Include full Lorentz dual force for monopoles

Author: Marco Giacalone

Common/SimConfig/include/SimConfig/G4Params.h

@@ -62,6 +62,10 @@ struct G4Params : public o2::conf::ConfigurableParamHelper<G4Params> {
   bool monopole = false;
   // Monopole magnetic charge in units of the Dirac charge g_D = eplus/(2*alpha)
   // (~68.5 eplus). 1.0 corresponds to a single classic Dirac monopole.
+  // The monopole is transported with the full dual Lorentz force
+  // F = g*(B - v x E/c^2). The electric part acts inside the TPC field cage,
+  // the only volume with an electric field, and its magnitude is the TPC's own
+  // TPCGEMParam.ElectricField[0]
   float monopoleMagneticCharge = 1.f;
 
   O2ParamDef(G4Params, "G4");

Detectors/TPC/simulation/src/Detector.cxx

@@ -198,7 +198,7 @@ Bool_t Detector::ProcessHits(FairVolume* vol)
   // TODO: Add discussion about drawback
 
   Int_t numberOfElectrons = 0;
-  // I.H. - the type expected in addHit is short
+  // I.H. - the type expected in addHit is float
 
   // ---| Stepsize in cm |---
   const double stepSize = fMC->TrackStep();
@@ -219,9 +219,9 @@ Bool_t Detector::ProcessHits(FairVolume* vol)
     // Ionisation electrons calculated directly from the energy deposited in this step: Nel = Edep / Wion.
     // To check by TPC experts if this is actually the best way...
     numberOfElectrons = static_cast<int>(fMC->Edep() / static_cast<double>(gasParam.Wion));
-    // The number of electrons is stored as a short in the HitGroup; cap it to
-    // avoid overflow for the very high monopole dE/dx.
-    numberOfElectrons = TMath::Min(numberOfElectrons, 32000);
+    // The number of electrons is stored as a float in the HitGroup: maximum cap at
+    // 2^24 (16777216) ==> largest integer a IEEE-754 float can represent exactly
+    numberOfElectrons = TMath::Min(numberOfElectrons, 16777216);
   } else {
     // ---| mean number of collisions and random for this event |---
     const double meanNcoll = stepSize * trackCharge * trackCharge * primaryElectronsPerCM;
@@ -244,7 +244,7 @@ Bool_t Detector::ProcessHits(FairVolume* vol)
       const double rndm = fMC->GetRandom()->Rndm();
       const double eDep = TMath::Power((kMax - kMin) * rndm + kMin, oneOverAlpha_p1);
       int nel_step = static_cast<int>(((eDep - eMin) / wIon) + 1);
-      nel_step = TMath::Min(nel_step, 300); // 300 electrons corresponds to 10 keV
+      nel_step = TMath::Min(nel_step, gasParam.MaxElePerStep); // 300 electrons corresponds to 10 keV
       numberOfElectrons += nel_step;
     }
   }

Detectors/gconfig/src/O2MonopolePhysics.cxx

@@ -29,6 +29,11 @@
 /// Geant4 libraries (libG4processes)
 
 #include "SimSetup/O2MonopolePhysics.h"
+#include "CommonUtils/ConfigurableParam.h"
+
+#include <boost/property_tree/ptree.hpp> // needed to instantiate getValueAs<>
+
+#include <TGeoManager.h>
 
 #include <fairlogger/Logger.h>
 
@@ -43,10 +48,24 @@
 #include <G4VEnergyLossProcess.hh>
 #include <G4mplIonisation.hh>
 
+#include <G4ChargeState.hh>
+#include <G4ChordFinder.hh>
+#include <G4ClassicalRK4.hh>
+#include <G4EquationOfMotion.hh>
+#include <G4EventManager.hh>
+#include <G4FieldManager.hh>
+#include <G4MagIntegratorStepper.hh>
+#include <G4MagneticField.hh>
+#include <G4Track.hh>
+#include <G4TrackingManager.hh>
+#include <G4Transportation.hh>
+#include <G4TransportationManager.hh>
+
 #include <CLHEP/Units/SystemOfUnits.h>
 #include <CLHEP/Units/PhysicalConstants.h>
 
 #include <array>
+#include <cmath>
 #include <vector>
 
 namespace o2
@@ -61,8 +80,213 @@ namespace
 //   +-4110000 : "symmetric"  monopoles
 //   +-4120000 : "asymmetric" monopoles
 constexpr std::array<int, 4> gMonopolePDGs = {4110000, -4110000, 4120000, -4120000};
+
+inline bool isMonopolePDG(int pdg)
+{
+  const int abspdg = std::abs(pdg);
+  return abspdg == 4110000 || abspdg == 4120000;
+}
+
+/// GEANT4 only queries the magnetic field when a particle has non-zero electric
+/// charge or non-zero magnetic moment (μ) and the monopole has neither. So this is a workaround
+/// so that G4Transportation queries the field for it
+constexpr G4double gMonopoleFieldGateMoment = 1.0e-20;
+
+// Extent of the TPC drift region
+constexpr G4double gTPCFieldCageRMin = 83.5 * CLHEP::cm;
+constexpr G4double gTPCFieldCageRMax = 254.5 * CLHEP::cm;
+constexpr G4double gTPCFieldCageZMax = 249.525 * CLHEP::cm;
+
+/// Magnitude of the TPC drift field, in Geant4 units; 0 when there is no TPC.
+inline double tpcDriftFieldMagnitude()
+{
+  if (gGeoManager == nullptr || gGeoManager->GetVolume("TPC_Drift") == nullptr) {
+    LOG(info) << "O2MonopolePhysics: no TPC in the geometry of this run, "
+                 "the monopole is not coupled to a drift field";
+    return 0.;
+  }
+  try {
+    const double valueKVPerCm = o2::conf::ConfigurableParam::getValueAs<float>("TPCGEMParam.ElectricField[0]");
+    return valueKVPerCm * CLHEP::kilovolt / CLHEP::cm;
+  } catch (...) {
+    LOG(warn) << "O2MonopolePhysics: the TPC is in the geometry but TPCGEMParam is not "
+                 "registered; no drift-field coupling for the monopole";
+    return 0.;
+  }
+}
+
+/// Electric field of the TPC drift region at a specific position.
+/// Returns false outside the field cage.
+inline bool tpcDriftField(const G4double position[3], G4double driftField, G4double E[3])
+{
+  const G4double z = position[2];
+  if (std::fabs(z) >= gTPCFieldCageZMax) {
+    return false;
+  }
+  const G4double r2 = position[0] * position[0] + position[1] * position[1];
+  if (r2 < gTPCFieldCageRMin * gTPCFieldCageRMin || r2 > gTPCFieldCageRMax * gTPCFieldCageRMax) {
+    return false;
+  }
+  E[0] = 0.;
+  E[1] = 0.;
+  E[2] = (z >= 0.) ? -driftField : driftField;
+  return true;
+}
 } // namespace
 
+//____________________________________________________________________________
+/// Equation of motion implementing the dual Lorentz force of a magnetic charge.
+class O2MonopoleEquation : public G4EquationOfMotion
+{
+ public:
+  /// \param field                    the magnetic field to integrate in
+  /// \param magneticChargeEplusUnits monopole magnetic charge expressed in eplus
+  ///                                 units (one Dirac charge = 1/(2*alpha) ~ 68.5)
+  /// \param tpcDriftFieldGeant4      TPC drift field in Geant4 units
+  O2MonopoleEquation(G4Field* field, double magneticChargeEplusUnits, double tpcDriftFieldGeant4)
+    : G4EquationOfMotion(field),
+      mMagneticChargeEplus(magneticChargeEplusUnits),
+      mTPCDriftField(tpcDriftFieldGeant4)
+  {
+  }
+
+  void SetChargeMomentumMass(G4ChargeState particleChargeState,
+                             G4double /*momentum*/, G4double particleMass) override
+  {
+    mElCharge = CLHEP::eplus * particleChargeState.GetCharge() * CLHEP::c_light;
+    mMassCof = particleMass * particleMass;
+
+    // Non-zero only while an O2 monopole is being transported. The sign follows
+    // the PDG sign, so monopole and anti-monopole are pushed in opposite
+    // directions along B.
+    double signedMagneticCharge = 0.;
+    int pdg = 0;
+    if (const G4Track* track = currentTrack()) {
+      pdg = track->GetDefinition()->GetPDGEncoding();
+      if (isMonopolePDG(pdg)) {
+        signedMagneticCharge = (pdg > 0) ? mMagneticChargeEplus : -mMagneticChargeEplus;
+      }
+    }
+    mMagCharge = CLHEP::eplus * signedMagneticCharge * CLHEP::c_light;
+  }
+
+  void EvaluateRhsGivenB(const G4double y[], const G4double B[3], G4double dydx[]) const override
+  {
+    const G4double pSquared = y[3] * y[3] + y[4] * y[4] + y[5] * y[5];
+    if (pSquared <= 0.) {
+      for (int i = 0; i < 8; ++i) {
+        dydx[i] = 0.;
+      }
+      return;
+    }
+    const G4double energy = std::sqrt(pSquared + mMassCof);
+    const G4double pModuleInverse = 1.0 / std::sqrt(pSquared);
+    const G4double cofEl = mElCharge * pModuleInverse;
+    const G4double cofMag = mMagCharge * energy * pModuleInverse;
+
+    dydx[0] = y[3] * pModuleInverse;
+    dydx[1] = y[4] * pModuleInverse;
+    dydx[2] = y[5] * pModuleInverse;
+
+    // magnetic charge -> force along B; electric charge -> the usual v x B
+    dydx[3] = cofMag * B[0] + cofEl * (y[4] * B[2] - y[5] * B[1]);
+    dydx[4] = cofMag * B[1] + cofEl * (y[5] * B[0] - y[3] * B[2]);
+    dydx[5] = cofMag * B[2] + cofEl * (y[3] * B[1] - y[4] * B[0]);
+
+    // Coupling of the magnetic charge to an electric field: the full dual
+    // Lorentz force is F = g*(B - v x E/c^2).
+    // mMagCharge is zero for every non-monopole, so nothing else is affected.
+    if (mMagCharge != 0. && mTPCDriftField > 0.) {
+      G4double E[3] = {0., 0., 0.};
+      if (tpcDriftField(y, mTPCDriftField, E)) {
+        // Relative to cofMag this carries 1/(c*energy), so the term is of order
+        // beta*E/(c*B) compared with the g*B term (similar to G4MonopoleEq, which uses
+        // d(p)/ds = g*(c*energy*B - p x E)/(p*c)).
+        const G4double cofMagE = mMagCharge * pModuleInverse / CLHEP::c_light;
+        const G4double dEx = cofMagE * (y[4] * E[2] - y[5] * E[1]);
+        const G4double dEy = cofMagE * (y[5] * E[0] - y[3] * E[2]);
+        const G4double dEz = cofMagE * (y[3] * E[1] - y[4] * E[0]);
+        dydx[3] -= dEx;
+        dydx[4] -= dEy;
+        dydx[5] -= dEz;
+      }
+    }
+
+    dydx[6] = 0.;                                       // not used
+    dydx[7] = energy * pModuleInverse / CLHEP::c_light; // inverse velocity
+  }
+
+ private:
+  static const G4Track* currentTrack()
+  {
+    auto* eventManager = G4EventManager::GetEventManager();
+    if (eventManager == nullptr) {
+      return nullptr;
+    }
+    auto* trackingManager = eventManager->GetTrackingManager();
+    return trackingManager != nullptr ? trackingManager->GetTrack() : nullptr;
+  }
+
+  double mMagneticChargeEplus;  ///< |g| in eplus units (1 g_D = 1/(2*alpha) ~ 68.5)
+  G4double mTPCDriftField = 0.; ///< TPC drift field, Geant4 units; 0 disables the coupling
+  G4double mElCharge = 0.;
+  G4double mMagCharge = 0.;
+  G4double mMassCof = 0.;
+};
+
+//____________________________________________________________________________
+/// Make the global field integrate O2MonopoleEquation instead of the default
+/// electric-charge-only equation.
+///
+/// SetUserEquationOfMotion() in Geant4-VMC is not usable here: it
+/// registers the object with TG4GeometryManager, and the field integrator is
+/// built before that registration is consulted, so the equation is never
+/// actually called.
+///
+/// \param magneticChargeEplusUnits monopole magnetic charge in eplus units
+/// \param tpcDriftFieldGeant4      TPC drift field in Geant4 units (0 = disabled)
+inline void installMonopoleFieldIntegrator(double magneticChargeEplusUnits, double tpcDriftFieldGeant4)
+{
+  auto* transportationManager = G4TransportationManager::GetTransportationManager();
+  auto* fieldManager = transportationManager != nullptr ? transportationManager->GetFieldManager() : nullptr;
+  if (fieldManager == nullptr) {
+    LOG(error) << "O2MonopolePhysics: no G4FieldManager, monopole equation of motion NOT installed";
+    return;
+  }
+  auto* magneticField =
+    const_cast<G4MagneticField*>(dynamic_cast<const G4MagneticField*>(fieldManager->GetDetectorField()));
+  if (magneticField == nullptr) {
+    LOG(error) << "O2MonopolePhysics: no magnetic field attached to the field manager, "
+                  "monopole equation of motion NOT installed";
+    return;
+  }
+
+  auto* equation = new O2MonopoleEquation(magneticField, magneticChargeEplusUnits, tpcDriftFieldGeant4);
+  // A generic (non-helix) integrator is required: the helix steppers hard-code
+  // the constant-curvature motion of an electric charge. 8 variables so that the
+  // time-of-flight component is integrated too.
+  auto* stepper = new G4ClassicalRK4(equation, 8);
+
+  // keep the accuracy Geant4-VMC configured for this field
+  auto* previous = fieldManager->GetChordFinder();
+  const G4double stepMinimum = 1.0e-2 * CLHEP::mm;
+  auto* chordFinder = new G4ChordFinder(magneticField, stepMinimum, stepper);
+  if (previous != nullptr) {
+    chordFinder->SetDeltaChord(previous->GetDeltaChord());
+  }
+  fieldManager->SetChordFinder(chordFinder);
+
+  if (tpcDriftFieldGeant4 > 0.) {
+    LOG(info) << "O2MonopolePhysics: monopole equation of motion installed (F = g*(B - v x E/c^2)), "
+                 "magnetic charge = "
+              << magneticChargeEplusUnits << " eplus, TPC drift field = "
+              << tpcDriftFieldGeant4 / (CLHEP::volt / CLHEP::cm) << " V/cm";
+  } else {
+    LOG(info) << "O2MonopolePhysics: monopole equation of motion installed (F = g*B), magnetic charge = "
+              << magneticChargeEplusUnits << " eplus (TPC drift field coupling disabled)";
+  }
+}
+
 //____________________________________________________________________________
 /// Minimal physics list whose only job is to attach the magnetic-monopole
 /// ionisation process to the already-defined O2 monopole particles.
@@ -126,6 +350,14 @@ class O2MonopolePhysics : public G4VUserPhysicsList
       // Ordering (AtRest, AlongStep, PostStep) = (-1, 1, 1) as in the Geant4
       // monopole example: continuous-and-discrete energy loss, not active at rest.
       pmanager->AddProcess(new G4mplIonisation(mMagneticCharge), -1, 1, 1);
+
+      // G4Transportation only looks up the field when the particle has a
+      // non-zero electric charge or a non-zero magnetic moment (μ) and a monopole has
+      // neither, so the field would never be queried. Hence a gate magnetic moment is set
+      // to allow the query to happen.
+      if (particle->GetPDGMagneticMoment() == 0.) {
+        particle->SetPDGMagneticMoment(gMonopoleFieldGateMoment);
+      }
       ++nAttached;
       LOG(info) << "O2MonopolePhysics: attached G4mplIonisation to "
                 << particle->GetParticleName() << " (PDG " << pdg
@@ -134,6 +366,17 @@ class O2MonopolePhysics : public G4VUserPhysicsList
     if (nAttached == 0) {
       LOG(warning) << "O2MonopolePhysics: no monopole particle found; no ionisation attached";
     }
+
+    // This static switch is what makes G4Transportation consider the μ of the monopole
+    // It is global, so electrically neutral particles that already carry a momentum (neutrons) are
+    // now propagated through the field as well; O2MonopoleEquation gives them
+    // exactly zero force, so their trajectories are unchanged.
+    G4Transportation::EnableMagneticMoment(true);
+
+    // Deflect the monopole in the field as well; without this only the energy
+    // loss above would act and the monopole would fly straight through, since
+    // its electric charge (and hence the usual Lorentz force) is zero.
+    installMonopoleFieldIntegrator(mMagneticCharge / CLHEP::eplus, tpcDriftFieldMagnitude());
   }
 
  private: