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G4IonFluctuations.cc
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25 //
26 // $Id$
27 //
28 // -------------------------------------------------------------------
29 //
30 // GEANT4 Class file
31 //
32 //
33 // File name: G4IonFluctuation
34 //
35 // Author: Vladimir Ivanchenko
36 //
37 // Creation date: 03.01.2002
38 //
39 // Modifications:
40 //
41 // 28-12-02 add method Dispersion (V.Ivanchenko)
42 // 07-02-03 change signature (V.Ivanchenko)
43 // 13-02-03 Add name (V.Ivanchenko)
44 // 23-05-03 Add control on parthalogical cases (V.Ivanchenko)
45 // 16-10-03 Changed interface to Initialisation (V.Ivanchenko)
46 // 27-09-07 Use FermiEnergy from material, add cut dependence (V.Ivanchenko)
47 // 01-02-08 Add protection for small energies and optimise the code (V.Ivanchenko)
48 // 01-06-08 Added initialisation of effective charge prestep (V.Ivanchenko)
49 //
50 // Class Description:
51 //
52 // -------------------------------------------------------------------
53 //
54 
55 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
56 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
57 
58 #include "G4IonFluctuations.hh"
59 #include "G4PhysicalConstants.hh"
60 #include "G4SystemOfUnits.hh"
61 #include "Randomize.hh"
62 #include "G4Poisson.hh"
63 #include "G4Material.hh"
64 #include "G4DynamicParticle.hh"
65 
66 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
67 
68 using namespace std;
69 
70 G4IonFluctuations::G4IonFluctuations(const G4String& nam)
71  : G4VEmFluctuationModel(nam),
72  particle(0),
73  particleMass(proton_mass_c2),
74  charge(1.0),
75  chargeSquare(1.0),
76  effChargeSquare(1.0),
77  parameter(10.0*CLHEP::MeV/CLHEP::proton_mass_c2),
78  minNumberInteractionsBohr(0.0),
79  theBohrBeta2(50.0*keV/CLHEP::proton_mass_c2),
80  minFraction(0.2),
81  xmin(0.2),
82  minLoss(0.001*eV)
83 {
84  kineticEnergy = 0.0;
85  beta2 = 0.0;
86 }
87 
88 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
89 
90 G4IonFluctuations::~G4IonFluctuations()
91 {}
92 
93 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
94 
95 void G4IonFluctuations::InitialiseMe(const G4ParticleDefinition* part)
96 {
97  particle = part;
98  particleMass = part->GetPDGMass();
99  charge = part->GetPDGCharge()/eplus;
100  chargeSquare = charge*charge;
101  effChargeSquare= chargeSquare;
102  uniFluct.InitialiseMe(part);
103 }
104 
105 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
106 
107 G4double G4IonFluctuations::SampleFluctuations(const G4Material* material,
108  const G4DynamicParticle* dp,
109  G4double& tmax,
110  G4double& length,
111  G4double& meanLoss)
112 {
113  // G4cout << "### meanLoss= " << meanLoss << G4endl;
114  if(meanLoss <= minLoss) return meanLoss;
115 
116  //G4cout << "G4IonFluctuations::SampleFluctuations E(MeV)= " << dp->GetKineticEnergy()
117  // << " Elim(MeV)= " << parameter*charge*particleMass << G4endl;
118 
119  // Vavilov fluctuations
120  if(dp->GetKineticEnergy() > parameter*charge*particleMass) {
121  return uniFluct.SampleFluctuations(material,dp,tmax,length,meanLoss);
122  }
123 
124  G4double siga = Dispersion(material,dp,tmax,length);
125  G4double loss = meanLoss;
126 
127  //G4cout << "### siga= " << sqrt(siga) << " navr= " << navr << G4endl;
128 
129  // Gaussian fluctuation
130 
131  // Increase fluctuations for big fractional energy loss
132  //G4cout << "siga= " << siga << G4endl;
133  if ( meanLoss > minFraction*kineticEnergy ) {
134  G4double gam = (kineticEnergy - meanLoss)/particleMass + 1.0;
135  G4double b2 = 1.0 - 1.0/(gam*gam);
136  if(b2 < xmin*beta2) b2 = xmin*beta2;
137  G4double x = b2/beta2;
138  G4double x3 = 1.0/(x*x*x);
139  siga *= 0.25*(1.0 + x)*(x3 + (1.0/b2 - 0.5)/(1.0/beta2 - 0.5) );
140  }
141  siga = sqrt(siga);
142  G4double sn = meanLoss/siga;
143  G4double twomeanLoss = meanLoss + meanLoss;
144  // G4cout << "siga= " << siga << " sn= " << sn << G4endl;
145 
146  // thick target case
147  if (sn >= 2.0) {
148 
149  do {
150  loss = G4RandGauss::shoot(meanLoss,siga);
151  } while (0.0 > loss || twomeanLoss < loss);
152 
153  // Gamma distribution
154  } else if(sn > 0.1) {
155 
156  G4double neff = sn*sn;
157  loss = meanLoss*CLHEP::RandGamma::shoot(neff,1.0)/neff;
158 
159  // uniform distribution for very small steps
160  } else {
161  loss = twomeanLoss*G4UniformRand();
162  }
163 
164  //G4cout << "meanLoss= " << meanLoss << " loss= " << loss << G4endl;
165  return loss;
166 }
167 
168 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
169 
170 G4double G4IonFluctuations::Dispersion(const G4Material* material,
171  const G4DynamicParticle* dp,
172  G4double& tmax,
173  G4double& length)
174 {
175  kineticEnergy = dp->GetKineticEnergy();
176  G4double etot = kineticEnergy + particleMass;
177  beta2 = kineticEnergy*(kineticEnergy + 2.*particleMass)/(etot*etot);
178 
179  G4double electronDensity = material->GetElectronDensity();
180 
181  /*
182  G4cout << "e= " << kineticEnergy << " m= " << particleMass
183  << " tmax= " << tmax << " l= " << length
184  << " q^2= " << effChargeSquare << " beta2=" << beta2<< G4endl;
185  */
186  G4double siga = (1. - beta2*0.5)*tmax*length*electronDensity*
187  twopi_mc2_rcl2*chargeSquare/beta2;
188 
189  // Low velocity - additional ion charge fluctuations according to
190  // Q.Yang et al., NIM B61(1991)149-155.
191  //G4cout << "sigE= " << sqrt(siga) << " charge= " << charge <<G4endl;
192 
193  G4double Z = electronDensity/material->GetTotNbOfAtomsPerVolume();
194 
195  G4double fac = Factor(material, Z);
196 
197  // heavy ion correction
198 // G4double f1 = 1.065e-4*chargeSquare;
199 // if(beta2 > theBohrBeta2) f1/= beta2;
200 // else f1/= theBohrBeta2;
201 // if(f1 > 2.5) f1 = 2.5;
202 // fac *= (1.0 + f1);
203 
204  // taking into account the cut
205  G4double fac_cut = 1.0 + (fac - 1.0)*2.0*electron_mass_c2*beta2/(tmax*(1.0 - beta2));
206  if(fac_cut > 0.01 && fac > 0.01) {
207  siga *= fac_cut;
208  }
209 
210  //G4cout << "siga(keV)= " << sqrt(siga)/keV << " fac= " << fac
211  // << " f1= " << f1 << G4endl;
212 
213  return siga;
214 }
215 
216 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
217 
218 G4double G4IonFluctuations::Factor(const G4Material* material, G4double Z)
219 {
220  // The aproximation of energy loss fluctuations
221  // Q.Yang et al., NIM B61(1991)149-155.
222 
223  // Reduced energy in MeV/AMU
224  G4double energy = kineticEnergy *amu_c2/(particleMass*MeV) ;
225 
226  // simple approximation for higher beta2
227  G4double s1 = RelativisticFactor(material, Z);
228 
229  // tabulation for lower beta2
230  if( beta2 < 3.0*theBohrBeta2*Z ) {
231 
232  static G4double a[96][4] = {
233  {-0.3291, -0.8312, 0.2460, -1.0220},
234  {-0.5615, -0.5898, 0.5205, -0.7258},
235  {-0.5280, -0.4981, 0.5519, -0.5865},
236  {-0.5125, -0.4625, 0.5660, -0.5190},
237  {-0.5127, -0.8595, 0.5626, -0.8721},
238  {-0.5174, -1.1930, 0.5565, -1.1980},
239  {-0.5179, -1.1850, 0.5560, -1.2070},
240  {-0.5209, -0.9355, 0.5590, -1.0250},
241  {-0.5255, -0.7766, 0.5720, -0.9412},
242 
243  {-0.5776, -0.6665, 0.6598, -0.8484},
244  {-0.6013, -0.6045, 0.7321, -0.7671},
245  {-0.5781, -0.5518, 0.7605, -0.6919},
246  {-0.5587, -0.4981, 0.7835, -0.6195},
247  {-0.5466, -0.4656, 0.7978, -0.5771},
248  {-0.5406, -0.4690, 0.8031, -0.5718},
249  {-0.5391, -0.5061, 0.8024, -0.5974},
250  {-0.5380, -0.6483, 0.7962, -0.6970},
251  {-0.5355, -0.7722, 0.7962, -0.7839},
252  {-0.5329, -0.7720, 0.7988, -0.7846},
253 
254  {-0.5335, -0.7671, 0.7984, -0.7933},
255  {-0.5324, -0.7612, 0.7998, -0.8031},
256  {-0.5305, -0.7300, 0.8031, -0.7990},
257  {-0.5307, -0.7178, 0.8049, -0.8216},
258  {-0.5248, -0.6621, 0.8165, -0.7919},
259  {-0.5180, -0.6502, 0.8266, -0.7986},
260  {-0.5084, -0.6408, 0.8396, -0.8048},
261  {-0.4967, -0.6331, 0.8549, -0.8093},
262  {-0.4861, -0.6508, 0.8712, -0.8432},
263  {-0.4700, -0.6186, 0.8961, -0.8132},
264 
265  {-0.4545, -0.5720, 0.9227, -0.7710},
266  {-0.4404, -0.5226, 0.9481, -0.7254},
267  {-0.4288, -0.4778, 0.9701, -0.6850},
268  {-0.4199, -0.4425, 0.9874, -0.6539},
269  {-0.4131, -0.4188, 0.9998, -0.6332},
270  {-0.4089, -0.4057, 1.0070, -0.6218},
271  {-0.4039, -0.3913, 1.0150, -0.6107},
272  {-0.3987, -0.3698, 1.0240, -0.5938},
273  {-0.3977, -0.3608, 1.0260, -0.5852},
274  {-0.3972, -0.3600, 1.0260, -0.5842},
275 
276  {-0.3985, -0.3803, 1.0200, -0.6013},
277  {-0.3985, -0.3979, 1.0150, -0.6168},
278  {-0.3968, -0.3990, 1.0160, -0.6195},
279  {-0.3971, -0.4432, 1.0050, -0.6591},
280  {-0.3944, -0.4665, 1.0010, -0.6825},
281  {-0.3924, -0.5109, 0.9921, -0.7235},
282  {-0.3882, -0.5158, 0.9947, -0.7343},
283  {-0.3838, -0.5125, 0.9999, -0.7370},
284  {-0.3786, -0.4976, 1.0090, -0.7310},
285  {-0.3741, -0.4738, 1.0200, -0.7155},
286 
287  {-0.3969, -0.4496, 1.0320, -0.6982},
288  {-0.3663, -0.4297, 1.0430, -0.6828},
289  {-0.3630, -0.4120, 1.0530, -0.6689},
290  {-0.3597, -0.3964, 1.0620, -0.6564},
291  {-0.3555, -0.3809, 1.0720, -0.6454},
292  {-0.3525, -0.3607, 1.0820, -0.6289},
293  {-0.3505, -0.3465, 1.0900, -0.6171},
294  {-0.3397, -0.3570, 1.1020, -0.6384},
295  {-0.3314, -0.3552, 1.1130, -0.6441},
296  {-0.3235, -0.3531, 1.1230, -0.6498},
297 
298  {-0.3150, -0.3483, 1.1360, -0.6539},
299  {-0.3060, -0.3441, 1.1490, -0.6593},
300  {-0.2968, -0.3396, 1.1630, -0.6649},
301  {-0.2935, -0.3225, 1.1760, -0.6527},
302  {-0.2797, -0.3262, 1.1940, -0.6722},
303  {-0.2704, -0.3202, 1.2100, -0.6770},
304  {-0.2815, -0.3227, 1.2480, -0.6775},
305  {-0.2880, -0.3245, 1.2810, -0.6801},
306  {-0.3034, -0.3263, 1.3270, -0.6778},
307  {-0.2936, -0.3215, 1.3430, -0.6835},
308 
309  {-0.3282, -0.3200, 1.3980, -0.6650},
310  {-0.3260, -0.3070, 1.4090, -0.6552},
311  {-0.3511, -0.3074, 1.4470, -0.6442},
312  {-0.3501, -0.3064, 1.4500, -0.6442},
313  {-0.3490, -0.3027, 1.4550, -0.6418},
314  {-0.3487, -0.3048, 1.4570, -0.6447},
315  {-0.3478, -0.3074, 1.4600, -0.6483},
316  {-0.3501, -0.3283, 1.4540, -0.6669},
317  {-0.3494, -0.3373, 1.4550, -0.6765},
318  {-0.3485, -0.3373, 1.4570, -0.6774},
319 
320  {-0.3462, -0.3300, 1.4630, -0.6728},
321  {-0.3462, -0.3225, 1.4690, -0.6662},
322  {-0.3453, -0.3094, 1.4790, -0.6553},
323  {-0.3844, -0.3134, 1.5240, -0.6412},
324  {-0.3848, -0.3018, 1.5310, -0.6303},
325  {-0.3862, -0.2955, 1.5360, -0.6237},
326  {-0.4262, -0.2991, 1.5860, -0.6115},
327  {-0.4278, -0.2910, 1.5900, -0.6029},
328  {-0.4303, -0.2817, 1.5940, -0.5927},
329  {-0.4315, -0.2719, 1.6010, -0.5829},
330 
331  {-0.4359, -0.2914, 1.6050, -0.6010},
332  {-0.4365, -0.2982, 1.6080, -0.6080},
333  {-0.4253, -0.3037, 1.6120, -0.6150},
334  {-0.4335, -0.3245, 1.6160, -0.6377},
335  {-0.4307, -0.3292, 1.6210, -0.6447},
336  {-0.4284, -0.3204, 1.6290, -0.6380},
337  {-0.4227, -0.3217, 1.6360, -0.6438}
338  } ;
339 
340  G4int iz = G4int(Z) - 2;
341  if( 0 > iz ) iz = 0;
342  else if(95 < iz ) iz = 95;
343 
344  G4double ss = 1.0 + a[iz][0]*pow(energy,a[iz][1])+
345  + a[iz][2]*pow(energy,a[iz][3]);
346 
347  // protection for the validity range for low beta
348  G4double slim = 0.001;
349  if(ss < slim) s1 = 1.0/slim;
350  // for high value of beta
351  else if(s1*ss < 1.0) s1 = 1.0/ss;
352  }
353 
354  G4int i = 0 ;
355  G4double factor = 1.0 ;
356 
357  // The index of set of parameters i = 0 for protons(hadrons) in gases
358  // 1 for protons(hadrons) in solids
359  // 2 for ions in atomic gases
360  // 3 for ions in molecular gases
361  // 4 for ions in solids
362  static G4double b[5][4] = {
363  {0.1014, 0.3700, 0.9642, 3.987},
364  {0.1955, 0.6941, 2.522, 1.040},
365  {0.05058, 0.08975, 0.1419, 10.80},
366  {0.05009, 0.08660, 0.2751, 3.787},
367  {0.01273, 0.03458, 0.3951, 3.812}
368  } ;
369 
370  // protons (hadrons)
371  if(1.5 > charge) {
372  if( kStateGas != material->GetState() ) i = 1 ;
373 
374  // ions
375  } else {
376 
377  factor = charge * pow(charge/Z, 0.33333333);
378 
379  if( kStateGas == material->GetState() ) {
380  energy /= (charge * sqrt(charge)) ;
381 
382  if(1 == (material->GetNumberOfElements())) {
383  i = 2 ;
384  } else {
385  i = 3 ;
386  }
387 
388  } else {
389  energy /= (charge * sqrt(charge*Z)) ;
390  i = 4 ;
391  }
392  }
393 
394  G4double x = b[i][2];
395  G4double y = energy * b[i][3];
396  if(y <= 0.2) x *= (y*(1.0 - 0.5*y));
397  else x *= (1.0 - exp(-y));
398 
399  y = energy - b[i][1];
400 
401  G4double s2 = factor * x * b[i][0] / (y*y + x*x);
402  /*
403  G4cout << "s1= " << s1 << " s2= " << s2 << " q^2= " << effChargeSquare
404  << " e= " << energy << G4endl;
405  */
406  return s1*effChargeSquare/chargeSquare + s2;
407 }
408 
409 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
410 
411 G4double G4IonFluctuations::RelativisticFactor(const G4Material* mat,
412  G4double Z)
413 {
414  G4double eF = mat->GetIonisation()->GetFermiEnergy();
415  G4double I = mat->GetIonisation()->GetMeanExcitationEnergy();
416 
417  // H.Geissel et al. NIM B, 195 (2002) 3.
418  G4double bF2= 2.0*eF/electron_mass_c2;
419  G4double f = 0.4*(1.0 - beta2)/((1.0 - 0.5*beta2)*Z);
420  if(beta2 > bF2) f *= log(2.0*electron_mass_c2*beta2/I)*bF2/beta2;
421  else f *= log(4.0*eF/I);
422 
423  // G4cout << "f= " << f << " beta2= " << beta2
424  // << " bf2= " << bF2 << " q^2= " << chargeSquare << G4endl;
425 
426  return 1.0 + f;
427 }
428 
429 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
430 
431 void G4IonFluctuations::SetParticleAndCharge(const G4ParticleDefinition* part,
432  G4double q2)
433 {
434  if(part != particle) {
435  particle = part;
436  particleMass = part->GetPDGMass();
437  charge = part->GetPDGCharge()/eplus;
438  chargeSquare = charge*charge;
439  }
440  effChargeSquare = q2;
441  uniFluct.SetParticleAndCharge(part, q2);
442 }
443 
444 //....oooOO0OOooo........oooOO0OOooo........oooOO0OOooo........oooOO0OOooo....
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