G4EqEMFieldWithEDM.cc

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//
// $Id: G4EqEMFieldWithEDM.cc 69786 2013-05-15 09:38:51Z gcosmo $
//
//
//  This is the standard right-hand side for equation of motion.
//
//  19.02.2009 Kevin Lynch, based on G4EqEMFieldWithSpin
//  06.11.2009 Hiromi Iinuma see:
//  http://hypernews.slac.stanford.edu/HyperNews/geant4/get/emfields/161.html
//
// -------------------------------------------------------------------

#include "G4EqEMFieldWithEDM.hh"
#include "G4ElectroMagneticField.hh"
#include "G4ThreeVector.hh"
#include "globals.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"

G4EqEMFieldWithEDM::G4EqEMFieldWithEDM(G4ElectroMagneticField *emField )
      : G4EquationOfMotion( emField ), fElectroMagCof(0.), fMassCof(0.),
        omegac(0.), anomaly(0.0011659208), eta(0.), pcharge(0.), E(0.),
        gamma(0.), beta(0.)
{
}

G4EqEMFieldWithEDM::~G4EqEMFieldWithEDM()
{
} 

void  
G4EqEMFieldWithEDM::SetChargeMomentumMass(G4double particleCharge, // e+ units
                                            G4double MomentumXc,
                                            G4double particleMass)
{
   fElectroMagCof =  eplus*particleCharge*c_light ;
   fMassCof = particleMass*particleMass ;

   omegac = (eplus/particleMass)*c_light;

   pcharge = particleCharge;

   E = std::sqrt(sqr(MomentumXc)+sqr(particleMass));
   beta  = MomentumXc/E;
   gamma = E/particleMass;

}

void
G4EqEMFieldWithEDM::EvaluateRhsGivenB(const G4double y[],
                                       const G4double Field[],
                                             G4double dydx[] ) const
{

   // Components of y:
   //    0-2 dr/ds,
   //    3-5 dp/ds - momentum derivatives
   //    9-11 dSpin/ds = (1/beta) dSpin/dt - spin derivatives

   // The BMT equation, following J.D.Jackson, Classical
   // Electrodynamics, Second Edition, with additions for EDM
   // evolution from 
   // M.Nowakowski, et.al. Eur.J.Phys.26, pp 545-560, (2005)
   // or
   // Silenko, Phys.Rev.ST Accel.Beams 9:034003, (2006)

   // dS/dt = (e/m) S \cross 
   // MDM:         [ (g/2-1 +1/\gamma) B
   //               -(g/2-1)\gamma/(\gamma+1) (\beta \cdot B)\beta 
   //               -(g/2-\gamma/(\gamma+1) \beta \cross E 
   //
   // EDM:        eta/2( E - gamma/(gamma+1) \beta (\beta \cdot E)
   //                    + \beta \cross B ) ]
   //
   // where
   // S = \vec{s}, where S^2 = 1
   // B = \vec{B}
   // \beta = \vec{\beta} = \beta \vec{u} with u^2 = 1
   // E = \vec{E}

   G4double pSquared = y[3]*y[3] + y[4]*y[4] + y[5]*y[5] ;

   G4double Energy   = std::sqrt( pSquared + fMassCof );
   G4double cof2     = Energy/c_light ;

   G4double pModuleInverse  = 1.0/std::sqrt(pSquared) ;

   G4double inverse_velocity = Energy * pModuleInverse / c_light;

   G4double cof1     = fElectroMagCof*pModuleInverse ;

   dydx[0] = y[3]*pModuleInverse ;                         
   dydx[1] = y[4]*pModuleInverse ;                         
   dydx[2] = y[5]*pModuleInverse ;                        

   dydx[3] = cof1*(cof2*Field[3] + (y[4]*Field[2] - y[5]*Field[1])) ;
   
   dydx[4] = cof1*(cof2*Field[4] + (y[5]*Field[0] - y[3]*Field[2])) ; 
 
   dydx[5] = cof1*(cof2*Field[5] + (y[3]*Field[1] - y[4]*Field[0])) ;  
   
   dydx[6] = dydx[8] = 0.;//not used

   // Lab Time of flight
   dydx[7] = inverse_velocity;
   
   G4ThreeVector BField(Field[0],Field[1],Field[2]);
   G4ThreeVector EField(Field[3],Field[4],Field[5]);

   EField /= c_light;

   G4ThreeVector u(y[3], y[4], y[5]);
   u *= pModuleInverse;

   G4double udb = anomaly*beta*gamma/(1.+gamma) * (BField * u);
   G4double ucb = (anomaly+1./gamma)/beta;
   G4double uce = anomaly + 1./(gamma+1.);
   G4double ude = beta*gamma/(1.+gamma)*(EField*u);

   G4ThreeVector Spin(y[9],y[10],y[11]);

   G4ThreeVector dSpin
     = pcharge*omegac*( ucb*(Spin.cross(BField))-udb*(Spin.cross(u))
                               // from Jackson
                               // -uce*Spin.cross(u.cross(EField)) )
                               // but this form has one less operation
                       - uce*(u*(Spin*EField) - EField*(Spin*u))
                       + eta/2.*(Spin.cross(EField) - ude*(Spin.cross(u))
                               // +Spin.cross(u.cross(Bfield))
                       + (u*(Spin*BField) - BField*(Spin*u)) ) );
      
   dydx[ 9] = dSpin.x();
   dydx[10] = dSpin.y();
   dydx[11] = dSpin.z();

   return ;
}