G4SynchrotronRadiationInMat.cc

Go to the documentation of this file.

//
// ********************************************************************
// * License and Disclaimer                                           *
// *                                                                  *
// * The  Geant4 software  is  copyright of the Copyright Holders  of *
// * the Geant4 Collaboration.  It is provided  under  the terms  and *
// * conditions of the Geant4 Software License,  included in the file *
// * LICENSE and available at  http://cern.ch/geant4/license .  These *
// * include a list of copyright holders.                             *
// *                                                                  *
// * Neither the authors of this software system, nor their employing *
// * institutes,nor the agencies providing financial support for this *
// * work  make  any representation or  warranty, express or implied, *
// * regarding  this  software system or assume any liability for its *
// * use.  Please see the license in the file  LICENSE  and URL above *
// * for the full disclaimer and the limitation of liability.         *
// *                                                                  *
// * This  code  implementation is the result of  the  scientific and *
// * technical work of the GEANT4 collaboration.                      *
// * By using,  copying,  modifying or  distributing the software (or *
// * any work based  on the software)  you  agree  to acknowledge its *
// * use  in  resulting  scientific  publications,  and indicate your *
// * acceptance of all terms of the Geant4 Software license.          *
// ********************************************************************
//
//
// $Id: G4SynchrotronRadiationInMat.cc 97385 2016-06-02 09:59:53Z gcosmo $
//
// --------------------------------------------------------------
//      GEANT 4 class implementation file
//      CERN Geneva Switzerland
//
//      History: first implementation,
//      21-5-98 V.Grichine
//      28-05-01, V.Ivanchenko minor changes to provide ANSI -wall compilation
//      04.03.05, V.Grichine: get local field interface
//      19-05-06, V.Ivanchenko rename from G4SynchrotronRadiation
//
//

#include "G4SynchrotronRadiationInMat.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4Integrator.hh"
#include "G4EmProcessSubType.hh"

//
// Constant for calculation of mean free path
//

const G4double
G4SynchrotronRadiationInMat::fLambdaConst = std::sqrt(3.0)*electron_mass_c2/
                                       (2.5*fine_structure_const*eplus*c_light) ;

//
// Constant for calculation of characterictic energy
//

const G4double
G4SynchrotronRadiationInMat::fEnergyConst = 1.5*c_light*c_light*eplus*hbar_Planck/
                                       electron_mass_c2  ;

//
// Array of integral probability of synchrotron photons:
//
// the corresponding energy = 0.0001*i*i*(characteristic energy)
//

const G4double
G4SynchrotronRadiationInMat::fIntegralProbabilityOfSR[200] =
{
  1.000000e+00, 9.428859e-01,   9.094095e-01,   8.813971e-01,   8.565154e-01,
  8.337008e-01, 8.124961e-01,   7.925217e-01,   7.735517e-01,   7.554561e-01,
  7.381233e-01, 7.214521e-01,   7.053634e-01,   6.898006e-01,   6.747219e-01,
  6.600922e-01, 6.458793e-01,   6.320533e-01,   6.185872e-01,   6.054579e-01,
  5.926459e-01, 5.801347e-01,   5.679103e-01,   5.559604e-01,   5.442736e-01,
  5.328395e-01, 5.216482e-01,   5.106904e-01,   4.999575e-01,   4.894415e-01,
  4.791351e-01, 4.690316e-01,   4.591249e-01,   4.494094e-01,   4.398800e-01,
  4.305320e-01, 4.213608e-01,   4.123623e-01,   4.035325e-01,   3.948676e-01,
  3.863639e-01, 3.780179e-01,   3.698262e-01,   3.617858e-01,   3.538933e-01,
  3.461460e-01, 3.385411e-01,   3.310757e-01,   3.237474e-01,   3.165536e-01,
  3.094921e-01, 3.025605e-01,   2.957566e-01,   2.890784e-01,   2.825237e-01,
  2.760907e-01, 2.697773e-01,   2.635817e-01,   2.575020e-01,   2.515365e-01,
  2.456834e-01, 2.399409e-01,   2.343074e-01,   2.287812e-01,   2.233607e-01,
  2.180442e-01, 2.128303e-01,   2.077174e-01,   2.027040e-01,   1.977885e-01,
  1.929696e-01, 1.882457e-01,   1.836155e-01,   1.790775e-01,   1.746305e-01,
  1.702730e-01, 1.660036e-01,   1.618212e-01,   1.577243e-01,   1.537117e-01,
  1.497822e-01, 1.459344e-01,   1.421671e-01,   1.384791e-01,   1.348691e-01,
  1.313360e-01, 1.278785e-01,   1.244956e-01,   1.211859e-01,   1.179483e-01,
  1.147818e-01, 1.116850e-01,   1.086570e-01,   1.056966e-01,   1.028026e-01,
  9.997405e-02, 9.720975e-02,   9.450865e-02,   9.186969e-02,   8.929179e-02,
  8.677391e-02, 8.431501e-02,   8.191406e-02,   7.957003e-02,   7.728192e-02,
  7.504872e-02, 7.286944e-02,   7.074311e-02,   6.866874e-02,   6.664538e-02,
  6.467208e-02, 6.274790e-02,   6.087191e-02,   5.904317e-02,   5.726079e-02,
  5.552387e-02, 5.383150e-02,   5.218282e-02,   5.057695e-02,   4.901302e-02,
  4.749020e-02, 4.600763e-02,   4.456450e-02,   4.315997e-02,   4.179325e-02,
  4.046353e-02, 3.917002e-02,   3.791195e-02,   3.668855e-02,   3.549906e-02,
  3.434274e-02, 3.321884e-02,   3.212665e-02,   3.106544e-02,   3.003452e-02,
  2.903319e-02, 2.806076e-02,   2.711656e-02,   2.619993e-02,   2.531021e-02,
  2.444677e-02, 2.360897e-02,   2.279620e-02,   2.200783e-02,   2.124327e-02,
  2.050194e-02, 1.978324e-02,   1.908662e-02,   1.841151e-02,   1.775735e-02,
  1.712363e-02, 1.650979e-02,   1.591533e-02,   1.533973e-02,   1.478250e-02,
  1.424314e-02, 1.372117e-02,   1.321613e-02,   1.272755e-02,   1.225498e-02,
  1.179798e-02, 1.135611e-02,   1.092896e-02,   1.051609e-02,   1.011712e-02,
  9.731635e-03, 9.359254e-03,   8.999595e-03,   8.652287e-03,   8.316967e-03,
  7.993280e-03, 7.680879e-03,   7.379426e-03,   7.088591e-03,   6.808051e-03,
  6.537491e-03, 6.276605e-03,   6.025092e-03,   5.782661e-03,   5.549027e-03,
  5.323912e-03, 5.107045e-03,   4.898164e-03,   4.697011e-03,   4.503336e-03,
  4.316896e-03, 4.137454e-03,   3.964780e-03,   3.798649e-03,   3.638843e-03,
  3.485150e-03, 3.337364e-03,   3.195284e-03,   3.058715e-03,   2.927469e-03,
  2.801361e-03, 2.680213e-03,   2.563852e-03,   2.452110e-03,   2.344824e-03
};
 
//
//  Constructor
//

G4SynchrotronRadiationInMat::G4SynchrotronRadiationInMat(const G4String& processName,
  G4ProcessType type):G4VDiscreteProcess (processName, type),
  LowestKineticEnergy (10.*keV),
  //HighestKineticEnergy (100.*TeV),
  //TotBin(200),
  theGamma (G4Gamma::Gamma() ),
  theElectron ( G4Electron::Electron() ),
  thePositron ( G4Positron::Positron() ), 
  //GammaCutInKineticEnergy(nullptr),
  //ElectronCutInKineticEnergy(nullptr),
  //PositronCutInKineticEnergy(nullptr),
  //ParticleCutInKineticEnergy(nullptr),
  fAlpha(0.0), fRootNumber(80),
  fVerboseLevel( verboseLevel )
{
  G4TransportationManager* transportMgr = G4TransportationManager::GetTransportationManager();

  fFieldPropagator = transportMgr->GetPropagatorInField();
  SetProcessSubType(fSynchrotronRadiation);
  CutInRange = GammaCutInKineticEnergyNow = ElectronCutInKineticEnergyNow = 
    PositronCutInKineticEnergyNow =  ParticleCutInKineticEnergyNow = fKsi = 
    fPsiGamma = fEta = fOrderAngleK = 0.0;
}
 
//
// Destructor
//
 
G4SynchrotronRadiationInMat::~G4SynchrotronRadiationInMat()
{}
 

G4bool
G4SynchrotronRadiationInMat::IsApplicable( const G4ParticleDefinition& particle )
{

  return ( ( &particle == (const G4ParticleDefinition *)theElectron ) ||
       ( &particle == (const G4ParticleDefinition *)thePositron )    );

}
 
//
//
// Production of synchrotron X-ray photon
// GEANT4 internal units.
//


G4double 
G4SynchrotronRadiationInMat::GetMeanFreePath( const G4Track& trackData,
                                               G4double,
                                               G4ForceCondition* condition)
{
  // gives the MeanFreePath in GEANT4 internal units
  G4double MeanFreePath;

  const G4DynamicParticle* aDynamicParticle = trackData.GetDynamicParticle();
  // G4Material* aMaterial = trackData.GetMaterial();

  //G4bool isOutRange ;
 
  *condition = NotForced ;

  G4double gamma = aDynamicParticle->GetTotalEnergy()/
                   aDynamicParticle->GetMass();

  G4double particleCharge = aDynamicParticle->GetDefinition()->GetPDGCharge();

  G4double KineticEnergy = aDynamicParticle->GetKineticEnergy();

  if ( KineticEnergy <  LowestKineticEnergy || gamma < 1.0e3 )  MeanFreePath = DBL_MAX; 
  else
  {

    G4ThreeVector  FieldValue;
    const G4Field*   pField = nullptr;

    G4FieldManager* fieldMgr=nullptr;
    G4bool          fieldExertsForce = false;

    if( (particleCharge != 0.0) )
    {
      fieldMgr = fFieldPropagator->FindAndSetFieldManager( trackData.GetVolume() );

      if ( fieldMgr != nullptr ) 
      {
        // If the field manager has no field, there is no field !

        fieldExertsForce = ( fieldMgr->GetDetectorField() != nullptr );
      }
    }
    if ( fieldExertsForce )
    {  
      pField = fieldMgr->GetDetectorField() ;
      G4ThreeVector  globPosition = trackData.GetPosition();

      G4double  globPosVec[4], FieldValueVec[6];

      globPosVec[0] = globPosition.x();
      globPosVec[1] = globPosition.y();
      globPosVec[2] = globPosition.z();
      globPosVec[3] = trackData.GetGlobalTime();

      pField->GetFieldValue( globPosVec, FieldValueVec );

      FieldValue = G4ThreeVector( FieldValueVec[0], 
                                   FieldValueVec[1], 
                                   FieldValueVec[2]   );

       

      G4ThreeVector unitMomentum = aDynamicParticle->GetMomentumDirection(); 
      G4ThreeVector unitMcrossB  = FieldValue.cross(unitMomentum) ;
      G4double perpB             = unitMcrossB.mag() ;
      G4double beta              = aDynamicParticle->GetTotalMomentum()/
                                   (aDynamicParticle->GetTotalEnergy()    );

      if( perpB > 0.0 ) MeanFreePath = fLambdaConst*beta/perpB;
      else              MeanFreePath = DBL_MAX;       
    }
    else  MeanFreePath = DBL_MAX;    
  }
  if(fVerboseLevel > 0)
  {
    G4cout<<"G4SynchrotronRadiationInMat::MeanFreePath = "<<MeanFreePath/m<<" m"<<G4endl;
  }
  return MeanFreePath; 
} 

//
//

G4VParticleChange*
G4SynchrotronRadiationInMat::PostStepDoIt(const G4Track& trackData,
                                     const G4Step&  stepData      )

{
  aParticleChange.Initialize(trackData);

  const G4DynamicParticle* aDynamicParticle=trackData.GetDynamicParticle();

  G4double gamma = aDynamicParticle->GetTotalEnergy()/
                   (aDynamicParticle->GetMass()              );

  if(gamma <= 1.0e3 ) 
  {
    return G4VDiscreteProcess::PostStepDoIt(trackData,stepData);
  }
  G4double particleCharge = aDynamicParticle->GetDefinition()->GetPDGCharge();

  G4ThreeVector  FieldValue;
  const G4Field*   pField = nullptr ;

  G4FieldManager* fieldMgr=nullptr;
  G4bool          fieldExertsForce = false;

  if( (particleCharge != 0.0) )
  {
    fieldMgr = fFieldPropagator->FindAndSetFieldManager( trackData.GetVolume() );
    if ( fieldMgr != nullptr ) 
    {
      // If the field manager has no field, there is no field !

      fieldExertsForce = ( fieldMgr->GetDetectorField() != nullptr );
    }
  }
  if ( fieldExertsForce )
  {
    pField = fieldMgr->GetDetectorField() ;
    G4ThreeVector  globPosition = trackData.GetPosition() ;
    G4double  globPosVec[4], FieldValueVec[6] ;
    globPosVec[0] = globPosition.x() ;
    globPosVec[1] = globPosition.y() ;
    globPosVec[2] = globPosition.z() ;
    globPosVec[3] = trackData.GetGlobalTime();

    pField->GetFieldValue( globPosVec, FieldValueVec ) ;
    FieldValue = G4ThreeVector( FieldValueVec[0], 
                                   FieldValueVec[1], 
                                   FieldValueVec[2]   );
       
    G4ThreeVector unitMomentum = aDynamicParticle->GetMomentumDirection(); 
    G4ThreeVector unitMcrossB = FieldValue.cross(unitMomentum);
    G4double perpB = unitMcrossB.mag() ;
    if(perpB > 0.0)
    {
      // M-C of synchrotron photon energy

      G4double energyOfSR = GetRandomEnergySR(gamma,perpB);

      if(fVerboseLevel > 0)
      {
        G4cout<<"SR photon energy = "<<energyOfSR/keV<<" keV"<<G4endl;
      }
      // check against insufficient energy

      if( energyOfSR <= 0.0 )
      {
        return G4VDiscreteProcess::PostStepDoIt(trackData,stepData);
      }
      G4double kineticEnergy = aDynamicParticle->GetKineticEnergy();
      G4ParticleMomentum 
      particleDirection = aDynamicParticle->GetMomentumDirection();

      // M-C of its direction, simplified dipole busted approach
      
      // G4double Teta = G4UniformRand()/gamma ;    // Very roughly

      G4double cosTheta, sinTheta, fcos, beta;

  do
  { 
    cosTheta = 1. - 2.*G4UniformRand();
    fcos     = (1 + cosTheta*cosTheta)*0.5;
  }
  // Loop checking, 07-Aug-2015, Vladimir Ivanchenko
  while( fcos < G4UniformRand() );

  beta = std::sqrt(1. - 1./(gamma*gamma));

  cosTheta = (cosTheta + beta)/(1. + beta*cosTheta);

  if( cosTheta >  1. ) cosTheta =  1.;
  if( cosTheta < -1. ) cosTheta = -1.;

  sinTheta = std::sqrt(1. - cosTheta*cosTheta );

      G4double Phi  = twopi * G4UniformRand() ;

      G4double dirx = sinTheta*std::cos(Phi) , 
               diry = sinTheta*std::sin(Phi) , 
               dirz = cosTheta;

      G4ThreeVector gammaDirection ( dirx, diry, dirz);
      gammaDirection.rotateUz(particleDirection);   
 
      // polarization of new gamma

      // G4double sx =  std::cos(Teta)*std::cos(Phi);
      // G4double sy =  std::cos(Teta)*std::sin(Phi);
      // G4double sz = -std::sin(Teta);

      G4ThreeVector gammaPolarization = FieldValue.cross(gammaDirection);
      gammaPolarization = gammaPolarization.unit();

      // (sx, sy, sz);
      // gammaPolarization.rotateUz(particleDirection);

      // create G4DynamicParticle object for the SR photon
 
      G4DynamicParticle* aGamma= new G4DynamicParticle ( G4Gamma::Gamma(),
                                                         gammaDirection, 
                                                         energyOfSR      );
      aGamma->SetPolarization( gammaPolarization.x(),
                               gammaPolarization.y(),
                               gammaPolarization.z() );


      aParticleChange.SetNumberOfSecondaries(1);
      aParticleChange.AddSecondary(aGamma); 

      // Update the incident particle 
   
      G4double newKinEnergy = kineticEnergy - energyOfSR ;
      
      if (newKinEnergy > 0.)
      {
        aParticleChange.ProposeMomentumDirection( particleDirection );
        aParticleChange.ProposeEnergy( newKinEnergy );
        aParticleChange.ProposeLocalEnergyDeposit (0.); 
      } 
      else
      { 
        aParticleChange.ProposeEnergy( 0. );
        aParticleChange.ProposeLocalEnergyDeposit (0.);
        G4double charge = aDynamicParticle->GetDefinition()->GetPDGCharge();   
        if (charge<0.)
        {
           aParticleChange.ProposeTrackStatus(fStopAndKill) ;
    }
        else      
        {
          aParticleChange.ProposeTrackStatus(fStopButAlive) ;
    }
      } 
    }       
    else
    {
      return G4VDiscreteProcess::PostStepDoIt(trackData,stepData);
    }
  }     
  return G4VDiscreteProcess::PostStepDoIt(trackData,stepData);
}


G4double 
G4SynchrotronRadiationInMat::GetPhotonEnergy( const G4Track& trackData,
                                         const G4Step&  )

{
  G4int i ;
  G4double energyOfSR = -1.0 ;
  //G4Material* aMaterial=trackData.GetMaterial() ;

  const G4DynamicParticle* aDynamicParticle=trackData.GetDynamicParticle();

  G4double gamma = aDynamicParticle->GetTotalEnergy()/
                   (aDynamicParticle->GetMass()              ) ;

  G4double particleCharge = aDynamicParticle->GetDefinition()->GetPDGCharge();

  G4ThreeVector  FieldValue;
  const G4Field*   pField = nullptr ;

  G4FieldManager* fieldMgr=nullptr;
  G4bool          fieldExertsForce = false;

  if( (particleCharge != 0.0) )
  {
    fieldMgr = fFieldPropagator->FindAndSetFieldManager( trackData.GetVolume() );
    if ( fieldMgr != nullptr ) 
    {
      // If the field manager has no field, there is no field !

      fieldExertsForce = ( fieldMgr->GetDetectorField() != 0 );
    }
  }
  if ( fieldExertsForce )
  {  
    pField = fieldMgr->GetDetectorField();
    G4ThreeVector  globPosition = trackData.GetPosition();
    G4double  globPosVec[3], FieldValueVec[3];

    globPosVec[0] = globPosition.x();
    globPosVec[1] = globPosition.y();
    globPosVec[2] = globPosition.z();

    pField->GetFieldValue( globPosVec, FieldValueVec );
    FieldValue = G4ThreeVector( FieldValueVec[0], 
                                   FieldValueVec[1], 
                                   FieldValueVec[2]   );
       
    G4ThreeVector unitMomentum = aDynamicParticle->GetMomentumDirection(); 
    G4ThreeVector unitMcrossB  = FieldValue.cross(unitMomentum) ;
    G4double perpB             = unitMcrossB.mag();
    if( perpB > 0.0 )
    {
      // M-C of synchrotron photon energy

      G4double random = G4UniformRand() ;
      for(i=0;i<200;i++)
      {
        if(random >= fIntegralProbabilityOfSR[i]) break ;
      }
      energyOfSR = 0.0001*i*i*fEnergyConst*gamma*gamma*perpB ;

      // check against insufficient energy

      if(energyOfSR <= 0.0)
      {
        return -1.0 ;
      }
      //G4double kineticEnergy = aDynamicParticle->GetKineticEnergy();
      //G4ParticleMomentum 
      //particleDirection = aDynamicParticle->GetMomentumDirection();

      // Gamma production cut in this material
      //G4double 
      //gammaEnergyCut = (G4Gamma::GetCutsInEnergy())[aMaterial->GetIndex()];

      // SR photon has energy more than the current material cut
      // M-C of its direction
      
      //G4double Teta = G4UniformRand()/gamma ;    // Very roughly

      //G4double Phi  = twopi * G4UniformRand() ;
    }       
    else
    {
      return -1.0 ;
    }
  }     
  return energyOfSR ;
}

//
//

G4double G4SynchrotronRadiationInMat::GetRandomEnergySR(G4double gamma, G4double perpB)
{
  G4int i, iMax;
  G4double energySR, random, position;

  iMax = 200;
  random = G4UniformRand();

  for( i = 0; i < iMax; i++ )
  {
    if( random >= fIntegralProbabilityOfSR[i] ) break;
  }
  if(i <= 0 )        position = G4UniformRand(); // 0.
  else if( i>= iMax) position = G4double(iMax);
  else position = i + G4UniformRand(); // -1
  // 
  // it was in initial implementation:
  //       energyOfSR = 0.0001*i*i*fEnergyConst*gamma*gamma*perpB ;

  energySR = 0.0001*position*position*fEnergyConst*gamma*gamma*perpB;

  if( energySR  < 0. ) energySR = 0.;

  return energySR;
}

//
// return

G4double G4SynchrotronRadiationInMat::GetProbSpectrumSRforInt( G4double t)
{
  G4double result, hypCos2, hypCos=std::cosh(t);

  hypCos2 = hypCos*hypCos;  
  result = std::cosh(5.*t/3.)*std::exp(t-fKsi*hypCos); // fKsi > 0. !
  result /= hypCos2;
  return result;
}

//
// return the probability to emit SR photon with relative energy
// energy/energy_c >= ksi
// for ksi <= 0. P = 1., however the method works for ksi > 0 only!

G4double G4SynchrotronRadiationInMat::GetIntProbSR( G4double ksi)
{
  if (ksi <= 0.) return 1.0;
  fKsi = ksi; // should be > 0. !
  G4int n;
  G4double result, a;

  a = fAlpha;        // always = 0.
  n = fRootNumber;   // around default = 80

  G4Integrator<G4SynchrotronRadiationInMat, G4double(G4SynchrotronRadiationInMat::*)(G4double)> integral;

  result = integral.Laguerre(this, 
           &G4SynchrotronRadiationInMat::GetProbSpectrumSRforInt, a, n);

  result *= 3./5./pi;

  return result;
}

//
// return an auxiliary function for K_5/3 integral representation

G4double G4SynchrotronRadiationInMat::GetProbSpectrumSRforEnergy( G4double t)
{
  G4double result, hypCos=std::cosh(t);
  
  result = std::cosh(5.*t/3.)*std::exp(t - fKsi*hypCos); // fKsi > 0. !
  result /= hypCos;
  return result;
}

//
// return the probability to emit SR photon energy with relative energy
// energy/energy_c >= ksi
// for ksi <= 0. P = 1., however the method works for ksi > 0 only!

G4double G4SynchrotronRadiationInMat::GetEnergyProbSR( G4double ksi)
{
  if (ksi <= 0.) return 1.0;
  fKsi = ksi; // should be > 0. !
  G4int n;
  G4double result, a;

  a = fAlpha;        // always = 0.
  n = fRootNumber;   // around default = 80

  G4Integrator<G4SynchrotronRadiationInMat, G4double(G4SynchrotronRadiationInMat::*)(G4double)> integral;

  result = integral.Laguerre(this, 
           &G4SynchrotronRadiationInMat::GetProbSpectrumSRforEnergy, a, n);

  result *= 9.*std::sqrt(3.)*ksi/8./pi;

  return result;
}

//
// 

G4double G4SynchrotronRadiationInMat::GetIntegrandForAngleK( G4double t)
{
  G4double result, hypCos=std::cosh(t);
  
  result  = std::cosh(fOrderAngleK*t)*std::exp(t - fEta*hypCos); // fEta > 0. !
  result /= hypCos;
  return result;
}

//
// Return K 1/3 or 2/3 for angular distribution

G4double G4SynchrotronRadiationInMat::GetAngleK( G4double eta)
{
  fEta = eta; // should be > 0. !
  G4int n;
  G4double result, a;

  a = fAlpha;        // always = 0.
  n = fRootNumber;   // around default = 80

  G4Integrator<G4SynchrotronRadiationInMat, G4double(G4SynchrotronRadiationInMat::*)(G4double)> integral;

  result = integral.Laguerre(this, 
           &G4SynchrotronRadiationInMat::GetIntegrandForAngleK, a, n);

  return result;
}

//
// Relative angle diff distribution for given fKsi, which is set externally

G4double G4SynchrotronRadiationInMat::GetAngleNumberAtGammaKsi( G4double gpsi)
{
  G4double result, funK, funK2, gpsi2 = gpsi*gpsi;

  fPsiGamma    = gpsi;
  fEta         = 0.5*fKsi*(1. + gpsi2)*std::sqrt(1. + gpsi2);
 
  fOrderAngleK = 1./3.;
  funK         = GetAngleK(fEta); 
  funK2        = funK*funK;

  result       = gpsi2*funK2/(1. + gpsi2);

  fOrderAngleK = 2./3.;
  funK         = GetAngleK(fEta); 
  funK2        = funK*funK;

  result      += funK2;
  result      *= (1. + gpsi2)*fKsi;
     
  return result;
}