Geant4 Cross Reference

Cross-Referencing   Geant4
Geant4/processes/electromagnetic/xrays/src/G4SynchrotronRadiationInMat.cc

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 24 // ********************************************************************
 25 //
 26 // --------------------------------------------------------------
 27 //      GEANT 4 class implementation file
 28 //
 29 //      History: first implementation,
 30 //      21-5-98 V.Grichine
 31 //      28-05-01, V.Ivanchenko minor changes to provide ANSI -wall compilation
 32 //      04.03.05, V.Grichine: get local field interface
 33 //      19-05-06, V.Ivanchenko rename from G4SynchrotronRadiation
 34 //
 35 ///////////////////////////////////////////////////////////////////////////
 36 
 37 #include "G4SynchrotronRadiationInMat.hh"
 38 
 39 #include "G4EmProcessSubType.hh"
 40 #include "G4Field.hh"
 41 #include "G4FieldManager.hh"
 42 #include "G4Integrator.hh"
 43 #include "G4PhysicalConstants.hh"
 44 #include "G4PropagatorInField.hh"
 45 #include "G4SystemOfUnits.hh"
 46 #include "G4PhysicsModelCatalog.hh"
 47 
 48 const G4double G4SynchrotronRadiationInMat::fIntegralProbabilityOfSR[200] = {
 49   1.000000e+00, 9.428859e-01, 9.094095e-01, 8.813971e-01, 8.565154e-01,
 50   8.337008e-01, 8.124961e-01, 7.925217e-01, 7.735517e-01, 7.554561e-01,
 51   7.381233e-01, 7.214521e-01, 7.053634e-01, 6.898006e-01, 6.747219e-01,
 52   6.600922e-01, 6.458793e-01, 6.320533e-01, 6.185872e-01, 6.054579e-01,
 53   5.926459e-01, 5.801347e-01, 5.679103e-01, 5.559604e-01, 5.442736e-01,
 54   5.328395e-01, 5.216482e-01, 5.106904e-01, 4.999575e-01, 4.894415e-01,
 55   4.791351e-01, 4.690316e-01, 4.591249e-01, 4.494094e-01, 4.398800e-01,
 56   4.305320e-01, 4.213608e-01, 4.123623e-01, 4.035325e-01, 3.948676e-01,
 57   3.863639e-01, 3.780179e-01, 3.698262e-01, 3.617858e-01, 3.538933e-01,
 58   3.461460e-01, 3.385411e-01, 3.310757e-01, 3.237474e-01, 3.165536e-01,
 59   3.094921e-01, 3.025605e-01, 2.957566e-01, 2.890784e-01, 2.825237e-01,
 60   2.760907e-01, 2.697773e-01, 2.635817e-01, 2.575020e-01, 2.515365e-01,
 61   2.456834e-01, 2.399409e-01, 2.343074e-01, 2.287812e-01, 2.233607e-01,
 62   2.180442e-01, 2.128303e-01, 2.077174e-01, 2.027040e-01, 1.977885e-01,
 63   1.929696e-01, 1.882457e-01, 1.836155e-01, 1.790775e-01, 1.746305e-01,
 64   1.702730e-01, 1.660036e-01, 1.618212e-01, 1.577243e-01, 1.537117e-01,
 65   1.497822e-01, 1.459344e-01, 1.421671e-01, 1.384791e-01, 1.348691e-01,
 66   1.313360e-01, 1.278785e-01, 1.244956e-01, 1.211859e-01, 1.179483e-01,
 67   1.147818e-01, 1.116850e-01, 1.086570e-01, 1.056966e-01, 1.028026e-01,
 68   9.997405e-02, 9.720975e-02, 9.450865e-02, 9.186969e-02, 8.929179e-02,
 69   8.677391e-02, 8.431501e-02, 8.191406e-02, 7.957003e-02, 7.728192e-02,
 70   7.504872e-02, 7.286944e-02, 7.074311e-02, 6.866874e-02, 6.664538e-02,
 71   6.467208e-02, 6.274790e-02, 6.087191e-02, 5.904317e-02, 5.726079e-02,
 72   5.552387e-02, 5.383150e-02, 5.218282e-02, 5.057695e-02, 4.901302e-02,
 73   4.749020e-02, 4.600763e-02, 4.456450e-02, 4.315997e-02, 4.179325e-02,
 74   4.046353e-02, 3.917002e-02, 3.791195e-02, 3.668855e-02, 3.549906e-02,
 75   3.434274e-02, 3.321884e-02, 3.212665e-02, 3.106544e-02, 3.003452e-02,
 76   2.903319e-02, 2.806076e-02, 2.711656e-02, 2.619993e-02, 2.531021e-02,
 77   2.444677e-02, 2.360897e-02, 2.279620e-02, 2.200783e-02, 2.124327e-02,
 78   2.050194e-02, 1.978324e-02, 1.908662e-02, 1.841151e-02, 1.775735e-02,
 79   1.712363e-02, 1.650979e-02, 1.591533e-02, 1.533973e-02, 1.478250e-02,
 80   1.424314e-02, 1.372117e-02, 1.321613e-02, 1.272755e-02, 1.225498e-02,
 81   1.179798e-02, 1.135611e-02, 1.092896e-02, 1.051609e-02, 1.011712e-02,
 82   9.731635e-03, 9.359254e-03, 8.999595e-03, 8.652287e-03, 8.316967e-03,
 83   7.993280e-03, 7.680879e-03, 7.379426e-03, 7.088591e-03, 6.808051e-03,
 84   6.537491e-03, 6.276605e-03, 6.025092e-03, 5.782661e-03, 5.549027e-03,
 85   5.323912e-03, 5.107045e-03, 4.898164e-03, 4.697011e-03, 4.503336e-03,
 86   4.316896e-03, 4.137454e-03, 3.964780e-03, 3.798649e-03, 3.638843e-03,
 87   3.485150e-03, 3.337364e-03, 3.195284e-03, 3.058715e-03, 2.927469e-03,
 88   2.801361e-03, 2.680213e-03, 2.563852e-03, 2.452110e-03, 2.344824e-03
 89 };
 90 
 91 ///////////////////////////////////////////////////////////////////////
 92 //  Constructor
 93 G4SynchrotronRadiationInMat::G4SynchrotronRadiationInMat(
 94   const G4String& processName, G4ProcessType type)
 95   : G4VDiscreteProcess(processName, type)
 96   , theGamma(G4Gamma::Gamma())
 97   , theElectron(G4Electron::Electron())
 98   , thePositron(G4Positron::Positron())
 99   , LowestKineticEnergy(10. * keV)
100   , fAlpha(0.0)
101   , fRootNumber(80)
102   , fVerboseLevel(verboseLevel)
103 {
104   G4TransportationManager* transportMgr =
105     G4TransportationManager::GetTransportationManager();
106 
107   fFieldPropagator = transportMgr->GetPropagatorInField();
108   secID = G4PhysicsModelCatalog::GetModelID("model_SynchrotronRadiation");
109   SetProcessSubType(fSynchrotronRadiation);
110   CutInRange = GammaCutInKineticEnergyNow = ElectronCutInKineticEnergyNow =
111     PositronCutInKineticEnergyNow = ParticleCutInKineticEnergyNow = fKsi =
112       fPsiGamma = fEta = fOrderAngleK = 0.0;
113 }
114 
115 /////////////////////////////////////////////////////////////////////////
116 // Destructor
117 G4SynchrotronRadiationInMat::~G4SynchrotronRadiationInMat() = default;
118 
119 G4bool G4SynchrotronRadiationInMat::IsApplicable(
120   const G4ParticleDefinition& particle)
121 {
122   return ((&particle == (const G4ParticleDefinition*) theElectron) ||
123           (&particle == (const G4ParticleDefinition*) thePositron));
124 }
125 
126 G4double G4SynchrotronRadiationInMat::GetLambdaConst() { return fLambdaConst; }
127 
128 G4double G4SynchrotronRadiationInMat::GetEnergyConst() { return fEnergyConst; }
129 
130 // Production of synchrotron X-ray photon
131 // Geant4 internal units.
132 G4double G4SynchrotronRadiationInMat::GetMeanFreePath(
133   const G4Track& trackData, G4double, G4ForceCondition* condition)
134 {
135   // gives the MeanFreePath in GEANT4 internal units
136   G4double MeanFreePath;
137 
138   const G4DynamicParticle* aDynamicParticle = trackData.GetDynamicParticle();
139 
140   *condition = NotForced;
141 
142   G4double gamma =
143     aDynamicParticle->GetTotalEnergy() / aDynamicParticle->GetMass();
144 
145   G4double particleCharge = aDynamicParticle->GetDefinition()->GetPDGCharge();
146 
147   G4double KineticEnergy = aDynamicParticle->GetKineticEnergy();
148 
149   if(KineticEnergy < LowestKineticEnergy || gamma < 1.0e3)
150     MeanFreePath = DBL_MAX;
151   else
152   {
153     G4ThreeVector FieldValue;
154     const G4Field* pField = nullptr;
155 
156     G4FieldManager* fieldMgr = nullptr;
157     G4bool fieldExertsForce  = false;
158 
159     if((particleCharge != 0.0))
160     {
161       fieldMgr =
162         fFieldPropagator->FindAndSetFieldManager(trackData.GetVolume());
163 
164       if(fieldMgr != nullptr)
165       {
166         // If the field manager has no field, there is no field !
167         fieldExertsForce = (fieldMgr->GetDetectorField() != nullptr);
168       }
169     }
170     if(fieldExertsForce)
171     {
172       pField                     = fieldMgr->GetDetectorField();
173       G4ThreeVector globPosition = trackData.GetPosition();
174 
175       G4double globPosVec[4], FieldValueVec[6];
176 
177       globPosVec[0] = globPosition.x();
178       globPosVec[1] = globPosition.y();
179       globPosVec[2] = globPosition.z();
180       globPosVec[3] = trackData.GetGlobalTime();
181 
182       pField->GetFieldValue(globPosVec, FieldValueVec);
183 
184       FieldValue =
185         G4ThreeVector(FieldValueVec[0], FieldValueVec[1], FieldValueVec[2]);
186 
187       G4ThreeVector unitMomentum = aDynamicParticle->GetMomentumDirection();
188       G4ThreeVector unitMcrossB  = FieldValue.cross(unitMomentum);
189       G4double perpB             = unitMcrossB.mag();
190       G4double beta              = aDynamicParticle->GetTotalMomentum() /
191                       (aDynamicParticle->GetTotalEnergy());
192 
193       if(perpB > 0.0)
194         MeanFreePath = fLambdaConst * beta / perpB;
195       else
196         MeanFreePath = DBL_MAX;
197     }
198     else
199       MeanFreePath = DBL_MAX;
200   }
201   if(fVerboseLevel > 0)
202   {
203     G4cout << "G4SynchrotronRadiationInMat::MeanFreePath = " << MeanFreePath / m
204            << " m" << G4endl;
205   }
206   return MeanFreePath;
207 }
208 
209 ////////////////////////////////////////////////////////////////////////////////
210 G4VParticleChange* G4SynchrotronRadiationInMat::PostStepDoIt(
211   const G4Track& trackData, const G4Step& stepData)
212 
213 {
214   aParticleChange.Initialize(trackData);
215 
216   const G4DynamicParticle* aDynamicParticle = trackData.GetDynamicParticle();
217 
218   G4double gamma =
219     aDynamicParticle->GetTotalEnergy() / (aDynamicParticle->GetMass());
220 
221   if(gamma <= 1.0e3)
222   {
223     return G4VDiscreteProcess::PostStepDoIt(trackData, stepData);
224   }
225   G4double particleCharge = aDynamicParticle->GetDefinition()->GetPDGCharge();
226 
227   G4ThreeVector FieldValue;
228   const G4Field* pField = nullptr;
229 
230   G4FieldManager* fieldMgr = nullptr;
231   G4bool fieldExertsForce  = false;
232 
233   if((particleCharge != 0.0))
234   {
235     fieldMgr = fFieldPropagator->FindAndSetFieldManager(trackData.GetVolume());
236     if(fieldMgr != nullptr)
237     {
238       // If the field manager has no field, there is no field !
239       fieldExertsForce = (fieldMgr->GetDetectorField() != nullptr);
240     }
241   }
242   if(fieldExertsForce)
243   {
244     pField                     = fieldMgr->GetDetectorField();
245     G4ThreeVector globPosition = trackData.GetPosition();
246     G4double globPosVec[4], FieldValueVec[6];
247     globPosVec[0] = globPosition.x();
248     globPosVec[1] = globPosition.y();
249     globPosVec[2] = globPosition.z();
250     globPosVec[3] = trackData.GetGlobalTime();
251 
252     pField->GetFieldValue(globPosVec, FieldValueVec);
253     FieldValue =
254       G4ThreeVector(FieldValueVec[0], FieldValueVec[1], FieldValueVec[2]);
255 
256     G4ThreeVector unitMomentum = aDynamicParticle->GetMomentumDirection();
257     G4ThreeVector unitMcrossB  = FieldValue.cross(unitMomentum);
258     G4double perpB             = unitMcrossB.mag();
259     if(perpB > 0.0)
260     {
261       // M-C of synchrotron photon energy
262       G4double energyOfSR = GetRandomEnergySR(gamma, perpB);
263 
264       if(fVerboseLevel > 0)
265       {
266         G4cout << "SR photon energy = " << energyOfSR / keV << " keV" << G4endl;
267       }
268 
269       // check against insufficient energy
270       if(energyOfSR <= 0.0)
271       {
272         return G4VDiscreteProcess::PostStepDoIt(trackData, stepData);
273       }
274       G4double kineticEnergy = aDynamicParticle->GetKineticEnergy();
275       G4ParticleMomentum particleDirection =
276         aDynamicParticle->GetMomentumDirection();
277 
278       // M-C of its direction, simplified dipole busted approach
279       G4double cosTheta, sinTheta, fcos, beta;
280 
281       do
282       {
283         cosTheta = 1. - 2. * G4UniformRand();
284         fcos     = (1 + cosTheta * cosTheta) * 0.5;
285       }
286       // Loop checking, 07-Aug-2015, Vladimir Ivanchenko
287       while(fcos < G4UniformRand());
288 
289       beta = std::sqrt(1. - 1. / (gamma * gamma));
290 
291       cosTheta = (cosTheta + beta) / (1. + beta * cosTheta);
292 
293       if(cosTheta > 1.)
294         cosTheta = 1.;
295       if(cosTheta < -1.)
296         cosTheta = -1.;
297 
298       sinTheta = std::sqrt(1. - cosTheta * cosTheta);
299 
300       G4double Phi = twopi * G4UniformRand();
301 
302       G4double dirx = sinTheta * std::cos(Phi);
303       G4double diry = sinTheta * std::sin(Phi);
304       G4double dirz = cosTheta;
305 
306       G4ThreeVector gammaDirection(dirx, diry, dirz);
307       gammaDirection.rotateUz(particleDirection);
308 
309       // polarization of new gamma
310       G4ThreeVector gammaPolarization = FieldValue.cross(gammaDirection);
311       gammaPolarization               = gammaPolarization.unit();
312 
313       // create G4DynamicParticle object for the SR photon
314       auto aGamma =
315         new G4DynamicParticle(G4Gamma::Gamma(), gammaDirection, energyOfSR);
316       aGamma->SetPolarization(gammaPolarization.x(), gammaPolarization.y(),
317                               gammaPolarization.z());
318 
319       aParticleChange.SetNumberOfSecondaries(1);
320 
321       // Update the incident particle
322       G4double newKinEnergy = kineticEnergy - energyOfSR;
323 
324       if(newKinEnergy > 0.)
325       {
326         aParticleChange.ProposeMomentumDirection(particleDirection);
327         aParticleChange.ProposeEnergy(newKinEnergy);
328         aParticleChange.ProposeLocalEnergyDeposit(0.);
329       }
330       else
331       {
332         aParticleChange.ProposeEnergy(0.);
333         aParticleChange.ProposeLocalEnergyDeposit(0.);
334         G4double charge = aDynamicParticle->GetDefinition()->GetPDGCharge();
335         if(charge < 0.)
336         {
337           aParticleChange.ProposeTrackStatus(fStopAndKill);
338         }
339         else
340         {
341           aParticleChange.ProposeTrackStatus(fStopButAlive);
342         }
343       }
344       
345       // Create the G4Track
346       G4Track* aSecondaryTrack = new G4Track(aGamma, trackData.GetGlobalTime(), trackData.GetPosition());
347       aSecondaryTrack->SetTouchableHandle(stepData.GetPostStepPoint()->GetTouchableHandle());
348       aSecondaryTrack->SetParentID(trackData.GetTrackID());
349       aSecondaryTrack->SetCreatorModelID(secID);
350       aParticleChange.AddSecondary(aSecondaryTrack);
351     }
352     else
353     {
354       return G4VDiscreteProcess::PostStepDoIt(trackData, stepData);
355     }
356   }
357   return G4VDiscreteProcess::PostStepDoIt(trackData, stepData);
358 }
359 
360 G4double G4SynchrotronRadiationInMat::GetPhotonEnergy(const G4Track& trackData,
361                                                       const G4Step&)
362 {
363   G4int i;
364   G4double energyOfSR = -1.0;
365 
366   const G4DynamicParticle* aDynamicParticle = trackData.GetDynamicParticle();
367 
368   G4double gamma =
369     aDynamicParticle->GetTotalEnergy() / (aDynamicParticle->GetMass());
370 
371   G4double particleCharge = aDynamicParticle->GetDefinition()->GetPDGCharge();
372 
373   G4ThreeVector FieldValue;
374   const G4Field* pField = nullptr;
375 
376   G4FieldManager* fieldMgr = nullptr;
377   G4bool fieldExertsForce  = false;
378 
379   if((particleCharge != 0.0))
380   {
381     fieldMgr = fFieldPropagator->FindAndSetFieldManager(trackData.GetVolume());
382     if(fieldMgr != nullptr)
383     {
384       // If the field manager has no field, there is no field !
385       fieldExertsForce = (fieldMgr->GetDetectorField() != nullptr);
386     }
387   }
388   if(fieldExertsForce)
389   {
390     pField                     = fieldMgr->GetDetectorField();
391     G4ThreeVector globPosition = trackData.GetPosition();
392     G4double globPosVec[3], FieldValueVec[3];
393 
394     globPosVec[0] = globPosition.x();
395     globPosVec[1] = globPosition.y();
396     globPosVec[2] = globPosition.z();
397 
398     pField->GetFieldValue(globPosVec, FieldValueVec);
399     FieldValue =
400       G4ThreeVector(FieldValueVec[0], FieldValueVec[1], FieldValueVec[2]);
401 
402     G4ThreeVector unitMomentum = aDynamicParticle->GetMomentumDirection();
403     G4ThreeVector unitMcrossB  = FieldValue.cross(unitMomentum);
404     G4double perpB             = unitMcrossB.mag();
405     if(perpB > 0.0)
406     {
407       // M-C of synchrotron photon energy
408       G4double random = G4UniformRand();
409       for(i = 0; i < 200; ++i)
410       {
411         if(random >= fIntegralProbabilityOfSR[i])
412           break;
413       }
414       energyOfSR = 0.0001 * i * i * fEnergyConst * gamma * gamma * perpB;
415 
416       // check against insufficient energy
417       if(energyOfSR <= 0.0)
418       {
419         return -1.0;
420       }
421     }
422     else
423     {
424       return -1.0;
425     }
426   }
427   return energyOfSR;
428 }
429 
430 /////////////////////////////////////////////////////////////////////////////////
431 G4double G4SynchrotronRadiationInMat::GetRandomEnergySR(G4double gamma,
432                                                         G4double perpB)
433 {
434   G4int i;
435   static constexpr G4int iMax = 200;
436   G4double energySR, random, position;
437 
438   random = G4UniformRand();
439 
440   for(i = 0; i < iMax; ++i)
441   {
442     if(random >= fIntegralProbabilityOfSR[i])
443       break;
444   }
445   if(i <= 0)
446     position = G4UniformRand();
447   else if(i >= iMax)
448     position = G4double(iMax);
449   else
450     position = i + G4UniformRand();
451 
452   energySR =
453     0.0001 * position * position * fEnergyConst * gamma * gamma * perpB;
454 
455   if(energySR < 0.)
456     energySR = 0.;
457 
458   return energySR;
459 }
460 
461 /////////////////////////////////////////////////////////////////////////
462 G4double G4SynchrotronRadiationInMat::GetProbSpectrumSRforInt(G4double t)
463 {
464   G4double result, hypCos2, hypCos = std::cosh(t);
465 
466   hypCos2 = hypCos * hypCos;
467   result = std::cosh(5. * t / 3.) * std::exp(t - fKsi * hypCos);  // fKsi > 0. !
468   result /= hypCos2;
469   return result;
470 }
471 
472 ///////////////////////////////////////////////////////////////////////////
473 // return the probability to emit SR photon with relative energy
474 // energy/energy_c >= ksi
475 // for ksi <= 0. P = 1., however the method works for ksi > 0 only!
476 G4double G4SynchrotronRadiationInMat::GetIntProbSR(G4double ksi)
477 {
478   if(ksi <= 0.)
479     return 1.0;
480   fKsi = ksi;  // should be > 0. !
481   G4int n;
482   G4double result, a;
483 
484   a = fAlpha;       // always = 0.
485   n = fRootNumber;  // around default = 80
486 
487   G4Integrator<G4SynchrotronRadiationInMat,
488                G4double (G4SynchrotronRadiationInMat::*)(G4double)>
489     integral;
490 
491   result = integral.Laguerre(
492     this, &G4SynchrotronRadiationInMat::GetProbSpectrumSRforInt, a, n);
493 
494   result *= 3. / 5. / pi;
495 
496   return result;
497 }
498 
499 /////////////////////////////////////////////////////////////////////////
500 // return an auxiliary function for K_5/3 integral representation
501 G4double G4SynchrotronRadiationInMat::GetProbSpectrumSRforEnergy(G4double t)
502 {
503   G4double result, hypCos = std::cosh(t);
504 
505   result = std::cosh(5. * t / 3.) * std::exp(t - fKsi * hypCos);  // fKsi > 0. !
506   result /= hypCos;
507   return result;
508 }
509 
510 ///////////////////////////////////////////////////////////////////////////
511 // return the probability to emit SR photon energy with relative energy
512 // energy/energy_c >= ksi
513 // for ksi <= 0. P = 1., however the method works for ksi > 0 only!
514 G4double G4SynchrotronRadiationInMat::GetEnergyProbSR(G4double ksi)
515 {
516   if(ksi <= 0.)
517     return 1.0;
518   fKsi = ksi;  // should be > 0. !
519   G4int n;
520   G4double result, a;
521 
522   a = fAlpha;       // always = 0.
523   n = fRootNumber;  // around default = 80
524 
525   G4Integrator<G4SynchrotronRadiationInMat,
526                G4double (G4SynchrotronRadiationInMat::*)(G4double)>
527     integral;
528 
529   result = integral.Laguerre(
530     this, &G4SynchrotronRadiationInMat::GetProbSpectrumSRforEnergy, a, n);
531 
532   result *= 9. * std::sqrt(3.) * ksi / 8. / pi;
533 
534   return result;
535 }
536 
537 /////////////////////////////////////////////////////////////////////////////
538 G4double G4SynchrotronRadiationInMat::GetIntegrandForAngleK(G4double t)
539 {
540   G4double result, hypCos = std::cosh(t);
541 
542   result =
543     std::cosh(fOrderAngleK * t) * std::exp(t - fEta * hypCos);  // fEta > 0. !
544   result /= hypCos;
545   return result;
546 }
547 
548 //////////////////////////////////////////////////////////////////////////
549 // Return K 1/3 or 2/3 for angular distribution
550 G4double G4SynchrotronRadiationInMat::GetAngleK(G4double eta)
551 {
552   fEta = eta;  // should be > 0. !
553   G4int n;
554   G4double result, a;
555 
556   a = fAlpha;       // always = 0.
557   n = fRootNumber;  // around default = 80
558 
559   G4Integrator<G4SynchrotronRadiationInMat,
560                G4double (G4SynchrotronRadiationInMat::*)(G4double)>
561     integral;
562 
563   result = integral.Laguerre(
564     this, &G4SynchrotronRadiationInMat::GetIntegrandForAngleK, a, n);
565 
566   return result;
567 }
568 
569 /////////////////////////////////////////////////////////////////////////
570 // Relative angle diff distribution for given fKsi, which is set externally
571 G4double G4SynchrotronRadiationInMat::GetAngleNumberAtGammaKsi(G4double gpsi)
572 {
573   G4double result, funK, funK2, gpsi2 = gpsi * gpsi;
574 
575   fPsiGamma = gpsi;
576   fEta      = 0.5 * fKsi * (1. + gpsi2) * std::sqrt(1. + gpsi2);
577 
578   fOrderAngleK = 1. / 3.;
579   funK         = GetAngleK(fEta);
580   funK2        = funK * funK;
581 
582   result = gpsi2 * funK2 / (1. + gpsi2);
583 
584   fOrderAngleK = 2. / 3.;
585   funK         = GetAngleK(fEta);
586   funK2        = funK * funK;
587 
588   result += funK2;
589   result *= (1. + gpsi2) * fKsi;
590 
591   return result;
592 }
593