G4BorisScheme.cc

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// G4BorisScheme implementation
//
// Author: Divyansh Tiwari (CERN, Google Summer of Code 2022), 05.11.2022
// Supervision: John Apostolakis (CERN), Renee Fatemi, Soon Yung Jun (FNAL)
// --------------------------------------------------------------------
 
#include "G4BorisScheme.hh"
#include "G4FieldUtils.hh"
#include"G4SystemOfUnits.hh"
#include "globals.hh"
#include "G4PhysicalConstants.hh"
 
#include "G4EquationOfMotion.hh"
 
using namespace field_utils;
 
G4BorisScheme::G4BorisScheme( G4EquationOfMotion* equation, G4int nvar )
  : fEquation(equation), fnvar(nvar)
{
  if (nvar <= 0)
  {
    G4Exception("G4BorisScheme::G4BorisScheme()",
                "GeomField0002", FatalException,
                "Invalid number of variables; must be greater than zero!");
  }
}
 
void G4BorisScheme::DoStep(const G4double restMass,const G4double charge,
                           const G4double yIn[], G4double yOut[],
                           G4double hstep) const
{
  G4double yOut1Temp[G4FieldTrack::ncompSVEC];
  G4double yOut2Temp[G4FieldTrack::ncompSVEC];
  
  // Used the scheme described in the following paper:
  // https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/153167/eth-5175-01.pdf?sequence=1
  UpdatePosition(restMass, charge, yIn, yOut1Temp, hstep/2);
  UpdateVelocity(restMass, charge, yOut1Temp, yOut2Temp, hstep);
  UpdatePosition(restMass, charge, yOut2Temp, yOut, hstep/2);
}
 
void G4BorisScheme::UpdatePosition(const G4double restMass,
                                   const G4double /*crg*/, const G4double yIn[],
                                   G4double yOut[], G4double hstep) const
{
  // Particle information
  copy(yOut, yIn);
    
  // Obtaining velocity
  G4ThreeVector momentum_vec =G4ThreeVector(yIn[3],yIn[4],yIn[5]);
  G4double momentum_mag = momentum_vec.mag();
  G4ThreeVector momentum_dir =(1.0/momentum_mag)*momentum_vec;
 
  G4double velocity_mag = momentum_mag*(c_l)/(std::sqrt(sqr(momentum_mag) +sqr(restMass)));
  G4ThreeVector velocity = momentum_dir*velocity_mag;
 
  // Obtaining the time step from the length step
 
  hstep /= velocity_mag*CLHEP::m;
 
  // Updating the Position
  for(G4int i = 0; i <3; i++ )
  {
    G4double pos = yIn[i]/CLHEP::m;
    pos += hstep*velocity[i];
    yOut[i] = pos*CLHEP::m;
  }   
}
 
void G4BorisScheme::UpdateVelocity(const G4double restMass,
                                   const G4double charge, const G4double yIn[], 
                                   G4double yOut[], G4double hstep) const
{
  // Particle information
 
  G4ThreeVector momentum_vec = G4ThreeVector(yIn[3],yIn[4],yIn[5]);
  G4double momentum_mag = momentum_vec.mag();
  G4ThreeVector momentum_dir =(1.0/momentum_mag)*momentum_vec;
 
  G4double gamma = std::sqrt(sqr(momentum_mag) + sqr(restMass))/restMass;  
 
  G4double mass = (restMass/c_squared)/CLHEP::kg;
 
  // Obtaining velocity
 
  G4double velocity_mag = momentum_mag*(c_l)/(std::sqrt(sqr(momentum_mag) +sqr(restMass)));
  G4ThreeVector velocity = momentum_dir*velocity_mag;
 
  // Obtaining the time step from the length step
 
  hstep /= velocity_mag*CLHEP::m; 
 
  // Obtaining the field values
 
  G4double dydx[G4FieldTrack::ncompSVEC];
  G4double fieldValue[6] ={0,0,0,0,0,0};
  fEquation->EvaluateRhsReturnB(yIn, dydx, fieldValue);
 
  // Initializing Vectors
 
  G4ThreeVector B;
  G4ThreeVector E;
  copy(yOut, yIn);
  for( G4int i = 0; i < 3; i++)
  {
    E[i] = fieldValue[i+3]/CLHEP::volt*CLHEP::meter;// FIXME - Check Units
    B[i] = fieldValue[i]/CLHEP::tesla;   
  }
 
  // Boris Algorithm
 
  G4double qd = hstep*(charge/(2*mass*gamma));
  G4ThreeVector h = qd*B;
  G4ThreeVector u = velocity + qd*E;
  G4double h_l = h[0]*h[0] + h[1]*h[1] + h[2]*h[2];
  G4ThreeVector s_1 = (2*h)/(1 + h_l);
  G4ThreeVector ud = u + (u + u.cross(h)).cross(s_1);
  G4ThreeVector v_fi = ud +qd*E;
  G4double v_mag = std::sqrt(v_fi.mag2());
  G4ThreeVector v_dir = v_fi/v_mag;
  G4double momen_mag = (restMass*v_mag)/(std::sqrt(c_l*c_l - v_mag*v_mag));
  G4ThreeVector momen = momen_mag*v_dir;
 
  // Storing the updated momentum
 
  for(G4int i = 3; i < 6; i++)
  {
    yOut[i] = momen[i-3];   
  }
}
 
// ----------------------------------------------------------------------------------
 
void G4BorisScheme::copy(G4double dst[], const G4double src[]) const
{
  std::memcpy(dst, src, sizeof(G4double) * fnvar);
}
 
// ----------------------------------------------------------------------------------
// - Methods using the Boris Scheme Stepping to estimate integration error
// ----------------------------------------------------------------------------------
void G4BorisScheme::
StepWithErrorEstimate(const G4double yIn[], G4double restMass,
                      G4double charge, G4double hstep,
                      G4double yOut[], G4double yErr[]) const
{
  // Use two half-steps (comparing to a full step) to obtain output
  // and error estimate
 
  G4double yMid[G4FieldTrack::ncompSVEC];
  StepWithMidAndErrorEstimate(yIn, restMass, charge, hstep, yMid, yOut, yErr);
}
 
// ----------------------------------------------------------------------------------
 
void G4BorisScheme::
StepWithMidAndErrorEstimate(const G4double yIn[], G4double restMass,
                            G4double charge, G4double hstep, G4double yMid[],
                            G4double yOut[], G4double yErr[]) const
{
  G4double halfStep= 0.5*hstep;
  G4double yOutAlt[G4FieldTrack::ncompSVEC];   
 
  // In a single step
  DoStep(restMass, charge, yIn,  yOutAlt, hstep );
 
  // Same, and also return mid-point evaluation
  DoStep(restMass, charge, yIn,  yMid, halfStep );
  DoStep(restMass, charge, yMid, yOut, halfStep );
 
  for( G4int i = 0; i < fnvar; i++ )
  {
    yErr[i] = yOutAlt[i] - yOut[i];
  }
}