x,&fkLook[(((i*fkNY+j)*fkNZ+k)*2+0)*3]);
256 void AliTPCExBExact::GetE(Double_t *e,const Double_t *x) const {
258 // Helper function returning the E field in SI units (V/m).
262 e[2]=(x[2]<0.?-1.:1.)*fgkDriftField; // in V/m
265 void AliTPCExBExact::GetB(Double_t *b,const Double_t *x) const {
267 // Helper function returning the B field in SI units (T).
270 // the beautiful m to cm (and the ugly "const_cast") and Double_t
271 // to Float_t read the NRs introduction!:
272 for (int i=0;i<3;++i) xm[i]=x[i]*100.;
275 // fkMap->Field(xm,bf);
277 ((AliMagF*)fkField)->Field(xm,bf);
278 for (int i=0;i<3;++i) b[i]=bf[i]/10.;
281 void AliTPCExBExact::Motion(const Double_t *x,Double_t,
282 Double_t *dxdt) const {
284 // The differential equation of motion of the electrons.
286 Double_t tau=fDriftVelocity/fgkDriftField/fgkEM;
287 Double_t tau2=tau*tau;
292 Double_t wx=fgkEM*b[0];
293 Double_t wy=fgkEM*b[1];
294 Double_t wz=fgkEM*b[2];
295 Double_t ex=fgkEM*e[0];
296 Double_t ey=fgkEM*e[1];
297 Double_t ez=fgkEM*e[2];
298 Double_t w2=(wx*wx+wy*wy+wz*wz);
299 dxdt[0]=(1.+wx*wx*tau2)*ex+(wz*tau+wx*wy*tau2)*ey+(-wy*tau+wx*wz*tau2)*ez;
300 dxdt[1]=(-wz*tau+wx*wy*tau2)*ex+(1.+wy*wy*tau2)*ey+(wx*tau+wy*wz*tau2)*ez;
301 dxdt[2]=(wy*tau+wx*wz*tau2)*ex+(-wx*tau+wy*wz*tau2)*ey+(1.+wz*wz*tau2)*ez;
302 Double_t fac=tau/(1.+w2*tau2);
308 void AliTPCExBExact::CalculateDistortion(const Double_t *x0,
309 Double_t *dist) const {
311 // Helper function that calculates one distortion by integration
312 // (only used to fill the lookup table).
314 Double_t h=0.01*250./fDriftVelocity/fkN;
318 for (int i=0;i<3;++i)
319 xo[i]=xt[i]=x0[i]*0.01;
320 while (TMath::Abs(xt[2])<250.*0.01) {
321 for (int i=0;i<3;++i)
327 Double_t p=((xt[2]<0.?-1.:1.)*250.*0.01-xo[2])/(xt[2]-xo[2]);
328 dist[0]=(xo[0]+p*(xt[0]-xo[0]))*100.;
329 dist[1]=(xo[1]+p*(xt[1]-xo[1]))*100.;
330 // dist[2]=(xo[2]+p*(xt[2]-xo[2]))*100.;
331 dist[2]=(x0[2]>0.?-1:1.)*(t-h+p*h)*fDriftVelocity*100.;
332 dist[2]+=(x0[2]<0.?-1:1.)*250.;
339 // reverse the distortion, i.e. get the correction
340 dist[0]=x0[0]-(dist[0]-x0[0]);
341 dist[1]=x0[1]-(dist[1]-x0[1]);
344 void AliTPCExBExact::DGLStep(Double_t *x,Double_t t,Double_t h) const {
346 // An elementary integration step.
347 // (simple Euler Method)
351 for (int i=0;i<3;++i)
354 /* suggestions about how to write it this way are welcome!
355 void DGLStep(void (*f)(const Double_t *x,Double_t t,Double_t *dxdt),
356 Double_t *x,Double_t t,Double_t h,Int_t n) const;