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CMSUrbanMscModel95.cc
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25 //
26 //
27 // GEANT4 Class file
28 //
29 //
30 // File name: CMSUrbanMscModel95
31 //
32 // Author: Laszlo Urban
33 //
34 // Creation date: 20.03.2011
35 //
36 // Created from G4UrbanMscModel93
37 //
38 // 01-08-2011 L.Urban
39 // new parametrization of the tail parameter c. Some of the timing
40 // optimization has been removed (facsafety)
41 // 04-09-2011 L.Urban
42 // facsafety optimization is back for UseSafety
43 // 10-10-2011 L.Urban
44 // facsafety=0.5 instead of 0.3
45 //
46 // Class Description:
47 //
48 // Implementation of the model of multiple scattering based on
49 // H.W.Lewis Phys Rev 78 (1950) 526 and others
50 
51 // -------------------------------------------------------------------
52 // In its present form the model can be used for simulation
53 // of the e-/e+ multiple scattering
54 //
55 
56 
57 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
58 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
59 
60 #include "CMSUrbanMscModel95.hh"
61 #include "Randomize.hh"
62 #include "G4Electron.hh"
63 #include "G4LossTableManager.hh"
64 #include "G4ParticleChangeForMSC.hh"
65 
66 #include "G4Poisson.hh"
67 #include "globals.hh"
68 
69 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
70 
71 using namespace std;
72 
73 CMSUrbanMscModel95::CMSUrbanMscModel95(const G4String& nam)
74  : G4VMscModel(nam),
75  isInitialized(false)
76 {
77  masslimite = 0.6*MeV;
78  lambdalimit = 1.*mm;
79  fr = 0.02;
80  taubig = 8.0;
81  tausmall = 1.e-16;
82  taulim = 1.e-6;
83  currentTau = taulim;
84  tlimitminfix = 1.e-6*mm;
85  stepmin = tlimitminfix;
86  smallstep = 1.e10;
87  currentRange = 0. ;
88  rangeinit = 0.;
89  tlimit = 1.e10*mm;
90  tlimitmin = 10.*tlimitminfix;
91  tgeom = 1.e50*mm;
92  geombig = 1.e50*mm;
93  geommin = 1.e-3*mm;
94  geomlimit = geombig;
95  presafety = 0.*mm;
96  //facsafety = 0.50 ;
97 
98  y = 0.;
99 
100  Zold = 0.;
101  Zeff = 1.;
102  Z2 = 1.;
103  Z23 = 1.;
104  lnZ = 0.;
105  coeffth1 = 0.;
106  coeffth2 = 0.;
107  coeffc1 = 0.;
108  coeffc2 = 0.;
109  coeffc3 = 0.;
110  coeffc4 = 0.;
111  scr1ini = fine_structure_const*fine_structure_const*
112  electron_mass_c2*electron_mass_c2/(0.885*0.885*4.*pi);
113  scr2ini = 3.76*fine_structure_const*fine_structure_const;
114  scr1 = 0.;
115  scr2 = 0.;
116 
117  theta0max = pi/6.;
118  rellossmax = 0.50;
119  third = 1./3.;
120  particle = 0;
121  theManager = G4LossTableManager::Instance();
122  inside = false;
123  insideskin = false;
124 
125  skindepth = skin*stepmin;
126 
127  mass = proton_mass_c2;
128  charge = ChargeSquare = 1.0;
129  currentKinEnergy = currentRadLength = lambda0 = lambdaeff = tPathLength
130  = zPathLength = par1 = par2 = par3 = 0;
131 
132  currentMaterialIndex = -1;
133  fParticleChange = 0;
134  theLambdaTable = 0;
135  couple = 0;
136  samplez = true;
137 }
138 
139 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
140 
141 CMSUrbanMscModel95::~CMSUrbanMscModel95()
142 {}
143 
144 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
145 
146 void CMSUrbanMscModel95::Initialise(const G4ParticleDefinition* p,
147  const G4DataVector&)
148 {
149  skindepth = skin*stepmin;
150 
151  if(isInitialized) { return; }
152  // set values of some data members
153  SetParticle(p);
154 
155  if(p->GetPDGMass() > MeV) {
156  G4cout << "### WARNING: CMSUrbanMscModel95 model is used for "
157  << p->GetParticleName() << " !!! " << G4endl;
158  G4cout << "### This model should be used only for e+-"
159  << G4endl;
160  }
161 
162  fParticleChange = GetParticleChangeForMSC();
163  InitialiseSafetyHelper();
164 
165  //samplez = true;
166 
167  isInitialized = true;
168 }
169 
170 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
171 
172 G4double CMSUrbanMscModel95::ComputeCrossSectionPerAtom(
173  const G4ParticleDefinition* part,
174  G4double KineticEnergy,
175  G4double AtomicNumber,G4double,
176  G4double, G4double)
177 {
178  const G4double sigmafactor = twopi*classic_electr_radius*classic_electr_radius;
179  const G4double epsfactor = 2.*electron_mass_c2*electron_mass_c2*
180  Bohr_radius*Bohr_radius/(hbarc*hbarc);
181  const G4double epsmin = 1.e-4 , epsmax = 1.e10;
182 
183  const G4double Zdat[15] = { 4., 6., 13., 20., 26., 29., 32., 38., 47.,
184  50., 56., 64., 74., 79., 82. };
185 
186  const G4double Tdat[22] = { 100*eV, 200*eV, 400*eV, 700*eV,
187  1*keV, 2*keV, 4*keV, 7*keV,
188  10*keV, 20*keV, 40*keV, 70*keV,
189  100*keV, 200*keV, 400*keV, 700*keV,
190  1*MeV, 2*MeV, 4*MeV, 7*MeV,
191  10*MeV, 20*MeV};
192 
193  // corr. factors for e-/e+ lambda for T <= Tlim
194  G4double celectron[15][22] =
195  {{1.125,1.072,1.051,1.047,1.047,1.050,1.052,1.054,
196  1.054,1.057,1.062,1.069,1.075,1.090,1.105,1.111,
197  1.112,1.108,1.100,1.093,1.089,1.087 },
198  {1.408,1.246,1.143,1.096,1.077,1.059,1.053,1.051,
199  1.052,1.053,1.058,1.065,1.072,1.087,1.101,1.108,
200  1.109,1.105,1.097,1.090,1.086,1.082 },
201  {2.833,2.268,1.861,1.612,1.486,1.309,1.204,1.156,
202  1.136,1.114,1.106,1.106,1.109,1.119,1.129,1.132,
203  1.131,1.124,1.113,1.104,1.099,1.098 },
204  {3.879,3.016,2.380,2.007,1.818,1.535,1.340,1.236,
205  1.190,1.133,1.107,1.099,1.098,1.103,1.110,1.113,
206  1.112,1.105,1.096,1.089,1.085,1.098 },
207  {6.937,4.330,2.886,2.256,1.987,1.628,1.395,1.265,
208  1.203,1.122,1.080,1.065,1.061,1.063,1.070,1.073,
209  1.073,1.070,1.064,1.059,1.056,1.056 },
210  {9.616,5.708,3.424,2.551,2.204,1.762,1.485,1.330,
211  1.256,1.155,1.099,1.077,1.070,1.068,1.072,1.074,
212  1.074,1.070,1.063,1.059,1.056,1.052 },
213  {11.72,6.364,3.811,2.806,2.401,1.884,1.564,1.386,
214  1.300,1.180,1.112,1.082,1.073,1.066,1.068,1.069,
215  1.068,1.064,1.059,1.054,1.051,1.050 },
216  {18.08,8.601,4.569,3.183,2.662,2.025,1.646,1.439,
217  1.339,1.195,1.108,1.068,1.053,1.040,1.039,1.039,
218  1.039,1.037,1.034,1.031,1.030,1.036 },
219  {18.22,10.48,5.333,3.713,3.115,2.367,1.898,1.631,
220  1.498,1.301,1.171,1.105,1.077,1.048,1.036,1.033,
221  1.031,1.028,1.024,1.022,1.021,1.024 },
222  {14.14,10.65,5.710,3.929,3.266,2.453,1.951,1.669,
223  1.528,1.319,1.178,1.106,1.075,1.040,1.027,1.022,
224  1.020,1.017,1.015,1.013,1.013,1.020 },
225  {14.11,11.73,6.312,4.240,3.478,2.566,2.022,1.720,
226  1.569,1.342,1.186,1.102,1.065,1.022,1.003,0.997,
227  0.995,0.993,0.993,0.993,0.993,1.011 },
228  {22.76,20.01,8.835,5.287,4.144,2.901,2.219,1.855,
229  1.677,1.410,1.224,1.121,1.073,1.014,0.986,0.976,
230  0.974,0.972,0.973,0.974,0.975,0.987 },
231  {50.77,40.85,14.13,7.184,5.284,3.435,2.520,2.059,
232  1.837,1.512,1.283,1.153,1.091,1.010,0.969,0.954,
233  0.950,0.947,0.949,0.952,0.954,0.963 },
234  {65.87,59.06,15.87,7.570,5.567,3.650,2.682,2.182,
235  1.939,1.579,1.325,1.178,1.108,1.014,0.965,0.947,
236  0.941,0.938,0.940,0.944,0.946,0.954 },
237  {55.60,47.34,15.92,7.810,5.755,3.767,2.760,2.239,
238  1.985,1.609,1.343,1.188,1.113,1.013,0.960,0.939,
239  0.933,0.930,0.933,0.936,0.939,0.949 }};
240 
241  G4double cpositron[15][22] = {
242  {2.589,2.044,1.658,1.446,1.347,1.217,1.144,1.110,
243  1.097,1.083,1.080,1.086,1.092,1.108,1.123,1.131,
244  1.131,1.126,1.117,1.108,1.103,1.100 },
245  {3.904,2.794,2.079,1.710,1.543,1.325,1.202,1.145,
246  1.122,1.096,1.089,1.092,1.098,1.114,1.130,1.137,
247  1.138,1.132,1.122,1.113,1.108,1.102 },
248  {7.970,6.080,4.442,3.398,2.872,2.127,1.672,1.451,
249  1.357,1.246,1.194,1.179,1.178,1.188,1.201,1.205,
250  1.203,1.190,1.173,1.159,1.151,1.145 },
251  {9.714,7.607,5.747,4.493,3.815,2.777,2.079,1.715,
252  1.553,1.353,1.253,1.219,1.211,1.214,1.225,1.228,
253  1.225,1.210,1.191,1.175,1.166,1.174 },
254  {17.97,12.95,8.628,6.065,4.849,3.222,2.275,1.820,
255  1.624,1.382,1.259,1.214,1.202,1.202,1.214,1.219,
256  1.217,1.203,1.184,1.169,1.160,1.151 },
257  {24.83,17.06,10.84,7.355,5.767,3.707,2.546,1.996,
258  1.759,1.465,1.311,1.252,1.234,1.228,1.238,1.241,
259  1.237,1.222,1.201,1.184,1.174,1.159 },
260  {23.26,17.15,11.52,8.049,6.375,4.114,2.792,2.155,
261  1.880,1.535,1.353,1.281,1.258,1.247,1.254,1.256,
262  1.252,1.234,1.212,1.194,1.183,1.170 },
263  {22.33,18.01,12.86,9.212,7.336,4.702,3.117,2.348,
264  2.015,1.602,1.385,1.297,1.268,1.251,1.256,1.258,
265  1.254,1.237,1.214,1.195,1.185,1.179 },
266  {33.91,24.13,15.71,10.80,8.507,5.467,3.692,2.808,
267  2.407,1.873,1.564,1.425,1.374,1.330,1.324,1.320,
268  1.312,1.288,1.258,1.235,1.221,1.205 },
269  {32.14,24.11,16.30,11.40,9.015,5.782,3.868,2.917,
270  2.490,1.925,1.596,1.447,1.391,1.342,1.332,1.327,
271  1.320,1.294,1.264,1.240,1.226,1.214 },
272  {29.51,24.07,17.19,12.28,9.766,6.238,4.112,3.066,
273  2.602,1.995,1.641,1.477,1.414,1.356,1.342,1.336,
274  1.328,1.302,1.270,1.245,1.231,1.233 },
275  {38.19,30.85,21.76,15.35,12.07,7.521,4.812,3.498,
276  2.926,2.188,1.763,1.563,1.484,1.405,1.382,1.371,
277  1.361,1.330,1.294,1.267,1.251,1.239 },
278  {49.71,39.80,27.96,19.63,15.36,9.407,5.863,4.155,
279  3.417,2.478,1.944,1.692,1.589,1.480,1.441,1.423,
280  1.409,1.372,1.330,1.298,1.280,1.258 },
281  {59.25,45.08,30.36,20.83,16.15,9.834,6.166,4.407,
282  3.641,2.648,2.064,1.779,1.661,1.531,1.482,1.459,
283  1.442,1.400,1.354,1.319,1.299,1.272 },
284  {56.38,44.29,30.50,21.18,16.51,10.11,6.354,4.542,
285  3.752,2.724,2.116,1.817,1.692,1.554,1.499,1.474,
286  1.456,1.412,1.364,1.328,1.307,1.282 }};
287 
288  //data/corrections for T > Tlim
289  G4double Tlim = 10.*MeV;
290  G4double beta2lim = Tlim*(Tlim+2.*electron_mass_c2)/
291  ((Tlim+electron_mass_c2)*(Tlim+electron_mass_c2));
292  G4double bg2lim = Tlim*(Tlim+2.*electron_mass_c2)/
293  (electron_mass_c2*electron_mass_c2);
294 
295  G4double sig0[15] = {0.2672*barn, 0.5922*barn, 2.653*barn, 6.235*barn,
296  11.69*barn , 13.24*barn , 16.12*barn, 23.00*barn ,
297  35.13*barn , 39.95*barn , 50.85*barn, 67.19*barn ,
298  91.15*barn , 104.4*barn , 113.1*barn};
299 
300  G4double hecorr[15] = {120.70, 117.50, 105.00, 92.92, 79.23, 74.510, 68.29,
301  57.39, 41.97, 36.14, 24.53, 10.21, -7.855, -16.84,
302  -22.30};
303 
304  G4double sigma;
305  SetParticle(part);
306 
307  G4double Z23 = 2.*log(AtomicNumber)/3.; Z23 = exp(Z23);
308 
309  // correction if particle .ne. e-/e+
310  // compute equivalent kinetic energy
311  // lambda depends on p*beta ....
312 
313  G4double eKineticEnergy = KineticEnergy;
314 
315  if(mass > electron_mass_c2)
316  {
317  G4double TAU = KineticEnergy/mass ;
318  G4double c = mass*TAU*(TAU+2.)/(electron_mass_c2*(TAU+1.)) ;
319  G4double w = c-2. ;
320  G4double tau = 0.5*(w+sqrt(w*w+4.*c)) ;
321  eKineticEnergy = electron_mass_c2*tau ;
322  }
323 
324  G4double eTotalEnergy = eKineticEnergy + electron_mass_c2 ;
325  G4double beta2 = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
326  /(eTotalEnergy*eTotalEnergy);
327  G4double bg2 = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
328  /(electron_mass_c2*electron_mass_c2);
329 
330  G4double eps = epsfactor*bg2/Z23;
331 
332  if (eps<epsmin) sigma = 2.*eps*eps;
333  else if(eps<epsmax) sigma = log(1.+2.*eps)-2.*eps/(1.+2.*eps);
334  else sigma = log(2.*eps)-1.+1./eps;
335 
336  sigma *= ChargeSquare*AtomicNumber*AtomicNumber/(beta2*bg2);
337 
338  // interpolate in AtomicNumber and beta2
339  G4double c1,c2,cc1,cc2,corr;
340 
341  // get bin number in Z
342  G4int iZ = 14;
343  while ((iZ>=0)&&(Zdat[iZ]>=AtomicNumber)) iZ -= 1;
344  if (iZ==14) iZ = 13;
345  if (iZ==-1) iZ = 0 ;
346 
347  G4double Z1 = Zdat[iZ];
348  G4double Z2 = Zdat[iZ+1];
349  G4double ratZ = (AtomicNumber-Z1)*(AtomicNumber+Z1)/
350  ((Z2-Z1)*(Z2+Z1));
351 
352  if(eKineticEnergy <= Tlim)
353  {
354  // get bin number in T (beta2)
355  G4int iT = 21;
356  while ((iT>=0)&&(Tdat[iT]>=eKineticEnergy)) iT -= 1;
357  if(iT==21) iT = 20;
358  if(iT==-1) iT = 0 ;
359 
360  // calculate betasquare values
361  G4double T = Tdat[iT], E = T + electron_mass_c2;
362  G4double b2small = T*(E+electron_mass_c2)/(E*E);
363 
364  T = Tdat[iT+1]; E = T + electron_mass_c2;
365  G4double b2big = T*(E+electron_mass_c2)/(E*E);
366  G4double ratb2 = (beta2-b2small)/(b2big-b2small);
367 
368  if (charge < 0.)
369  {
370  c1 = celectron[iZ][iT];
371  c2 = celectron[iZ+1][iT];
372  cc1 = c1+ratZ*(c2-c1);
373 
374  c1 = celectron[iZ][iT+1];
375  c2 = celectron[iZ+1][iT+1];
376  cc2 = c1+ratZ*(c2-c1);
377 
378  corr = cc1+ratb2*(cc2-cc1);
379 
380  sigma *= sigmafactor/corr;
381  }
382  else
383  {
384  c1 = cpositron[iZ][iT];
385  c2 = cpositron[iZ+1][iT];
386  cc1 = c1+ratZ*(c2-c1);
387 
388  c1 = cpositron[iZ][iT+1];
389  c2 = cpositron[iZ+1][iT+1];
390  cc2 = c1+ratZ*(c2-c1);
391 
392  corr = cc1+ratb2*(cc2-cc1);
393 
394  sigma *= sigmafactor/corr;
395  }
396  }
397  else
398  {
399  c1 = bg2lim*sig0[iZ]*(1.+hecorr[iZ]*(beta2-beta2lim))/bg2;
400  c2 = bg2lim*sig0[iZ+1]*(1.+hecorr[iZ+1]*(beta2-beta2lim))/bg2;
401  if((AtomicNumber >= Z1) && (AtomicNumber <= Z2))
402  sigma = c1+ratZ*(c2-c1) ;
403  else if(AtomicNumber < Z1)
404  sigma = AtomicNumber*AtomicNumber*c1/(Z1*Z1);
405  else if(AtomicNumber > Z2)
406  sigma = AtomicNumber*AtomicNumber*c2/(Z2*Z2);
407  }
408  return sigma;
409 
410 }
411 
412 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
413 
414 G4double CMSUrbanMscModel95::ComputeTruePathLengthLimit(
415  const G4Track& track,
416  G4PhysicsTable* theTable,
417  G4double currentMinimalStep)
418 {
419  tPathLength = currentMinimalStep;
420  G4StepPoint* sp = track.GetStep()->GetPreStepPoint();
421  G4StepStatus stepStatus = sp->GetStepStatus();
422 
423  const G4DynamicParticle* dp = track.GetDynamicParticle();
424 
425  if(stepStatus == fUndefined) {
426  inside = false;
427  insideskin = false;
428  tlimit = geombig;
429  SetParticle( dp->GetDefinition() );
430  }
431 
432  theLambdaTable = theTable;
433  couple = track.GetMaterialCutsCouple();
434  currentMaterialIndex = couple->GetIndex();
435  currentKinEnergy = dp->GetKineticEnergy();
436  currentRange =
437  theManager->GetRangeFromRestricteDEDX(particle,currentKinEnergy,couple);
438  lambda0 = GetLambda(currentKinEnergy);
439 
440  // stop here if small range particle
441  if(inside) { return tPathLength; }
442 
443  if(tPathLength > currentRange) { tPathLength = currentRange; }
444 
445  presafety = sp->GetSafety();
446 
447  // G4cout << "G4Urban2::StepLimit tPathLength= "
448  // <<tPathLength<<" safety= " << presafety
449  // << " range= " <<currentRange<< " lambda= "<<lambda0
450  // << " Alg: " << steppingAlgorithm <<G4endl;
451 
452  // far from geometry boundary
453  if(currentRange < presafety)
454  {
455  inside = true;
456  return tPathLength;
457  }
458 
459  // standard version
460  //
461  if (steppingAlgorithm == fUseDistanceToBoundary)
462  {
463  //compute geomlimit and presafety
464  G4double geomlimit = ComputeGeomLimit(track, presafety, currentRange);
465 
466  // is it far from boundary ?
467  if(currentRange < presafety)
468  {
469  inside = true;
470  return tPathLength;
471  }
472 
473  smallstep += 1.;
474  insideskin = false;
475 
476  if((stepStatus == fGeomBoundary) || (stepStatus == fUndefined))
477  {
478  rangeinit = currentRange;
479  if(stepStatus == fUndefined) smallstep = 1.e10;
480  else smallstep = 1.;
481 
482  //define stepmin here (it depends on lambda!)
483  //rough estimation of lambda_elastic/lambda_transport
484  G4double rat = currentKinEnergy/MeV ;
485  rat = 1.e-3/(rat*(10.+rat)) ;
486  //stepmin ~ lambda_elastic
487  stepmin = rat*lambda0;
488  skindepth = skin*stepmin;
489  //define tlimitmin
490  tlimitmin = 10.*stepmin;
491  if(tlimitmin < tlimitminfix) tlimitmin = tlimitminfix;
492  //G4cout << "rangeinit= " << rangeinit << " stepmin= " << stepmin
493  // << " tlimitmin= " << tlimitmin << " geomlimit= " << geomlimit <<G4endl;
494  // constraint from the geometry
495  if((geomlimit < geombig) && (geomlimit > geommin))
496  {
497  // geomlimit is a geometrical step length
498  // transform it to true path length (estimation)
499  if((1.-geomlimit/lambda0) > 0.)
500  geomlimit = -lambda0*log(1.-geomlimit/lambda0)+tlimitmin ;
501 
502  if(stepStatus == fGeomBoundary)
503  tgeom = geomlimit/facgeom;
504  else
505  tgeom = 2.*geomlimit/facgeom;
506  }
507  else
508  tgeom = geombig;
509  }
510 
511 
512  //step limit
513  tlimit = facrange*rangeinit;
514 
515  //lower limit for tlimit
516  if(tlimit < tlimitmin) tlimit = tlimitmin;
517 
518  if(tlimit > tgeom) tlimit = tgeom;
519 
520  //G4cout << "tgeom= " << tgeom << " geomlimit= " << geomlimit
521  // << " tlimit= " << tlimit << " presafety= " << presafety << G4endl;
522 
523  // shortcut
524  if((tPathLength < tlimit) && (tPathLength < presafety) &&
525  (smallstep >= skin) && (tPathLength < geomlimit-0.999*skindepth))
526  return tPathLength;
527 
528  // step reduction near to boundary
529  if(smallstep < skin)
530  {
531  tlimit = stepmin;
532  insideskin = true;
533  }
534  else if(geomlimit < geombig)
535  {
536  if(geomlimit > skindepth)
537  {
538  if(tlimit > geomlimit-0.999*skindepth)
539  tlimit = geomlimit-0.999*skindepth;
540  }
541  else
542  {
543  insideskin = true;
544  if(tlimit > stepmin) tlimit = stepmin;
545  }
546  }
547 
548  if(tlimit < stepmin) tlimit = stepmin;
549 
550  // randomize 1st step or 1st 'normal' step in volume
551  if((stepStatus == fUndefined) ||
552  ((smallstep == skin) && !insideskin))
553  {
554  G4double temptlimit = tlimit;
555  if(temptlimit > tlimitmin)
556  {
557  do {
558  temptlimit = G4RandGauss::shoot(tlimit,0.3*tlimit);
559  } while ((temptlimit < tlimitmin) ||
560  (temptlimit > 2.*tlimit-tlimitmin));
561  }
562  else
563  temptlimit = tlimitmin;
564  if(tPathLength > temptlimit) tPathLength = temptlimit;
565  }
566  else
567  {
568  if(tPathLength > tlimit) tPathLength = tlimit ;
569  }
570 
571  }
572  // for 'normal' simulation with or without magnetic field
573  // there no small step/single scattering at boundaries
574  else if(steppingAlgorithm == fUseSafety)
575  {
576  // compute presafety again if presafety <= 0 and no boundary
577  // i.e. when it is needed for optimization purposes
578  if((stepStatus != fGeomBoundary) && (presafety < tlimitminfix))
579  presafety = ComputeSafety(sp->GetPosition(),tPathLength);
580 
581  // is far from boundary
582  if(currentRange < presafety)
583  {
584  inside = true;
585  return tPathLength;
586  }
587 
588  if((stepStatus == fGeomBoundary) || (stepStatus == fUndefined))
589  {
590  rangeinit = currentRange;
591  fr = facrange;
592  // 9.1 like stepping for e+/e- only (not for muons,hadrons)
593  if(mass < masslimite)
594  {
595  if(lambda0 > currentRange)
596  rangeinit = lambda0;
597  if(lambda0 > lambdalimit)
598  fr *= 0.75+0.25*lambda0/lambdalimit;
599  }
600 
601  //lower limit for tlimit
602  G4double rat = currentKinEnergy/MeV ;
603  rat = 1.e-3/(rat*(10.+rat)) ;
604  tlimitmin = 10.*lambda0*rat;
605  if(tlimitmin < tlimitminfix) tlimitmin = tlimitminfix;
606  }
607  //step limit
608  tlimit = fr*rangeinit;
609 
610  if(tlimit < facsafety*presafety)
611  tlimit = facsafety*presafety;
612 
613  //lower limit for tlimit
614  if(tlimit < tlimitmin) tlimit = tlimitmin;
615 
616  if(tPathLength > tlimit) tPathLength = tlimit;
617 
618  }
619 
620  // version similar to 7.1 (needed for some experiments)
621  else
622  {
623  if (stepStatus == fGeomBoundary)
624  {
625  if (currentRange > lambda0) tlimit = facrange*currentRange;
626  else tlimit = facrange*lambda0;
627 
628  if(tlimit < tlimitmin) tlimit = tlimitmin;
629  if(tPathLength > tlimit) tPathLength = tlimit;
630  }
631  }
632  //G4cout << "tPathLength= " << tPathLength
633  // << " currentMinimalStep= " << currentMinimalStep << G4endl;
634  return tPathLength ;
635 }
636 
637 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
638 
639 G4double CMSUrbanMscModel95::ComputeGeomPathLength(G4double)
640 {
641  lambdaeff = lambda0;
642  par1 = -1. ;
643  par2 = par3 = 0. ;
644 
645  // do the true -> geom transformation
646  zPathLength = tPathLength;
647 
648  // z = t for very small tPathLength
649  if(tPathLength < tlimitminfix) return zPathLength;
650 
651  // this correction needed to run MSC with eIoni and eBrem inactivated
652  // and makes no harm for a normal run
653  if(tPathLength > currentRange)
654  tPathLength = currentRange ;
655 
656  G4double tau = tPathLength/lambda0 ;
657 
658  if ((tau <= tausmall) || insideskin) {
659  zPathLength = tPathLength;
660  if(zPathLength > lambda0) zPathLength = lambda0;
661  return zPathLength;
662  }
663 
664  G4double zmean = tPathLength;
665  if (tPathLength < currentRange*dtrl) {
666  if(tau < taulim) zmean = tPathLength*(1.-0.5*tau) ;
667  else zmean = lambda0*(1.-exp(-tau));
668  zPathLength = zmean ;
669  return zPathLength;
670 
671  } else if(currentKinEnergy < mass || tPathLength == currentRange) {
672  par1 = 1./currentRange ;
673  par2 = 1./(par1*lambda0) ;
674  par3 = 1.+par2 ;
675  if(tPathLength < currentRange)
676  zmean = (1.-exp(par3*log(1.-tPathLength/currentRange)))/(par1*par3) ;
677  else {
678  zmean = 1./(par1*par3) ;
679  }
680  zPathLength = zmean ;
681  return zPathLength;
682 
683  } else {
684  G4double T1 = theManager->GetEnergy(particle,currentRange-tPathLength,couple);
685  G4double lambda1 = GetLambda(T1);
686 
687  par1 = (lambda0-lambda1)/(lambda0*tPathLength) ;
688  par2 = 1./(par1*lambda0) ;
689  par3 = 1.+par2 ;
690  zmean = (1.-exp(par3*log(lambda1/lambda0)))/(par1*par3) ;
691  }
692 
693  zPathLength = zmean ;
694 
695  // sample z
696  if(samplez)
697  {
698  const G4double ztmax = 0.999 ;
699  G4double zt = zmean/tPathLength ;
700 
701  if (tPathLength > stepmin && zt < ztmax)
702  {
703  G4double u,cz1;
704  if(zt >= third)
705  {
706  G4double cz = 0.5*(3.*zt-1.)/(1.-zt) ;
707  cz1 = 1.+cz ;
708  G4double u0 = cz/cz1 ;
709  G4double grej ;
710  do {
711  u = exp(log(G4UniformRand())/cz1) ;
712  grej = exp(cz*log(u/u0))*(1.-u)/(1.-u0) ;
713  } while (grej < G4UniformRand()) ;
714  }
715  else
716  {
717  u = 2.*zt*G4UniformRand();
718  }
719  zPathLength = tPathLength*u ;
720  }
721  }
722 
723  if(zPathLength > lambda0) { zPathLength = lambda0; }
724  //G4cout << "zPathLength= " << zPathLength << " lambda1= " << lambda0 << G4endl;
725  return zPathLength;
726 }
727 
728 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
729 
730 G4double CMSUrbanMscModel95::ComputeTrueStepLength(G4double geomStepLength)
731 {
732  // step defined other than transportation
733  if(geomStepLength == zPathLength && tPathLength <= currentRange)
734  { return tPathLength; }
735 
736  // t = z for very small step
737  zPathLength = geomStepLength;
738  tPathLength = geomStepLength;
739  if(geomStepLength < tlimitminfix) { return tPathLength; }
740 
741  // recalculation
742  if((geomStepLength > lambda0*tausmall) && !insideskin)
743  {
744  if(par1 < 0.)
745  tPathLength = -lambda0*log(1.-geomStepLength/lambda0) ;
746  else
747  {
748  if(par1*par3*geomStepLength < 1.)
749  tPathLength = (1.-exp(log(1.-par1*par3*geomStepLength)/par3))/par1 ;
750  else
751  tPathLength = currentRange;
752  }
753  }
754  if(tPathLength < geomStepLength) tPathLength = geomStepLength;
755  //G4cout << "tPathLength= " << tPathLength << " step= " << geomStepLength << G4endl;
756 
757  return tPathLength;
758 }
759 
760 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
761 
762 G4double CMSUrbanMscModel95::ComputeTheta0(G4double trueStepLength,
763  G4double KineticEnergy)
764 {
765  // for all particles take the width of the central part
766  // from a parametrization similar to the Highland formula
767  // ( Highland formula: Particle Physics Booklet, July 2002, eq. 26.10)
768  const G4double c_highland = 13.6*MeV ;
769  G4double betacp = sqrt(currentKinEnergy*(currentKinEnergy+2.*mass)*
770  KineticEnergy*(KineticEnergy+2.*mass)/
771  ((currentKinEnergy+mass)*(KineticEnergy+mass)));
772  y = trueStepLength/currentRadLength;
773  G4double theta0 = c_highland*std::abs(charge)*sqrt(y)/betacp;
774  y = log(y);
775  // correction factor from e- scattering data
776  G4double corr = coeffth1+coeffth2*y;
777 
778  theta0 *= corr ;
779 
780  return theta0;
781 }
782 
783 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
784 
785 void CMSUrbanMscModel95::SampleScattering(const G4DynamicParticle* dynParticle,
786  G4double safety)
787 {
788  G4double kineticEnergy = dynParticle->GetKineticEnergy();
789 
790  if((kineticEnergy <= 0.0) || (tPathLength <= tlimitminfix) ||
791  (tPathLength/tausmall < lambda0)) return;
792 
793  G4double cth = SampleCosineTheta(tPathLength,kineticEnergy);
794 
795  // protection against 'bad' cth values
796  if(std::fabs(cth) > 1.) return;
797 
798  // extra protection agaist high energy particles backscattered
799  if(cth < 1.0 - 1000*tPathLength/lambda0 && kineticEnergy > 20*MeV) {
800  //G4cout << "Warning: large scattering E(MeV)= " << kineticEnergy
801  // << " s(mm)= " << tPathLength/mm
802  // << " 1-cosTheta= " << 1.0 - cth << G4endl;
803  // do Gaussian central scattering
804  do {
805  cth = 1.0 + 2*log(G4UniformRand())*tPathLength/lambda0;
806  } while(cth < -1.0);
807  }
808 
809  G4double sth = sqrt((1.0 - cth)*(1.0 + cth));
810  G4double phi = twopi*G4UniformRand();
811  G4double dirx = sth*cos(phi);
812  G4double diry = sth*sin(phi);
813 
814  G4ThreeVector oldDirection = dynParticle->GetMomentumDirection();
815  G4ThreeVector newDirection(dirx,diry,cth);
816  newDirection.rotateUz(oldDirection);
817  fParticleChange->ProposeMomentumDirection(newDirection);
818 
819  if (latDisplasment && safety > tlimitminfix) {
820 
821  G4double r = SampleDisplacement();
822  /*
823  G4cout << "CMSUrbanMscModel95::SampleSecondaries: e(MeV)= " << kineticEnergy
824  << " sinTheta= " << sth << " r(mm)= " << r
825  << " trueStep(mm)= " << tPathLength
826  << " geomStep(mm)= " << zPathLength
827  << G4endl;
828  */
829  if(r > 0.)
830  {
831  G4double latcorr = LatCorrelation();
832  if(latcorr > r) latcorr = r;
833 
834  // sample direction of lateral displacement
835  // compute it from the lateral correlation
836  G4double Phi = 0.;
837  if(std::abs(r*sth) < latcorr)
838  Phi = twopi*G4UniformRand();
839  else
840  {
841  G4double psi = std::acos(latcorr/(r*sth));
842  if(G4UniformRand() < 0.5)
843  Phi = phi+psi;
844  else
845  Phi = phi-psi;
846  }
847 
848  dirx = std::cos(Phi);
849  diry = std::sin(Phi);
850 
851  G4ThreeVector latDirection(dirx,diry,0.0);
852  latDirection.rotateUz(oldDirection);
853 
854  ComputeDisplacement(fParticleChange, latDirection, r, safety);
855  }
856  }
857 }
858 
859 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
860 
861 G4double CMSUrbanMscModel95::SampleCosineTheta(G4double trueStepLength,
862  G4double KineticEnergy)
863 {
864  G4double cth = 1. ;
865  G4double tau = trueStepLength/lambda0 ;
866 
867  Zeff = couple->GetMaterial()->GetTotNbOfElectPerVolume()/
868  couple->GetMaterial()->GetTotNbOfAtomsPerVolume() ;
869 
870  if(Zold != Zeff)
871  UpdateCache();
872 
873  if(insideskin)
874  {
875  //no scattering, single or plural scattering
876  G4double mean = trueStepLength/stepmin ;
877 
878  G4int n = G4Poisson(mean);
879  if(n > 0)
880  {
881  //screening (Moliere-Bethe)
882  G4double mom2 = KineticEnergy*(2.*mass+KineticEnergy);
883  G4double beta2 = mom2/((KineticEnergy+mass)*(KineticEnergy+mass));
884  G4double ascr = scr1/mom2;
885  ascr *= 1.13+scr2/beta2;
886  G4double ascr1 = 1.+2.*ascr;
887  G4double bp1=ascr1+1.;
888  G4double bm1=ascr1-1.;
889 
890  // single scattering from screened Rutherford x-section
891  G4double ct,st,phi;
892  G4double sx=0.,sy=0.,sz=0.;
893  for(G4int i=1; i<=n; i++)
894  {
895  ct = ascr1-bp1*bm1/(2.*G4UniformRand()+bm1);
896  if(ct < -1.) ct = -1.;
897  if(ct > 1.) ct = 1.;
898  st = sqrt(1.-ct*ct);
899  phi = twopi*G4UniformRand();
900  sx += st*cos(phi);
901  sy += st*sin(phi);
902  sz += ct;
903  }
904  cth = sz/sqrt(sx*sx+sy*sy+sz*sz);
905  }
906  }
907  else
908  {
909  G4double lambda1 = GetLambda(KineticEnergy);
910  if(std::fabs(lambda1/lambda0 - 1) > 0.01 && lambda1 > 0.)
911  {
912  // mean tau value
913  tau = trueStepLength*log(lambda0/lambda1)/(lambda0-lambda1);
914  }
915 
916  currentTau = tau ;
917  lambdaeff = trueStepLength/currentTau;
918  currentRadLength = couple->GetMaterial()->GetRadlen();
919 
920  if (tau >= taubig) cth = -1.+2.*G4UniformRand();
921  else if (tau >= tausmall)
922  {
923  G4double x0 = 1.;
924  G4double a = 1., ea = 0., eaa = 1.;
925  G4double b=1.,b1=2.,bx=1.,eb1=3.,ebx=1.;
926  G4double prob = 1. ;
927  G4double xmean1 = 1., xmean2 = 0.;
928  G4double xmeanth = exp(-tau);
929  G4double x2meanth = (1.+2.*exp(-2.5*tau))/3.;
930 
931  G4double relloss = 1.-KineticEnergy/currentKinEnergy;
932  if(relloss > rellossmax)
933  return SimpleScattering(xmeanth,x2meanth);
934 
935  G4double theta0 = ComputeTheta0(trueStepLength,KineticEnergy);
936 
937  // protection for very small angles
938  if(theta0*theta0 < tausmall) return cth;
939 
940  if(theta0 > theta0max)
941  return SimpleScattering(xmeanth,x2meanth);
942  G4double sth = sin(0.5*theta0);
943  a = 0.25/(sth*sth);
944 
945  // parameter for tail
946  G4double u = exp(log(tau)/6.);
947  G4double x = log(lambdaeff/currentRadLength);
948  G4double c = coeffc1+u*(coeffc2+coeffc3*u)+coeffc4*x;
949 
950  if(abs(c-3.) < 0.001) c = 3.001;
951  if(abs(c-2.) < 0.001) c = 2.001;
952  if(abs(c-1.) < 0.001) c = 1.001;
953 
954  ea = exp(-c);
955  eaa = 1.-ea ;
956  xmean1 = 1.-(1.-(1.+c)*ea)/(a*eaa);
957  x0 = 1.-c/a;
958 
959  if(xmean1 <= 0.999*xmeanth)
960  return SimpleScattering(xmeanth,x2meanth);
961 
962  G4double c1 = c-1.;
963 
964  bx = c/a;
965  eb1 = exp(c1*log(b1));
966  ebx = exp(c1*log(bx));
967 
968  xmean2 = (x0*eb1+ebx-(eb1*bx-b1*ebx)/(c-2.))/(eb1-ebx);
969 
970  G4double f1x0 = a*ea/eaa;
971  G4double f2x0 = c1*eb1/(bx*(eb1-ebx));
972  prob = f2x0/(f1x0+f2x0);
973 
974  // sampling of costheta
975  G4double qprob = xmeanth/(prob*xmean1+(1.-prob)*xmean2);
976  if(G4UniformRand() < qprob)
977  {
978  if(G4UniformRand() < prob)
979  cth = 1.+log(ea+G4UniformRand()*eaa)/a ;
980  else
981  cth = b-b1*bx/exp(log(ebx+(eb1-ebx)*G4UniformRand())/c1) ;
982  }
983  else
984  cth = 2.*G4UniformRand()-1.;
985  }
986  }
987  return cth ;
988 }
989 
990 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
991 
992 G4double CMSUrbanMscModel95::SimpleScattering(G4double xmeanth,G4double x2meanth)
993 {
994  // 'large angle scattering'
995  // 2 model functions with correct xmean and x2mean
996  G4double a = (2.*xmeanth+9.*x2meanth-3.)/(2.*xmeanth-3.*x2meanth+1.);
997  G4double prob = (a+2.)*xmeanth/a;
998 
999  // sampling
1000  G4double cth = 1.;
1001  if(G4UniformRand() < prob)
1002  cth = -1.+2.*exp(log(G4UniformRand())/(a+1.));
1003  else
1004  cth = -1.+2.*G4UniformRand();
1005  return cth;
1006 }
1007 
1008 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1009 
1010 G4double CMSUrbanMscModel95::SampleDisplacement()
1011 {
1012  G4double r = 0.0;
1013  if ((currentTau >= tausmall) && !insideskin) {
1014  G4double rmax = sqrt((tPathLength-zPathLength)*(tPathLength+zPathLength));
1015  r = rmax*exp(log(G4UniformRand())/3.);
1016  }
1017  return r;
1018 }
1019 
1020 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1021 
1022 G4double CMSUrbanMscModel95::LatCorrelation()
1023 {
1024  const G4double kappa = 2.5;
1025  const G4double kappami1 = kappa-1.;
1026 
1027  G4double latcorr = 0.;
1028  if((currentTau >= tausmall) && !insideskin)
1029  {
1030  if(currentTau < taulim)
1031  latcorr = lambdaeff*kappa*currentTau*currentTau*
1032  (1.-(kappa+1.)*currentTau/3.)/3.;
1033  else
1034  {
1035  G4double etau = 0.;
1036  if(currentTau < taubig) etau = exp(-currentTau);
1037  latcorr = -kappa*currentTau;
1038  latcorr = exp(latcorr)/kappami1;
1039  latcorr += 1.-kappa*etau/kappami1 ;
1040  latcorr *= 2.*lambdaeff/3. ;
1041  }
1042  }
1043 
1044  return latcorr;
1045 }
1046 
1047 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
i
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