source: trunk/source/processes/electromagnetic/standard/src/G4UrbanMscModel93.cc @ 1353

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26//
27// $Id: G4UrbanMscModel93.cc,v 1.7 2010/11/04 17:30:32 vnivanch Exp $
28// GEANT4 tag $Name: emstand-V09-03-25 $
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  skindepth = skin*stepmin;
169
170  mass = proton_mass_c2;
171  charge = ChargeSquare = 1.0;
172  currentKinEnergy = currentRadLength = lambda0 = lambdaeff = tPathLength
173    = zPathLength = par1 = par2 = par3 = 0;
174
175  currentMaterialIndex = -1;
176}
177
178//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
179
180G4UrbanMscModel93::~G4UrbanMscModel93()
181{}
182
183//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
184
185void G4UrbanMscModel93::Initialise(const G4ParticleDefinition* p,
186                                   const G4DataVector&)
187{
188  skindepth = skin*stepmin;
189
190  if(isInitialized) { return; }
191  // set values of some data members
192  SetParticle(p);
193
194  fParticleChange = GetParticleChangeForMSC();
195  InitialiseSafetyHelper();
196
197  isInitialized = true;
198}
199
200//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
201
202G4double G4UrbanMscModel93::ComputeCrossSectionPerAtom( 
203                             const G4ParticleDefinition* part,
204                                   G4double KineticEnergy,
205                                   G4double AtomicNumber,G4double,
206                                   G4double, G4double)
207{
208  const G4double sigmafactor = twopi*classic_electr_radius*classic_electr_radius;
209  const G4double epsfactor = 2.*electron_mass_c2*electron_mass_c2*
210                            Bohr_radius*Bohr_radius/(hbarc*hbarc);
211  const G4double epsmin = 1.e-4 , epsmax = 1.e10;
212
213  const G4double Zdat[15] = { 4.,  6., 13., 20., 26., 29., 32., 38., 47.,
214                             50., 56., 64., 74., 79., 82. };
215
216  const G4double Tdat[22] = { 100*eV,  200*eV,  400*eV,  700*eV,
217                               1*keV,   2*keV,   4*keV,   7*keV,
218                              10*keV,  20*keV,  40*keV,  70*keV,
219                             100*keV, 200*keV, 400*keV, 700*keV,
220                               1*MeV,   2*MeV,   4*MeV,   7*MeV,
221                              10*MeV,  20*MeV};
222
223  // corr. factors for e-/e+ lambda for T <= Tlim
224          G4double celectron[15][22] =
225          {{1.125,1.072,1.051,1.047,1.047,1.050,1.052,1.054,
226            1.054,1.057,1.062,1.069,1.075,1.090,1.105,1.111,
227            1.112,1.108,1.100,1.093,1.089,1.087            },
228           {1.408,1.246,1.143,1.096,1.077,1.059,1.053,1.051,
229            1.052,1.053,1.058,1.065,1.072,1.087,1.101,1.108,
230            1.109,1.105,1.097,1.090,1.086,1.082            },
231           {2.833,2.268,1.861,1.612,1.486,1.309,1.204,1.156,
232            1.136,1.114,1.106,1.106,1.109,1.119,1.129,1.132,
233            1.131,1.124,1.113,1.104,1.099,1.098            },
234           {3.879,3.016,2.380,2.007,1.818,1.535,1.340,1.236,
235            1.190,1.133,1.107,1.099,1.098,1.103,1.110,1.113,
236            1.112,1.105,1.096,1.089,1.085,1.098            },
237           {6.937,4.330,2.886,2.256,1.987,1.628,1.395,1.265,
238            1.203,1.122,1.080,1.065,1.061,1.063,1.070,1.073,
239            1.073,1.070,1.064,1.059,1.056,1.056            },
240           {9.616,5.708,3.424,2.551,2.204,1.762,1.485,1.330,
241            1.256,1.155,1.099,1.077,1.070,1.068,1.072,1.074,
242            1.074,1.070,1.063,1.059,1.056,1.052            },
243           {11.72,6.364,3.811,2.806,2.401,1.884,1.564,1.386,
244            1.300,1.180,1.112,1.082,1.073,1.066,1.068,1.069,
245            1.068,1.064,1.059,1.054,1.051,1.050            },
246           {18.08,8.601,4.569,3.183,2.662,2.025,1.646,1.439,
247            1.339,1.195,1.108,1.068,1.053,1.040,1.039,1.039,
248            1.039,1.037,1.034,1.031,1.030,1.036            },
249           {18.22,10.48,5.333,3.713,3.115,2.367,1.898,1.631,
250            1.498,1.301,1.171,1.105,1.077,1.048,1.036,1.033,
251            1.031,1.028,1.024,1.022,1.021,1.024            },
252           {14.14,10.65,5.710,3.929,3.266,2.453,1.951,1.669,
253            1.528,1.319,1.178,1.106,1.075,1.040,1.027,1.022,
254            1.020,1.017,1.015,1.013,1.013,1.020            },
255           {14.11,11.73,6.312,4.240,3.478,2.566,2.022,1.720,
256            1.569,1.342,1.186,1.102,1.065,1.022,1.003,0.997,
257            0.995,0.993,0.993,0.993,0.993,1.011            },
258           {22.76,20.01,8.835,5.287,4.144,2.901,2.219,1.855,
259            1.677,1.410,1.224,1.121,1.073,1.014,0.986,0.976,
260            0.974,0.972,0.973,0.974,0.975,0.987            },
261           {50.77,40.85,14.13,7.184,5.284,3.435,2.520,2.059,
262            1.837,1.512,1.283,1.153,1.091,1.010,0.969,0.954,
263            0.950,0.947,0.949,0.952,0.954,0.963            },
264           {65.87,59.06,15.87,7.570,5.567,3.650,2.682,2.182,
265            1.939,1.579,1.325,1.178,1.108,1.014,0.965,0.947,
266            0.941,0.938,0.940,0.944,0.946,0.954            },
267           {55.60,47.34,15.92,7.810,5.755,3.767,2.760,2.239,
268            1.985,1.609,1.343,1.188,1.113,1.013,0.960,0.939,
269            0.933,0.930,0.933,0.936,0.939,0.949            }};
270           
271           G4double cpositron[15][22] = {
272           {2.589,2.044,1.658,1.446,1.347,1.217,1.144,1.110,
273            1.097,1.083,1.080,1.086,1.092,1.108,1.123,1.131,
274            1.131,1.126,1.117,1.108,1.103,1.100            },
275           {3.904,2.794,2.079,1.710,1.543,1.325,1.202,1.145,
276            1.122,1.096,1.089,1.092,1.098,1.114,1.130,1.137,
277            1.138,1.132,1.122,1.113,1.108,1.102            },
278           {7.970,6.080,4.442,3.398,2.872,2.127,1.672,1.451,
279            1.357,1.246,1.194,1.179,1.178,1.188,1.201,1.205,
280            1.203,1.190,1.173,1.159,1.151,1.145            },
281           {9.714,7.607,5.747,4.493,3.815,2.777,2.079,1.715,
282            1.553,1.353,1.253,1.219,1.211,1.214,1.225,1.228,
283            1.225,1.210,1.191,1.175,1.166,1.174            },
284           {17.97,12.95,8.628,6.065,4.849,3.222,2.275,1.820,
285            1.624,1.382,1.259,1.214,1.202,1.202,1.214,1.219,
286            1.217,1.203,1.184,1.169,1.160,1.151            },
287           {24.83,17.06,10.84,7.355,5.767,3.707,2.546,1.996,
288            1.759,1.465,1.311,1.252,1.234,1.228,1.238,1.241,
289            1.237,1.222,1.201,1.184,1.174,1.159            },
290           {23.26,17.15,11.52,8.049,6.375,4.114,2.792,2.155,
291            1.880,1.535,1.353,1.281,1.258,1.247,1.254,1.256,
292            1.252,1.234,1.212,1.194,1.183,1.170            },
293           {22.33,18.01,12.86,9.212,7.336,4.702,3.117,2.348,
294            2.015,1.602,1.385,1.297,1.268,1.251,1.256,1.258,
295            1.254,1.237,1.214,1.195,1.185,1.179            },
296           {33.91,24.13,15.71,10.80,8.507,5.467,3.692,2.808,
297            2.407,1.873,1.564,1.425,1.374,1.330,1.324,1.320,
298            1.312,1.288,1.258,1.235,1.221,1.205            },
299           {32.14,24.11,16.30,11.40,9.015,5.782,3.868,2.917,
300            2.490,1.925,1.596,1.447,1.391,1.342,1.332,1.327,
301            1.320,1.294,1.264,1.240,1.226,1.214            },
302           {29.51,24.07,17.19,12.28,9.766,6.238,4.112,3.066,
303            2.602,1.995,1.641,1.477,1.414,1.356,1.342,1.336,
304            1.328,1.302,1.270,1.245,1.231,1.233            },
305           {38.19,30.85,21.76,15.35,12.07,7.521,4.812,3.498,
306            2.926,2.188,1.763,1.563,1.484,1.405,1.382,1.371,
307            1.361,1.330,1.294,1.267,1.251,1.239            },
308           {49.71,39.80,27.96,19.63,15.36,9.407,5.863,4.155,
309            3.417,2.478,1.944,1.692,1.589,1.480,1.441,1.423,
310            1.409,1.372,1.330,1.298,1.280,1.258            },
311           {59.25,45.08,30.36,20.83,16.15,9.834,6.166,4.407,
312            3.641,2.648,2.064,1.779,1.661,1.531,1.482,1.459,
313            1.442,1.400,1.354,1.319,1.299,1.272            },
314           {56.38,44.29,30.50,21.18,16.51,10.11,6.354,4.542,
315            3.752,2.724,2.116,1.817,1.692,1.554,1.499,1.474,
316            1.456,1.412,1.364,1.328,1.307,1.282            }};
317
318  //data/corrections for T > Tlim 
319  G4double Tlim = 10.*MeV;
320  G4double beta2lim = Tlim*(Tlim+2.*electron_mass_c2)/
321                      ((Tlim+electron_mass_c2)*(Tlim+electron_mass_c2));
322  G4double bg2lim   = Tlim*(Tlim+2.*electron_mass_c2)/
323                      (electron_mass_c2*electron_mass_c2);
324
325  G4double sig0[15] = {0.2672*barn,  0.5922*barn, 2.653*barn,  6.235*barn,
326                      11.69*barn  , 13.24*barn  , 16.12*barn, 23.00*barn ,
327                      35.13*barn  , 39.95*barn  , 50.85*barn, 67.19*barn ,
328                      91.15*barn  , 104.4*barn  , 113.1*barn};
329                                       
330  G4double hecorr[15] = {120.70, 117.50, 105.00, 92.92, 79.23,  74.510,  68.29,
331                          57.39,  41.97,  36.14, 24.53, 10.21,  -7.855, -16.84,
332                         -22.30};
333
334  G4double sigma;
335  SetParticle(part);
336
337  G4double Z23 = 2.*log(AtomicNumber)/3.; Z23 = exp(Z23);
338
339  // correction if particle .ne. e-/e+
340  // compute equivalent kinetic energy
341  // lambda depends on p*beta ....
342
343  G4double eKineticEnergy = KineticEnergy;
344
345  if(mass > electron_mass_c2)
346  {
347     G4double TAU = KineticEnergy/mass ;
348     G4double c = mass*TAU*(TAU+2.)/(electron_mass_c2*(TAU+1.)) ;
349     G4double w = c-2. ;
350     G4double tau = 0.5*(w+sqrt(w*w+4.*c)) ;
351     eKineticEnergy = electron_mass_c2*tau ;
352  }
353
354  G4double eTotalEnergy = eKineticEnergy + electron_mass_c2 ;
355  G4double beta2 = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
356                                 /(eTotalEnergy*eTotalEnergy);
357  G4double bg2   = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
358                                 /(electron_mass_c2*electron_mass_c2);
359
360  G4double eps = epsfactor*bg2/Z23;
361
362  if     (eps<epsmin)  sigma = 2.*eps*eps;
363  else if(eps<epsmax)  sigma = log(1.+2.*eps)-2.*eps/(1.+2.*eps);
364  else                 sigma = log(2.*eps)-1.+1./eps;
365
366  sigma *= ChargeSquare*AtomicNumber*AtomicNumber/(beta2*bg2);
367
368  // interpolate in AtomicNumber and beta2
369  G4double c1,c2,cc1,cc2,corr;
370
371  // get bin number in Z
372  G4int iZ = 14;
373  while ((iZ>=0)&&(Zdat[iZ]>=AtomicNumber)) iZ -= 1;
374  if (iZ==14)                               iZ = 13;
375  if (iZ==-1)                               iZ = 0 ;
376
377  G4double Z1 = Zdat[iZ];
378  G4double Z2 = Zdat[iZ+1];
379  G4double ratZ = (AtomicNumber-Z1)*(AtomicNumber+Z1)/
380                  ((Z2-Z1)*(Z2+Z1));
381
382  if(eKineticEnergy <= Tlim) 
383  {
384    // get bin number in T (beta2)
385    G4int iT = 21;
386    while ((iT>=0)&&(Tdat[iT]>=eKineticEnergy)) iT -= 1;
387    if(iT==21)                                  iT = 20;
388    if(iT==-1)                                  iT = 0 ;
389
390    //  calculate betasquare values
391    G4double T = Tdat[iT],   E = T + electron_mass_c2;
392    G4double b2small = T*(E+electron_mass_c2)/(E*E);
393
394    T = Tdat[iT+1]; E = T + electron_mass_c2;
395    G4double b2big = T*(E+electron_mass_c2)/(E*E);
396    G4double ratb2 = (beta2-b2small)/(b2big-b2small);
397
398    if (charge < 0.)
399    {
400       c1 = celectron[iZ][iT];
401       c2 = celectron[iZ+1][iT];
402       cc1 = c1+ratZ*(c2-c1);
403
404       c1 = celectron[iZ][iT+1];
405       c2 = celectron[iZ+1][iT+1];
406       cc2 = c1+ratZ*(c2-c1);
407
408       corr = cc1+ratb2*(cc2-cc1);
409
410       sigma *= sigmafactor/corr;
411    }
412    else             
413    {
414       c1 = cpositron[iZ][iT];
415       c2 = cpositron[iZ+1][iT];
416       cc1 = c1+ratZ*(c2-c1);
417
418       c1 = cpositron[iZ][iT+1];
419       c2 = cpositron[iZ+1][iT+1];
420       cc2 = c1+ratZ*(c2-c1);
421
422       corr = cc1+ratb2*(cc2-cc1);
423
424       sigma *= sigmafactor/corr;
425    }
426  }
427  else
428  {
429    c1 = bg2lim*sig0[iZ]*(1.+hecorr[iZ]*(beta2-beta2lim))/bg2;
430    c2 = bg2lim*sig0[iZ+1]*(1.+hecorr[iZ+1]*(beta2-beta2lim))/bg2;
431    if((AtomicNumber >= Z1) && (AtomicNumber <= Z2))
432      sigma = c1+ratZ*(c2-c1) ;
433    else if(AtomicNumber < Z1)
434      sigma = AtomicNumber*AtomicNumber*c1/(Z1*Z1);
435    else if(AtomicNumber > Z2)
436      sigma = AtomicNumber*AtomicNumber*c2/(Z2*Z2);
437  }
438  return sigma;
439
440}
441
442//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
443
444G4double G4UrbanMscModel93::ComputeTruePathLengthLimit(
445                             const G4Track& track,
446                             G4PhysicsTable* theTable,
447                             G4double currentMinimalStep)
448{
449  tPathLength = currentMinimalStep;
450  G4StepPoint* sp = track.GetStep()->GetPreStepPoint();
451  G4StepStatus stepStatus = sp->GetStepStatus();
452
453  const G4DynamicParticle* dp = track.GetDynamicParticle();
454
455  if(stepStatus == fUndefined) {
456    inside = false;
457    insideskin = false;
458    tlimit = geombig;
459    SetParticle( dp->GetDefinition() );
460  }
461
462  theLambdaTable = theTable;
463  couple = track.GetMaterialCutsCouple();
464  currentMaterialIndex = couple->GetIndex();
465  currentKinEnergy = dp->GetKineticEnergy();
466  currentRange = 
467    theManager->GetRangeFromRestricteDEDX(particle,currentKinEnergy,couple);
468  lambda0 = GetLambda(currentKinEnergy);
469
470  // stop here if small range particle
471  if(inside) { return tPathLength; }           
472 
473  if(tPathLength > currentRange) { tPathLength = currentRange; }
474
475  presafety = sp->GetSafety();
476
477  // G4cout << "G4Urban2::StepLimit tPathLength= "
478  //     <<tPathLength<<" safety= " << presafety
479  //        << " range= " <<currentRange<< " lambda= "<<lambda0
480  //     << " Alg: " << steppingAlgorithm <<G4endl;
481
482  // far from geometry boundary
483  if(currentRange < presafety)
484    {
485      inside = true;
486      return tPathLength; 
487    }
488
489  // standard  version
490  //
491  if (steppingAlgorithm == fUseDistanceToBoundary)
492    {
493      //compute geomlimit and presafety
494      G4double geomlimit = ComputeGeomLimit(track, presafety, currentRange);
495
496      // is it far from boundary ?
497      if(currentRange < presafety)
498        {
499          inside = true;
500          return tPathLength;   
501        }
502
503      smallstep += 1.;
504      insideskin = false;
505
506      if((stepStatus == fGeomBoundary) || (stepStatus == fUndefined))
507        {
508          rangeinit = currentRange;
509          if(stepStatus == fUndefined) smallstep = 1.e10;
510          else  smallstep = 1.;
511
512          //define stepmin here (it depends on lambda!)
513          //rough estimation of lambda_elastic/lambda_transport
514          G4double rat = currentKinEnergy/MeV ;
515          rat = 1.e-3/(rat*(10.+rat)) ;
516          //stepmin ~ lambda_elastic
517          stepmin = rat*lambda0;
518          skindepth = skin*stepmin;
519          //define tlimitmin
520          tlimitmin = 10.*stepmin;
521          if(tlimitmin < tlimitminfix) tlimitmin = tlimitminfix;
522          //G4cout << "rangeinit= " << rangeinit << " stepmin= " << stepmin
523          //     << " tlimitmin= " << tlimitmin << " geomlimit= " << geomlimit <<G4endl;
524          // constraint from the geometry
525          if((geomlimit < geombig) && (geomlimit > geommin))
526            {
527              // geomlimit is a geometrical step length
528              // transform it to true path length (estimation)
529              if((1.-geomlimit/lambda0) > 0.)
530                geomlimit = -lambda0*log(1.-geomlimit/lambda0)+tlimitmin ;
531
532              if(stepStatus == fGeomBoundary)
533                tgeom = geomlimit/facgeom;
534              else
535                tgeom = 2.*geomlimit/facgeom;
536            }
537            else
538              tgeom = geombig;
539        }
540
541
542      //step limit
543      tlimit = facrange*rangeinit;             
544      if(tlimit < facsafety*presafety)
545        tlimit = facsafety*presafety; 
546
547      //lower limit for tlimit
548      if(tlimit < tlimitmin) tlimit = tlimitmin;
549
550      if(tlimit > tgeom) tlimit = tgeom;
551
552      //G4cout << "tgeom= " << tgeom << " geomlimit= " << geomlimit 
553      //      << " tlimit= " << tlimit << " presafety= " << presafety << G4endl;
554
555      // shortcut
556      if((tPathLength < tlimit) && (tPathLength < presafety) &&
557         (smallstep >= skin) && (tPathLength < geomlimit-0.999*skindepth))
558        return tPathLength;   
559
560      // step reduction near to boundary
561      if(smallstep < skin)
562        {
563          tlimit = stepmin;
564          insideskin = true;
565        }
566      else if(geomlimit < geombig)
567        {
568          if(geomlimit > skindepth)
569            {
570              if(tlimit > geomlimit-0.999*skindepth)
571                tlimit = geomlimit-0.999*skindepth;
572            }
573          else
574            {
575              insideskin = true;
576              if(tlimit > stepmin) tlimit = stepmin;
577            }
578        }
579
580      if(tlimit < stepmin) tlimit = stepmin;
581
582      // randomize 1st step or 1st 'normal' step in volume
583      if((stepStatus == fUndefined) ||
584         ((smallstep == skin) && !insideskin)) 
585        { 
586          G4double temptlimit = tlimit;
587          if(temptlimit > tlimitmin)
588          {
589            do {
590              temptlimit = G4RandGauss::shoot(tlimit,0.3*tlimit);       
591               } while ((temptlimit < tlimitmin) || 
592                        (temptlimit > 2.*tlimit-tlimitmin));
593          }
594          else
595            temptlimit = tlimitmin;
596          if(tPathLength > temptlimit) tPathLength = temptlimit;
597        }
598      else
599        { 
600          if(tPathLength > tlimit) tPathLength = tlimit  ; 
601        }
602
603    }
604    // for 'normal' simulation with or without magnetic field
605    //  there no small step/single scattering at boundaries
606  else if(steppingAlgorithm == fUseSafety)
607    {
608      // compute presafety again if presafety <= 0 and no boundary
609      // i.e. when it is needed for optimization purposes
610      if((stepStatus != fGeomBoundary) && (presafety < tlimitminfix)) 
611        presafety = ComputeSafety(sp->GetPosition(),tPathLength); 
612
613      // is far from boundary
614      if(currentRange < presafety)
615        {
616          inside = true;
617          return tPathLength; 
618        }
619
620      if((stepStatus == fGeomBoundary) || (stepStatus == fUndefined))
621      {
622        rangeinit = currentRange;
623        fr = facrange;
624        // 9.1 like stepping for e+/e- only (not for muons,hadrons)
625        if(mass < masslimite) 
626        {
627          if(lambda0 > currentRange)
628            rangeinit = lambda0;
629          if(lambda0 > lambdalimit)
630            fr *= 0.75+0.25*lambda0/lambdalimit;
631        }
632
633        //lower limit for tlimit
634        G4double rat = currentKinEnergy/MeV ;
635        rat = 1.e-3/(rat*(10.+rat)) ;
636        tlimitmin = 10.*lambda0*rat;
637        if(tlimitmin < tlimitminfix) tlimitmin = tlimitminfix;
638      }
639      //step limit
640      tlimit = fr*rangeinit;               
641
642      if(tlimit < facsafety*presafety)
643        tlimit = facsafety*presafety;
644
645      //lower limit for tlimit
646      if(tlimit < tlimitmin) tlimit = tlimitmin;
647     
648      if(tPathLength > tlimit) tPathLength = tlimit;
649
650    }
651 
652  // version similar to 7.1 (needed for some experiments)
653  else
654    {
655      if (stepStatus == fGeomBoundary)
656        {
657          if (currentRange > lambda0) tlimit = facrange*currentRange;
658          else                        tlimit = facrange*lambda0;
659
660          if(tlimit < tlimitmin) tlimit = tlimitmin;
661          if(tPathLength > tlimit) tPathLength = tlimit;
662        }
663    }
664  //G4cout << "tPathLength= " << tPathLength
665  //     << " currentMinimalStep= " << currentMinimalStep << G4endl;
666  return tPathLength ;
667}
668
669//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
670
671G4double G4UrbanMscModel93::ComputeGeomPathLength(G4double)
672{
673  lambdaeff = lambda0;
674  par1 = -1. ; 
675  par2 = par3 = 0. ; 
676
677  //  do the true -> geom transformation
678  zPathLength = tPathLength;
679
680  // z = t for very small tPathLength
681  if(tPathLength < tlimitminfix) return zPathLength;
682
683  // this correction needed to run MSC with eIoni and eBrem inactivated
684  // and makes no harm for a normal run
685  if(tPathLength > currentRange)
686    tPathLength = currentRange ;
687
688  G4double tau   = tPathLength/lambda0 ;
689
690  if ((tau <= tausmall) || insideskin) {
691    zPathLength  = tPathLength;
692    if(zPathLength > lambda0) zPathLength = lambda0;
693    return zPathLength;
694  }
695
696  G4double zmean = tPathLength;
697  if (tPathLength < currentRange*dtrl) {
698    if(tau < taulim) zmean = tPathLength*(1.-0.5*tau) ;
699    else             zmean = lambda0*(1.-exp(-tau));
700  } else if(currentKinEnergy < mass)  {
701    par1 = 1./currentRange ;
702    par2 = 1./(par1*lambda0) ;
703    par3 = 1.+par2 ;
704    if(tPathLength < currentRange)
705      zmean = (1.-exp(par3*log(1.-tPathLength/currentRange)))/(par1*par3) ;
706    else
707      zmean = 1./(par1*par3) ;
708  } else {
709    G4double T1 = theManager->GetEnergy(particle,currentRange-tPathLength,couple);
710    G4double lambda1 = GetLambda(T1);
711
712    par1 = (lambda0-lambda1)/(lambda0*tPathLength) ;
713    par2 = 1./(par1*lambda0) ;
714    par3 = 1.+par2 ;
715    zmean = (1.-exp(par3*log(lambda1/lambda0)))/(par1*par3) ;
716  }
717
718  zPathLength = zmean ;
719
720  //  sample z
721  if(samplez)
722  {
723    const G4double  ztmax = 0.99 ;
724    G4double zt = zmean/tPathLength ;
725
726    if (tPathLength > stepmin && zt < ztmax)             
727    {
728      G4double u,cz1;
729      if(zt >= third)
730      {
731        G4double cz = 0.5*(3.*zt-1.)/(1.-zt) ;
732        cz1 = 1.+cz ;
733        G4double u0 = cz/cz1 ;
734        G4double grej ;
735        do {
736            u = exp(log(G4UniformRand())/cz1) ;
737            grej = exp(cz*log(u/u0))*(1.-u)/(1.-u0) ;
738           } while (grej < G4UniformRand()) ;
739      }
740      else
741      {
742        cz1 = 1./zt-1.;
743        u = 1.-exp(log(G4UniformRand())/cz1) ;
744      }
745      zPathLength = tPathLength*u ;
746    }
747  }
748
749  if(zPathLength > lambda0) zPathLength = lambda0;
750  //G4cout << "zPathLength= " << zPathLength << " lambda1= " << lambda0 << G4endl;
751  return zPathLength;
752}
753
754//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
755
756G4double G4UrbanMscModel93::ComputeTrueStepLength(G4double geomStepLength)
757{
758  // step defined other than transportation
759  if(geomStepLength == zPathLength && tPathLength <= currentRange)
760    return tPathLength;
761
762  // t = z for very small step
763  zPathLength = geomStepLength;
764  tPathLength = geomStepLength;
765  if(geomStepLength < tlimitminfix) return tPathLength;
766 
767  // recalculation
768  if((geomStepLength > lambda0*tausmall) && !insideskin)
769  {
770    if(par1 <  0.)
771      tPathLength = -lambda0*log(1.-geomStepLength/lambda0) ;
772    else 
773    {
774      if(par1*par3*geomStepLength < 1.)
775        tPathLength = (1.-exp(log(1.-par1*par3*geomStepLength)/par3))/par1 ;
776      else 
777        tPathLength = currentRange;
778    } 
779  }
780  if(tPathLength < geomStepLength) tPathLength = geomStepLength;
781  //G4cout << "tPathLength= " << tPathLength << " step= " << geomStepLength << G4endl;
782
783  return tPathLength;
784}
785
786//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
787
788G4double G4UrbanMscModel93::ComputeTheta0(G4double trueStepLength,
789                                          G4double KineticEnergy)
790{
791  // for all particles take the width of the central part
792  //  from a  parametrization similar to the Highland formula
793  // ( Highland formula: Particle Physics Booklet, July 2002, eq. 26.10)
794  const G4double c_highland = 13.6*MeV ;
795  G4double betacp = sqrt(currentKinEnergy*(currentKinEnergy+2.*mass)*
796                         KineticEnergy*(KineticEnergy+2.*mass)/
797                      ((currentKinEnergy+mass)*(KineticEnergy+mass)));
798  y = trueStepLength/currentRadLength;
799  G4double theta0 = c_highland*std::abs(charge)*sqrt(y)/betacp;
800  y = log(y);
801  // correction factor from e- scattering data
802  G4double corr = coeffth1+coeffth2*y;               
803
804  theta0 *= corr ;                                               
805
806  return theta0;
807}
808
809//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
810
811void G4UrbanMscModel93::SampleScattering(const G4DynamicParticle* dynParticle,
812                                         G4double safety)
813{
814  G4double kineticEnergy = dynParticle->GetKineticEnergy();
815
816  if((kineticEnergy <= 0.0) || (tPathLength <= tlimitminfix) ||
817     (tPathLength/tausmall < lambda0)) return;
818
819  G4double cth  = SampleCosineTheta(tPathLength,kineticEnergy);
820
821  // protection against 'bad' cth values
822  if(std::abs(cth) > 1.) return;
823
824  G4double sth  = sqrt((1.0 - cth)*(1.0 + cth));
825  G4double phi  = twopi*G4UniformRand();
826  G4double dirx = sth*cos(phi);
827  G4double diry = sth*sin(phi);
828
829  G4ThreeVector oldDirection = dynParticle->GetMomentumDirection();
830  G4ThreeVector newDirection(dirx,diry,cth);
831  newDirection.rotateUz(oldDirection);
832  fParticleChange->ProposeMomentumDirection(newDirection);
833
834  if (latDisplasment && safety > tlimitminfix) {
835
836    G4double r = SampleDisplacement();
837    /*   
838    G4cout << "G4UrbanMscModel93::SampleSecondaries: e(MeV)= " << kineticEnergy
839           << " sinTheta= " << sth << " r(mm)= " << r
840           << " trueStep(mm)= " << tPathLength
841           << " geomStep(mm)= " << zPathLength
842           << G4endl;
843    */
844    if(r > 0.)
845      {
846        G4double latcorr = LatCorrelation();
847        if(latcorr > r) latcorr = r;
848
849        // sample direction of lateral displacement
850        // compute it from the lateral correlation
851        G4double Phi = 0.;
852        if(std::abs(r*sth) < latcorr)
853          Phi  = twopi*G4UniformRand();
854        else
855        {
856          G4double psi = std::acos(latcorr/(r*sth));
857          if(G4UniformRand() < 0.5)
858            Phi = phi+psi;
859          else
860            Phi = phi-psi;
861        }
862
863        dirx = std::cos(Phi);
864        diry = std::sin(Phi);
865
866        G4ThreeVector latDirection(dirx,diry,0.0);
867        latDirection.rotateUz(oldDirection);
868
869        ComputeDisplacement(fParticleChange, latDirection, r, safety);
870      }
871  }
872}
873
874//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
875
876G4double G4UrbanMscModel93::SampleCosineTheta(G4double trueStepLength,
877                                              G4double KineticEnergy)
878{
879  G4double cth = 1. ;
880  G4double tau = trueStepLength/lambda0 ;
881
882  Zeff = couple->GetMaterial()->GetTotNbOfElectPerVolume()/
883         couple->GetMaterial()->GetTotNbOfAtomsPerVolume() ;
884
885  if(Zold != Zeff) 
886    UpdateCache();
887
888  if(insideskin)
889  {
890    //no scattering, single or plural scattering
891    G4double mean = trueStepLength/stepmin ;
892
893    G4int n = G4Poisson(mean);
894    if(n > 0)
895    {
896      //screening (Moliere-Bethe)
897      G4double mom2 = KineticEnergy*(2.*mass+KineticEnergy);
898      G4double beta2 = mom2/((KineticEnergy+mass)*(KineticEnergy+mass));
899      G4double ascr = scr1/mom2;
900      ascr *= 1.13+scr2/beta2;
901      G4double ascr1 = 1.+2.*ascr;
902      G4double bp1=ascr1+1.;
903      G4double bm1=ascr1-1.;
904
905      // single scattering from screened Rutherford x-section
906      G4double ct,st,phi;
907      G4double sx=0.,sy=0.,sz=0.;
908      for(G4int i=1; i<=n; i++)
909      {
910        ct = ascr1-bp1*bm1/(2.*G4UniformRand()+bm1);
911        if(ct < -1.) ct = -1.;
912        if(ct >  1.) ct =  1.; 
913        st = sqrt(1.-ct*ct);
914        phi = twopi*G4UniformRand();
915        sx += st*cos(phi);
916        sy += st*sin(phi);
917        sz += ct;
918      }
919      cth = sz/sqrt(sx*sx+sy*sy+sz*sz);
920    }
921  }
922  else
923  {
924    if(trueStepLength >= currentRange*dtrl) 
925    {
926      if(par1*trueStepLength < 1.)
927        tau = -par2*log(1.-par1*trueStepLength) ;
928      // for the case if ioni/brems are inactivated
929      // see the corresponding condition in ComputeGeomPathLength
930      else if(1.-KineticEnergy/currentKinEnergy > taulim)
931        tau = taubig ;
932    }
933    currentTau = tau ;
934    lambdaeff = trueStepLength/currentTau;
935    currentRadLength = couple->GetMaterial()->GetRadlen();
936
937    if (tau >= taubig) cth = -1.+2.*G4UniformRand();
938    else if (tau >= tausmall)
939    {
940      G4double xsi = 3.;
941      G4double x0 = 1.;
942      G4double a = 1., ea = 0., eaa = 1.;
943      G4double b=2.,b1=3.,bx=1.,eb1=3.,ebx=1.;
944      G4double prob = 1. , qprob = 1. ;
945      G4double xmean1 = 1., xmean2 = 0.;
946      G4double xmeanth = exp(-tau);
947      G4double x2meanth = (1.+2.*exp(-2.5*tau))/3.;
948
949      G4double relloss = 1.-KineticEnergy/currentKinEnergy;
950      if(relloss > rellossmax) 
951        return SimpleScattering(xmeanth,x2meanth);
952
953      G4double theta0 = ComputeTheta0(trueStepLength,KineticEnergy);
954
955      // protection for very small angles
956      if(theta0 < tausmall) return cth;
957   
958      if(theta0 > theta0max)
959        return SimpleScattering(xmeanth,x2meanth);
960      G4double sth = sin(0.5*theta0);
961      a = 0.25/(sth*sth);
962
963      ea = exp(-xsi);
964      eaa = 1.-ea ;
965      xmean1 = 1.-(1.-(1.+xsi)*ea)/(a*eaa);
966      x0 = 1.-xsi/a;
967
968      if(xmean1 <= 0.999*xmeanth)
969        return SimpleScattering(xmeanth,x2meanth);
970
971      // from e- and muon scattering data                   
972      G4double c = coeffc1+coeffc2*y; ;                         
973
974      if(abs(c-3.) < 0.001)  c = 3.001;     
975      if(abs(c-2.) < 0.001)  c = 2.001;     
976      if(abs(c-1.) < 0.001)  c = 1.001;     
977
978      G4double c1 = c-1.;
979
980      //from continuity of derivatives
981      b = 1.+(c-xsi)/a;
982
983      b1 = b+1.;
984      bx = c/a;
985      eb1 = exp(c1*log(b1));
986      ebx = exp(c1*log(bx));
987
988      xmean2 = (x0*eb1+ebx-(eb1*bx-b1*ebx)/(c-2.))/(eb1-ebx);
989     
990      G4double f1x0 = a*ea/eaa;
991      G4double f2x0 = c1*eb1/(bx*(eb1-ebx));
992      prob = f2x0/(f1x0+f2x0);
993
994      qprob = xmeanth/(prob*xmean1+(1.-prob)*xmean2);
995
996      // sampling of costheta
997      if(G4UniformRand() < qprob)
998      {
999        if(G4UniformRand() < prob)
1000          cth = 1.+log(ea+G4UniformRand()*eaa)/a ;
1001        else
1002          cth = b-b1*bx/exp(log(ebx+(eb1-ebx)*G4UniformRand())/c1) ;
1003      }
1004      else
1005        cth = -1.+2.*G4UniformRand();
1006    }
1007  } 
1008  return cth ;
1009}
1010
1011//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1012
1013G4double G4UrbanMscModel93::SimpleScattering(G4double xmeanth,G4double x2meanth)
1014{
1015  // 'large angle scattering'
1016  // 2 model functions with correct xmean and x2mean
1017  G4double a = (2.*xmeanth+9.*x2meanth-3.)/(2.*xmeanth-3.*x2meanth+1.);
1018  G4double prob = (a+2.)*xmeanth/a;
1019
1020  // sampling
1021  G4double cth = 1.;
1022  if(G4UniformRand() < prob)
1023    cth = -1.+2.*exp(log(G4UniformRand())/(a+1.));
1024  else
1025    cth = -1.+2.*G4UniformRand();
1026  return cth;
1027}
1028
1029//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1030
1031G4double G4UrbanMscModel93::SampleDisplacement()
1032{
1033  // compute rmean = sqrt(<r**2>) from theory
1034  const G4double kappa = 2.5;
1035  const G4double kappapl1 = kappa+1.;
1036  const G4double kappami1 = kappa-1.;
1037  // Compute rmean = sqrt(<r**2>) from theory
1038  G4double rmean = 0.0;
1039  if ((currentTau >= tausmall) && !insideskin) {
1040    if (currentTau < taulim) {
1041      rmean = kappa*currentTau*currentTau*currentTau*
1042             (1.-kappapl1*currentTau*0.25)/6. ;
1043
1044    } else {
1045      G4double etau = 0.0;
1046      if (currentTau<taubig) etau = exp(-currentTau);
1047      rmean = -kappa*currentTau;
1048      rmean = -exp(rmean)/(kappa*kappami1);
1049      rmean += currentTau-kappapl1/kappa+kappa*etau/kappami1;
1050    }
1051    if (rmean>0.) rmean = 2.*lambdaeff*sqrt(rmean/3.0);
1052    else          rmean = 0.;
1053  }
1054
1055  if(rmean == 0.) return rmean;
1056
1057  // protection against z > t ...........................
1058  G4double rmax = (tPathLength-zPathLength)*(tPathLength+zPathLength);
1059    if(rmax <= 0.)
1060      rmax = 0.;
1061    else
1062      rmax = sqrt(rmax);
1063
1064  if(rmean >= rmax) return rmax;
1065     
1066  return rmean;
1067  // VI comment out for the time being
1068  /*
1069  //sample r (Gaussian distribution with a mean of rmean )
1070  G4double r = 0.;
1071  G4double sigma = min(rmean,rmax-rmean);
1072  sigma /= 3.;
1073  G4double rlow  = rmean-3.*sigma;
1074  G4double rhigh = rmean+3.*sigma;
1075  do {
1076      r = G4RandGauss::shoot(rmean,sigma); 
1077     } while ((r < rlow) || (r > rhigh));   
1078
1079  return r;
1080  */
1081}
1082
1083//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1084
1085G4double G4UrbanMscModel93::LatCorrelation()
1086{
1087  const G4double kappa = 2.5;
1088  const G4double kappami1 = kappa-1.;
1089
1090  G4double latcorr = 0.;
1091  if((currentTau >= tausmall) && !insideskin)
1092  {
1093    if(currentTau < taulim)
1094      latcorr = lambdaeff*kappa*currentTau*currentTau*
1095                (1.-(kappa+1.)*currentTau/3.)/3.;
1096    else
1097    {
1098      G4double etau = 0.;
1099      if(currentTau < taubig) etau = exp(-currentTau);
1100      latcorr = -kappa*currentTau;
1101      latcorr = exp(latcorr)/kappami1;
1102      latcorr += 1.-kappa*etau/kappami1 ;
1103      latcorr *= 2.*lambdaeff/3. ;
1104    }
1105  }
1106
1107  return latcorr;
1108}
1109
1110//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
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