G4MagHelicalStepper Class Reference

#include <G4MagHelicalStepper.hh>

Inheritance diagram for G4MagHelicalStepper:

Public Member Functions
	G4MagHelicalStepper (G4Mag_EqRhs *EqRhs)
virtual	~G4MagHelicalStepper ()
virtual void	Stepper (const G4double y[], const G4double dydx[], G4double h, G4double yout[], G4double yerr[])
virtual void	DumbStepper (const G4double y[], G4ThreeVector Bfld, G4double h, G4double yout[])=0
G4double	DistChord () const
Public Member Functions inherited from G4MagIntegratorStepper
	G4MagIntegratorStepper (G4EquationOfMotion *Equation, G4int numIntegrationVariables, G4int numStateVariables=12)
virtual	~G4MagIntegratorStepper ()
virtual void	Stepper (const G4double y[], const G4double dydx[], G4double h, G4double yout[], G4double yerr[])=0
virtual G4double	DistChord () const =0
virtual void	ComputeRightHandSide (const G4double y[], G4double dydx[])
void	NormaliseTangentVector (G4double vec[6])
void	NormalisePolarizationVector (G4double vec[12])
void	RightHandSide (const double y[], double dydx[])
G4int	GetNumberOfVariables () const
G4int	GetNumberOfStateVariables () const
virtual G4int	IntegratorOrder () const =0
G4EquationOfMotion *	GetEquationOfMotion ()
void	SetEquationOfMotion (G4EquationOfMotion *newEquation)

Protected Member Functions
void	LinearStep (const G4double yIn[], G4double h, G4double yHelix[]) const
void	AdvanceHelix (const G4double yIn[], G4ThreeVector Bfld, G4double h, G4double yHelix[], G4double yHelix2[]=0)
void	MagFieldEvaluate (const G4double y[], G4ThreeVector &Bfield)
G4double	GetInverseCurve (const G4double Momentum, const G4double Bmag)
void	SetAngCurve (const G4double Ang)
G4double	GetAngCurve () const
void	SetCurve (const G4double Curve)
G4double	GetCurve () const
void	SetRadHelix (const G4double Rad)
G4double	GetRadHelix () const

Detailed Description

Definition at line 53 of file G4MagHelicalStepper.hh.

Constructor & Destructor Documentation

G4MagHelicalStepper()

G4MagHelicalStepper::G4MagHelicalStepper

(

G4Mag_EqRhs *

EqRhs

)

Definition at line 47 of file G4MagHelicalStepper.cc.

   : G4MagIntegratorStepper(EqRhs, 6), // integrate over 6 variables only !!
                                       // position & velocity
     fPtrMagEqOfMot(EqRhs), fAngCurve(0.), frCurve(0.), frHelix(0.)
{
}

~G4MagHelicalStepper()

G4MagHelicalStepper::~G4MagHelicalStepper ( )

virtual

Definition at line 54 of file G4MagHelicalStepper.cc.

{
}

Member Function Documentation

AdvanceHelix()

void G4MagHelicalStepper::AdvanceHelix ( const G4double  yIn[], G4ThreeVector  Bfld, G4double  h, G4double  yHelix[], G4double  yHelix2[] = 0  )

protected

Definition at line 59 of file G4MagHelicalStepper.cc.

{
  // const G4int    nvar = 6;
 
  // OLD  const G4double approc_limit = 0.05;
  // OLD  approc_limit = 0.05 gives max.error=x^5/5!=(0.05)^5/5!=2.6*e-9
  // NEW  approc_limit = 0.005 gives max.error=x^5/5!=2.6*e-14
 
  const G4double approc_limit = 0.005;
  G4ThreeVector  Bnorm, B_x_P, vperp, vpar;
 
  G4double B_d_P;
  G4double B_v_P;
  G4double Theta;
  G4double R_1;
  G4double R_Helix;
  G4double CosT2, SinT2, CosT, SinT;
  G4ThreeVector positionMove, endTangent;
 
  G4double Bmag = Bfld.mag();
  const G4double *pIn = yIn+3;
  G4ThreeVector initVelocity= G4ThreeVector( pIn[0], pIn[1], pIn[2]);
  G4double      velocityVal = initVelocity.mag();
  G4ThreeVector initTangent = (1.0/velocityVal) * initVelocity;
  
  R_1=GetInverseCurve(velocityVal,Bmag);
 
  // for too small magnetic fields there is no curvature
  // (include momentum here) FIXME
 
  if( (std::fabs(R_1) < 1e-10)||(Bmag<1e-12) )
  {
    LinearStep( yIn, h, yHelix );
 
    // Store and/or calculate parameters for chord distance
 
    SetAngCurve(1.);     
    SetCurve(h);
    SetRadHelix(0.);
  }
  else
  {
    Bnorm = (1.0/Bmag)*Bfld;
 
    // calculate the direction of the force
    
    B_x_P = Bnorm.cross(initTangent);
 
    // parallel and perp vectors
 
    B_d_P = Bnorm.dot(initTangent); // this is the fraction of P parallel to B
 
    vpar = B_d_P * Bnorm;       // the component parallel      to B
    vperp= initTangent - vpar;  // the component perpendicular to B
    
    B_v_P  = std::sqrt( 1 - B_d_P * B_d_P); // Fraction of P perp to B
 
    // calculate  the stepping angle
  
    Theta   = R_1 * h; // * B_v_P;
 
    // Trigonometrix
      
    if( std::fabs(Theta) > approc_limit )
    {
       SinT     = std::sin(Theta);
       CosT     = std::cos(Theta);
    }
    else
    {
      G4double Theta2 = Theta*Theta;
      G4double Theta3 = Theta2 * Theta;
      G4double Theta4 = Theta2 * Theta2;
      SinT     = Theta - 1.0/6.0 * Theta3;
      CosT     = 1 - 0.5 * Theta2 + 1.0/24.0 * Theta4;
    }
 
    // the actual "rotation"
 
    G4double R = 1.0 / R_1;
 
    positionMove  = R * ( SinT * vperp + (1-CosT) * B_x_P) + h * vpar;
    endTangent    = CosT * vperp + SinT * B_x_P + vpar;
 
    // Store the resulting position and tangent
 
    yHelix[0]   = yIn[0] + positionMove.x(); 
    yHelix[1]   = yIn[1] + positionMove.y(); 
    yHelix[2]   = yIn[2] + positionMove.z();
    yHelix[3] = velocityVal * endTangent.x();
    yHelix[4] = velocityVal * endTangent.y();
    yHelix[5] = velocityVal * endTangent.z();
 
    // Store 2*h step Helix if exist
 
    if(yHelix2)
    {
      SinT2     = 2.0 * SinT * CosT;
      CosT2     = 1.0 - 2.0 * SinT * SinT;
      endTangent    = (CosT2 * vperp + SinT2 * B_x_P + vpar);
      positionMove  = R * ( SinT2 * vperp + (1-CosT2) * B_x_P) + h*2 * vpar;
      
      yHelix2[0]   = yIn[0] + positionMove.x(); 
      yHelix2[1]   = yIn[1] + positionMove.y(); 
      yHelix2[2]   = yIn[2] + positionMove.z(); 
      yHelix2[3] = velocityVal * endTangent.x();
      yHelix2[4] = velocityVal * endTangent.y();
      yHelix2[5] = velocityVal * endTangent.z();
    }
 
    // Store and/or calculate parameters for chord distance
 
    G4double ptan=velocityVal*B_v_P;
 
    G4double particleCharge = fPtrMagEqOfMot->FCof() / (eplus*c_light); 
    R_Helix =std::abs( ptan/(fUnitConstant  * particleCharge*Bmag));
       
    SetAngCurve(std::abs(Theta));
    SetCurve(std::abs(R));
    SetRadHelix(R_Helix);
  }
}

Referenced by G4ExactHelixStepper::DumbStepper(), G4HelixExplicitEuler::DumbStepper(), G4HelixHeum::DumbStepper(), G4HelixImplicitEuler::DumbStepper(), G4HelixMixedStepper::DumbStepper(), G4HelixSimpleRunge::DumbStepper(), G4HelixExplicitEuler::Stepper(), G4ExactHelixStepper::Stepper(), and G4HelixMixedStepper::Stepper().

DistChord()

G4double G4MagHelicalStepper::DistChord ( ) const

virtual

Implements G4MagIntegratorStepper.

Definition at line 238 of file G4MagHelicalStepper.cc.

{
  // Check whether h/R >  pi  !!
  // Method DistLine is good only for <  pi
 
  G4double Ang=GetAngCurve();
  if(Ang<=pi)
  {
    return GetRadHelix()*(1-std::cos(0.5*Ang));
  }
  else
  {
    if(Ang<twopi)
    {
      return GetRadHelix()*(1+std::cos(0.5*(twopi-Ang)));
    }
    else  // return Diameter of projected circle
    {
      return 2*GetRadHelix();
    }
  }
}

DumbStepper()

virtual void G4MagHelicalStepper::DumbStepper ( const G4double  y[], G4ThreeVector  Bfld, G4double  h, G4double  yout[]  )

pure virtual

Implemented in G4ExactHelixStepper, G4HelixExplicitEuler, G4HelixHeum, G4HelixImplicitEuler, G4HelixMixedStepper, and G4HelixSimpleRunge.

Referenced by Stepper().

GetAngCurve()

G4double G4MagHelicalStepper::GetAngCurve ( ) const

inlineprotected

Referenced by G4ExactHelixStepper::DistChord(), G4HelixExplicitEuler::DistChord(), G4HelixMixedStepper::DistChord(), and DistChord().

GetCurve()

G4double G4MagHelicalStepper::GetCurve ( ) const

inlineprotected

GetInverseCurve()

G4double G4MagHelicalStepper::GetInverseCurve ( const G4double  Momentum, const G4double  Bmag  )

inlineprotected

Referenced by AdvanceHelix(), and G4HelixMixedStepper::Stepper().

GetRadHelix()

G4double G4MagHelicalStepper::GetRadHelix ( ) const

inlineprotected

Referenced by G4ExactHelixStepper::DistChord(), G4HelixExplicitEuler::DistChord(), G4HelixMixedStepper::DistChord(), and DistChord().

LinearStep()

void G4MagHelicalStepper::LinearStep ( const G4double  yIn[], G4double  h, G4double  yHelix[]  ) const

inlineprotected

Referenced by AdvanceHelix().

MagFieldEvaluate()

void G4MagHelicalStepper::MagFieldEvaluate ( const G4double  y[], G4ThreeVector &  Bfield  )

inlineprotected

Referenced by G4HelixHeum::DumbStepper(), G4HelixImplicitEuler::DumbStepper(), G4HelixSimpleRunge::DumbStepper(), G4HelixExplicitEuler::Stepper(), G4ExactHelixStepper::Stepper(), G4HelixMixedStepper::Stepper(), and Stepper().

SetAngCurve()

void G4MagHelicalStepper::SetAngCurve ( const G4double  Ang )

inlineprotected

Referenced by AdvanceHelix(), and G4HelixMixedStepper::Stepper().

SetCurve()

void G4MagHelicalStepper::SetCurve ( const G4double  Curve )

inlineprotected

Referenced by AdvanceHelix(), and G4HelixMixedStepper::Stepper().

SetRadHelix()

void G4MagHelicalStepper::SetRadHelix ( const G4double  Rad )

inlineprotected

Referenced by AdvanceHelix().

Stepper()

void G4MagHelicalStepper::Stepper ( const G4double  y[], const G4double  dydx[], G4double  h, G4double  yout[], G4double  yerr[]  )

virtual

Implements G4MagIntegratorStepper.

Reimplemented in G4ExactHelixStepper, and G4HelixMixedStepper.

Definition at line 192 of file G4MagHelicalStepper.cc.

{  
   const G4int nvar = 6;
 
   G4int i;
 
   // correction for Richardson Extrapolation.
   // G4double  correction = 1. / ( (1 << IntegratorOrder()) -1 );
   
   G4double      yTemp[7], yIn[7] ;
   G4ThreeVector Bfld_initial, Bfld_midpoint;
   
   //  Saving yInput because yInput and yOut can be aliases for same array
 
   for(i=0;i<nvar;i++) { yIn[i]=yInput[i]; }
 
   G4double h = hstep * 0.5; 
 
   MagFieldEvaluate(yIn, Bfld_initial) ;      
 
   // Do two half steps
 
   DumbStepper(yIn,   Bfld_initial,  h, yTemp);
   MagFieldEvaluate(yTemp, Bfld_midpoint) ;     
   DumbStepper(yTemp, Bfld_midpoint, h, yOut); 
 
   // Do a full Step
 
   h = hstep ;
   DumbStepper(yIn, Bfld_initial, h, yTemp);
 
   // Error estimation
 
   for(i=0;i<nvar;i++)
   {
     yErr[i] = yOut[i] - yTemp[i] ;
   }
   
   return;
}

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The documentation for this class was generated from the following files:

• G4MagHelicalStepper.hh
• G4MagHelicalStepper.cc