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G4UrbanMscModel92.cc
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26 //
27 // $Id: G4UrbanMscModel92.cc 66592 2012-12-23 09:34:55Z vnivanch $
28 //
29 // -------------------------------------------------------------------
30 //
31 // GEANT4 Class file
32 //
33 //
34 // File name: G4UrbanMscModel92
35 //
36 // Author: Laszlo Urban
37 //
38 // Creation date: 06.03.2008
39 //
40 // Modifications:
41 //
42 // 06-03-2008 starting point : G4UrbanMscModel2 = G4UrbanMscModel 9.1 ref 02
43 //
44 // 13-03-08 Bug in SampleScattering (which caused lateral asymmetry) fixed
45 // (L.Urban)
46 //
47 // 14-03-08 Simplification of step limitation in ComputeTruePathLengthLimit,
48 // + tlimitmin is the same for UseDistancetoBoundary and
49 // UseSafety (L.Urban)
50 //
51 // 16-03-08 Reorganization of SampleCosineTheta + new method SimpleScattering
52 // SimpleScattering is used if the relative energy loss is too big
53 // or theta0 is too big (see data members rellossmax, theta0max)
54 // (L.Urban)
55 //
56 // 17-03-08 tuning of the correction factor in ComputeTheta0 (L.Urban)
57 //
58 // 19-03-08 exponent c of the 'tail' model function is not equal to 2 any more,
59 // value of c has been extracted from some e- scattering data (L.Urban)
60 //
61 // 24-03-08 Step limitation in ComputeTruePathLengthLimit has been
62 // simplified further + some data members have been removed (L.Urban)
63 //
64 // 24-07-08 central part of scattering angle (theta0) has been tuned
65 // tail of the scattering angle distribution has been tuned
66 // using some e- and proton scattering data
67 //
68 // 05-08-08 bugfix in ComputeTruePathLengthLimit (L.Urban)
69 //
70 // 09-10-08 theta0 and tail have been retuned using some e-,mu,proton
71 // scattering data (L.Urban)
72 // + single scattering without path length correction for
73 // small steps (t < tlimitmin, for UseDistanceToBoundary only)
74 //
75 // 15-10-08 Moliere-Bethe screening in the single scattering part(L.Urban)
76 //
77 // 17-10-08 stepping similar to that in model (9.1) for UseSafety case
78 // for e+/e- in order to speed up the code for calorimeters
79 //
80 // 23-10-08 bugfix in the screeningparameter of the single scattering part,
81 // some technical change in order to speed up the code (UpdateCache)
82 //
83 // 27-10-08 bugfix in ComputeTruePathLengthLimit (affects UseDistanceToBoundary
84 // stepping type only) (L.Urban)
85 //
86 // 28-10-09 V.Ivanchenko moved G4UrbanMscModel to G4UrbanMscModel92,
87 // now it is a frozen version of the Urban model corresponding
88 // to g4 9.2
89 
90 // Class Description:
91 //
92 // Implementation of the model of multiple scattering based on
93 // H.W.Lewis Phys Rev 78 (1950) 526 and others
94 
95 // -------------------------------------------------------------------
96 // In its present form the model can be used for simulation
97 // of the e-/e+, muon and charged hadron multiple scattering
98 //
99 
100 
101 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
102 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
103 
104 #include "G4UrbanMscModel92.hh"
105 #include "G4PhysicalConstants.hh"
106 #include "G4SystemOfUnits.hh"
107 #include "Randomize.hh"
108 #include "G4Electron.hh"
109 #include "G4LossTableManager.hh"
110 #include "G4ParticleChangeForMSC.hh"
111 
112 #include "G4Poisson.hh"
113 #include "globals.hh"
114 
115 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
116 
117 using namespace std;
118 
119 G4UrbanMscModel92::G4UrbanMscModel92(const G4String& nam)
120  : G4VMscModel(nam)
121 {
122  masslimite = 0.6*MeV;
123  lambdalimit = 1.*mm;
124  fr = 0.02;
125  // facsafety = 0.3;
126  taubig = 8.0;
127  tausmall = 1.e-16;
128  taulim = 1.e-6;
129  currentTau = taulim;
130  tlimitminfix = 1.e-6*mm;
131  stepmin = tlimitminfix;
132  smallstep = 1.e10;
133  currentRange = 0. ;
134  rangeinit = 0.;
135  tlimit = 1.e10*mm;
136  tlimitmin = 10.*tlimitminfix;
137  tgeom = 1.e50*mm;
138  geombig = 1.e50*mm;
139  geommin = 1.e-3*mm;
140  geomlimit = geombig;
141  presafety = 0.*mm;
142 
143  y = 0.;
144 
145  Zold = 0.;
146  Zeff = 1.;
147  Z2 = 1.;
148  Z23 = 1.;
149  lnZ = 0.;
150  coeffth1 = 0.;
151  coeffth2 = 0.;
152  coeffc1 = 0.;
153  coeffc2 = 0.;
154  scr1ini = fine_structure_const*fine_structure_const*
155  electron_mass_c2*electron_mass_c2/(0.885*0.885*4.*pi);
156  scr2ini = 3.76*fine_structure_const*fine_structure_const;
157  scr1 = 0.;
158  scr2 = 0.;
159 
160  theta0max = pi/6.;
161  rellossmax = 0.50;
162  third = 1./3.;
163  particle = 0;
164  theManager = G4LossTableManager::Instance();
165  firstStep = true;
166  inside = false;
167  insideskin = false;
168 
169  skindepth = skin*stepmin;
170 
171  mass = proton_mass_c2;
172  charge = ChargeSquare = 1.0;
173  currentKinEnergy = currentRadLength = lambda0 = lambdaeff = tPathLength
174  = zPathLength = par1 = par2 = par3 = 0;
175 
176  currentMaterialIndex = -1;
177  fParticleChange = 0;
178  couple = 0;
179  G4cout << "### G4UrbanMscModel92 is obsolete and will be removed for "
180  << "the next Geant4 version" << G4endl;
181 }
182 
183 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
184 
185 G4UrbanMscModel92::~G4UrbanMscModel92()
186 {}
187 
188 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
189 
190 void G4UrbanMscModel92::Initialise(const G4ParticleDefinition* p,
191  const G4DataVector&)
192 {
193  skindepth = skin*stepmin;
194  // set values of some data members
195  SetParticle(p);
196 
197  if(p->GetPDGMass() > MeV) {
198  G4cout << "### WARNING: G4UrbanMscModel92 model is used for "
199  << p->GetParticleName() << " !!! " << G4endl;
200  G4cout << "### This model should be used only for e+-"
201  << G4endl;
202  }
203 
204  fParticleChange = GetParticleChangeForMSC(p);
205 }
206 
207 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
208 
209 G4double G4UrbanMscModel92::ComputeCrossSectionPerAtom(
210  const G4ParticleDefinition* part,
211  G4double KineticEnergy,
212  G4double AtomicNumber,G4double,
213  G4double, G4double)
214 {
215  const G4double sigmafactor = twopi*classic_electr_radius*classic_electr_radius;
216  const G4double epsfactor = 2.*electron_mass_c2*electron_mass_c2*
217  Bohr_radius*Bohr_radius/(hbarc*hbarc);
218  const G4double epsmin = 1.e-4 , epsmax = 1.e10;
219 
220  const G4double Zdat[15] = { 4., 6., 13., 20., 26., 29., 32., 38., 47.,
221  50., 56., 64., 74., 79., 82. };
222 
223  const G4double Tdat[22] = { 100*eV, 200*eV, 400*eV, 700*eV,
224  1*keV, 2*keV, 4*keV, 7*keV,
225  10*keV, 20*keV, 40*keV, 70*keV,
226  100*keV, 200*keV, 400*keV, 700*keV,
227  1*MeV, 2*MeV, 4*MeV, 7*MeV,
228  10*MeV, 20*MeV};
229 
230  // corr. factors for e-/e+ lambda for T <= Tlim
231  G4double celectron[15][22] =
232  {{1.125,1.072,1.051,1.047,1.047,1.050,1.052,1.054,
233  1.054,1.057,1.062,1.069,1.075,1.090,1.105,1.111,
234  1.112,1.108,1.100,1.093,1.089,1.087 },
235  {1.408,1.246,1.143,1.096,1.077,1.059,1.053,1.051,
236  1.052,1.053,1.058,1.065,1.072,1.087,1.101,1.108,
237  1.109,1.105,1.097,1.090,1.086,1.082 },
238  {2.833,2.268,1.861,1.612,1.486,1.309,1.204,1.156,
239  1.136,1.114,1.106,1.106,1.109,1.119,1.129,1.132,
240  1.131,1.124,1.113,1.104,1.099,1.098 },
241  {3.879,3.016,2.380,2.007,1.818,1.535,1.340,1.236,
242  1.190,1.133,1.107,1.099,1.098,1.103,1.110,1.113,
243  1.112,1.105,1.096,1.089,1.085,1.098 },
244  {6.937,4.330,2.886,2.256,1.987,1.628,1.395,1.265,
245  1.203,1.122,1.080,1.065,1.061,1.063,1.070,1.073,
246  1.073,1.070,1.064,1.059,1.056,1.056 },
247  {9.616,5.708,3.424,2.551,2.204,1.762,1.485,1.330,
248  1.256,1.155,1.099,1.077,1.070,1.068,1.072,1.074,
249  1.074,1.070,1.063,1.059,1.056,1.052 },
250  {11.72,6.364,3.811,2.806,2.401,1.884,1.564,1.386,
251  1.300,1.180,1.112,1.082,1.073,1.066,1.068,1.069,
252  1.068,1.064,1.059,1.054,1.051,1.050 },
253  {18.08,8.601,4.569,3.183,2.662,2.025,1.646,1.439,
254  1.339,1.195,1.108,1.068,1.053,1.040,1.039,1.039,
255  1.039,1.037,1.034,1.031,1.030,1.036 },
256  {18.22,10.48,5.333,3.713,3.115,2.367,1.898,1.631,
257  1.498,1.301,1.171,1.105,1.077,1.048,1.036,1.033,
258  1.031,1.028,1.024,1.022,1.021,1.024 },
259  {14.14,10.65,5.710,3.929,3.266,2.453,1.951,1.669,
260  1.528,1.319,1.178,1.106,1.075,1.040,1.027,1.022,
261  1.020,1.017,1.015,1.013,1.013,1.020 },
262  {14.11,11.73,6.312,4.240,3.478,2.566,2.022,1.720,
263  1.569,1.342,1.186,1.102,1.065,1.022,1.003,0.997,
264  0.995,0.993,0.993,0.993,0.993,1.011 },
265  {22.76,20.01,8.835,5.287,4.144,2.901,2.219,1.855,
266  1.677,1.410,1.224,1.121,1.073,1.014,0.986,0.976,
267  0.974,0.972,0.973,0.974,0.975,0.987 },
268  {50.77,40.85,14.13,7.184,5.284,3.435,2.520,2.059,
269  1.837,1.512,1.283,1.153,1.091,1.010,0.969,0.954,
270  0.950,0.947,0.949,0.952,0.954,0.963 },
271  {65.87,59.06,15.87,7.570,5.567,3.650,2.682,2.182,
272  1.939,1.579,1.325,1.178,1.108,1.014,0.965,0.947,
273  0.941,0.938,0.940,0.944,0.946,0.954 },
274  {55.60,47.34,15.92,7.810,5.755,3.767,2.760,2.239,
275  1.985,1.609,1.343,1.188,1.113,1.013,0.960,0.939,
276  0.933,0.930,0.933,0.936,0.939,0.949 }};
277 
278  G4double cpositron[15][22] = {
279  {2.589,2.044,1.658,1.446,1.347,1.217,1.144,1.110,
280  1.097,1.083,1.080,1.086,1.092,1.108,1.123,1.131,
281  1.131,1.126,1.117,1.108,1.103,1.100 },
282  {3.904,2.794,2.079,1.710,1.543,1.325,1.202,1.145,
283  1.122,1.096,1.089,1.092,1.098,1.114,1.130,1.137,
284  1.138,1.132,1.122,1.113,1.108,1.102 },
285  {7.970,6.080,4.442,3.398,2.872,2.127,1.672,1.451,
286  1.357,1.246,1.194,1.179,1.178,1.188,1.201,1.205,
287  1.203,1.190,1.173,1.159,1.151,1.145 },
288  {9.714,7.607,5.747,4.493,3.815,2.777,2.079,1.715,
289  1.553,1.353,1.253,1.219,1.211,1.214,1.225,1.228,
290  1.225,1.210,1.191,1.175,1.166,1.174 },
291  {17.97,12.95,8.628,6.065,4.849,3.222,2.275,1.820,
292  1.624,1.382,1.259,1.214,1.202,1.202,1.214,1.219,
293  1.217,1.203,1.184,1.169,1.160,1.151 },
294  {24.83,17.06,10.84,7.355,5.767,3.707,2.546,1.996,
295  1.759,1.465,1.311,1.252,1.234,1.228,1.238,1.241,
296  1.237,1.222,1.201,1.184,1.174,1.159 },
297  {23.26,17.15,11.52,8.049,6.375,4.114,2.792,2.155,
298  1.880,1.535,1.353,1.281,1.258,1.247,1.254,1.256,
299  1.252,1.234,1.212,1.194,1.183,1.170 },
300  {22.33,18.01,12.86,9.212,7.336,4.702,3.117,2.348,
301  2.015,1.602,1.385,1.297,1.268,1.251,1.256,1.258,
302  1.254,1.237,1.214,1.195,1.185,1.179 },
303  {33.91,24.13,15.71,10.80,8.507,5.467,3.692,2.808,
304  2.407,1.873,1.564,1.425,1.374,1.330,1.324,1.320,
305  1.312,1.288,1.258,1.235,1.221,1.205 },
306  {32.14,24.11,16.30,11.40,9.015,5.782,3.868,2.917,
307  2.490,1.925,1.596,1.447,1.391,1.342,1.332,1.327,
308  1.320,1.294,1.264,1.240,1.226,1.214 },
309  {29.51,24.07,17.19,12.28,9.766,6.238,4.112,3.066,
310  2.602,1.995,1.641,1.477,1.414,1.356,1.342,1.336,
311  1.328,1.302,1.270,1.245,1.231,1.233 },
312  {38.19,30.85,21.76,15.35,12.07,7.521,4.812,3.498,
313  2.926,2.188,1.763,1.563,1.484,1.405,1.382,1.371,
314  1.361,1.330,1.294,1.267,1.251,1.239 },
315  {49.71,39.80,27.96,19.63,15.36,9.407,5.863,4.155,
316  3.417,2.478,1.944,1.692,1.589,1.480,1.441,1.423,
317  1.409,1.372,1.330,1.298,1.280,1.258 },
318  {59.25,45.08,30.36,20.83,16.15,9.834,6.166,4.407,
319  3.641,2.648,2.064,1.779,1.661,1.531,1.482,1.459,
320  1.442,1.400,1.354,1.319,1.299,1.272 },
321  {56.38,44.29,30.50,21.18,16.51,10.11,6.354,4.542,
322  3.752,2.724,2.116,1.817,1.692,1.554,1.499,1.474,
323  1.456,1.412,1.364,1.328,1.307,1.282 }};
324 
325  //data/corrections for T > Tlim
326  G4double Tlim = 10.*MeV;
327  G4double beta2lim = Tlim*(Tlim+2.*electron_mass_c2)/
328  ((Tlim+electron_mass_c2)*(Tlim+electron_mass_c2));
329  G4double bg2lim = Tlim*(Tlim+2.*electron_mass_c2)/
330  (electron_mass_c2*electron_mass_c2);
331 
332  G4double sig0[15] = {0.2672*barn, 0.5922*barn, 2.653*barn, 6.235*barn,
333  11.69*barn , 13.24*barn , 16.12*barn, 23.00*barn ,
334  35.13*barn , 39.95*barn , 50.85*barn, 67.19*barn ,
335  91.15*barn , 104.4*barn , 113.1*barn};
336 
337  G4double hecorr[15] = {120.70, 117.50, 105.00, 92.92, 79.23, 74.510, 68.29,
338  57.39, 41.97, 36.14, 24.53, 10.21, -7.855, -16.84,
339  -22.30};
340 
341  G4double sigma;
342  SetParticle(part);
343 
344  Z23 = pow(AtomicNumber,2./3.);
345 
346  // correction if particle .ne. e-/e+
347  // compute equivalent kinetic energy
348  // lambda depends on p*beta ....
349 
350  G4double eKineticEnergy = KineticEnergy;
351 
352  if(mass > electron_mass_c2)
353  {
354  G4double TAU = KineticEnergy/mass ;
355  G4double c = mass*TAU*(TAU+2.)/(electron_mass_c2*(TAU+1.)) ;
356  G4double w = c-2. ;
357  G4double tau = 0.5*(w+sqrt(w*w+4.*c)) ;
358  eKineticEnergy = electron_mass_c2*tau ;
359  }
360 
361  G4double eTotalEnergy = eKineticEnergy + electron_mass_c2 ;
362  G4double beta2 = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
363  /(eTotalEnergy*eTotalEnergy);
364  G4double bg2 = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
365  /(electron_mass_c2*electron_mass_c2);
366 
367  G4double eps = epsfactor*bg2/Z23;
368 
369  if (eps<epsmin) sigma = 2.*eps*eps;
370  else if(eps<epsmax) sigma = log(1.+2.*eps)-2.*eps/(1.+2.*eps);
371  else sigma = log(2.*eps)-1.+1./eps;
372 
373  sigma *= ChargeSquare*AtomicNumber*AtomicNumber/(beta2*bg2);
374 
375  // interpolate in AtomicNumber and beta2
376  G4double c1,c2,cc1,cc2,corr;
377 
378  // get bin number in Z
379  G4int iZ = 14;
380  while ((iZ>=0)&&(Zdat[iZ]>=AtomicNumber)) iZ -= 1;
381  if (iZ==14) iZ = 13;
382  if (iZ==-1) iZ = 0 ;
383 
384  G4double ZZ1 = Zdat[iZ];
385  G4double ZZ2 = Zdat[iZ+1];
386  G4double ratZ = (AtomicNumber-ZZ1)*(AtomicNumber+ZZ1)/
387  ((ZZ2-ZZ1)*(ZZ2+ZZ1));
388 
389  if(eKineticEnergy <= Tlim)
390  {
391  // get bin number in T (beta2)
392  G4int iT = 21;
393  while ((iT>=0)&&(Tdat[iT]>=eKineticEnergy)) iT -= 1;
394  if(iT==21) iT = 20;
395  if(iT==-1) iT = 0 ;
396 
397  // calculate betasquare values
398  G4double T = Tdat[iT], E = T + electron_mass_c2;
399  G4double b2small = T*(E+electron_mass_c2)/(E*E);
400 
401  T = Tdat[iT+1]; E = T + electron_mass_c2;
402  G4double b2big = T*(E+electron_mass_c2)/(E*E);
403  G4double ratb2 = (beta2-b2small)/(b2big-b2small);
404 
405  if (charge < 0.)
406  {
407  c1 = celectron[iZ][iT];
408  c2 = celectron[iZ+1][iT];
409  cc1 = c1+ratZ*(c2-c1);
410 
411  c1 = celectron[iZ][iT+1];
412  c2 = celectron[iZ+1][iT+1];
413  cc2 = c1+ratZ*(c2-c1);
414 
415  corr = cc1+ratb2*(cc2-cc1);
416 
417  sigma *= sigmafactor/corr;
418  }
419  else
420  {
421  c1 = cpositron[iZ][iT];
422  c2 = cpositron[iZ+1][iT];
423  cc1 = c1+ratZ*(c2-c1);
424 
425  c1 = cpositron[iZ][iT+1];
426  c2 = cpositron[iZ+1][iT+1];
427  cc2 = c1+ratZ*(c2-c1);
428 
429  corr = cc1+ratb2*(cc2-cc1);
430 
431  sigma *= sigmafactor/corr;
432  }
433  }
434  else
435  {
436  c1 = bg2lim*sig0[iZ]*(1.+hecorr[iZ]*(beta2-beta2lim))/bg2;
437  c2 = bg2lim*sig0[iZ+1]*(1.+hecorr[iZ+1]*(beta2-beta2lim))/bg2;
438  if((AtomicNumber >= ZZ1) && (AtomicNumber <= ZZ2))
439  sigma = c1+ratZ*(c2-c1) ;
440  else if(AtomicNumber < ZZ1)
441  sigma = AtomicNumber*AtomicNumber*c1/(ZZ1*ZZ1);
442  else if(AtomicNumber > ZZ2)
443  sigma = AtomicNumber*AtomicNumber*c2/(ZZ2*ZZ2);
444  }
445  return sigma;
446 
447 }
448 
449 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
450 
451 void G4UrbanMscModel92::StartTracking(G4Track* track)
452 {
453  SetParticle(track->GetDynamicParticle()->GetDefinition());
454  firstStep = true;
455  inside = false;
456  insideskin = false;
457  tlimit = geombig;
458 }
459 
460 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
461 
462 G4double G4UrbanMscModel92::ComputeTruePathLengthLimit(
463  const G4Track& track,
464  G4double& currentMinimalStep)
465 {
466  tPathLength = currentMinimalStep;
467  const G4DynamicParticle* dp = track.GetDynamicParticle();
468  G4StepPoint* sp = track.GetStep()->GetPreStepPoint();
469  G4StepStatus stepStatus = sp->GetStepStatus();
470  couple = track.GetMaterialCutsCouple();
471  SetCurrentCouple(couple);
472  currentMaterialIndex = couple->GetIndex();
473  currentKinEnergy = dp->GetKineticEnergy();
474  currentRange = GetRange(particle,currentKinEnergy,couple);
475  lambda0 = GetTransportMeanFreePath(particle,currentKinEnergy);
476 
477  // stop here if small range particle
478  if(inside || tPathLength < tlimitminfix) {
479  return ConvertTrueToGeom(tPathLength, currentMinimalStep);
480  }
481 
482  if(tPathLength > currentRange) tPathLength = currentRange;
483 
484  presafety = sp->GetSafety();
485 
486  // G4cout << "G4UrbanMscModel92::ComputeTruePathLengthLimit tPathLength= "
487  // <<tPathLength<<" safety= " << presafety
488  // << " range= " <<currentRange<<G4endl;
489 
490  // far from geometry boundary
491  if(currentRange < presafety)
492  {
493  inside = true;
494  return ConvertTrueToGeom(tPathLength, currentMinimalStep);
495  }
496 
497  // standard version
498  //
499  if (steppingAlgorithm == fUseDistanceToBoundary)
500  {
501  //compute geomlimit and presafety
502  geomlimit = ComputeGeomLimit(track, presafety, currentRange);
503 
504  // is it far from boundary ?
505  if(currentRange < presafety)
506  {
507  inside = true;
508  return ConvertTrueToGeom(tPathLength, currentMinimalStep);
509  }
510 
511  smallstep += 1.;
512  insideskin = false;
513 
514  if(firstStep || stepStatus == fGeomBoundary)
515  {
516  rangeinit = currentRange;
517  if(firstStep) smallstep = 1.e10;
518  else smallstep = 1.;
519 
520  // constraint from the geometry
521  if((geomlimit < geombig) && (geomlimit > geommin))
522  {
523  if(stepStatus == fGeomBoundary)
524  tgeom = geomlimit/facgeom;
525  else
526  tgeom = 2.*geomlimit/facgeom;
527  }
528  else
529  tgeom = geombig;
530 
531  //define stepmin here (it depends on lambda!)
532  //rough estimation of lambda_elastic/lambda_transport
533  G4double rat = currentKinEnergy/MeV ;
534  rat = 1.e-3/(rat*(10.+rat)) ;
535  //stepmin ~ lambda_elastic
536  stepmin = rat*lambda0;
537  skindepth = skin*stepmin;
538 
539  //define tlimitmin
540  tlimitmin = 10.*stepmin;
541  if(tlimitmin < tlimitminfix) tlimitmin = tlimitminfix;
542 
543  }
544 
545  //step limit
546  tlimit = facrange*rangeinit;
547  if(tlimit < facsafety*presafety)
548  tlimit = facsafety*presafety;
549 
550  //lower limit for tlimit
551  if(tlimit < tlimitmin) tlimit = tlimitmin;
552 
553  if(tlimit > tgeom) tlimit = tgeom;
554 
555  // G4cout << "tgeom= " << tgeom << " geomlimit= " << geomlimit
556  // << " tlimit= " << tlimit << " presafety= " << presafety << G4endl;
557 
558  // shortcut
559  if((tPathLength < tlimit) && (tPathLength < presafety) &&
560  (smallstep >= skin) && (tPathLength < geomlimit-0.999*skindepth))
561  return ConvertTrueToGeom(tPathLength, currentMinimalStep);
562 
563  // step reduction near to boundary
564  if(smallstep < skin)
565  {
566  tlimit = stepmin;
567  insideskin = true;
568  }
569  else if(geomlimit < geombig)
570  {
571  if(geomlimit > skindepth)
572  {
573  if(tlimit > geomlimit-0.999*skindepth)
574  tlimit = geomlimit-0.999*skindepth;
575  }
576  else
577  {
578  insideskin = true;
579  if(tlimit > stepmin) tlimit = stepmin;
580  }
581  }
582 
583  if(tlimit < stepmin) tlimit = stepmin;
584 
585  if(tPathLength > tlimit) tPathLength = tlimit ;
586 
587  }
588  // for 'normal' simulation with or without magnetic field
589  // there no small step/single scattering at boundaries
590  else if(steppingAlgorithm == fUseSafety)
591  {
592  // compute presafety again if presafety <= 0 and no boundary
593  // i.e. when it is needed for optimization purposes
594  if((stepStatus != fGeomBoundary) && (presafety < tlimitminfix))
595  presafety = ComputeSafety(sp->GetPosition(),tPathLength);
596 
597  // is far from boundary
598  if(currentRange < presafety)
599  {
600  inside = true;
601  return ConvertTrueToGeom(tPathLength, currentMinimalStep);
602  }
603 
604  if(firstStep || stepStatus == fGeomBoundary)
605  {
606  rangeinit = currentRange;
607  fr = facrange;
608  // 9.1 like stepping for e+/e- only (not for muons,hadrons)
609  if(mass < masslimite)
610  {
611  if(lambda0 > currentRange)
612  rangeinit = lambda0;
613  if(lambda0 > lambdalimit)
614  fr *= 0.75+0.25*lambda0/lambdalimit;
615  }
616 
617  //lower limit for tlimit
618  G4double rat = currentKinEnergy/MeV ;
619  rat = 1.e-3/(rat*(10.+rat)) ;
620  tlimitmin = 10.*lambda0*rat;
621  if(tlimitmin < tlimitminfix) tlimitmin = tlimitminfix;
622  }
623  //step limit
624  tlimit = fr*rangeinit;
625 
626  if(tlimit < facsafety*presafety)
627  tlimit = facsafety*presafety;
628 
629  //lower limit for tlimit
630  if(tlimit < tlimitmin) tlimit = tlimitmin;
631 
632  if(tPathLength > tlimit) tPathLength = tlimit;
633  }
634 
635  // version similar to 7.1 (needed for some experiments)
636  else
637  {
638  if (stepStatus == fGeomBoundary)
639  {
640  if (currentRange > lambda0) tlimit = facrange*currentRange;
641  else tlimit = facrange*lambda0;
642 
643  if(tlimit < tlimitmin) tlimit = tlimitmin;
644  if(tPathLength > tlimit) tPathLength = tlimit;
645  }
646  }
647  // G4cout << "tPathLength= " << tPathLength << " geomlimit= " << geomlimit
648  // << " currentMinimalStep= " << currentMinimalStep << G4endl;
649  return ConvertTrueToGeom(tPathLength, currentMinimalStep);
650 }
651 
652 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
653 
654 G4double G4UrbanMscModel92::ComputeGeomPathLength(G4double)
655 {
656  firstStep = false;
657  lambdaeff = lambda0;
658  par1 = -1. ;
659  par2 = par3 = 0. ;
660 
661  // do the true -> geom transformation
662  zPathLength = tPathLength;
663 
664  // z = t for very small tPathLength
665  if(tPathLength < tlimitminfix) return zPathLength;
666 
667  // this correction needed to run MSC with eIoni and eBrem inactivated
668  // and makes no harm for a normal run
669  if(tPathLength > currentRange)
670  tPathLength = currentRange ;
671 
672  G4double tau = tPathLength/lambda0 ;
673 
674  if ((tau <= tausmall) || insideskin) {
675  zPathLength = tPathLength;
676  if(zPathLength > lambda0) zPathLength = lambda0;
677  return zPathLength;
678  }
679 
680  G4double zmean = tPathLength;
681  if (tPathLength < currentRange*dtrl) {
682  if(tau < taulim) zmean = tPathLength*(1.-0.5*tau) ;
683  else zmean = lambda0*(1.-exp(-tau));
684  } else if(currentKinEnergy < mass || tPathLength == currentRange) {
685  par1 = 1./currentRange ;
686  par2 = 1./(par1*lambda0) ;
687  par3 = 1.+par2 ;
688  if(tPathLength < currentRange)
689  zmean = (1.-exp(par3*log(1.-tPathLength/currentRange)))/(par1*par3) ;
690  else
691  zmean = 1./(par1*par3) ;
692  } else {
693  G4double T1 = GetEnergy(particle,currentRange-tPathLength,couple);
694  G4double lambda1 = GetTransportMeanFreePath(particle,T1);
695 
696  par1 = (lambda0-lambda1)/(lambda0*tPathLength) ;
697  par2 = 1./(par1*lambda0) ;
698  par3 = 1.+par2 ;
699  zmean = (1.-exp(par3*log(lambda1/lambda0)))/(par1*par3) ;
700  }
701 
702  zPathLength = zmean ;
703 
704  // sample z
705  if(samplez)
706  {
707  const G4double ztmax = 0.99 ;
708  G4double zt = zmean/tPathLength ;
709 
710  if (tPathLength > stepmin && zt < ztmax)
711  {
712  G4double u,cz1;
713  if(zt >= third)
714  {
715  G4double cz = 0.5*(3.*zt-1.)/(1.-zt) ;
716  cz1 = 1.+cz ;
717  G4double u0 = cz/cz1 ;
718  G4double grej ;
719  do {
720  u = exp(log(G4UniformRand())/cz1) ;
721  grej = exp(cz*log(u/u0))*(1.-u)/(1.-u0) ;
722  } while (grej < G4UniformRand()) ;
723  }
724  else
725  {
726  cz1 = 1./zt-1.;
727  u = 1.-exp(log(G4UniformRand())/cz1) ;
728  }
729  zPathLength = tPathLength*u ;
730  }
731  }
732 
733  if(zPathLength > lambda0) zPathLength = lambda0;
734 
735  return zPathLength;
736 }
737 
738 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
739 
740 G4double G4UrbanMscModel92::ComputeTrueStepLength(G4double geomStepLength)
741 {
742  // step defined other than transportation
743  if(geomStepLength == zPathLength && tPathLength <= currentRange)
744  return tPathLength;
745 
746  // t = z for very small step
747  zPathLength = geomStepLength;
748  tPathLength = geomStepLength;
749  if(geomStepLength < tlimitminfix) return tPathLength;
750 
751  // recalculation
752  if((geomStepLength > lambda0*tausmall) && !insideskin)
753  {
754  if(par1 < 0.)
755  tPathLength = -lambda0*log(1.-geomStepLength/lambda0) ;
756  else
757  {
758  if(par1*par3*geomStepLength < 1.)
759  tPathLength = (1.-exp(log(1.-par1*par3*geomStepLength)/par3))/par1 ;
760  else
761  tPathLength = currentRange;
762  }
763  }
764  if(tPathLength < geomStepLength) tPathLength = geomStepLength;
765 
766  return tPathLength;
767 }
768 
769 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
770 
771 G4double G4UrbanMscModel92::ComputeTheta0(G4double trueStepLength,
772  G4double KineticEnergy)
773 {
774  // for all particles take the width of the central part
775  // from a parametrization similar to the Highland formula
776  // ( Highland formula: Particle Physics Booklet, July 2002, eq. 26.10)
777  const G4double c_highland = 13.6*MeV ;
778  G4double betacp = sqrt(currentKinEnergy*(currentKinEnergy+2.*mass)*
779  KineticEnergy*(KineticEnergy+2.*mass)/
780  ((currentKinEnergy+mass)*(KineticEnergy+mass)));
781  y = trueStepLength/currentRadLength;
782  G4double theta0 = c_highland*std::abs(charge)*sqrt(y)/betacp;
783  y = log(y);
784  // correction factor from e-/proton scattering data
785  G4double corr = coeffth1+coeffth2*y;
786  if(y < -6.5) corr -= 0.011*(6.5+y);
787  theta0 *= corr ;
788 
789  return theta0;
790 }
791 
792 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
793 
794 G4ThreeVector&
795 G4UrbanMscModel92::SampleScattering(const G4ThreeVector& oldDirection,
796  G4double safety)
797 {
798  fDisplacement.set(0.0,0.0,0.0);
799  G4double kineticEnergy = currentKinEnergy;
800  if (tPathLength > currentRange*dtrl) {
801  kineticEnergy = GetEnergy(particle,currentRange-tPathLength,couple);
802  } else {
803  kineticEnergy -= tPathLength*GetDEDX(particle,currentKinEnergy,couple);
804  }
805  if((kineticEnergy <= 0.0) || (tPathLength <= tlimitminfix) ||
806  (tPathLength/tausmall < lambda0)) return fDisplacement;
807 
808  G4double cth = SampleCosineTheta(tPathLength,kineticEnergy);
809 
810  // protection against 'bad' cth values
811  if(std::abs(cth) > 1.) return fDisplacement;
812 
813  // extra protection agaist high energy particles backscattered
814  if(cth < 1.0 - 1000*tPathLength/lambda0 && kineticEnergy > 20*MeV) {
815  //G4cout << "Warning: large scattering E(MeV)= " << kineticEnergy
816  // << " s(mm)= " << tPathLength/mm
817  // << " 1-cosTheta= " << 1.0 - cth << G4endl;
818  // do Gaussian central scattering
819  if(kineticEnergy > GeV && cth < 0.0) {
820  G4ExceptionDescription ed;
821  ed << particle->GetParticleName()
822  << " E(MeV)= " << kineticEnergy/MeV
823  << " Step(mm)= " << tPathLength/mm
824  << " in " << CurrentCouple()->GetMaterial()->GetName()
825  << " CosTheta= " << cth
826  << " is too big - the angle is resampled" << G4endl;
827  G4Exception("G4UrbanMscModel92::SampleScattering","em0004",
828  JustWarning, ed,"");
829  }
830  do {
831  cth = 1.0 + 2*log(G4UniformRand())*tPathLength/lambda0;
832  } while(cth < -1.0);
833  }
834 
835  G4double sth = sqrt((1.0 - cth)*(1.0 + cth));
836  G4double phi = twopi*G4UniformRand();
837  G4double dirx = sth*cos(phi);
838  G4double diry = sth*sin(phi);
839 
840  // G4ThreeVector oldDirection = dynParticle->GetMomentumDirection();
841  G4ThreeVector newDirection(dirx,diry,cth);
842  newDirection.rotateUz(oldDirection);
843  fParticleChange->ProposeMomentumDirection(newDirection);
844 
845  if (latDisplasment && safety > tlimitminfix) {
846 
847  G4double r = SampleDisplacement();
848  /*
849  G4cout << "G4UrbanMscModel92::SampleSecondaries: e(MeV)= " << kineticEnergy
850  << " sinTheta= " << sth << " r(mm)= " << r
851  << " trueStep(mm)= " << tPathLength
852  << " geomStep(mm)= " << zPathLength
853  << G4endl;
854  */
855  if(r > 0.)
856  {
857  G4double latcorr = LatCorrelation();
858  if(latcorr > r) latcorr = r;
859 
860  // sample direction of lateral displacement
861  // compute it from the lateral correlation
862  G4double Phi = 0.;
863  if(std::abs(r*sth) < latcorr)
864  Phi = twopi*G4UniformRand();
865  else
866  {
867  G4double psi = std::acos(latcorr/(r*sth));
868  if(G4UniformRand() < 0.5)
869  Phi = phi+psi;
870  else
871  Phi = phi-psi;
872  }
873 
874  dirx = r*std::cos(Phi);
875  diry = r*std::sin(Phi);
876 
877  fDisplacement.set(dirx,diry,0.0);
878  fDisplacement.rotateUz(oldDirection);
879  }
880  }
881  return fDisplacement;
882 }
883 
884 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
885 
886 G4double G4UrbanMscModel92::SampleCosineTheta(G4double trueStepLength,
887  G4double KineticEnergy)
888 {
889  G4double cth = 1. ;
890  G4double tau = trueStepLength/lambda0 ;
891 
892  Zeff = couple->GetMaterial()->GetTotNbOfElectPerVolume()/
893  couple->GetMaterial()->GetTotNbOfAtomsPerVolume() ;
894 
895  if(Zold != Zeff)
896  UpdateCache();
897 
898  if(insideskin)
899  {
900  //no scattering, single or plural scattering
901  G4double mean = trueStepLength/stepmin ;
902 
903  G4int n = G4Poisson(mean);
904  if(n > 0)
905  {
906  //screening (Moliere-Bethe)
907  G4double mom2 = KineticEnergy*(2.*mass+KineticEnergy);
908  G4double beta2 = mom2/((KineticEnergy+mass)*(KineticEnergy+mass));
909  G4double ascr = scr1/mom2;
910  ascr *= 1.13+scr2/beta2;
911  G4double ascr1 = 1.+2.*ascr;
912  G4double bp1=ascr1+1.;
913  G4double bm1=ascr1-1.;
914 
915  // single scattering from screened Rutherford x-section
916  G4double ct,st,phi;
917  G4double sx=0.,sy=0.,sz=0.;
918  for(G4int i=1; i<=n; i++)
919  {
920  ct = ascr1-bp1*bm1/(2.*G4UniformRand()+bm1);
921  if(ct < -1.) ct = -1.;
922  if(ct > 1.) ct = 1.;
923  st = sqrt(1.-ct*ct);
924  phi = twopi*G4UniformRand();
925  sx += st*cos(phi);
926  sy += st*sin(phi);
927  sz += ct;
928  }
929  cth = sz/sqrt(sx*sx+sy*sy+sz*sz);
930  }
931  }
932  else
933  {
934  if(trueStepLength >= currentRange*dtrl)
935  {
936  if(par1*trueStepLength < 1.)
937  tau = -par2*log(1.-par1*trueStepLength) ;
938  // for the case if ioni/brems are inactivated
939  // see the corresponding condition in ComputeGeomPathLength
940  else if(1.-KineticEnergy/currentKinEnergy > taulim)
941  tau = taubig ;
942  }
943  currentTau = tau ;
944  lambdaeff = trueStepLength/currentTau;
945  currentRadLength = couple->GetMaterial()->GetRadlen();
946 
947  if (tau >= taubig) cth = -1.+2.*G4UniformRand();
948  else if (tau >= tausmall)
949  {
950  G4double xsi = 3.0;
951  G4double x0 = 1.;
952  G4double a = 1., ea = 0., eaa = 1.;
953  G4double b=2.,b1=3.,bx=1.,eb1=3.,ebx=1.;
954  G4double prob = 1. , qprob = 1. ;
955  G4double xmean1 = 1., xmean2 = 0.;
956  G4double xmeanth = exp(-tau);
957  G4double x2meanth = (1.+2.*exp(-2.5*tau))/3.;
958 
959  G4double relloss = 1.-KineticEnergy/currentKinEnergy;
960  if(relloss > rellossmax)
961  return SimpleScattering(xmeanth,x2meanth);
962 
963  G4double theta0 = ComputeTheta0(trueStepLength,KineticEnergy);
964 
965  // protection for very small angles
966  if(theta0*theta0 < tausmall) return cth;
967 
968  if(theta0 > theta0max)
969  return SimpleScattering(xmeanth,x2meanth);
970  G4double sth = sin(0.5*theta0);
971  a = 0.25/(sth*sth);
972 
973  ea = exp(-xsi);
974  eaa = 1.-ea ;
975  xmean1 = 1.-(1.-(1.+xsi)*ea)/(a*eaa);
976  x0 = 1.-xsi/a;
977 
978  if(xmean1 <= 0.999*xmeanth)
979  return SimpleScattering(xmeanth,x2meanth);
980 
981  // from MUSCAT H,Be,Fe data
982  G4double c = coeffc1;
983  if(y > -13.5)
984  c += coeffc2*exp(3.*log(y+13.5));
985 
986  if(abs(c-3.) < 0.001) c = 3.001;
987  if(abs(c-2.) < 0.001) c = 2.001;
988 
989  G4double c1 = c-1.;
990 
991  //from continuity of derivatives
992  b = 1.+(c-xsi)/a;
993 
994  b1 = b+1.;
995  bx = c/a;
996  eb1 = exp(c1*log(b1));
997  ebx = exp(c1*log(bx));
998 
999  xmean2 = (x0*eb1+ebx-(eb1*bx-b1*ebx)/(c-2.))/(eb1-ebx);
1000 
1001  G4double f1x0 = a*ea/eaa;
1002  G4double f2x0 = c1*eb1/(bx*(eb1-ebx));
1003  prob = f2x0/(f1x0+f2x0);
1004 
1005  qprob = xmeanth/(prob*xmean1+(1.-prob)*xmean2);
1006 
1007  // sampling of costheta
1008  if(G4UniformRand() < qprob)
1009  {
1010  if(G4UniformRand() < prob)
1011  cth = 1.+log(ea+G4UniformRand()*eaa)/a ;
1012  else
1013  cth = b-b1*bx/exp(log(ebx+(eb1-ebx)*G4UniformRand())/c1) ;
1014  }
1015  else
1016  cth = -1.+2.*G4UniformRand();
1017  }
1018  }
1019  return cth ;
1020 }
1021 
1022 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1023 
1024 G4double G4UrbanMscModel92::SimpleScattering(G4double xmeanth,G4double x2meanth)
1025 {
1026  // 'large angle scattering'
1027  // 2 model functions with correct xmean and x2mean
1028  G4double a = (2.*xmeanth+9.*x2meanth-3.)/(2.*xmeanth-3.*x2meanth+1.);
1029  G4double prob = (a+2.)*xmeanth/a;
1030 
1031  // sampling
1032  G4double cth = 1.;
1033  if(G4UniformRand() < prob)
1034  cth = -1.+2.*exp(log(G4UniformRand())/(a+1.));
1035  else
1036  cth = -1.+2.*G4UniformRand();
1037  return cth;
1038 }
1039 
1040 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1041 
1042 G4double G4UrbanMscModel92::SampleDisplacement()
1043 {
1044  const G4double kappa = 2.5;
1045  const G4double kappapl1 = kappa+1.;
1046  const G4double kappami1 = kappa-1.;
1047  G4double rmean = 0.0;
1048  if ((currentTau >= tausmall) && !insideskin) {
1049  if (currentTau < taulim) {
1050  rmean = kappa*currentTau*currentTau*currentTau*
1051  (1.-kappapl1*currentTau*0.25)/6. ;
1052 
1053  } else {
1054  G4double etau = 0.0;
1055  if (currentTau<taubig) etau = exp(-currentTau);
1056  rmean = -kappa*currentTau;
1057  rmean = -exp(rmean)/(kappa*kappami1);
1058  rmean += currentTau-kappapl1/kappa+kappa*etau/kappami1;
1059  }
1060  if (rmean>0.) rmean = 2.*lambdaeff*sqrt(rmean/3.0);
1061  else rmean = 0.;
1062  }
1063 
1064  // protection against z > t ...........................
1065  if(rmean > 0.) {
1066  G4double zt = (tPathLength-zPathLength)*(tPathLength+zPathLength);
1067  if(zt <= 0.)
1068  rmean = 0.;
1069  else if(rmean*rmean > zt)
1070  rmean = sqrt(zt);
1071  }
1072  return rmean;
1073 }
1074 
1075 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1076 
1077 G4double G4UrbanMscModel92::LatCorrelation()
1078 {
1079  const G4double kappa = 2.5;
1080  const G4double kappami1 = kappa-1.;
1081 
1082  G4double latcorr = 0.;
1083  if((currentTau >= tausmall) && !insideskin)
1084  {
1085  if(currentTau < taulim)
1086  latcorr = lambdaeff*kappa*currentTau*currentTau*
1087  (1.-(kappa+1.)*currentTau/3.)/3.;
1088  else
1089  {
1090  G4double etau = 0.;
1091  if(currentTau < taubig) etau = exp(-currentTau);
1092  latcorr = -kappa*currentTau;
1093  latcorr = exp(latcorr)/kappami1;
1094  latcorr += 1.-kappa*etau/kappami1 ;
1095  latcorr *= 2.*lambdaeff/3. ;
1096  }
1097  }
1098 
1099  return latcorr;
1100 }
1101 
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