source: trunk/source/processes/electromagnetic/standard/src/G4UrbanMscModel93.cc @ 1315

Last change on this file since 1315 was 1315, checked in by garnier, 14 years ago

update geant4-09-04-beta-cand-01 interfaces-V09-03-09 vis-V09-03-08
File size: 36.6 KB
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26//
27// $Id: G4UrbanMscModel93.cc,v 1.4 2010/05/20 13:17:25 vnivanch Exp $
28// GEANT4 tag $Name: geant4-09-04-beta-cand-01 $
29//
30// -------------------------------------------------------------------
31//   
32// GEANT4 Class file
33//   
34//
35// File name:   G4UrbanMscModel93
36//
37// Author:      Laszlo Urban
38//
39// Creation date: 06.03.2008
40//
41// Modifications:
42//
43// 06-03-2008 starting point : G4UrbanMscModel2 = G4UrbanMscModel 9.1 ref 02
44//
45// 13-03-08  Bug in SampleScattering (which caused lateral asymmetry) fixed
46//           (L.Urban)
47//
48// 14-03-08  Simplification of step limitation in ComputeTruePathLengthLimit,
49//           + tlimitmin is the same for UseDistancetoBoundary and
50//           UseSafety (L.Urban)           
51//
52// 16-03-08  Reorganization of SampleCosineTheta + new method SimpleScattering
53//           SimpleScattering is used if the relative energy loss is too big
54//           or theta0 is too big (see data members rellossmax, theta0max)
55//           (L.Urban)         
56//
57// 17-03-08  tuning of the correction factor in ComputeTheta0 (L.Urban)
58//
59// 19-03-08  exponent c of the 'tail' model function is not equal to 2 any more,
60//           value of c has been extracted from some e- scattering data (L.Urban)
61//
62// 24-03-08  Step limitation in ComputeTruePathLengthLimit has been
63//           simplified further + some data members have been removed (L.Urban)
64//
65// 24-07-08  central part of scattering angle (theta0) has been tuned
66//           tail of the scattering angle distribution has been tuned
67//           using some e- and proton scattering data
68//
69// 05-08-08  bugfix in ComputeTruePathLengthLimit (L.Urban)
70//
71// 09-10-08  theta0 and tail have been retuned using some e-,mu,proton
72//           scattering data (L.Urban)
73//           + single scattering without path length correction for
74//           small steps (t < tlimitmin, for UseDistanceToBoundary only)
75//
76// 15-10-08  Moliere-Bethe screening in the single scattering part(L.Urban)         
77//
78// 17-10-08  stepping similar to that in model (9.1) for UseSafety case
79//           for e+/e- in order to speed up the code for calorimeters
80//
81// 23-10-08  bugfix in the screeningparameter of the single scattering part,
82//           some technical change in order to speed up the code (UpdateCache)
83//
84// 27-10-08  bugfix in ComputeTruePathLengthLimit (affects UseDistanceToBoundary
85//           stepping type only) (L.Urban)         
86//
87// 28-10-09  V.Ivanchenko moved G4UrbanMscModel2 to G4UrbanMscModel93,
88//           now it is a frozen version of the Urban model corresponding
89//           to g4 9.3
90
91// Class Description:
92//
93// Implementation of the model of multiple scattering based on
94// H.W.Lewis Phys Rev 78 (1950) 526 and others
95
96// -------------------------------------------------------------------
97// In its present form the model can be  used for simulation
98//   of the e-/e+, muon and charged hadron multiple scattering
99//
100
101
102//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
103//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
104
105#include "G4UrbanMscModel93.hh"
106#include "Randomize.hh"
107#include "G4Electron.hh"
108#include "G4LossTableManager.hh"
109#include "G4ParticleChangeForMSC.hh"
110
111#include "G4Poisson.hh"
112#include "globals.hh"
113
114//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
115
116using namespace std;
117
118G4UrbanMscModel93::G4UrbanMscModel93(const G4String& nam)
119  : G4VMscModel(nam),
120    isInitialized(false)
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  inside        = false; 
166  insideskin    = false;
167
168}
169
170//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
171
172G4UrbanMscModel93::~G4UrbanMscModel93()
173{}
174
175//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
176
177void G4UrbanMscModel93::Initialise(const G4ParticleDefinition* p,
178                                   const G4DataVector&)
179{
180  skindepth = skin*stepmin;
181  if(isInitialized) return;
182  // set values of some data members
183  SetParticle(p);
184
185  fParticleChange = GetParticleChangeForMSC();
186  InitialiseSafetyHelper();
187
188  isInitialized = true;
189}
190
191//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
192
193G4double G4UrbanMscModel93::ComputeCrossSectionPerAtom( 
194                             const G4ParticleDefinition* part,
195                                   G4double KineticEnergy,
196                                   G4double AtomicNumber,G4double,
197                                   G4double, G4double)
198{
199  const G4double sigmafactor = twopi*classic_electr_radius*classic_electr_radius;
200  const G4double epsfactor = 2.*electron_mass_c2*electron_mass_c2*
201                            Bohr_radius*Bohr_radius/(hbarc*hbarc);
202  const G4double epsmin = 1.e-4 , epsmax = 1.e10;
203
204  const G4double Zdat[15] = { 4.,  6., 13., 20., 26., 29., 32., 38., 47.,
205                             50., 56., 64., 74., 79., 82. };
206
207  const G4double Tdat[22] = { 100*eV,  200*eV,  400*eV,  700*eV,
208                               1*keV,   2*keV,   4*keV,   7*keV,
209                              10*keV,  20*keV,  40*keV,  70*keV,
210                             100*keV, 200*keV, 400*keV, 700*keV,
211                               1*MeV,   2*MeV,   4*MeV,   7*MeV,
212                              10*MeV,  20*MeV};
213
214  // corr. factors for e-/e+ lambda for T <= Tlim
215          G4double celectron[15][22] =
216          {{1.125,1.072,1.051,1.047,1.047,1.050,1.052,1.054,
217            1.054,1.057,1.062,1.069,1.075,1.090,1.105,1.111,
218            1.112,1.108,1.100,1.093,1.089,1.087            },
219           {1.408,1.246,1.143,1.096,1.077,1.059,1.053,1.051,
220            1.052,1.053,1.058,1.065,1.072,1.087,1.101,1.108,
221            1.109,1.105,1.097,1.090,1.086,1.082            },
222           {2.833,2.268,1.861,1.612,1.486,1.309,1.204,1.156,
223            1.136,1.114,1.106,1.106,1.109,1.119,1.129,1.132,
224            1.131,1.124,1.113,1.104,1.099,1.098            },
225           {3.879,3.016,2.380,2.007,1.818,1.535,1.340,1.236,
226            1.190,1.133,1.107,1.099,1.098,1.103,1.110,1.113,
227            1.112,1.105,1.096,1.089,1.085,1.098            },
228           {6.937,4.330,2.886,2.256,1.987,1.628,1.395,1.265,
229            1.203,1.122,1.080,1.065,1.061,1.063,1.070,1.073,
230            1.073,1.070,1.064,1.059,1.056,1.056            },
231           {9.616,5.708,3.424,2.551,2.204,1.762,1.485,1.330,
232            1.256,1.155,1.099,1.077,1.070,1.068,1.072,1.074,
233            1.074,1.070,1.063,1.059,1.056,1.052            },
234           {11.72,6.364,3.811,2.806,2.401,1.884,1.564,1.386,
235            1.300,1.180,1.112,1.082,1.073,1.066,1.068,1.069,
236            1.068,1.064,1.059,1.054,1.051,1.050            },
237           {18.08,8.601,4.569,3.183,2.662,2.025,1.646,1.439,
238            1.339,1.195,1.108,1.068,1.053,1.040,1.039,1.039,
239            1.039,1.037,1.034,1.031,1.030,1.036            },
240           {18.22,10.48,5.333,3.713,3.115,2.367,1.898,1.631,
241            1.498,1.301,1.171,1.105,1.077,1.048,1.036,1.033,
242            1.031,1.028,1.024,1.022,1.021,1.024            },
243           {14.14,10.65,5.710,3.929,3.266,2.453,1.951,1.669,
244            1.528,1.319,1.178,1.106,1.075,1.040,1.027,1.022,
245            1.020,1.017,1.015,1.013,1.013,1.020            },
246           {14.11,11.73,6.312,4.240,3.478,2.566,2.022,1.720,
247            1.569,1.342,1.186,1.102,1.065,1.022,1.003,0.997,
248            0.995,0.993,0.993,0.993,0.993,1.011            },
249           {22.76,20.01,8.835,5.287,4.144,2.901,2.219,1.855,
250            1.677,1.410,1.224,1.121,1.073,1.014,0.986,0.976,
251            0.974,0.972,0.973,0.974,0.975,0.987            },
252           {50.77,40.85,14.13,7.184,5.284,3.435,2.520,2.059,
253            1.837,1.512,1.283,1.153,1.091,1.010,0.969,0.954,
254            0.950,0.947,0.949,0.952,0.954,0.963            },
255           {65.87,59.06,15.87,7.570,5.567,3.650,2.682,2.182,
256            1.939,1.579,1.325,1.178,1.108,1.014,0.965,0.947,
257            0.941,0.938,0.940,0.944,0.946,0.954            },
258           {55.60,47.34,15.92,7.810,5.755,3.767,2.760,2.239,
259            1.985,1.609,1.343,1.188,1.113,1.013,0.960,0.939,
260            0.933,0.930,0.933,0.936,0.939,0.949            }};
261           
262           G4double cpositron[15][22] = {
263           {2.589,2.044,1.658,1.446,1.347,1.217,1.144,1.110,
264            1.097,1.083,1.080,1.086,1.092,1.108,1.123,1.131,
265            1.131,1.126,1.117,1.108,1.103,1.100            },
266           {3.904,2.794,2.079,1.710,1.543,1.325,1.202,1.145,
267            1.122,1.096,1.089,1.092,1.098,1.114,1.130,1.137,
268            1.138,1.132,1.122,1.113,1.108,1.102            },
269           {7.970,6.080,4.442,3.398,2.872,2.127,1.672,1.451,
270            1.357,1.246,1.194,1.179,1.178,1.188,1.201,1.205,
271            1.203,1.190,1.173,1.159,1.151,1.145            },
272           {9.714,7.607,5.747,4.493,3.815,2.777,2.079,1.715,
273            1.553,1.353,1.253,1.219,1.211,1.214,1.225,1.228,
274            1.225,1.210,1.191,1.175,1.166,1.174            },
275           {17.97,12.95,8.628,6.065,4.849,3.222,2.275,1.820,
276            1.624,1.382,1.259,1.214,1.202,1.202,1.214,1.219,
277            1.217,1.203,1.184,1.169,1.160,1.151            },
278           {24.83,17.06,10.84,7.355,5.767,3.707,2.546,1.996,
279            1.759,1.465,1.311,1.252,1.234,1.228,1.238,1.241,
280            1.237,1.222,1.201,1.184,1.174,1.159            },
281           {23.26,17.15,11.52,8.049,6.375,4.114,2.792,2.155,
282            1.880,1.535,1.353,1.281,1.258,1.247,1.254,1.256,
283            1.252,1.234,1.212,1.194,1.183,1.170            },
284           {22.33,18.01,12.86,9.212,7.336,4.702,3.117,2.348,
285            2.015,1.602,1.385,1.297,1.268,1.251,1.256,1.258,
286            1.254,1.237,1.214,1.195,1.185,1.179            },
287           {33.91,24.13,15.71,10.80,8.507,5.467,3.692,2.808,
288            2.407,1.873,1.564,1.425,1.374,1.330,1.324,1.320,
289            1.312,1.288,1.258,1.235,1.221,1.205            },
290           {32.14,24.11,16.30,11.40,9.015,5.782,3.868,2.917,
291            2.490,1.925,1.596,1.447,1.391,1.342,1.332,1.327,
292            1.320,1.294,1.264,1.240,1.226,1.214            },
293           {29.51,24.07,17.19,12.28,9.766,6.238,4.112,3.066,
294            2.602,1.995,1.641,1.477,1.414,1.356,1.342,1.336,
295            1.328,1.302,1.270,1.245,1.231,1.233            },
296           {38.19,30.85,21.76,15.35,12.07,7.521,4.812,3.498,
297            2.926,2.188,1.763,1.563,1.484,1.405,1.382,1.371,
298            1.361,1.330,1.294,1.267,1.251,1.239            },
299           {49.71,39.80,27.96,19.63,15.36,9.407,5.863,4.155,
300            3.417,2.478,1.944,1.692,1.589,1.480,1.441,1.423,
301            1.409,1.372,1.330,1.298,1.280,1.258            },
302           {59.25,45.08,30.36,20.83,16.15,9.834,6.166,4.407,
303            3.641,2.648,2.064,1.779,1.661,1.531,1.482,1.459,
304            1.442,1.400,1.354,1.319,1.299,1.272            },
305           {56.38,44.29,30.50,21.18,16.51,10.11,6.354,4.542,
306            3.752,2.724,2.116,1.817,1.692,1.554,1.499,1.474,
307            1.456,1.412,1.364,1.328,1.307,1.282            }};
308
309  //data/corrections for T > Tlim 
310  G4double Tlim = 10.*MeV;
311  G4double beta2lim = Tlim*(Tlim+2.*electron_mass_c2)/
312                      ((Tlim+electron_mass_c2)*(Tlim+electron_mass_c2));
313  G4double bg2lim   = Tlim*(Tlim+2.*electron_mass_c2)/
314                      (electron_mass_c2*electron_mass_c2);
315
316  G4double sig0[15] = {0.2672*barn,  0.5922*barn, 2.653*barn,  6.235*barn,
317                      11.69*barn  , 13.24*barn  , 16.12*barn, 23.00*barn ,
318                      35.13*barn  , 39.95*barn  , 50.85*barn, 67.19*barn ,
319                      91.15*barn  , 104.4*barn  , 113.1*barn};
320                                       
321  G4double hecorr[15] = {120.70, 117.50, 105.00, 92.92, 79.23,  74.510,  68.29,
322                          57.39,  41.97,  36.14, 24.53, 10.21,  -7.855, -16.84,
323                         -22.30};
324
325  G4double sigma;
326  SetParticle(part);
327
328  G4double Z23 = 2.*log(AtomicNumber)/3.; Z23 = exp(Z23);
329
330  // correction if particle .ne. e-/e+
331  // compute equivalent kinetic energy
332  // lambda depends on p*beta ....
333
334  G4double eKineticEnergy = KineticEnergy;
335
336  if(mass > electron_mass_c2)
337  {
338     G4double TAU = KineticEnergy/mass ;
339     G4double c = mass*TAU*(TAU+2.)/(electron_mass_c2*(TAU+1.)) ;
340     G4double w = c-2. ;
341     G4double tau = 0.5*(w+sqrt(w*w+4.*c)) ;
342     eKineticEnergy = electron_mass_c2*tau ;
343  }
344
345  G4double eTotalEnergy = eKineticEnergy + electron_mass_c2 ;
346  G4double beta2 = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
347                                 /(eTotalEnergy*eTotalEnergy);
348  G4double bg2   = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
349                                 /(electron_mass_c2*electron_mass_c2);
350
351  G4double eps = epsfactor*bg2/Z23;
352
353  if     (eps<epsmin)  sigma = 2.*eps*eps;
354  else if(eps<epsmax)  sigma = log(1.+2.*eps)-2.*eps/(1.+2.*eps);
355  else                 sigma = log(2.*eps)-1.+1./eps;
356
357  sigma *= ChargeSquare*AtomicNumber*AtomicNumber/(beta2*bg2);
358
359  // interpolate in AtomicNumber and beta2
360  G4double c1,c2,cc1,cc2,corr;
361
362  // get bin number in Z
363  G4int iZ = 14;
364  while ((iZ>=0)&&(Zdat[iZ]>=AtomicNumber)) iZ -= 1;
365  if (iZ==14)                               iZ = 13;
366  if (iZ==-1)                               iZ = 0 ;
367
368  G4double Z1 = Zdat[iZ];
369  G4double Z2 = Zdat[iZ+1];
370  G4double ratZ = (AtomicNumber-Z1)*(AtomicNumber+Z1)/
371                  ((Z2-Z1)*(Z2+Z1));
372
373  if(eKineticEnergy <= Tlim) 
374  {
375    // get bin number in T (beta2)
376    G4int iT = 21;
377    while ((iT>=0)&&(Tdat[iT]>=eKineticEnergy)) iT -= 1;
378    if(iT==21)                                  iT = 20;
379    if(iT==-1)                                  iT = 0 ;
380
381    //  calculate betasquare values
382    G4double T = Tdat[iT],   E = T + electron_mass_c2;
383    G4double b2small = T*(E+electron_mass_c2)/(E*E);
384
385    T = Tdat[iT+1]; E = T + electron_mass_c2;
386    G4double b2big = T*(E+electron_mass_c2)/(E*E);
387    G4double ratb2 = (beta2-b2small)/(b2big-b2small);
388
389    if (charge < 0.)
390    {
391       c1 = celectron[iZ][iT];
392       c2 = celectron[iZ+1][iT];
393       cc1 = c1+ratZ*(c2-c1);
394
395       c1 = celectron[iZ][iT+1];
396       c2 = celectron[iZ+1][iT+1];
397       cc2 = c1+ratZ*(c2-c1);
398
399       corr = cc1+ratb2*(cc2-cc1);
400
401       sigma *= sigmafactor/corr;
402    }
403    else             
404    {
405       c1 = cpositron[iZ][iT];
406       c2 = cpositron[iZ+1][iT];
407       cc1 = c1+ratZ*(c2-c1);
408
409       c1 = cpositron[iZ][iT+1];
410       c2 = cpositron[iZ+1][iT+1];
411       cc2 = c1+ratZ*(c2-c1);
412
413       corr = cc1+ratb2*(cc2-cc1);
414
415       sigma *= sigmafactor/corr;
416    }
417  }
418  else
419  {
420    c1 = bg2lim*sig0[iZ]*(1.+hecorr[iZ]*(beta2-beta2lim))/bg2;
421    c2 = bg2lim*sig0[iZ+1]*(1.+hecorr[iZ+1]*(beta2-beta2lim))/bg2;
422    if((AtomicNumber >= Z1) && (AtomicNumber <= Z2))
423      sigma = c1+ratZ*(c2-c1) ;
424    else if(AtomicNumber < Z1)
425      sigma = AtomicNumber*AtomicNumber*c1/(Z1*Z1);
426    else if(AtomicNumber > Z2)
427      sigma = AtomicNumber*AtomicNumber*c2/(Z2*Z2);
428  }
429  return sigma;
430
431}
432
433//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
434
435G4double G4UrbanMscModel93::ComputeTruePathLengthLimit(
436                             const G4Track& track,
437                             G4PhysicsTable* theTable,
438                             G4double currentMinimalStep)
439{
440  tPathLength = currentMinimalStep;
441  G4StepPoint* sp = track.GetStep()->GetPreStepPoint();
442  G4StepStatus stepStatus = sp->GetStepStatus();
443
444  const G4DynamicParticle* dp = track.GetDynamicParticle();
445
446  if(stepStatus == fUndefined) {
447    inside = false;
448    insideskin = false;
449    tlimit = geombig;
450    SetParticle( dp->GetDefinition() );
451  }
452
453  theLambdaTable = theTable;
454  couple = track.GetMaterialCutsCouple();
455  currentMaterialIndex = couple->GetIndex();
456  currentKinEnergy = dp->GetKineticEnergy();
457  currentRange = 
458    theManager->GetRangeFromRestricteDEDX(particle,currentKinEnergy,couple);
459  lambda0 = GetLambda(currentKinEnergy);
460
461  // stop here if small range particle
462  if(inside) return tPathLength;           
463 
464  if(tPathLength > currentRange) tPathLength = currentRange;
465
466  presafety = sp->GetSafety();
467
468 // G4cout << "G4Urban2::StepLimit tPathLength= "
469 //      <<tPathLength<<" safety= " << presafety
470 //        << " range= " <<currentRange<< " lambda= "<<lambda0
471 //      << " Alg: " << steppingAlgorithm <<G4endl;
472
473  // far from geometry boundary
474  if(currentRange < presafety)
475    {
476      inside = true;
477      return tPathLength; 
478    }
479
480  // standard  version
481  //
482  if (steppingAlgorithm == fUseDistanceToBoundary)
483    {
484      //compute geomlimit and presafety
485      G4double geomlimit = ComputeGeomLimit(track, presafety, currentRange);
486
487      // is it far from boundary ?
488      if(currentRange < presafety)
489        {
490          inside = true;
491          return tPathLength;   
492        }
493
494      smallstep += 1.;
495      insideskin = false;
496
497      if((stepStatus == fGeomBoundary) || (stepStatus == fUndefined))
498        {
499          rangeinit = currentRange;
500          if(stepStatus == fUndefined) smallstep = 1.e10;
501          else  smallstep = 1.;
502
503          //define stepmin here (it depends on lambda!)
504          //rough estimation of lambda_elastic/lambda_transport
505          G4double rat = currentKinEnergy/MeV ;
506          rat = 1.e-3/(rat*(10.+rat)) ;
507          //stepmin ~ lambda_elastic
508          stepmin = rat*lambda0;
509          skindepth = skin*stepmin;
510          //define tlimitmin
511          tlimitmin = 10.*stepmin;
512          if(tlimitmin < tlimitminfix) tlimitmin = tlimitminfix;
513          //G4cout << "rangeinit= " << rangeinit << " stepmin= " << stepmin
514          //     << " tlimitmin= " << tlimitmin << " geomlimit= " << geomlimit <<G4endl;
515          // constraint from the geometry
516          if((geomlimit < geombig) && (geomlimit > geommin))
517            {
518              // geomlimit is a geometrical step length
519              // transform it to true path length (estimation)
520              if((1.-geomlimit/lambda0) > 0.)
521                geomlimit = -lambda0*log(1.-geomlimit/lambda0)+tlimitmin ;
522
523              if(stepStatus == fGeomBoundary)
524                tgeom = geomlimit/facgeom;
525              else
526                tgeom = 2.*geomlimit/facgeom;
527            }
528            else
529              tgeom = geombig;
530        }
531
532
533      //step limit
534      tlimit = facrange*rangeinit;             
535      if(tlimit < facsafety*presafety)
536        tlimit = facsafety*presafety; 
537
538      //lower limit for tlimit
539      if(tlimit < tlimitmin) tlimit = tlimitmin;
540
541      if(tlimit > tgeom) tlimit = tgeom;
542
543      //G4cout << "tgeom= " << tgeom << " geomlimit= " << geomlimit 
544      //      << " tlimit= " << tlimit << " presafety= " << presafety << G4endl;
545
546      // shortcut
547      if((tPathLength < tlimit) && (tPathLength < presafety) &&
548         (smallstep >= skin) && (tPathLength < geomlimit-0.999*skindepth))
549        return tPathLength;   
550
551      // step reduction near to boundary
552      if(smallstep < skin)
553        {
554          tlimit = stepmin;
555          insideskin = true;
556        }
557      else if(geomlimit < geombig)
558        {
559          if(geomlimit > skindepth)
560            {
561              if(tlimit > geomlimit-0.999*skindepth)
562                tlimit = geomlimit-0.999*skindepth;
563            }
564          else
565            {
566              insideskin = true;
567              if(tlimit > stepmin) tlimit = stepmin;
568            }
569        }
570
571      if(tlimit < stepmin) tlimit = stepmin;
572
573      // randomize 1st step or 1st 'normal' step in volume
574      if((stepStatus == fUndefined) ||
575         ((smallstep == skin) && !insideskin)) 
576        { 
577          G4double temptlimit = tlimit;
578          if(temptlimit > tlimitmin)
579          {
580            do {
581              temptlimit = G4RandGauss::shoot(tlimit,0.3*tlimit);       
582               } while ((temptlimit < tlimitmin) || 
583                        (temptlimit > 2.*tlimit-tlimitmin));
584          }
585          else
586            temptlimit = tlimitmin;
587          if(tPathLength > temptlimit) tPathLength = temptlimit;
588        }
589      else
590        { 
591          if(tPathLength > tlimit) tPathLength = tlimit  ; 
592        }
593
594    }
595    // for 'normal' simulation with or without magnetic field
596    //  there no small step/single scattering at boundaries
597  else if(steppingAlgorithm == fUseSafety)
598    {
599      // compute presafety again if presafety <= 0 and no boundary
600      // i.e. when it is needed for optimization purposes
601      if((stepStatus != fGeomBoundary) && (presafety < tlimitminfix)) 
602        presafety = ComputeSafety(sp->GetPosition(),tPathLength); 
603
604      // is far from boundary
605      if(currentRange < presafety)
606        {
607          inside = true;
608          return tPathLength; 
609        }
610
611      if((stepStatus == fGeomBoundary) || (stepStatus == fUndefined))
612      {
613        rangeinit = currentRange;
614        fr = facrange;
615        // 9.1 like stepping for e+/e- only (not for muons,hadrons)
616        if(mass < masslimite) 
617        {
618          if(lambda0 > currentRange)
619            rangeinit = lambda0;
620          if(lambda0 > lambdalimit)
621            fr *= 0.75+0.25*lambda0/lambdalimit;
622        }
623
624        //lower limit for tlimit
625        G4double rat = currentKinEnergy/MeV ;
626        rat = 1.e-3/(rat*(10.+rat)) ;
627        tlimitmin = 10.*lambda0*rat;
628        if(tlimitmin < tlimitminfix) tlimitmin = tlimitminfix;
629      }
630      //step limit
631      tlimit = fr*rangeinit;               
632
633      if(tlimit < facsafety*presafety)
634        tlimit = facsafety*presafety;
635
636      //lower limit for tlimit
637      if(tlimit < tlimitmin) tlimit = tlimitmin;
638     
639      if(tPathLength > tlimit) tPathLength = tlimit;
640
641    }
642 
643  // version similar to 7.1 (needed for some experiments)
644  else
645    {
646      if (stepStatus == fGeomBoundary)
647        {
648          if (currentRange > lambda0) tlimit = facrange*currentRange;
649          else                        tlimit = facrange*lambda0;
650
651          if(tlimit < tlimitmin) tlimit = tlimitmin;
652          if(tPathLength > tlimit) tPathLength = tlimit;
653        }
654    }
655  //G4cout << "tPathLength= " << tPathLength
656  //     << " currentMinimalStep= " << currentMinimalStep << G4endl;
657  return tPathLength ;
658}
659
660//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
661
662G4double G4UrbanMscModel93::ComputeGeomPathLength(G4double)
663{
664  lambdaeff = lambda0;
665  par1 = -1. ; 
666  par2 = par3 = 0. ; 
667
668  //  do the true -> geom transformation
669  zPathLength = tPathLength;
670
671  // z = t for very small tPathLength
672  if(tPathLength < tlimitminfix) return zPathLength;
673
674  // this correction needed to run MSC with eIoni and eBrem inactivated
675  // and makes no harm for a normal run
676  if(tPathLength > currentRange)
677    tPathLength = currentRange ;
678
679  G4double tau   = tPathLength/lambda0 ;
680
681  if ((tau <= tausmall) || insideskin) {
682    zPathLength  = tPathLength;
683    if(zPathLength > lambda0) zPathLength = lambda0;
684    return zPathLength;
685  }
686
687  G4double zmean = tPathLength;
688  if (tPathLength < currentRange*dtrl) {
689    if(tau < taulim) zmean = tPathLength*(1.-0.5*tau) ;
690    else             zmean = lambda0*(1.-exp(-tau));
691  } else if(currentKinEnergy < mass)  {
692    par1 = 1./currentRange ;
693    par2 = 1./(par1*lambda0) ;
694    par3 = 1.+par2 ;
695    if(tPathLength < currentRange)
696      zmean = (1.-exp(par3*log(1.-tPathLength/currentRange)))/(par1*par3) ;
697    else
698      zmean = 1./(par1*par3) ;
699  } else {
700    G4double T1 = theManager->GetEnergy(particle,currentRange-tPathLength,couple);
701    G4double lambda1 = GetLambda(T1);
702
703    par1 = (lambda0-lambda1)/(lambda0*tPathLength) ;
704    par2 = 1./(par1*lambda0) ;
705    par3 = 1.+par2 ;
706    zmean = (1.-exp(par3*log(lambda1/lambda0)))/(par1*par3) ;
707  }
708
709  zPathLength = zmean ;
710
711  //  sample z
712  if(samplez)
713  {
714    const G4double  ztmax = 0.99 ;
715    G4double zt = zmean/tPathLength ;
716
717    if (tPathLength > stepmin && zt < ztmax)             
718    {
719      G4double u,cz1;
720      if(zt >= third)
721      {
722        G4double cz = 0.5*(3.*zt-1.)/(1.-zt) ;
723        cz1 = 1.+cz ;
724        G4double u0 = cz/cz1 ;
725        G4double grej ;
726        do {
727            u = exp(log(G4UniformRand())/cz1) ;
728            grej = exp(cz*log(u/u0))*(1.-u)/(1.-u0) ;
729           } while (grej < G4UniformRand()) ;
730      }
731      else
732      {
733        cz1 = 1./zt-1.;
734        u = 1.-exp(log(G4UniformRand())/cz1) ;
735      }
736      zPathLength = tPathLength*u ;
737    }
738  }
739
740  if(zPathLength > lambda0) zPathLength = lambda0;
741  //G4cout << "zPathLength= " << zPathLength << " lambda1= " << lambda0 << G4endl;
742  return zPathLength;
743}
744
745//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
746
747G4double G4UrbanMscModel93::ComputeTrueStepLength(G4double geomStepLength)
748{
749  // step defined other than transportation
750  if(geomStepLength == zPathLength && tPathLength <= currentRange)
751    return tPathLength;
752
753  // t = z for very small step
754  zPathLength = geomStepLength;
755  tPathLength = geomStepLength;
756  if(geomStepLength < tlimitminfix) return tPathLength;
757 
758  // recalculation
759  if((geomStepLength > lambda0*tausmall) && !insideskin)
760  {
761    if(par1 <  0.)
762      tPathLength = -lambda0*log(1.-geomStepLength/lambda0) ;
763    else 
764    {
765      if(par1*par3*geomStepLength < 1.)
766        tPathLength = (1.-exp(log(1.-par1*par3*geomStepLength)/par3))/par1 ;
767      else 
768        tPathLength = currentRange;
769    } 
770  }
771  if(tPathLength < geomStepLength) tPathLength = geomStepLength;
772  //G4cout << "tPathLength= " << tPathLength << " step= " << geomStepLength << G4endl;
773
774  return tPathLength;
775}
776
777//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
778
779G4double G4UrbanMscModel93::ComputeTheta0(G4double trueStepLength,
780                                          G4double KineticEnergy)
781{
782  // for all particles take the width of the central part
783  //  from a  parametrization similar to the Highland formula
784  // ( Highland formula: Particle Physics Booklet, July 2002, eq. 26.10)
785  const G4double c_highland = 13.6*MeV ;
786  G4double betacp = sqrt(currentKinEnergy*(currentKinEnergy+2.*mass)*
787                         KineticEnergy*(KineticEnergy+2.*mass)/
788                      ((currentKinEnergy+mass)*(KineticEnergy+mass)));
789  y = trueStepLength/currentRadLength;
790  G4double theta0 = c_highland*std::abs(charge)*sqrt(y)/betacp;
791  y = log(y);
792  // correction factor from e- scattering data
793  G4double corr = coeffth1+coeffth2*y;               
794
795  theta0 *= corr ;                                               
796
797  return theta0;
798}
799
800//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
801
802void G4UrbanMscModel93::SampleScattering(const G4DynamicParticle* dynParticle,
803                                         G4double safety)
804{
805  G4double kineticEnergy = dynParticle->GetKineticEnergy();
806
807  if((kineticEnergy <= 0.0) || (tPathLength <= tlimitminfix) ||
808     (tPathLength/tausmall < lambda0)) return;
809
810  G4double cth  = SampleCosineTheta(tPathLength,kineticEnergy);
811
812  // protection against 'bad' cth values
813  if(std::abs(cth) > 1.) return;
814
815  G4double sth  = sqrt((1.0 - cth)*(1.0 + cth));
816  G4double phi  = twopi*G4UniformRand();
817  G4double dirx = sth*cos(phi);
818  G4double diry = sth*sin(phi);
819
820  G4ThreeVector oldDirection = dynParticle->GetMomentumDirection();
821  G4ThreeVector newDirection(dirx,diry,cth);
822  newDirection.rotateUz(oldDirection);
823  fParticleChange->ProposeMomentumDirection(newDirection);
824
825  if (latDisplasment && safety > tlimitminfix) {
826
827    G4double r = SampleDisplacement();
828    /*   
829    G4cout << "G4UrbanMscModel93::SampleSecondaries: e(MeV)= " << kineticEnergy
830           << " sinTheta= " << sth << " r(mm)= " << r
831           << " trueStep(mm)= " << tPathLength
832           << " geomStep(mm)= " << zPathLength
833           << G4endl;
834    */
835    if(r > 0.)
836      {
837        G4double latcorr = LatCorrelation();
838        if(latcorr > r) latcorr = r;
839
840        // sample direction of lateral displacement
841        // compute it from the lateral correlation
842        G4double Phi = 0.;
843        if(std::abs(r*sth) < latcorr)
844          Phi  = twopi*G4UniformRand();
845        else
846        {
847          G4double psi = std::acos(latcorr/(r*sth));
848          if(G4UniformRand() < 0.5)
849            Phi = phi+psi;
850          else
851            Phi = phi-psi;
852        }
853
854        dirx = std::cos(Phi);
855        diry = std::sin(Phi);
856
857        G4ThreeVector latDirection(dirx,diry,0.0);
858        latDirection.rotateUz(oldDirection);
859
860        ComputeDisplacement(fParticleChange, latDirection, r, safety);
861      }
862  }
863}
864
865//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
866
867G4double G4UrbanMscModel93::SampleCosineTheta(G4double trueStepLength,
868                                              G4double KineticEnergy)
869{
870  G4double cth = 1. ;
871  G4double tau = trueStepLength/lambda0 ;
872
873  Zeff = couple->GetMaterial()->GetTotNbOfElectPerVolume()/
874         couple->GetMaterial()->GetTotNbOfAtomsPerVolume() ;
875
876  if(Zold != Zeff) 
877    UpdateCache();
878
879  if(insideskin)
880  {
881    //no scattering, single or plural scattering
882    G4double mean = trueStepLength/stepmin ;
883
884    G4int n = G4Poisson(mean);
885    if(n > 0)
886    {
887      //screening (Moliere-Bethe)
888      G4double mom2 = KineticEnergy*(2.*mass+KineticEnergy);
889      G4double beta2 = mom2/((KineticEnergy+mass)*(KineticEnergy+mass));
890      G4double ascr = scr1/mom2;
891      ascr *= 1.13+scr2/beta2;
892      G4double ascr1 = 1.+2.*ascr;
893      G4double bp1=ascr1+1.;
894      G4double bm1=ascr1-1.;
895
896      // single scattering from screened Rutherford x-section
897      G4double ct,st,phi;
898      G4double sx=0.,sy=0.,sz=0.;
899      for(G4int i=1; i<=n; i++)
900      {
901        ct = ascr1-bp1*bm1/(2.*G4UniformRand()+bm1);
902        if(ct < -1.) ct = -1.;
903        if(ct >  1.) ct =  1.; 
904        st = sqrt(1.-ct*ct);
905        phi = twopi*G4UniformRand();
906        sx += st*cos(phi);
907        sy += st*sin(phi);
908        sz += ct;
909      }
910      cth = sz/sqrt(sx*sx+sy*sy+sz*sz);
911    }
912  }
913  else
914  {
915    if(trueStepLength >= currentRange*dtrl) 
916    {
917      if(par1*trueStepLength < 1.)
918        tau = -par2*log(1.-par1*trueStepLength) ;
919      // for the case if ioni/brems are inactivated
920      // see the corresponding condition in ComputeGeomPathLength
921      else if(1.-KineticEnergy/currentKinEnergy > taulim)
922        tau = taubig ;
923    }
924    currentTau = tau ;
925    lambdaeff = trueStepLength/currentTau;
926    currentRadLength = couple->GetMaterial()->GetRadlen();
927
928    if (tau >= taubig) cth = -1.+2.*G4UniformRand();
929    else if (tau >= tausmall)
930    {
931      G4double xsi = 3.;
932      G4double x0 = 1.;
933      G4double a = 1., ea = 0., eaa = 1.;
934      G4double b=2.,b1=3.,bx=1.,eb1=3.,ebx=1.;
935      G4double prob = 1. , qprob = 1. ;
936      G4double xmean1 = 1., xmean2 = 0.;
937      G4double xmeanth = exp(-tau);
938      G4double x2meanth = (1.+2.*exp(-2.5*tau))/3.;
939
940      G4double relloss = 1.-KineticEnergy/currentKinEnergy;
941      if(relloss > rellossmax) 
942        return SimpleScattering(xmeanth,x2meanth);
943
944      G4double theta0 = ComputeTheta0(trueStepLength,KineticEnergy);
945
946      // protection for very small angles
947      if(theta0 < tausmall) return cth;
948   
949      if(theta0 > theta0max)
950        return SimpleScattering(xmeanth,x2meanth);
951      G4double sth = sin(0.5*theta0);
952      a = 0.25/(sth*sth);
953
954      ea = exp(-xsi);
955      eaa = 1.-ea ;
956      xmean1 = 1.-(1.-(1.+xsi)*ea)/(a*eaa);
957      x0 = 1.-xsi/a;
958
959      if(xmean1 <= 0.999*xmeanth)
960        return SimpleScattering(xmeanth,x2meanth);
961
962      // from e- and muon scattering data                   
963      G4double c = coeffc1+coeffc2*y; ;                         
964
965      if(abs(c-3.) < 0.001)  c = 3.001;     
966      if(abs(c-2.) < 0.001)  c = 2.001;     
967      if(abs(c-1.) < 0.001)  c = 1.001;     
968
969      G4double c1 = c-1.;
970
971      //from continuity of derivatives
972      b = 1.+(c-xsi)/a;
973
974      b1 = b+1.;
975      bx = c/a;
976      eb1 = exp(c1*log(b1));
977      ebx = exp(c1*log(bx));
978
979      xmean2 = (x0*eb1+ebx-(eb1*bx-b1*ebx)/(c-2.))/(eb1-ebx);
980     
981      G4double f1x0 = a*ea/eaa;
982      G4double f2x0 = c1*eb1/(bx*(eb1-ebx));
983      prob = f2x0/(f1x0+f2x0);
984
985      qprob = xmeanth/(prob*xmean1+(1.-prob)*xmean2);
986
987      // sampling of costheta
988      if(G4UniformRand() < qprob)
989      {
990        if(G4UniformRand() < prob)
991          cth = 1.+log(ea+G4UniformRand()*eaa)/a ;
992        else
993          cth = b-b1*bx/exp(log(ebx+(eb1-ebx)*G4UniformRand())/c1) ;
994      }
995      else
996        cth = -1.+2.*G4UniformRand();
997    }
998  } 
999  return cth ;
1000}
1001
1002//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1003
1004G4double G4UrbanMscModel93::SimpleScattering(G4double xmeanth,G4double x2meanth)
1005{
1006  // 'large angle scattering'
1007  // 2 model functions with correct xmean and x2mean
1008  G4double a = (2.*xmeanth+9.*x2meanth-3.)/(2.*xmeanth-3.*x2meanth+1.);
1009  G4double prob = (a+2.)*xmeanth/a;
1010
1011  // sampling
1012  G4double cth = 1.;
1013  if(G4UniformRand() < prob)
1014    cth = -1.+2.*exp(log(G4UniformRand())/(a+1.));
1015  else
1016    cth = -1.+2.*G4UniformRand();
1017  return cth;
1018}
1019
1020//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1021
1022G4double G4UrbanMscModel93::SampleDisplacement()
1023{
1024  // compute rmean = sqrt(<r**2>) from theory
1025  const G4double kappa = 2.5;
1026  const G4double kappapl1 = kappa+1.;
1027  const G4double kappami1 = kappa-1.;
1028  // Compute rmean = sqrt(<r**2>) from theory
1029  G4double rmean = 0.0;
1030  if ((currentTau >= tausmall) && !insideskin) {
1031    if (currentTau < taulim) {
1032      rmean = kappa*currentTau*currentTau*currentTau*
1033             (1.-kappapl1*currentTau*0.25)/6. ;
1034
1035    } else {
1036      G4double etau = 0.0;
1037      if (currentTau<taubig) etau = exp(-currentTau);
1038      rmean = -kappa*currentTau;
1039      rmean = -exp(rmean)/(kappa*kappami1);
1040      rmean += currentTau-kappapl1/kappa+kappa*etau/kappami1;
1041    }
1042    if (rmean>0.) rmean = 2.*lambdaeff*sqrt(rmean/3.0);
1043    else          rmean = 0.;
1044  }
1045
1046  if(rmean == 0.) return rmean;
1047
1048  // protection against z > t ...........................
1049  G4double rmax = (tPathLength-zPathLength)*(tPathLength+zPathLength);
1050    if(rmax <= 0.)
1051      rmax = 0.;
1052    else
1053      rmax = sqrt(rmax);
1054
1055  if(rmean >= rmax) return rmax;
1056     
1057  return rmean;
1058  // VI comment out for the time being
1059  /*
1060  //sample r (Gaussian distribution with a mean of rmean )
1061  G4double r = 0.;
1062  G4double sigma = min(rmean,rmax-rmean);
1063  sigma /= 3.;
1064  G4double rlow  = rmean-3.*sigma;
1065  G4double rhigh = rmean+3.*sigma;
1066  do {
1067      r = G4RandGauss::shoot(rmean,sigma); 
1068     } while ((r < rlow) || (r > rhigh));   
1069
1070  return r;
1071  */
1072}
1073
1074//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1075
1076G4double G4UrbanMscModel93::LatCorrelation()
1077{
1078  const G4double kappa = 2.5;
1079  const G4double kappami1 = kappa-1.;
1080
1081  G4double latcorr = 0.;
1082  if((currentTau >= tausmall) && !insideskin)
1083  {
1084    if(currentTau < taulim)
1085      latcorr = lambdaeff*kappa*currentTau*currentTau*
1086                (1.-(kappa+1.)*currentTau/3.)/3.;
1087    else
1088    {
1089      G4double etau = 0.;
1090      if(currentTau < taubig) etau = exp(-currentTau);
1091      latcorr = -kappa*currentTau;
1092      latcorr = exp(latcorr)/kappami1;
1093      latcorr += 1.-kappa*etau/kappami1 ;
1094      latcorr *= 2.*lambdaeff/3. ;
1095    }
1096  }
1097
1098  return latcorr;
1099}
1100
1101//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
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