source: trunk/source/processes/electromagnetic/standard/src/G4UrbanMscModel.cc@ 900

Last change on this file since 900 was 819, checked in by garnier, 17 years ago

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25//
26// $Id: G4UrbanMscModel.cc,v 1.77.2.2 2008/04/25 00:34:55 vnivanch Exp $
27// GEANT4 tag $Name: geant4-09-01-patch-02 $
28//
29// -------------------------------------------------------------------
30//
31// GEANT4 Class file
32//
33//
34// File name: G4UrbanMscModel
35//
36// Author: Laszlo Urban
37//
38// Creation date: 03.03.2001
39//
40// Modifications:
41//
42// 27-03-03 Move model part from G4MultipleScattering80 (V.Ivanchenko)
43// 23-05-03 important change in angle distribution for muons/hadrons
44// the central part now is similar to the Highland parametrization +
45// minor correction in angle sampling algorithm (for all particles)
46// (L.Urban)
47// 30-05-03 misprint in SampleCosineTheta corrected(L.Urban)
48// 27-03-03 Rename (V.Ivanchenko)
49// 05-08-03 angle distribution has been modified (L.Urban)
50// 06-11-03 precision problems solved for high energy (PeV) particles
51// change in the tail of the angular distribution
52// highKinEnergy is set to 100 PeV (L.Urban)
53//
54// 10-11-03 highKinEnergy is set back to 100 TeV, some tail tuning +
55// cleaning (L.Urban)
56// 26-11-03 correction in TrueStepLength :
57// trueLength <= currentRange (L.Urban)
58// 01-03-04 signature changed in SampleCosineTheta,
59// energy dependence calculations has been simplified,
60// 11-03-04 corrections in GeomPathLength,TrueStepLength,
61// SampleCosineTheta
62// 23-04-04 true -> geom and geom -> true transformation has been
63// rewritten, changes in the angular distribution (L.Urban)
64// 19-07-04 correction in SampleCosineTheta in order to avoid
65// num. precision problems at high energy/small step(L.Urban)
66// 17-08-04 changes in the angle distribution (slightly modified
67// Highland formula for the width of the central part,
68// changes in the numerical values of some other parameters)
69// ---> approximately step independent distribution (L.Urban)
70// 21-09-04 change in the tail of the angular distribution (L.Urban)
71//
72// 03-11-04 precision problem for very high energy ions and small stepsize
73// solved in SampleCosineTheta (L.Urban).
74// 15-04-05 optimize internal interface
75// add SampleSecondaries method (V.Ivanchenko)
76// 11-08-05 computation of lateral correlation added (L.Urban)
77// 02-10-05 nuclear size correction computation removed, the correction
78// included in the (theoretical) tabulated values (L.Urban)
79// 17-01-06 computation of tail changed in SampleCosineTheta (l.Urban)
80// 16-02-06 code cleaning + revised 'z' sampling (L.Urban)
81// 17-02-06 Save table of transport cross sections not mfp (V.Ivanchenko)
82// 07-03-06 Create G4UrbanMscModel and move there step limit
83// calculation (V.Ivanchenko)
84// 23-03-06 Bugfix in SampleCosineTheta method (L.Urban)
85// 10-05-06 SetMscStepLimitation at initialisation (V.Ivantchenko)
86// 11-05-06 name of data member safety changed to presafety, some new data
87// members added (frscaling1,frscaling2,tlimitminfix,nstepmax)
88// changes in ComputeTruePathLengthLimit,SampleCosineTheta (L.Urban)
89// 17-05-06 parameters of theta0 in SampleCosineTheta changed
90// c_highland 13.6*MeV ---> 13.26*MeV,
91// corr_highland 0.555 ---> 0.54,
92// value of data member geommin changed (5 nm -> 1 nm) (L.Urban)
93// 13-10-06 data member factail removed, data member tkinlimit changed
94// to lambdalimit,
95// new data members tgeom,tnow,skin,skindepth,Zeff,geomlimit
96// G4double GeomLimit(const G4Track& track) changed to
97// void GeomLimit(const G4Track& track)
98// - important changes in ComputeTruePathLengthLimit:
99// possibility to have very small step(s) with single scattering
100// before boundary crossing (with skin > 0)
101// - changes in SampleCosineTheta :
102// single scattering if step <= stepmin, parameter theta0
103// slightly modified, tail modified (L.Urban)
104// 20-10-06 parameter theta0 now computed in the (public)
105// function ComputeTheta0,
106// single scattering modified allowing not small
107// angles as well (L.Urban)
108// 23-10-06 correction in SampleSecondaries, now safety update
109// computed in a simpler/faster way (L.Urban)
110// 06-11-06 corrections in ComputeTruePathLengthLimit, results are
111// more stable in calorimeters (L.Urban)
112// 07-11-06 fix in GeomPathLength and SampleCosineTheta (L.Urban)
113// 15-11-06 bugfix in SampleCosineTheta (L.Urban)
114// 20-11-06 bugfix in single scattering part of SampleCosineTheta,
115// single scattering just before boundary crossing now (L.Urban)
116// 04-12-06 fix in ComputeTruePathLengthLimit (L.Urban)
117// 17-01-07 remove LocatePoint from GeomLimit method (V.Ivanchenko)
118// 19-01-07 fix of true < geom problem (L.Urban)
119// 25-01-07 add protections from NaN vaues and for zero geometry step (VI)
120// 31-01-07 correction in SampleCosineTheta: screening parameter
121// corrected in single/plural scattering +
122// code cleaning (L.Urban)
123// 01-02-07 restore logic inside ComputeTrueStepLength (V.Ivanchenko)
124// 06-02-07 Move SetMscStepLimitation method into the source, add there
125// reinitialisation of some private members, add protection inside
126// SampleDisplacement(VI)
127// 07-02-07 fix single scattering for heavy particles, now skin=1 can be used
128// for heavy particles as well (L.Urban)
129// 08-02-07 randomization of tlimit removed (L.Urban)
130// 11-02-07 modified stepping algorithm for skin=0
131// 15-02-07 new data member: smallstep, small steps with single scattering
132// before + after boundary for skin > 1
133// 23-02-07 use tPathLength inside ComputeStep instead of geombig
134// 24-02-07 step reduction before boundary for 'small' geomlimit only
135// 03-03-07 single scattering around boundaries only (L.Urban)
136// 07-03-07 bugfix in ComputeTruePathLengthLimit (for skin > 0.) (L.Urban)
137// 10-04-07 optimize logic of ComputeTruePathLengthLimit, remove
138// unused members, use unique G4SafetyHelper (V.Ivanchenko)
139// 01-05-07 optimization for skin > 0 (L.Urban)
140// 05-07-07 modified model functions in SampleCosineTheta (L.Urban)
141// 06-07-07 theta0 is not the same for e-/e+ as for heavy particles (L.Urban)
142// 02-08-07 compare safety not with 0. but with tlimitminfix (V.Ivanchenko)
143// 09-08-07 tail of angular distribution has been modified (L.Urban)
144// 22-10-07 - corr. in ComputeGeomPathLength in order to get better low
145// energy behaviour for heavy particles,
146// - theta0 is slightly modified,
147// - some old inconsistency/bug is cured in SampleCosineTheta,
148// now 0 <= prob <= 1 in any case (L.Urban)
149// 26-10-07 different correction parameters for e/mu/hadrons in ComputeTheta0
150// 30-11-07 fix in ComputeTheta0 (L.Urban)
151//
152
153// Class Description:
154//
155// Implementation of the model of multiple scattering based on
156// H.W.Lewis Phys Rev 78 (1950) 526 and others
157
158// -------------------------------------------------------------------
159//
160
161
162//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
163//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
164
165#include "G4UrbanMscModel.hh"
166#include "Randomize.hh"
167#include "G4Electron.hh"
168
169#include "G4LossTableManager.hh"
170#include "G4ParticleChangeForMSC.hh"
171#include "G4TransportationManager.hh"
172#include "G4SafetyHelper.hh"
173
174#include "G4Poisson.hh"
175
176//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
177
178using namespace std;
179
180G4UrbanMscModel::G4UrbanMscModel(G4double m_facrange, G4double m_dtrl,
181 G4double m_lambdalimit,
182 G4double m_facgeom,G4double m_skin,
183 G4bool m_samplez, G4MscStepLimitType m_stepAlg,
184 const G4String& nam)
185 : G4VEmModel(nam),
186 dtrl(m_dtrl),
187 lambdalimit(m_lambdalimit),
188 facrange(m_facrange),
189 facgeom(m_facgeom),
190 skin(m_skin),
191 steppingAlgorithm(m_stepAlg),
192 samplez(m_samplez),
193 isInitialized(false)
194{
195 masslimite = 0.6*MeV;
196 masslimitmu = 110.*MeV;
197
198 taubig = 8.0;
199 tausmall = 1.e-16;
200 taulim = 1.e-6;
201 currentTau = taulim;
202 tlimitminfix = 1.e-6*mm;
203 stepmin = tlimitminfix;
204 skindepth = skin*stepmin;
205 smallstep = 1.e10;
206 currentRange = 0. ;
207 frscaling2 = 0.25;
208 frscaling1 = 1.-frscaling2;
209 tlimit = 1.e10*mm;
210 tlimitmin = 10.*tlimitminfix;
211 nstepmax = 25.;
212 geombig = 1.e50*mm;
213 geommin = 1.e-3*mm;
214 geomlimit = geombig;
215 facsafety = 0.25;
216 presafety = 0.*mm;
217 Zeff = 1.;
218 particle = 0;
219 theManager = G4LossTableManager::Instance();
220 inside = false;
221 insideskin = false;
222
223}
224
225//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
226
227G4UrbanMscModel::~G4UrbanMscModel()
228{}
229
230//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
231
232void G4UrbanMscModel::Initialise(const G4ParticleDefinition* p,
233 const G4DataVector&)
234{
235 skindepth = skin*stepmin;
236 if(isInitialized) return;
237
238 // set values of some data members
239 SetParticle(p);
240
241 if (pParticleChange)
242 fParticleChange = reinterpret_cast<G4ParticleChangeForMSC*>(pParticleChange);
243 else
244 fParticleChange = new G4ParticleChangeForMSC();
245
246 safetyHelper = G4TransportationManager::GetTransportationManager()
247 ->GetSafetyHelper();
248 safetyHelper->InitialiseHelper();
249
250 isInitialized = true;
251}
252
253//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
254
255G4double G4UrbanMscModel::ComputeCrossSectionPerAtom(
256 const G4ParticleDefinition* part,
257 G4double KineticEnergy,
258 G4double AtomicNumber,G4double,
259 G4double, G4double)
260{
261 const G4double sigmafactor = twopi*classic_electr_radius*classic_electr_radius;
262 const G4double epsfactor = 2.*electron_mass_c2*electron_mass_c2*
263 Bohr_radius*Bohr_radius/(hbarc*hbarc);
264 const G4double epsmin = 1.e-4 , epsmax = 1.e10;
265
266 const G4double Zdat[15] = { 4., 6., 13., 20., 26., 29., 32., 38., 47.,
267 50., 56., 64., 74., 79., 82. };
268
269 const G4double Tdat[22] = { 100*eV, 200*eV, 400*eV, 700*eV,
270 1*keV, 2*keV, 4*keV, 7*keV,
271 10*keV, 20*keV, 40*keV, 70*keV,
272 100*keV, 200*keV, 400*keV, 700*keV,
273 1*MeV, 2*MeV, 4*MeV, 7*MeV,
274 10*MeV, 20*MeV};
275
276 // corr. factors for e-/e+ lambda for T <= Tlim
277 G4double celectron[15][22] =
278 {{1.125,1.072,1.051,1.047,1.047,1.050,1.052,1.054,
279 1.054,1.057,1.062,1.069,1.075,1.090,1.105,1.111,
280 1.112,1.108,1.100,1.093,1.089,1.087 },
281 {1.408,1.246,1.143,1.096,1.077,1.059,1.053,1.051,
282 1.052,1.053,1.058,1.065,1.072,1.087,1.101,1.108,
283 1.109,1.105,1.097,1.090,1.086,1.082 },
284 {2.833,2.268,1.861,1.612,1.486,1.309,1.204,1.156,
285 1.136,1.114,1.106,1.106,1.109,1.119,1.129,1.132,
286 1.131,1.124,1.113,1.104,1.099,1.098 },
287 {3.879,3.016,2.380,2.007,1.818,1.535,1.340,1.236,
288 1.190,1.133,1.107,1.099,1.098,1.103,1.110,1.113,
289 1.112,1.105,1.096,1.089,1.085,1.098 },
290 {6.937,4.330,2.886,2.256,1.987,1.628,1.395,1.265,
291 1.203,1.122,1.080,1.065,1.061,1.063,1.070,1.073,
292 1.073,1.070,1.064,1.059,1.056,1.056 },
293 {9.616,5.708,3.424,2.551,2.204,1.762,1.485,1.330,
294 1.256,1.155,1.099,1.077,1.070,1.068,1.072,1.074,
295 1.074,1.070,1.063,1.059,1.056,1.052 },
296 {11.72,6.364,3.811,2.806,2.401,1.884,1.564,1.386,
297 1.300,1.180,1.112,1.082,1.073,1.066,1.068,1.069,
298 1.068,1.064,1.059,1.054,1.051,1.050 },
299 {18.08,8.601,4.569,3.183,2.662,2.025,1.646,1.439,
300 1.339,1.195,1.108,1.068,1.053,1.040,1.039,1.039,
301 1.039,1.037,1.034,1.031,1.030,1.036 },
302 {18.22,10.48,5.333,3.713,3.115,2.367,1.898,1.631,
303 1.498,1.301,1.171,1.105,1.077,1.048,1.036,1.033,
304 1.031,1.028,1.024,1.022,1.021,1.024 },
305 {14.14,10.65,5.710,3.929,3.266,2.453,1.951,1.669,
306 1.528,1.319,1.178,1.106,1.075,1.040,1.027,1.022,
307 1.020,1.017,1.015,1.013,1.013,1.020 },
308 {14.11,11.73,6.312,4.240,3.478,2.566,2.022,1.720,
309 1.569,1.342,1.186,1.102,1.065,1.022,1.003,0.997,
310 0.995,0.993,0.993,0.993,0.993,1.011 },
311 {22.76,20.01,8.835,5.287,4.144,2.901,2.219,1.855,
312 1.677,1.410,1.224,1.121,1.073,1.014,0.986,0.976,
313 0.974,0.972,0.973,0.974,0.975,0.987 },
314 {50.77,40.85,14.13,7.184,5.284,3.435,2.520,2.059,
315 1.837,1.512,1.283,1.153,1.091,1.010,0.969,0.954,
316 0.950,0.947,0.949,0.952,0.954,0.963 },
317 {65.87,59.06,15.87,7.570,5.567,3.650,2.682,2.182,
318 1.939,1.579,1.325,1.178,1.108,1.014,0.965,0.947,
319 0.941,0.938,0.940,0.944,0.946,0.954 },
320 {55.60,47.34,15.92,7.810,5.755,3.767,2.760,2.239,
321 1.985,1.609,1.343,1.188,1.113,1.013,0.960,0.939,
322 0.933,0.930,0.933,0.936,0.939,0.949 }};
323
324 G4double cpositron[15][22] = {
325 {2.589,2.044,1.658,1.446,1.347,1.217,1.144,1.110,
326 1.097,1.083,1.080,1.086,1.092,1.108,1.123,1.131,
327 1.131,1.126,1.117,1.108,1.103,1.100 },
328 {3.904,2.794,2.079,1.710,1.543,1.325,1.202,1.145,
329 1.122,1.096,1.089,1.092,1.098,1.114,1.130,1.137,
330 1.138,1.132,1.122,1.113,1.108,1.102 },
331 {7.970,6.080,4.442,3.398,2.872,2.127,1.672,1.451,
332 1.357,1.246,1.194,1.179,1.178,1.188,1.201,1.205,
333 1.203,1.190,1.173,1.159,1.151,1.145 },
334 {9.714,7.607,5.747,4.493,3.815,2.777,2.079,1.715,
335 1.553,1.353,1.253,1.219,1.211,1.214,1.225,1.228,
336 1.225,1.210,1.191,1.175,1.166,1.174 },
337 {17.97,12.95,8.628,6.065,4.849,3.222,2.275,1.820,
338 1.624,1.382,1.259,1.214,1.202,1.202,1.214,1.219,
339 1.217,1.203,1.184,1.169,1.160,1.151 },
340 {24.83,17.06,10.84,7.355,5.767,3.707,2.546,1.996,
341 1.759,1.465,1.311,1.252,1.234,1.228,1.238,1.241,
342 1.237,1.222,1.201,1.184,1.174,1.159 },
343 {23.26,17.15,11.52,8.049,6.375,4.114,2.792,2.155,
344 1.880,1.535,1.353,1.281,1.258,1.247,1.254,1.256,
345 1.252,1.234,1.212,1.194,1.183,1.170 },
346 {22.33,18.01,12.86,9.212,7.336,4.702,3.117,2.348,
347 2.015,1.602,1.385,1.297,1.268,1.251,1.256,1.258,
348 1.254,1.237,1.214,1.195,1.185,1.179 },
349 {33.91,24.13,15.71,10.80,8.507,5.467,3.692,2.808,
350 2.407,1.873,1.564,1.425,1.374,1.330,1.324,1.320,
351 1.312,1.288,1.258,1.235,1.221,1.205 },
352 {32.14,24.11,16.30,11.40,9.015,5.782,3.868,2.917,
353 2.490,1.925,1.596,1.447,1.391,1.342,1.332,1.327,
354 1.320,1.294,1.264,1.240,1.226,1.214 },
355 {29.51,24.07,17.19,12.28,9.766,6.238,4.112,3.066,
356 2.602,1.995,1.641,1.477,1.414,1.356,1.342,1.336,
357 1.328,1.302,1.270,1.245,1.231,1.233 },
358 {38.19,30.85,21.76,15.35,12.07,7.521,4.812,3.498,
359 2.926,2.188,1.763,1.563,1.484,1.405,1.382,1.371,
360 1.361,1.330,1.294,1.267,1.251,1.239 },
361 {49.71,39.80,27.96,19.63,15.36,9.407,5.863,4.155,
362 3.417,2.478,1.944,1.692,1.589,1.480,1.441,1.423,
363 1.409,1.372,1.330,1.298,1.280,1.258 },
364 {59.25,45.08,30.36,20.83,16.15,9.834,6.166,4.407,
365 3.641,2.648,2.064,1.779,1.661,1.531,1.482,1.459,
366 1.442,1.400,1.354,1.319,1.299,1.272 },
367 {56.38,44.29,30.50,21.18,16.51,10.11,6.354,4.542,
368 3.752,2.724,2.116,1.817,1.692,1.554,1.499,1.474,
369 1.456,1.412,1.364,1.328,1.307,1.282 }};
370
371 //data/corrections for T > Tlim
372 G4double Tlim = 10.*MeV;
373 G4double beta2lim = Tlim*(Tlim+2.*electron_mass_c2)/
374 ((Tlim+electron_mass_c2)*(Tlim+electron_mass_c2));
375 G4double bg2lim = Tlim*(Tlim+2.*electron_mass_c2)/
376 (electron_mass_c2*electron_mass_c2);
377
378 G4double sig0[15] = {0.2672*barn, 0.5922*barn, 2.653*barn, 6.235*barn,
379 11.69*barn , 13.24*barn , 16.12*barn, 23.00*barn ,
380 35.13*barn , 39.95*barn , 50.85*barn, 67.19*barn ,
381 91.15*barn , 104.4*barn , 113.1*barn};
382
383 G4double hecorr[15] = {120.70, 117.50, 105.00, 92.92, 79.23, 74.510, 68.29,
384 57.39, 41.97, 36.14, 24.53, 10.21, -7.855, -16.84,
385 -22.30};
386
387 G4double sigma;
388 SetParticle(part);
389
390 G4double Z23 = 2.*log(AtomicNumber)/3.; Z23 = exp(Z23);
391
392 // correction if particle .ne. e-/e+
393 // compute equivalent kinetic energy
394 // lambda depends on p*beta ....
395
396 G4double eKineticEnergy = KineticEnergy;
397
398 if((particle->GetParticleName() != "e-") &&
399 (particle->GetParticleName() != "e+") )
400 {
401 G4double TAU = KineticEnergy/mass ;
402 G4double c = mass*TAU*(TAU+2.)/(electron_mass_c2*(TAU+1.)) ;
403 G4double w = c-2. ;
404 G4double tau = 0.5*(w+sqrt(w*w+4.*c)) ;
405 eKineticEnergy = electron_mass_c2*tau ;
406 }
407
408 G4double ChargeSquare = charge*charge;
409
410 G4double eTotalEnergy = eKineticEnergy + electron_mass_c2 ;
411 G4double beta2 = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
412 /(eTotalEnergy*eTotalEnergy);
413 G4double bg2 = eKineticEnergy*(eTotalEnergy+electron_mass_c2)
414 /(electron_mass_c2*electron_mass_c2);
415
416 G4double eps = epsfactor*bg2/Z23;
417
418 if (eps<epsmin) sigma = 2.*eps*eps;
419 else if(eps<epsmax) sigma = log(1.+2.*eps)-2.*eps/(1.+2.*eps);
420 else sigma = log(2.*eps)-1.+1./eps;
421
422 sigma *= ChargeSquare*AtomicNumber*AtomicNumber/(beta2*bg2);
423
424 // interpolate in AtomicNumber and beta2
425 G4double c1,c2,cc1,cc2,corr;
426
427 // get bin number in Z
428 G4int iZ = 14;
429 while ((iZ>=0)&&(Zdat[iZ]>=AtomicNumber)) iZ -= 1;
430 if (iZ==14) iZ = 13;
431 if (iZ==-1) iZ = 0 ;
432
433 G4double Z1 = Zdat[iZ];
434 G4double Z2 = Zdat[iZ+1];
435 G4double ratZ = (AtomicNumber-Z1)*(AtomicNumber+Z1)/
436 ((Z2-Z1)*(Z2+Z1));
437
438 if(eKineticEnergy <= Tlim)
439 {
440 // get bin number in T (beta2)
441 G4int iT = 21;
442 while ((iT>=0)&&(Tdat[iT]>=eKineticEnergy)) iT -= 1;
443 if(iT==21) iT = 20;
444 if(iT==-1) iT = 0 ;
445
446 // calculate betasquare values
447 G4double T = Tdat[iT], E = T + electron_mass_c2;
448 G4double b2small = T*(E+electron_mass_c2)/(E*E);
449
450 T = Tdat[iT+1]; E = T + electron_mass_c2;
451 G4double b2big = T*(E+electron_mass_c2)/(E*E);
452 G4double ratb2 = (beta2-b2small)/(b2big-b2small);
453
454 if (charge < 0.)
455 {
456 c1 = celectron[iZ][iT];
457 c2 = celectron[iZ+1][iT];
458 cc1 = c1+ratZ*(c2-c1);
459
460 c1 = celectron[iZ][iT+1];
461 c2 = celectron[iZ+1][iT+1];
462 cc2 = c1+ratZ*(c2-c1);
463
464 corr = cc1+ratb2*(cc2-cc1);
465
466 sigma *= sigmafactor/corr;
467 }
468 else
469 {
470 c1 = cpositron[iZ][iT];
471 c2 = cpositron[iZ+1][iT];
472 cc1 = c1+ratZ*(c2-c1);
473
474 c1 = cpositron[iZ][iT+1];
475 c2 = cpositron[iZ+1][iT+1];
476 cc2 = c1+ratZ*(c2-c1);
477
478 corr = cc1+ratb2*(cc2-cc1);
479
480 sigma *= sigmafactor/corr;
481 }
482 }
483 else
484 {
485 c1 = bg2lim*sig0[iZ]*(1.+hecorr[iZ]*(beta2-beta2lim))/bg2;
486 c2 = bg2lim*sig0[iZ+1]*(1.+hecorr[iZ+1]*(beta2-beta2lim))/bg2;
487 if((AtomicNumber >= Z1) && (AtomicNumber <= Z2))
488 sigma = c1+ratZ*(c2-c1) ;
489 else if(AtomicNumber < Z1)
490 sigma = AtomicNumber*AtomicNumber*c1/(Z1*Z1);
491 else if(AtomicNumber > Z2)
492 sigma = AtomicNumber*AtomicNumber*c2/(Z2*Z2);
493 }
494 return sigma;
495
496}
497
498//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
499
500G4double G4UrbanMscModel::ComputeTruePathLengthLimit(
501 const G4Track& track,
502 G4PhysicsTable* theTable,
503 G4double currentMinimalStep)
504{
505 tPathLength = currentMinimalStep;
506 G4int stepNumber = track.GetCurrentStepNumber();
507 const G4DynamicParticle* dp = track.GetDynamicParticle();
508
509 if(stepNumber == 1) {
510 inside = false;
511 insideskin = false;
512 tlimit = geombig;
513 SetParticle( dp->GetDefinition() );
514 }
515
516 theLambdaTable = theTable;
517 couple = track.GetMaterialCutsCouple();
518 currentMaterialIndex = couple->GetIndex();
519 currentKinEnergy = dp->GetKineticEnergy();
520 currentRange =
521 theManager->GetRangeFromRestricteDEDX(particle,currentKinEnergy,couple);
522 lambda0 = GetLambda(currentKinEnergy);
523
524 // stop here if small range particle
525 if(inside) return tPathLength;
526
527 if(tPathLength > currentRange) tPathLength = currentRange;
528
529 G4StepPoint* sp = track.GetStep()->GetPreStepPoint();
530 presafety = sp->GetSafety();
531
532 // G4cout << "G4UrbanMscModel::ComputeTruePathLengthLimit tPathLength= "
533 // <<tPathLength<<" safety= " << presafety
534 // << " range= " <<currentRange<<G4endl;
535
536 // far from geometry boundary
537 if(currentRange < presafety)
538 {
539 inside = true;
540 return tPathLength;
541 }
542
543 G4StepStatus stepStatus = sp->GetStepStatus();
544
545 // standard version
546 //
547 if (steppingAlgorithm == fUseDistanceToBoundary)
548 {
549 //compute geomlimit and presafety
550 GeomLimit(track);
551
552 // is far from boundary
553 if(currentRange <= presafety)
554 {
555 inside = true;
556 return tPathLength;
557 }
558
559 smallstep += 1.;
560 insideskin = false;
561
562 if((stepStatus == fGeomBoundary) || (stepNumber == 1))
563 {
564 if(stepNumber == 1) smallstep = 1.e10;
565 else smallstep = 1.;
566
567 // facrange scaling in lambda
568 // not so strong step restriction above lambdalimit
569 G4double facr = facrange;
570 if(lambda0 > lambdalimit)
571 facr *= frscaling1+frscaling2*lambda0/lambdalimit;
572
573 // constraint from the physics
574 if (currentRange > lambda0) tlimit = facr*currentRange;
575 else tlimit = facr*lambda0;
576
577 if(tlimit > currentRange) tlimit = currentRange;
578
579 //define stepmin here (it depends on lambda!)
580 //rough estimation of lambda_elastic/lambda_transport
581 G4double rat = currentKinEnergy/MeV ;
582 rat = 1.e-3/(rat*(10.+rat)) ;
583 //stepmin ~ lambda_elastic
584 stepmin = rat*lambda0;
585 skindepth = skin*stepmin;
586
587 //define tlimitmin
588 tlimitmin = 10.*stepmin;
589 if(tlimitmin < tlimitminfix) tlimitmin = tlimitminfix;
590
591 //lower limit for tlimit
592 if(tlimit < tlimitmin) tlimit = tlimitmin;
593
594 // constraint from the geometry (if tlimit above is too big)
595 G4double tgeom = geombig;
596
597 if((geomlimit < geombig) && (geomlimit > geommin))
598 {
599 if(stepStatus == fGeomBoundary)
600 tgeom = geomlimit/facgeom;
601 else
602 tgeom = 2.*geomlimit/facgeom;
603
604 if(tlimit > tgeom) tlimit = tgeom;
605 }
606 }
607
608 //if track starts far from boundaries increase tlimit!
609 if(tlimit < facsafety*presafety) tlimit = facsafety*presafety ;
610
611 // G4cout << "tgeom= " << tgeom << " geomlimit= " << geomlimit
612 // << " tlimit= " << tlimit << " presafety= " << presafety << G4endl;
613
614 // shortcut
615 if((tPathLength < tlimit) && (tPathLength < presafety))
616 return tPathLength;
617
618 G4double tnow = tlimit;
619 // optimization ...
620 if(geomlimit < geombig) tnow = max(tlimit,facsafety*geomlimit);
621
622 // step reduction near to boundary
623 if(smallstep < skin)
624 {
625 tnow = stepmin;
626 insideskin = true;
627 }
628 else if(geomlimit < geombig)
629 {
630 if(geomlimit > skindepth)
631 {
632 if(tnow > geomlimit-0.999*skindepth)
633 tnow = geomlimit-0.999*skindepth;
634 }
635 else
636 {
637 insideskin = true;
638 if(tnow > stepmin) tnow = stepmin;
639 }
640 }
641
642 if(tnow < stepmin) tnow = stepmin;
643
644 if(tPathLength > tnow) tPathLength = tnow ;
645 }
646 // for 'normal' simulation with or without magnetic field
647 // there no small step/single scattering at boundaries
648 else if(steppingAlgorithm == fUseSafety)
649 {
650 // compute presafety again if presafety <= 0 and no boundary
651 // i.e. when it is needed for optimization purposes
652 if((stepStatus != fGeomBoundary) && (presafety < tlimitminfix))
653 presafety = safetyHelper->ComputeSafety(sp->GetPosition());
654
655 // is far from boundary
656 if(currentRange < presafety)
657 {
658 inside = true;
659 return tPathLength;
660 }
661
662 if((stepStatus == fGeomBoundary) || (stepNumber == 1))
663 {
664 // facrange scaling in lambda
665 // not so strong step restriction above lambdalimit
666 G4double facr = facrange;
667 if(lambda0 > lambdalimit)
668 facr *= frscaling1+frscaling2*lambda0/lambdalimit;
669
670 // constraint from the physics
671 if (currentRange > lambda0) tlimit = facr*currentRange;
672 else tlimit = facr*lambda0;
673
674 //lower limit for tlimit
675 tlimitmin = std::max(tlimitminfix,lambda0/nstepmax);
676 if(tlimit < tlimitmin) tlimit = tlimitmin;
677 }
678
679 //if track starts far from boundaries increase tlimit!
680 if(tlimit < facsafety*presafety) tlimit = facsafety*presafety ;
681
682 if(tPathLength > tlimit) tPathLength = tlimit;
683 }
684
685 // version similar to 7.1 (needed for some experiments)
686 else
687 {
688 if (stepStatus == fGeomBoundary)
689 {
690 if (currentRange > lambda0) tlimit = facrange*currentRange;
691 else tlimit = facrange*lambda0;
692
693 if(tlimit < tlimitmin) tlimit = tlimitmin;
694 if(tPathLength > tlimit) tPathLength = tlimit;
695 }
696 }
697 // G4cout << "tPathLength= " << tPathLength << " geomlimit= " << geomlimit
698 // << " currentMinimalStep= " << currentMinimalStep << G4endl;
699
700 return tPathLength ;
701}
702
703//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
704
705void G4UrbanMscModel::GeomLimit(const G4Track& track)
706{
707 geomlimit = geombig;
708
709 // no geomlimit for the World volume
710 if((track.GetVolume() != 0) &&
711 (track.GetVolume() != safetyHelper->GetWorldVolume()))
712 {
713 G4double cstep = currentRange;
714
715 geomlimit = safetyHelper->CheckNextStep(
716 track.GetStep()->GetPreStepPoint()->GetPosition(),
717 track.GetMomentumDirection(),
718 cstep,
719 presafety);
720 // G4cout << "!!!G4UrbanMscModel::GeomLimit presafety= " << presafety
721 // << " limit= " << geomlimit << G4endl;
722 }
723}
724
725//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
726
727G4double G4UrbanMscModel::ComputeGeomPathLength(G4double)
728{
729 lambdaeff = lambda0;
730 par1 = -1. ;
731 par2 = par3 = 0. ;
732
733 // do the true -> geom transformation
734 zPathLength = tPathLength;
735
736 // z = t for very small tPathLength
737 if(tPathLength < tlimitminfix) return zPathLength;
738
739 // this correction needed to run MSC with eIoni and eBrem inactivated
740 // and makes no harm for a normal run
741 if(tPathLength > currentRange)
742 tPathLength = currentRange ;
743
744 G4double tau = tPathLength/lambda0 ;
745
746 if ((tau <= tausmall) || insideskin) {
747 zPathLength = tPathLength;
748 if(zPathLength > lambda0) zPathLength = lambda0;
749 return zPathLength;
750 }
751
752 G4double zmean = tPathLength;
753 if (tPathLength < currentRange*dtrl) {
754 if(tau < taulim) zmean = tPathLength*(1.-0.5*tau) ;
755 else zmean = lambda0*(1.-exp(-tau));
756 } else if(currentKinEnergy < mass) {
757 par1 = 1./currentRange ;
758 par2 = 1./(par1*lambda0) ;
759 par3 = 1.+par2 ;
760 if(tPathLength < currentRange)
761 zmean = (1.-exp(par3*log(1.-tPathLength/currentRange)))/(par1*par3) ;
762 else
763 zmean = 1./(par1*par3) ;
764 } else {
765 G4double T1 = theManager->GetEnergy(particle,currentRange-tPathLength,couple);
766 G4double lambda1 = GetLambda(T1);
767
768 par1 = (lambda0-lambda1)/(lambda0*tPathLength) ;
769 par2 = 1./(par1*lambda0) ;
770 par3 = 1.+par2 ;
771 zmean = (1.-exp(par3*log(lambda1/lambda0)))/(par1*par3) ;
772 }
773
774 zPathLength = zmean ;
775
776 // sample z
777 if(samplez)
778 {
779 const G4double ztmax = 0.99, onethird = 1./3. ;
780 G4double zt = zmean/tPathLength ;
781
782 if (tPathLength > stepmin && zt < ztmax)
783 {
784 G4double u,cz1;
785 if(zt >= onethird)
786 {
787 G4double cz = 0.5*(3.*zt-1.)/(1.-zt) ;
788 cz1 = 1.+cz ;
789 G4double u0 = cz/cz1 ;
790 G4double grej ;
791 do {
792 u = exp(log(G4UniformRand())/cz1) ;
793 grej = exp(cz*log(u/u0))*(1.-u)/(1.-u0) ;
794 } while (grej < G4UniformRand()) ;
795 }
796 else
797 {
798 cz1 = 1./zt-1.;
799 u = 1.-exp(log(G4UniformRand())/cz1) ;
800 }
801 zPathLength = tPathLength*u ;
802 }
803 }
804
805 if(zPathLength > lambda0) zPathLength = lambda0;
806
807 return zPathLength;
808}
809
810//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
811
812G4double G4UrbanMscModel::ComputeTrueStepLength(G4double geomStepLength)
813{
814 // step defined other than transportation
815 if(geomStepLength == zPathLength && tPathLength <= currentRange)
816 return tPathLength;
817
818 // t = z for very small step
819 zPathLength = geomStepLength;
820 tPathLength = geomStepLength;
821 if(geomStepLength < tlimitminfix) return tPathLength;
822
823 // recalculation
824 if((geomStepLength > lambda0*tausmall) && !insideskin)
825 {
826 if(par1 < 0.)
827 tPathLength = -lambda0*log(1.-geomStepLength/lambda0) ;
828 else
829 {
830 if(par1*par3*geomStepLength < 1.)
831 tPathLength = (1.-exp(log(1.-par1*par3*geomStepLength)/par3))/par1 ;
832 else
833 tPathLength = currentRange;
834 }
835 }
836 if(tPathLength < geomStepLength) tPathLength = geomStepLength;
837
838 return tPathLength;
839}
840
841//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
842
843G4double G4UrbanMscModel::ComputeTheta0(G4double trueStepLength,
844 G4double KineticEnergy)
845{
846 // for all particles take the width of the central part
847 // from a parametrization similar to the Highland formula
848 // ( Highland formula: Particle Physics Booklet, July 2002, eq. 26.10)
849 const G4double c_highland = 13.6*MeV ;
850 G4double betacp = sqrt(currentKinEnergy*(currentKinEnergy+2.*mass)*
851 KineticEnergy*(KineticEnergy+2.*mass)/
852 ((currentKinEnergy+mass)*(KineticEnergy+mass)));
853 G4double y = trueStepLength/currentRadLength;
854 G4double theta0 = c_highland*std::abs(charge)*sqrt(y)/betacp;
855 y = log(y);
856 if(mass < masslimite)
857 theta0 *= (1.+0.051*y);
858 else if(mass < masslimitmu)
859 theta0 *= (1.+0.044*y);
860 else
861 theta0 *= (1.+0.038*y);
862
863 return theta0;
864}
865
866//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
867
868void G4UrbanMscModel::SampleScattering(const G4DynamicParticle* dynParticle,
869 G4double safety)
870{
871 G4double kineticEnergy = dynParticle->GetKineticEnergy();
872 if((kineticEnergy <= 0.0) || (tPathLength <= tlimitminfix)) return;
873
874 G4double cth = SampleCosineTheta(tPathLength,kineticEnergy);
875 // protection against 'bad' cth values
876 if(cth > 1.) cth = 1.;
877 if(cth < -1.) cth = -1.;
878 G4double sth = sqrt((1.0 - cth)*(1.0 + cth));
879 G4double phi = twopi*G4UniformRand();
880 G4double dirx = sth*cos(phi);
881 G4double diry = sth*sin(phi);
882
883 G4ThreeVector oldDirection = dynParticle->GetMomentumDirection();
884 G4ThreeVector newDirection(dirx,diry,cth);
885 newDirection.rotateUz(oldDirection);
886 fParticleChange->ProposeMomentumDirection(newDirection);
887
888 if (latDisplasment && safety > tlimitminfix) {
889
890 G4double r = SampleDisplacement();
891/*
892 G4cout << "G4UrbanMscModel::SampleSecondaries: e(MeV)= " << kineticEnergy
893 << " sinTheta= " << sth << " r(mm)= " << r
894 << " trueStep(mm)= " << tPathLength
895 << " geomStep(mm)= " << zPathLength
896 << G4endl;
897*/
898 if(r > 0.)
899 {
900 G4double latcorr = LatCorrelation();
901 if(latcorr > r) latcorr = r;
902
903 // sample direction of lateral displacement
904 // compute it from the lateral correlation
905 G4double Phi = 0.;
906 if(std::abs(r*sth) < latcorr) {
907 Phi = twopi*G4UniformRand();
908 } else {
909 G4double psi = std::acos(latcorr/(r*sth));
910 if(G4UniformRand() < 0.5) Phi = phi+psi;
911 else Phi = phi-psi;
912 }
913
914 dirx = std::cos(Phi);
915 diry = std::sin(Phi);
916
917 G4ThreeVector latDirection(dirx,diry,0.0);
918 latDirection.rotateUz(oldDirection);
919
920 G4ThreeVector Position = *(fParticleChange->GetProposedPosition());
921 G4double fac = 1.;
922 if(r > safety) {
923 // ******* so safety is computed at boundary too ************
924 G4double newsafety = safetyHelper->ComputeSafety(Position);
925 if(r > newsafety)
926 fac = newsafety/r ;
927 }
928
929 if(fac > 0.)
930 {
931 // compute new endpoint of the Step
932 G4ThreeVector newPosition = Position+fac*r*latDirection;
933
934 // definitely not on boundary
935 if(1. == fac) {
936 safetyHelper->ReLocateWithinVolume(newPosition);
937
938 } else {
939 // check safety after displacement
940 G4double postsafety = safetyHelper->ComputeSafety(newPosition);
941
942 // displacement to boundary
943 // if(postsafety < tlimitminfix) {
944 if(postsafety <= 0.0) {
945 safetyHelper->Locate(newPosition, newDirection);
946
947 // not on the boundary
948 } else {
949 safetyHelper->ReLocateWithinVolume(newPosition);
950 }
951 }
952 fParticleChange->ProposePosition(newPosition);
953 }
954 }
955 }
956}
957
958//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
959
960G4double G4UrbanMscModel::SampleCosineTheta(G4double trueStepLength,
961 G4double KineticEnergy)
962{
963 G4double cth = 1. ;
964 G4double tau = trueStepLength/lambda0 ;
965
966 Zeff = couple->GetMaterial()->GetTotNbOfElectPerVolume()/
967 couple->GetMaterial()->GetTotNbOfAtomsPerVolume() ;
968
969 if(insideskin)
970 {
971 //no scattering, single or plural scattering
972 G4double mean = trueStepLength/stepmin ;
973
974 G4int n = G4Poisson(mean);
975 if(n > 0)
976 {
977 G4double tm = KineticEnergy/electron_mass_c2;
978 // ascr - screening parameter
979 G4double ascr = exp(log(Zeff)/3.)/(137.*sqrt(tm*(tm+2.)));
980 G4double ascr1 = 1.+0.5*ascr*ascr;
981 G4double bp1=ascr1+1.;
982 G4double bm1=ascr1-1.;
983 // single scattering from screened Rutherford x-section
984 G4double ct,st,phi;
985 G4double sx=0.,sy=0.,sz=0.;
986 for(G4int i=1; i<=n; i++)
987 {
988 ct = ascr1-bp1*bm1/(2.*G4UniformRand()+bm1);
989 if(ct < -1.) ct = -1.;
990 if(ct > 1.) ct = 1.;
991 st = sqrt(1.-ct*ct);
992 phi = twopi*G4UniformRand();
993 sx += st*cos(phi);
994 sy += st*sin(phi);
995 sz += ct;
996 }
997 cth = sz/sqrt(sx*sx+sy*sy+sz*sz);
998 }
999 }
1000 else
1001 {
1002 if(trueStepLength >= currentRange*dtrl)
1003 {
1004 if(par1*trueStepLength < 1.)
1005 tau = -par2*log(1.-par1*trueStepLength) ;
1006 // for the case if ioni/brems are inactivated
1007 // see the corresponding condition in ComputeGeomPathLength
1008 else if(1.-KineticEnergy/currentKinEnergy > taulim)
1009 tau = taubig ;
1010 }
1011 currentTau = tau ;
1012 lambdaeff = trueStepLength/currentTau;
1013 currentRadLength = couple->GetMaterial()->GetRadlen();
1014
1015 if (tau >= taubig) cth = -1.+2.*G4UniformRand();
1016 else if (tau >= tausmall)
1017 {
1018 G4double b=2.,bp1=3.,bm1=1.;
1019 G4double prob = 0. ;
1020 G4double a = 1., ea = 0., eaa = 1.;
1021 G4double xmean1 = 1., xmean2 = 0.;
1022
1023 G4double theta0 = ComputeTheta0(trueStepLength,KineticEnergy);
1024
1025 // protexction for very small angles
1026 if(theta0 < tausmall) return cth;
1027
1028 G4double sth = sin(0.5*theta0);
1029 a = 0.25/(sth*sth);
1030
1031 ea = exp(-2.*a);
1032 eaa = 1.-ea ;
1033 xmean1 = (1.+ea)/eaa-1./a;
1034
1035 G4double xmeanth = exp(-tau);
1036 b = 1./xmeanth ;
1037 bp1 = b+1.;
1038 bm1 = b-1.;
1039 // protection
1040 if(bm1 > 0.)
1041 xmean2 = b-0.5*bp1*bm1*log(bp1/bm1);
1042 else
1043 {
1044 b = 1.+tau;
1045 bp1 = 2.+tau;
1046 bm1 = tau;
1047 xmean2 = 1.+tau*(1.-log(2./tau));
1048 }
1049
1050 if((xmean1 >= xmeanth) && (xmean2 <= xmeanth))
1051 {
1052 //normal case
1053 prob = (xmeanth-xmean2)/(xmean1-xmean2);
1054 }
1055 else
1056 {
1057 // x1 < xth ( x2 < xth automatically if b = 1/xth)
1058 // correct a (xmean1)
1059 if((xmeanth-xmean1)/xmeanth < 1.e-5)
1060 {
1061 // xmean1 is small probably due to precision problems
1062 xmean1 = 0.50*(1.+xmeanth);
1063 prob = (xmeanth-xmean2)/(xmean1-xmean2);
1064 }
1065 else
1066 {
1067 // correct a in order to have x1=xth
1068 G4int i=0, imax=10;
1069 do
1070 {
1071 a = 1./(1.-xmeanth+2.*ea/eaa);
1072 ea = exp(-2.*a);
1073 eaa = 1.-ea;
1074 xmean1 = (1.+ea)/eaa-1./a;
1075 i += 1;
1076 } while ((std::abs((xmeanth-xmean1)/xmeanth) > 0.05) && (i < imax));
1077 prob = 1.;
1078 }
1079 }
1080
1081 // sampling of costheta
1082 if (G4UniformRand() < prob)
1083 cth = 1.+log(ea+G4UniformRand()*eaa)/a ;
1084 else
1085 cth = b-bp1*bm1/(bm1+2.*G4UniformRand()) ;
1086 }
1087 }
1088 return cth ;
1089}
1090
1091//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1092
1093G4double G4UrbanMscModel::SampleDisplacement()
1094{
1095 const G4double kappa = 2.5;
1096 const G4double kappapl1 = kappa+1.;
1097 const G4double kappami1 = kappa-1.;
1098 G4double rmean = 0.0;
1099 if ((currentTau >= tausmall) && !insideskin) {
1100 if (currentTau < taulim) {
1101 rmean = kappa*currentTau*currentTau*currentTau*
1102 (1.-kappapl1*currentTau*0.25)/6. ;
1103
1104 } else {
1105 G4double etau = 0.0;
1106 if (currentTau<taubig) etau = exp(-currentTau);
1107 rmean = -kappa*currentTau;
1108 rmean = -exp(rmean)/(kappa*kappami1);
1109 rmean += currentTau-kappapl1/kappa+kappa*etau/kappami1;
1110 }
1111 if (rmean>0.) rmean = 2.*lambdaeff*sqrt(rmean/3.0);
1112 else rmean = 0.;
1113 }
1114
1115 // protection against z > t ...........................
1116 if(rmean > 0.) {
1117 G4double zt = (tPathLength-zPathLength)*(tPathLength+zPathLength);
1118 if(zt <= 0.)
1119 rmean = 0.;
1120 else if(rmean*rmean > zt)
1121 rmean = sqrt(zt);
1122 }
1123 return rmean;
1124}
1125
1126//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1127
1128G4double G4UrbanMscModel::LatCorrelation()
1129{
1130 const G4double kappa = 2.5;
1131 const G4double kappami1 = kappa-1.;
1132
1133 G4double latcorr = 0.;
1134 if((currentTau >= tausmall) && !insideskin)
1135 {
1136 if(currentTau < taulim)
1137 latcorr = lambdaeff*kappa*currentTau*currentTau*
1138 (1.-(kappa+1.)*currentTau/3.)/3.;
1139 else
1140 {
1141 G4double etau = 0.;
1142 if(currentTau < taubig) etau = exp(-currentTau);
1143 latcorr = -kappa*currentTau;
1144 latcorr = exp(latcorr)/kappami1;
1145 latcorr += 1.-kappa*etau/kappami1 ;
1146 latcorr *= 2.*lambdaeff/3. ;
1147 }
1148 }
1149
1150 return latcorr;
1151}
1152
1153//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
1154
1155void G4UrbanMscModel::SampleSecondaries(std::vector<G4DynamicParticle*>*,
1156 const G4MaterialCutsCouple*,
1157 const G4DynamicParticle*,
1158 G4double,
1159 G4double)
1160{}
1161
1162//....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo......
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