G4MagHelicalStepper.cc

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//
// G4MagHelicalStepper implementation
//
// Given a purely magnetic field a better approach than adding a straight line
// (as in the normal runge-kutta-methods) is to add helix segments to the
// current position
//
// Created: J.Apostolakis, CERN - 05.11.1998
// --------------------------------------------------------------------
 
#include "G4MagHelicalStepper.hh"
#include "G4PhysicalConstants.hh"
#include "G4SystemOfUnits.hh"
#include "G4LineSection.hh"
#include "G4Mag_EqRhs.hh"
 
// Constant for determining unit conversion when using normal as integrand.
//
const G4double G4MagHelicalStepper::fUnitConstant = 0.299792458*(GeV/(tesla*m));
 
G4MagHelicalStepper::G4MagHelicalStepper(G4Mag_EqRhs *EqRhs)
   : G4MagIntegratorStepper(EqRhs, 6), // integrate over 6 variables only !!
                                       // position & velocity
     fPtrMagEqOfMot(EqRhs)
{
}
 
G4MagHelicalStepper::~G4MagHelicalStepper()
{
}
 
void
G4MagHelicalStepper::AdvanceHelix( const G4double yIn[],
                                         G4ThreeVector Bfld,    
                                         G4double h,
                                         G4double yHelix[],
                                         G4double yHelix2[] )
{
  // 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);
  }
}
 
// Use the midpoint method to get an error estimate and correction
// modified from G4ClassicalRK4: W.Wander <wwc@mit.edu> 12/09/97
//
void
G4MagHelicalStepper::Stepper( const G4double yInput[],
                              const G4double*,
                                    G4double hstep,
                                    G4double yOut[],
                                    G4double yErr[]  )
{  
   const G4int nvar = 6;
 
   // correction for Richardson Extrapolation.
   // G4double  correction = 1. / ( (1 << IntegratorOrder()) -1 );
   
   G4double      yTemp[8], yIn[8] ;
   G4ThreeVector Bfld_initial, Bfld_midpoint;
   
   //  Saving yInput because yInput and yOut can be aliases for same array
   //
   for(G4int 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(G4int i=0; i<nvar; ++i)
   {
     yErr[i] = yOut[i] - yTemp[i] ;
   }
   
   return;
}
 
G4double
G4MagHelicalStepper::DistChord() const 
{
  // 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();
    }
  }
}