ParallelTTracker.cpp

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//
// Class ParallelTTracker
//   OPAL-T tracker.
//   The visitor class for tracking particles with time as independent
//   variable.
//
// Copyright (c) 200x - 2014, Christof Kraus, Paul Scherrer Institut, Villigen PSI, Switzerland
//               2015 - 2016, Christof Metzger-Kraus, Helmholtz-Zentrum Berlin, Germany
//               2017 - 2020, Christof Metzger-Kraus
// All rights reserved
//
// This file is part of OPAL.
//
// OPAL is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// You should have received a copy of the GNU General Public License
// along with OPAL. If not, see <https://www.gnu.org/licenses/>.
//
#include "Algorithms/ParallelTTracker.h"
 
#include <cfloat>
#include <cmath>
#include <fstream>
#include <limits>
#include <iomanip>
#include <iostream>
#include <sstream>
#include <string>
 
#include "AbsBeamline/Monitor.h"
#include "AbstractObjects/OpalData.h"
#include "Algorithms/OrbitThreader.h"
#include "Algorithms/CavityAutophaser.h"
#include "BasicActions/Option.h"
#ifdef ENABLE_OPAL_FEL
#include "BeamlineCore/UndulatorRep.h"
#endif
#include "Beamlines/Beamline.h"
#include "Beamlines/FlaggedBeamline.h"
#include "Distribution/Distribution.h"
#include "Elements/OpalBeamline.h"
#include "Physics/Units.h"
#include "Solvers/CSRWakeFunction.h"
#include "Solvers/ParticleMatterInteractionHandler.h"
#include "Structure/BoundaryGeometry.h"
#include "Structure/BoundingBox.h"
#include "Utilities/OpalException.h"
#include "Utilities/Options.h"
#include "Utilities/Timer.h"
#include "Utilities/Util.h"
#include "ValueDefinitions/RealVariable.h"
 
extern Inform* gmsg;
 
class PartData;
 
ParallelTTracker::ParallelTTracker(const Beamline &beamline,
                                   const PartData &reference,
                                   bool revBeam,
                                   bool revTrack):
    Tracker(beamline, reference, revBeam, revTrack),
    itsDataSink_m(nullptr),
    itsOpalBeamline_m(beamline.getOrigin3D(), beamline.getInitialDirection()),
    globalEOL_m(false),
    wakeStatus_m(false),
    wakeFunction_m(nullptr),
    pathLength_m(0.0),
    zstart_m(0.0),
    dtCurrentTrack_m(0.0),
    minStepforReBin_m(-1),
    minBinEmitted_m(std::numeric_limits<size_t>::max()),
    repartFreq_m(-1),
    emissionSteps_m(std::numeric_limits<unsigned int>::max()),
    numParticlesInSimulation_m(0),
    timeIntegrationTimer1_m(IpplTimings::getTimer("TIntegration1")),
    timeIntegrationTimer2_m(IpplTimings::getTimer("TIntegration2")),
    fieldEvaluationTimer_m(IpplTimings::getTimer("External field eval")),
    BinRepartTimer_m(IpplTimings::getTimer("Binaryrepart")),
    WakeFieldTimer_m(IpplTimings::getTimer("WakeField")),
    particleMatterStatus_m(false)
{}
 
ParallelTTracker::ParallelTTracker(const Beamline &beamline,
                                   PartBunchBase<double, 3> *bunch,
                                   DataSink &ds,
                                   const PartData &reference,
                                   bool revBeam,
                                   bool revTrack,
                                   const std::vector<unsigned long long> &maxSteps,
                                   double zstart,
                                   const std::vector<double> &zstop,
                                   const std::vector<double> &dt):
    Tracker(beamline, bunch, reference, revBeam, revTrack),
    itsDataSink_m(&ds),
    itsOpalBeamline_m(beamline.getOrigin3D(), beamline.getInitialDirection()),
    globalEOL_m(false),
    wakeStatus_m(false),
    wakeFunction_m(nullptr),
    pathLength_m(0.0),
    zstart_m(zstart),
    dtCurrentTrack_m(0.0),
    minStepforReBin_m(-1),
    minBinEmitted_m(std::numeric_limits<size_t>::max()),
    repartFreq_m(-1),
    emissionSteps_m(std::numeric_limits<unsigned int>::max()),
    numParticlesInSimulation_m(0),
    timeIntegrationTimer1_m(IpplTimings::getTimer("TIntegration1")),
    timeIntegrationTimer2_m(IpplTimings::getTimer("TIntegration2")),
    fieldEvaluationTimer_m(IpplTimings::getTimer("External field eval")),
    BinRepartTimer_m(IpplTimings::getTimer("Binaryrepart")),
    WakeFieldTimer_m(IpplTimings::getTimer("WakeField")),
    particleMatterStatus_m(false)
{
    for (unsigned int i = 0; i < zstop.size(); ++ i) {
        stepSizes_m.push_back(dt[i], zstop[i], maxSteps[i]);
    }
 
    stepSizes_m.sortAscendingZStop();
    stepSizes_m.resetIterator();
}
 
ParallelTTracker::~ParallelTTracker() {}
 
void ParallelTTracker::visitBeamline(const Beamline &bl) {
    const FlaggedBeamline* fbl = static_cast<const FlaggedBeamline*>(&bl);
    if (fbl->getRelativeFlag()) {
        OpalBeamline stash(fbl->getOrigin3D(), fbl->getInitialDirection());
        stash.swap(itsOpalBeamline_m);
        fbl->iterate(*this, false);
        itsOpalBeamline_m.prepareSections();
        itsOpalBeamline_m.compute3DLattice();
        stash.merge(itsOpalBeamline_m);
        stash.swap(itsOpalBeamline_m);
    } else {
        fbl->iterate(*this, false);
    }
}
 
void ParallelTTracker::updateRFElement(std::string elName, double maxPhase) {
    FieldList cavities = itsOpalBeamline_m.getElementByType(ElementType::RFCAVITY);
    FieldList travelingwaves = itsOpalBeamline_m.getElementByType(ElementType::TRAVELINGWAVE);
    cavities.insert(cavities.end(), travelingwaves.begin(), travelingwaves.end());
 
    for (FieldList::iterator fit = cavities.begin(); fit != cavities.end(); ++ fit) {
        if ((*fit).getElement()->getName() == elName) {
 
            RFCavity *element = static_cast<RFCavity *>((*fit).getElement().get());
 
            element->setPhasem(maxPhase);
            element->setAutophaseVeto();
 
            INFOMSG("Restored cavity phase from the h5 file. Name: " << element->getName() << ", phase: " << maxPhase << " rad" << endl);
            return;
        }
    }
}
 
void ParallelTTracker::saveCavityPhases() {
    itsDataSink_m->storeCavityInformation();
}
 
void ParallelTTracker::restoreCavityPhases() {
    typedef std::vector<MaxPhasesT>::iterator iterator_t;
 
    if (OpalData::getInstance()->hasPriorTrack() ||
        OpalData::getInstance()->inRestartRun()) {
        iterator_t it = OpalData::getInstance()->getFirstMaxPhases();
        iterator_t end = OpalData::getInstance()->getLastMaxPhases();
        for (; it < end; ++ it) {
            updateRFElement((*it).first, (*it).second);
        }
    }
}
 
void ParallelTTracker::execute() {
    Inform msg("ParallelTTracker ", *gmsg);
    OpalData::getInstance()->setInPrepState(true);
 
    BorisPusher pusher(itsReference);
    const double globalTimeShift = itsBunch_m->weHaveEnergyBins()? OpalData::getInstance()->getGlobalPhaseShift(): 0.0;
    OpalData::getInstance()->setGlobalPhaseShift(0.0);
 
    // the time step needs to be positive in the setup
    itsBunch_m->setdT(std::abs(itsBunch_m->getdT()));
    dtCurrentTrack_m = itsBunch_m->getdT();
 
    evenlyDistributeParticles();
 
    if (OpalData::getInstance()->hasPriorTrack() || OpalData::getInstance()->inRestartRun()) {
        OpalData::getInstance()->setOpenMode(OpalData::OpenMode::APPEND);
    }
 
    prepareSections();
 
    double minTimeStep = stepSizes_m.getMinTimeStep();
 
    itsOpalBeamline_m.activateElements();
 
    if ( OpalData::getInstance()->hasPriorTrack() ||
         OpalData::getInstance()->inRestartRun()) {
 
        pathLength_m = itsBunch_m->get_sPos();
        zstart_m = pathLength_m;
 
        restoreCavityPhases();
    } else {
 
        double momentum = euclidean_norm(itsBunch_m->get_pmean_Distribution());
        CoordinateSystemTrafo beamlineToLab = itsOpalBeamline_m.getCSTrafoLab2Local().inverted();
        itsBunch_m->toLabTrafo_m = beamlineToLab;
 
        itsBunch_m->RefPartR_m = beamlineToLab.transformTo(Vector_t(0.0));
        itsBunch_m->RefPartP_m = beamlineToLab.rotateTo(momentum * Vector_t(0, 0, 1));
 
        if (itsBunch_m->getTotalNum() > 0) {
            if (!itsOpalBeamline_m.containsSource()) {
                momentum = itsReference.getP() / itsBunch_m->getM();
                itsBunch_m->RefPartP_m = beamlineToLab.rotateTo(momentum * Vector_t(0, 0, 1));
            }
 
            if (zstart_m > pathLength_m) {
                findStartPosition(pusher);
            }
 
            itsBunch_m->set_sPos(pathLength_m);
        }
    }
 
    stepSizes_m.advanceToPos(zstart_m);
    if (back_track) {
        itsBunch_m->setdT(-std::abs(itsBunch_m->getdT()));
        stepSizes_m.reverseDirection();
        if (pathLength_m < stepSizes_m.getZStop()) {
            ++ stepSizes_m;
        }
    }
 
    Vector_t rmin(0.0), rmax(0.0);
    if (itsBunch_m->getTotalNum() > 0) {
        itsBunch_m->get_bounds(rmin, rmax);
    }
 
    OrbitThreader oth(itsReference,
                      itsBunch_m->RefPartR_m,
                      itsBunch_m->RefPartP_m,
                      pathLength_m,
                      -rmin(2),
                      itsBunch_m->getT(),
                      (back_track? -minTimeStep: minTimeStep),
                      stepSizes_m,
                      itsOpalBeamline_m);
 
    oth.execute();
    BoundingBox globalBoundingBox = oth.getBoundingBox();
 
    saveCavityPhases();
 
    numParticlesInSimulation_m = itsBunch_m->getTotalNum();
 
    setTime();
 
    double time = itsBunch_m->getT() - globalTimeShift;
    itsBunch_m->setT(time);
 
    *gmsg << level1 << *itsBunch_m << endl;
 
    unsigned long long step = itsBunch_m->getGlobalTrackStep();
    OPALTimer::Timer myt1;
    *gmsg << "* Track start at: " << myt1.time() << ", t= " << Util::getTimeString(time) << "; "
          << "zstart at: " << Util::getLengthString(pathLength_m)
          << endl;
 
    prepareEmission();
 
    *gmsg << "* Executing ParallelTTracker\n"
          << "* Initial dt = " << Util::getTimeString(itsBunch_m->getdT()) << "\n"
          << "* Max integration steps = " << stepSizes_m.getMaxSteps()
          << ", next step = " << step << endl << endl;
 
    setOptionalVariables();
 
    globalEOL_m = false;
    wakeStatus_m = false;
    deletedParticles_m = false;
    OpalData::getInstance()->setInPrepState(false);
    while (!stepSizes_m.reachedEnd()) {
        unsigned long long trackSteps = stepSizes_m.getNumSteps() + step;
        dtCurrentTrack_m = stepSizes_m.getdT();
        changeDT(back_track);
 
        for (; step < trackSteps; ++ step) {
            Vector_t rmin(0.0), rmax(0.0);
            if (itsBunch_m->getTotalNum() > 0) {
                itsBunch_m->get_bounds(rmin, rmax);
            }
 
            timeIntegration1(pusher);
 
            itsBunch_m->Ef = Vector_t(0.0);
            itsBunch_m->Bf = Vector_t(0.0);
 
            computeSpaceChargeFields(step);
 
            selectDT(back_track);
            emitParticles(step);
            selectDT(back_track);
 
            computeExternalFields(oth);
            
            timeIntegration2(pusher);
 
            itsBunch_m->incrementT();
 
            if (itsBunch_m->getT() > 0.0 ||
                itsBunch_m->getdT() < 0.0) {
                updateReference(pusher);
            }
 
            if (deletedParticles_m) {
                evenlyDistributeParticles();
                deletedParticles_m = false;
            }
            itsBunch_m->set_sPos(pathLength_m);
 
            if (hasEndOfLineReached(globalBoundingBox)) break;
 
            bool const psDump = ((itsBunch_m->getGlobalTrackStep() % Options::psDumpFreq) + 1 == Options::psDumpFreq);
            bool const statDump = ((itsBunch_m->getGlobalTrackStep() % Options::statDumpFreq) + 1 == Options::statDumpFreq);
            dumpStats(step, psDump, statDump);
 
            itsBunch_m->incTrackSteps();
 
            double beta = euclidean_norm(itsBunch_m->RefPartP_m / Util::getGamma(itsBunch_m->RefPartP_m));
            double driftPerTimeStep = std::abs(itsBunch_m->getdT()) * Physics::c * beta;
            if (std::abs(stepSizes_m.getZStop() - pathLength_m) < 0.5 * driftPerTimeStep) {
                break;
            }
        }
 
        if (globalEOL_m)
            break;
 
        ++ stepSizes_m;
    }
 
    itsBunch_m->set_sPos(pathLength_m);
 
    if (numParticlesInSimulation_m > minBinEmitted_m) {
        numParticlesInSimulation_m = itsBunch_m->getTotalNum();
    }
 
    bool const psDump = (((itsBunch_m->getGlobalTrackStep() - 1) % Options::psDumpFreq) + 1 != Options::psDumpFreq);
    bool const statDump = (((itsBunch_m->getGlobalTrackStep() - 1) % Options::statDumpFreq) + 1 != Options::statDumpFreq);
    writePhaseSpace((step + 1), psDump, statDump);
 
    msg << level2 << "Dump phase space of last step" << endl;
 
    itsOpalBeamline_m.switchElementsOff();
 
    OPALTimer::Timer myt3;
    *gmsg << endl << "* Done executing ParallelTTracker at "
          << myt3.time() << endl << endl;
 
    Monitor::writeStatistics();
 
    OpalData::getInstance()->setPriorTrack();
}
 
void ParallelTTracker::prepareSections() {
 
    itsBeamline_m.accept(*this);
 
    itsOpalBeamline_m.prepareSections();
 
    itsOpalBeamline_m.compute3DLattice();
    itsOpalBeamline_m.save3DLattice();
    itsOpalBeamline_m.save3DInput();
}
 
void ParallelTTracker::timeIntegration1(BorisPusher & pusher) {
 
    IpplTimings::startTimer(timeIntegrationTimer1_m);
    pushParticles(pusher);
    IpplTimings::stopTimer(timeIntegrationTimer1_m);
}
 
 
void ParallelTTracker::timeIntegration2(BorisPusher & pusher) {
    /*
      transport and emit particles
      that passed the cathode in the first
      half-step or that would pass it in the
      second half-step.
 
      to make IPPL and the field solver happy
      make sure that at least 10 particles are emitted
 
      also remember that node 0 has
      all the particles to be emitted
 
      this has to be done *after* the calculation of the
      space charges! thereby we neglect space charge effects
      in the very first step of a new-born particle.
 
    */
 
    IpplTimings::startTimer(timeIntegrationTimer2_m);
    kickParticles(pusher);
    //switchElements();
    pushParticles(pusher);
 
    const unsigned int localNum = itsBunch_m->getLocalNum();
    for (unsigned int i = 0; i < localNum; ++ i) {
        itsBunch_m->dt[i] = itsBunch_m->getdT();
    }
 
    IpplTimings::stopTimer(timeIntegrationTimer2_m);
}
 
void ParallelTTracker::selectDT(bool backTrack) {
 
    if (itsBunch_m->getIfBeamEmitting()) {
        double dt = itsBunch_m->getEmissionDeltaT();
        itsBunch_m->setdT(dt);
    } else {
        double dt = dtCurrentTrack_m;
        itsBunch_m->setdT(dt);
    }
    if (backTrack) {
        itsBunch_m->setdT(-std::abs(itsBunch_m->getdT()));
    }
}
 
void ParallelTTracker::changeDT(bool backTrack) {
    selectDT(backTrack);
    const unsigned int localNum = itsBunch_m->getLocalNum();
    for (unsigned int i = 0; i < localNum; ++ i) {
        itsBunch_m->dt[i] = itsBunch_m->getdT();
    }
}
 
void ParallelTTracker::emitParticles(long long step) {
    if (!itsBunch_m->weHaveEnergyBins()) return;
 
    if (itsBunch_m->getIfBeamEmitting()) {
        CoordinateSystemTrafo gunToLab = itsOpalBeamline_m.getCSTrafoLab2Local().inverted();
        CoordinateSystemTrafo refToGun = itsOpalBeamline_m.getCSTrafoLab2Local() * itsBunch_m->toLabTrafo_m;
 
        transformBunch(refToGun);
 
        itsBunch_m->switchToUnitlessPositions(true);
 
        Vector_t externalE = Vector_t(0.0);
        Vector_t externalB = Vector_t(0.0);
        itsOpalBeamline_m.getFieldAt(gunToLab.transformTo(Vector_t(0.0)),
                                     gunToLab.rotateTo(Vector_t(0.0)),
                                     itsBunch_m->getT() + 0.5 * itsBunch_m->getdT(),
                                     externalE,
                                     externalB);
        itsBunch_m->emitParticles(externalE(2));
 
        itsBunch_m->updateNumTotal();
        numParticlesInSimulation_m = itsBunch_m->getTotalNum();
        itsBunch_m->switchOffUnitlessPositions(true);
 
        transformBunch(refToGun.inverted());
    }
 
    if (step > minStepforReBin_m) {
        itsBunch_m->Rebin();
        itsBunch_m->resetInterpolationCache(true);
    }
}
 
 
void ParallelTTracker::computeSpaceChargeFields(unsigned long long step) {
    if (numParticlesInSimulation_m <= minBinEmitted_m || !itsBunch_m->hasFieldSolver()) {
        return;
    }
 
    itsBunch_m->calcBeamParameters();
    Quaternion alignment = getQuaternion(itsBunch_m->get_pmean(), Vector_t(0, 0, 1));
    CoordinateSystemTrafo beamToReferenceCSTrafo(Vector_t(0, 0, pathLength_m), alignment.conjugate());
    CoordinateSystemTrafo referenceToBeamCSTrafo = beamToReferenceCSTrafo.inverted();
    const unsigned int localNum1 = itsBunch_m->getLocalNum();
    for (unsigned int i = 0; i < localNum1; ++ i) {
        itsBunch_m->R[i] = referenceToBeamCSTrafo.transformTo(itsBunch_m->R[i]);
    }
 
    itsBunch_m->boundp();
 
    if (step % repartFreq_m + 1 == repartFreq_m) {
        doBinaryRepartition();
    }
 
    if (itsBunch_m->weHaveEnergyBins()) {
        itsBunch_m->calcGammas();
        itsBunch_m->resetInterpolationCache();
        ParticleAttrib<double> Q_back = itsBunch_m->Q;
        for (int binNumber = 0; binNumber < itsBunch_m->getLastEmittedEnergyBin() &&
                 binNumber < itsBunch_m->getNumberOfEnergyBins(); ++binNumber) {
 
            itsBunch_m->setBinCharge(binNumber);
            itsBunch_m->setGlobalMeanR(itsBunch_m->get_centroid());
            itsBunch_m->computeSelfFields(binNumber);
            itsBunch_m->Q = Q_back;
 
        }
 
    } else {
        itsBunch_m->setGlobalMeanR(itsBunch_m->get_centroid());
        itsBunch_m->computeSelfFields();
    }
 
    const unsigned int localNum2 = itsBunch_m->getLocalNum();
    for (unsigned int i = 0; i < localNum2; ++ i) {
        itsBunch_m->R[i] = beamToReferenceCSTrafo.transformTo(itsBunch_m->R[i]);
        itsBunch_m->Ef[i] = beamToReferenceCSTrafo.rotateTo(itsBunch_m->Ef[i]);
        itsBunch_m->Bf[i] = beamToReferenceCSTrafo.rotateTo(itsBunch_m->Bf[i]);
    }
}
 
 
void ParallelTTracker::computeExternalFields(OrbitThreader &oth) {
    IpplTimings::startTimer(fieldEvaluationTimer_m);
    Inform msg("ParallelTTracker ", *gmsg);
    const unsigned int localNum = itsBunch_m->getLocalNum();
    bool locPartOutOfBounds = false, globPartOutOfBounds = false;
    Vector_t rmin(0.0), rmax(0.0);
    if (itsBunch_m->getTotalNum() > 0)
        itsBunch_m->get_bounds(rmin, rmax);
    IndexMap::value_t elements;
 
    try {
        elements = oth.query(pathLength_m + 0.5 * (rmax(2) + rmin(2)), rmax(2) - rmin(2));
    } catch(IndexMap::OutOfBounds &e) {
        globalEOL_m = true;
        return;
    }
 
    IndexMap::value_t::const_iterator it = elements.begin();
    const IndexMap::value_t::const_iterator end = elements.end();
 
    for (; it != end; ++ it) {
        CoordinateSystemTrafo refToLocalCSTrafo = (itsOpalBeamline_m.getMisalignment((*it)) *
                                                   (itsOpalBeamline_m.getCSTrafoLab2Local((*it)) * itsBunch_m->toLabTrafo_m));
        CoordinateSystemTrafo localToRefCSTrafo = refToLocalCSTrafo.inverted();
 
        (*it)->setCurrentSCoordinate(pathLength_m + rmin(2));
 
        for (unsigned int i = 0; i < localNum; ++ i) {
            if (itsBunch_m->Bin[i] < 0) continue;
 
            itsBunch_m->R[i] = refToLocalCSTrafo.transformTo(itsBunch_m->R[i]);
            itsBunch_m->P[i] = refToLocalCSTrafo.rotateTo(itsBunch_m->P[i]);
            double &dt = itsBunch_m->dt[i];
 
            Vector_t localE(0.0), localB(0.0);
 
            if ((*it)->apply(i, itsBunch_m->getT() + 0.5 * dt, localE, localB)) {
                itsBunch_m->R[i] = localToRefCSTrafo.transformTo(itsBunch_m->R[i]);
                itsBunch_m->P[i] = localToRefCSTrafo.rotateTo(itsBunch_m->P[i]);
                itsBunch_m->Bin[i] = -1;
                locPartOutOfBounds = true;
 
                continue;
            }
 
            itsBunch_m->R[i] = localToRefCSTrafo.transformTo(itsBunch_m->R[i]);
            itsBunch_m->P[i] = localToRefCSTrafo.rotateTo(itsBunch_m->P[i]);
            itsBunch_m->Ef[i] += localToRefCSTrafo.rotateTo(localE);
            itsBunch_m->Bf[i] += localToRefCSTrafo.rotateTo(localB);
        }
    }
 
    IpplTimings::stopTimer(fieldEvaluationTimer_m);
 
    computeWakefield(elements);
#ifdef ENABLE_OPAL_FEL
    computeUndulator(elements);
#endif
    computeParticleMatterInteraction(elements, oth);
 
    reduce(locPartOutOfBounds, globPartOutOfBounds, OpOrAssign());
 
    size_t ne = 0;
    if (globPartOutOfBounds) {
        if (itsBunch_m->hasFieldSolver()) {
            ne = itsBunch_m->boundp_destroyT();
        } else {
            ne = itsBunch_m->destroyT();
        }
        numParticlesInSimulation_m  = itsBunch_m->getTotalNum();
        deletedParticles_m = true;
    }
 
    size_t totalNum = itsBunch_m->getTotalNum();
    if (numParticlesInSimulation_m > minBinEmitted_m || totalNum > minBinEmitted_m) {
        numParticlesInSimulation_m = totalNum;
    }
 
    if (ne > 0) {
        msg << level1 << "* Deleted " << ne << " particles, "
            << "remaining " << numParticlesInSimulation_m << " particles" << endl;
    }
}
 
#ifdef ENABLE_OPAL_FEL
void ParallelTTracker::computeUndulator(IndexMap::value_t &elements) {
    // Check if bunch has entered undulator field.
    UndulatorRep* und;
    IndexMap::value_t::const_iterator it = elements.begin();
    for (; it != elements.end(); ++ it)
        if ((*it)->getType() == ElementType::UNDULATOR) {
            und = dynamic_cast<UndulatorRep*>(it->get());
            if (!und->getHasBeenSimulated())
                break;
        }
    if (it == elements.end())
        return;
 
    // Apply MITHRA full wave solver for undulator.
    CoordinateSystemTrafo refToLocalCSTrafo = (itsOpalBeamline_m.getMisalignment((*it)) *
                                               (itsOpalBeamline_m.getCSTrafoLab2Local((*it)) * itsBunch_m->toLabTrafo_m));
 
    und->apply(itsBunch_m, refToLocalCSTrafo);
 
    evenlyDistributeParticles();
}
#endif
 
void ParallelTTracker::computeWakefield(IndexMap::value_t &elements) {
    bool hasWake = false;
    WakeFunction *wfInstance;
 
    Inform msg("ParallelTTracker ", *gmsg);
 
    const unsigned int localNum = itsBunch_m->getLocalNum();
 
    IndexMap::value_t::const_iterator it = elements.begin();
    const IndexMap::value_t::const_iterator end = elements.end();
 
    for (; it != end; ++ it) {
        if ((*it)->hasWake() && !hasWake) {
            IpplTimings::startTimer(WakeFieldTimer_m);
 
            hasWake = true;
 
            if ((*it)->getWake()->getType() == WakeType::CSRWakeFunction ||
                (*it)->getWake()->getType() == WakeType::CSRIGFWakeFunction) {
                if ((*it)->getType() == ElementType::RBEND ||
                    (*it)->getType() == ElementType::SBEND) {
                    wfInstance = (*it)->getWake();
                    wakeFunction_m = wfInstance;
                } else {
                    wfInstance = wakeFunction_m;
                }
            } else {
                wfInstance = (*it)->getWake();
            }
 
            if (!wfInstance) {
                throw OpalException("ParallelTTracker::computeWakefield",
                                    "empty wake function");
            }
 
            if (!wakeStatus_m) {
                msg << level2 << "============== START WAKE CALCULATION =============" << endl;
                wfInstance->initialize((*it).get());
                wakeStatus_m = true;
            }
 
            if (!itsBunch_m->hasFieldSolver()) itsBunch_m->calcBeamParameters();
 
            Quaternion alignment = getQuaternion(itsBunch_m->get_pmean(), Vector_t(0, 0, 1));
            CoordinateSystemTrafo referenceToBeamCSTrafo(Vector_t(0.0), alignment);
            CoordinateSystemTrafo beamToReferenceCSTrafo = referenceToBeamCSTrafo.inverted();
 
            for (unsigned int i = 0; i < localNum; ++ i) {
                itsBunch_m->R[i] = referenceToBeamCSTrafo.transformTo(itsBunch_m->R[i]);
                itsBunch_m->P[i] = referenceToBeamCSTrafo.rotateTo(itsBunch_m->P[i]);
                itsBunch_m->Ef[i] = referenceToBeamCSTrafo.rotateTo(itsBunch_m->Ef[i]);
            }
 
            wfInstance->apply(itsBunch_m);
 
            for (unsigned int i = 0; i < localNum; ++ i) {
                itsBunch_m->R[i] = beamToReferenceCSTrafo.transformTo(itsBunch_m->R[i]);
                itsBunch_m->P[i] = beamToReferenceCSTrafo.rotateTo(itsBunch_m->P[i]);
                itsBunch_m->Ef[i] = beamToReferenceCSTrafo.rotateTo(itsBunch_m->Ef[i]);
            }
 
            IpplTimings::stopTimer(WakeFieldTimer_m);
        }
    }
 
    if (wakeStatus_m && !hasWake) {
        msg << level2 << "=============== END WAKE CALCULATION ==============" << endl;
        wakeStatus_m = false;
    }
}
 
void ParallelTTracker::computeParticleMatterInteraction(IndexMap::value_t elements, OrbitThreader &oth) {
    Inform msg("ParallelTTracker ", *gmsg);
    std::set<IndexMap::value_t::value_type> elementsWithParticleMatterInteraction;
    std::set<ParticleMatterInteractionHandler*> particleMatterinteractionHandlers;
    IndexMap::key_t currentRange{0.0, 0.0};
 
    while (elements.size() > 0) {
        auto it = elements.begin();
        if ((*it)->hasParticleMatterInteraction()) {
            elementsWithParticleMatterInteraction.insert(*it);
            particleMatterinteractionHandlers.insert((*it)->getParticleMatterInteraction());
 
            IndexMap::key_t range = oth.getRange(*it, pathLength_m);
            currentRange.begin = std::min(currentRange.begin, range.begin);
            currentRange.end = std::max(currentRange.end, range.end);
 
            IndexMap::value_t touching = oth.getTouchingElements(range);
            elements.insert(touching.begin(), touching.end());
        }
 
        elements.erase(it);
    }
 
    if (!elementsWithParticleMatterInteraction.empty()) {
        std::set<ParticleMatterInteractionHandler*> oldSPHandlers;
        std::vector<ParticleMatterInteractionHandler*> leftBehindSPHandlers, newSPHandlers;
        for (auto it: activeParticleMatterInteractionHandlers_m) {
            oldSPHandlers.insert(it);
        }
 
        leftBehindSPHandlers.resize(std::max(oldSPHandlers.size(),
                                             particleMatterinteractionHandlers.size()));
        auto last = std::set_difference(oldSPHandlers.begin(), oldSPHandlers.end(),
                                        particleMatterinteractionHandlers.begin(), particleMatterinteractionHandlers.end(),
                                        leftBehindSPHandlers.begin());
        leftBehindSPHandlers.resize(last - leftBehindSPHandlers.begin());
 
        for (auto it: leftBehindSPHandlers) {
            if (!it->stillActive()) {
                activeParticleMatterInteractionHandlers_m.erase(it);
            }
        }
 
        newSPHandlers.resize(std::max(oldSPHandlers.size(),
                                      elementsWithParticleMatterInteraction.size()));
        last = std::set_difference(particleMatterinteractionHandlers.begin(), particleMatterinteractionHandlers.end(),
                                   oldSPHandlers.begin(), oldSPHandlers.end(),
                                   newSPHandlers.begin());
        newSPHandlers.resize(last - newSPHandlers.begin());
 
        for (auto it: newSPHandlers) {
            activeParticleMatterInteractionHandlers_m.insert(it);
        }
 
        if(!particleMatterStatus_m) {
            msg << level2 << "============== START PARTICLE MATTER INTERACTION CALCULATION =============" << endl;
            particleMatterStatus_m = true;
        }
    } else {
        for (auto it = activeParticleMatterInteractionHandlers_m.begin();
             it != activeParticleMatterInteractionHandlers_m.end();) {
            if (!(*it)->stillActive()) {
                auto next = std::next(it);
                activeParticleMatterInteractionHandlers_m.erase(it);
                it = next;
            } else {
                it = std::next(it);
            }
        }
    }
 
    if (particleMatterStatus_m) {
        do {
            //check if more than one degrader has particles
            ParticleMatterInteractionHandler* onlyDegraderWithParticles = nullptr;
            int degradersWithParticlesCount = 0;
            for (auto it: activeParticleMatterInteractionHandlers_m) {
                it->setFlagAllParticlesIn(false);
                if (it->getParticlesInMat() > 0) {
                    onlyDegraderWithParticles = it;
                    ++ degradersWithParticlesCount;
                }
            }
 
            //if max particles per node is 2, and only one degrader has particles set
            //AllParticlesIn for this degrader to true
            unsigned int localNum = itsBunch_m->getLocalNum();
            unsigned int totalNum = 0;
            reduce(localNum, totalNum, OpAddAssign());
            bool allParticlesInMat = (totalNum == 0 &&
                                      degradersWithParticlesCount == 1);
 
            if (allParticlesInMat) {
                onlyDegraderWithParticles->setFlagAllParticlesIn(true);
                msg << "All particles in degrader" << endl;
            }
 
            auto boundingSphere = itsBunch_m->getLocalBoundingSphere();
            unsigned int rediffusedParticles = 0;
            unsigned int numEnteredParticles = 0;
            for (auto it: activeParticleMatterInteractionHandlers_m) {
                ElementBase* element = it->getElement();
                CoordinateSystemTrafo refToLocalCSTrafo = (element->getMisalignment() *
                                                           (element->getCSTrafoGlobal2Local() * itsBunch_m->toLabTrafo_m));
                CoordinateSystemTrafo localToRefCSTrafo = refToLocalCSTrafo.inverted();
 
                const unsigned int localNum = itsBunch_m->getLocalNum();
                for (unsigned int i = 0; i < localNum; ++i) {
                    itsBunch_m->R[i] = refToLocalCSTrafo.transformTo(itsBunch_m->R[i]);
                    itsBunch_m->P[i] = refToLocalCSTrafo.rotateTo(itsBunch_m->P[i]);
                }
                boundingSphere.first = refToLocalCSTrafo.transformTo(boundingSphere.first);
 
                it->apply(itsBunch_m, boundingSphere);
                it->print(msg);
 
                boundingSphere.first = localToRefCSTrafo.transformTo(boundingSphere.first);
 
                const unsigned int newLocalNum = itsBunch_m->getLocalNum();
                for (unsigned int i = 0; i < newLocalNum; ++i) {
                    itsBunch_m->R[i] = localToRefCSTrafo.transformTo(itsBunch_m->R[i]);
                    itsBunch_m->P[i] = localToRefCSTrafo.rotateTo(itsBunch_m->P[i]);
                }
 
                rediffusedParticles += it->getRediffused();
                numEnteredParticles += it->getNumEntered();
 
                //if all particles were in material update time to time in degrader
                if (it->getFlagAllParticlesIn()) {
                    double timeDifference = it->getTime() - itsBunch_m->getdT() - itsBunch_m->getT();
                    if (timeDifference > 0.0) {
                        const unsigned int numSteps = std::ceil(timeDifference / itsBunch_m->getdT());
                        const double origdT = itsBunch_m->getdT();
                        itsBunch_m->setdT(timeDifference / numSteps);
                        BorisPusher pusher(itsReference);
                        for (unsigned int i = 0; i < numSteps; ++ i) {
                            updateReference(pusher);
                        }
                        itsBunch_m->setdT(origdT);
                    }
                    itsBunch_m->setT(it->getTime() - itsBunch_m->getdT());
                }
            }
 
            //perform boundp only if there are particles in the bunch, or there are particles
            //comming out of the degrader
            if (numEnteredParticles > 0 || rediffusedParticles > 0) {
                totalNum -= (numEnteredParticles + rediffusedParticles);
                if (totalNum > minBinEmitted_m && itsBunch_m->hasFieldSolver()) {
                    itsBunch_m->boundp();
                } else {
                    itsBunch_m->updateNumTotal();
                }
            }
 
            //if bunch has no particles update time to time in degrader
            if (itsBunch_m->getTotalNum() == 0)
                itsBunch_m->incrementT();
 
        } while (itsBunch_m->getTotalNum() == 0);
 
 
        if (activeParticleMatterInteractionHandlers_m.empty()) {
            msg << level2 << "============== END PARTICLE MATTER INTERACTION CALCULATION =============" << endl;
            particleMatterStatus_m = false;
        }
    }
}
 
void ParallelTTracker::doBinaryRepartition() {
    size_t particles_or_bins = std::max(minBinEmitted_m, size_t(1000));
    if (itsBunch_m->hasFieldSolver() && numParticlesInSimulation_m > particles_or_bins) {
 
        INFOMSG("*****************************************************************" << endl);
        INFOMSG("do repartition because of repartFreq_m" << endl);
        INFOMSG("*****************************************************************" << endl);
        IpplTimings::startTimer(BinRepartTimer_m);
        itsBunch_m->do_binaryRepart();
        Ippl::Comm->barrier();
        IpplTimings::stopTimer(BinRepartTimer_m);
        INFOMSG("*****************************************************************" << endl);
        INFOMSG("do repartition done" << endl);
        INFOMSG("*****************************************************************" << endl);
    }
}
 
void ParallelTTracker::dumpStats(long long step, bool psDump, bool statDump) {
    OPALTimer::Timer myt2;
    Inform msg("ParallelTTracker ", *gmsg);
 
    if (itsBunch_m->getGlobalTrackStep() % 1000 + 1 == 1000) {
        msg << level1;
    } else if (itsBunch_m->getGlobalTrackStep() % 100 + 1 == 100) {
        msg << level2;
    } else {
        msg << level3;
    }
 
    if (numParticlesInSimulation_m == 0) {
        msg << myt2.time() << " "
            << "Step " << std::setw(6) <<  itsBunch_m->getGlobalTrackStep() << "; "
            << "   -- no emission yet --     "
            << "t= "   << Util::getTimeString(itsBunch_m->getT())
            << endl;
        return;
    }
 
    itsBunch_m->calcEMean();
    size_t totalParticles_f = numParticlesInSimulation_m;
    if (totalParticles_f <= minBinEmitted_m) {
        msg << myt2.time() << " "
            << "Step " << std::setw(6) << itsBunch_m->getGlobalTrackStep() << "; "
            << "only " << std::setw(4) << totalParticles_f << " particles emitted; "
            << "t= "   << Util::getTimeString(itsBunch_m->getT()) << ", "
            << "E="    << Util::getEnergyString(itsBunch_m->get_meanKineticEnergy()) << ", "
            << endl;
    } else if (std::isnan(pathLength_m) || std::isinf(pathLength_m)) {
        throw OpalException("ParallelTTracker::dumpStats()",
                            "there seems to be something wrong with the position of the bunch!");
    } else {
 
        msg << myt2.time() << " "
            << "Step " << std::setw(6)  <<  itsBunch_m->getGlobalTrackStep() << " "
            << "at "   << Util::getLengthString(pathLength_m) << ", "
            << "t= "   << Util::getTimeString(itsBunch_m->getT()) << ", "
            << "E="    << Util::getEnergyString(itsBunch_m->get_meanKineticEnergy())
            << endl;
 
        writePhaseSpace(step, psDump, statDump);
    }
}
 
 
void ParallelTTracker::setOptionalVariables() {
    Inform msg("ParallelTTracker ", *gmsg);
 
    minBinEmitted_m  = Options::minBinEmitted;
    RealVariable *ar = dynamic_cast<RealVariable *>(OpalData::getInstance()->find("MINBINEMITTED"));
    if (ar)
        minBinEmitted_m = static_cast<size_t>(ar->getReal());
    msg << level2 << "MINBINEMITTED " << minBinEmitted_m << endl;
 
    minStepforReBin_m  = Options::minStepForRebin;
    RealVariable *br = dynamic_cast<RealVariable *>(OpalData::getInstance()->find("MINSTEPFORREBIN"));
    if (br)
        minStepforReBin_m = static_cast<int>(br->getReal());
    msg << level2 << "MINSTEPFORREBIN " << minStepforReBin_m << endl;
 
    // there is no point to do repartitioning with one node
    if (Ippl::getNodes() == 1) {
        repartFreq_m = std::numeric_limits<unsigned int>::max();
    } else {
        repartFreq_m = Options::repartFreq * 100;
        RealVariable *rep = dynamic_cast<RealVariable *>(OpalData::getInstance()->find("REPARTFREQ"));
        if (rep)
            repartFreq_m = static_cast<int>(rep->getReal());
        msg << level2 << "REPARTFREQ " << repartFreq_m << endl;
    }
}
 
 
bool ParallelTTracker::hasEndOfLineReached(const BoundingBox& globalBoundingBox) {
    reduce(&globalEOL_m, &globalEOL_m + 1, &globalEOL_m, OpBitwiseAndAssign());
    globalEOL_m = globalEOL_m || globalBoundingBox.isOutside(itsBunch_m->RefPartR_m);
    return globalEOL_m;
}
 
void ParallelTTracker::setTime() {
    const unsigned int localNum = itsBunch_m->getLocalNum();
    for (unsigned int i = 0; i < localNum; ++i) {
        itsBunch_m->dt[i] = itsBunch_m->getdT();
    }
}
 
void ParallelTTracker::prepareEmission() {
    Inform msg("ParallelTTracker ", *gmsg);
 
    if (!itsBunch_m->doEmission()) return;
 
    emissionSteps_m = itsBunch_m->getNumberOfEmissionSteps();
    msg << level2 << "Do emission for " << itsBunch_m->getTEmission() << " [s] using "
        << itsBunch_m->getNumberOfEnergyBins() << " energy bins " << endl
        << "Change dT from " <<  itsBunch_m->getdT() << " [s] to "
        <<  itsBunch_m->getEmissionDeltaT() << " [s] during emission " << endl;;
 
}
 
void ParallelTTracker::writePhaseSpace(const long long /*step*/, bool psDump, bool statDump) {
    extern Inform *gmsg;
    Inform msg("OPAL ", *gmsg);
    Vector_t externalE, externalB;
    Vector_t FDext[2];  // FDext = {BHead, EHead, BRef, ERef, BTail, ETail}.
 
    // Sample fields at (xmin, ymin, zmin), (xmax, ymax, zmax) and the centroid location. We
    // are sampling the electric and magnetic fields at the back, front and
    // center of the beam.
    Vector_t rmin, rmax;
    itsBunch_m->get_bounds(rmin, rmax);
 
    if (psDump || statDump) {
        externalB = Vector_t(0.0);
        externalE = Vector_t(0.0);
        itsOpalBeamline_m.getFieldAt(itsBunch_m->RefPartR_m,
                                     itsBunch_m->RefPartP_m,
                                     itsBunch_m->getT() - 0.5 * itsBunch_m->getdT(),
                                     externalE,
                                     externalB);
        FDext[0] = itsBunch_m->toLabTrafo_m.rotateFrom(externalB);
        FDext[1] = itsBunch_m->toLabTrafo_m.rotateFrom(externalE * Units::Vpm2MVpm);
    }
 
    if (statDump) {
        std::vector<std::pair<std::string, unsigned int> > collimatorLosses;
        FieldList collimators = itsOpalBeamline_m.getElementByType(ElementType::CCOLLIMATOR);
        if (!collimators.empty()) {
            for (FieldList::iterator it = collimators.begin(); it != collimators.end(); ++ it) {
                FlexibleCollimator* coll = static_cast<FlexibleCollimator*>(it->getElement().get());
                std::string name = coll->getName();
                unsigned int losses = coll->getLosses();
                collimatorLosses.push_back(std::make_pair(name, losses));
            }
            std::sort(collimatorLosses.begin(), collimatorLosses.end(),
                      [](const std::pair<std::string, unsigned int>& a, const std::pair<std::string, unsigned int>& b) ->bool {
                          return a.first < b.first;
                      });
            std::vector<unsigned int> bareLosses(collimatorLosses.size(),0);
            for (size_t i = 0; i < collimatorLosses.size(); ++ i){
                bareLosses[i] = collimatorLosses[i].second;
            }
 
            reduce(&bareLosses[0], &bareLosses[0] + bareLosses.size(), &bareLosses[0], OpAddAssign());
 
            for (size_t i = 0; i < collimatorLosses.size(); ++ i){
                collimatorLosses[i].second = bareLosses[i];
            }
        }
        // Write statistical data.
        itsDataSink_m->dumpSDDS(itsBunch_m, FDext, collimatorLosses);
 
        msg << level3 << "* Wrote beam statistics." << endl;
    }
 
    if (psDump && (itsBunch_m->getTotalNum() > 0)) {
        // Write fields to .h5 file.
        const size_t localNum = itsBunch_m->getLocalNum();
        double distToLastStop = stepSizes_m.getFinalZStop() - pathLength_m;
        Vector_t beta = itsBunch_m->RefPartP_m / Util::getGamma(itsBunch_m->RefPartP_m);
        Vector_t driftPerTimeStep = itsBunch_m->getdT() * Physics::c * itsBunch_m->toLabTrafo_m.rotateFrom(beta);
        bool driftToCorrectPosition = std::abs(distToLastStop) < 0.5 * euclidean_norm(driftPerTimeStep);
        Ppos_t stashedR;
        Vector_t stashedRefPartR;
 
        if (driftToCorrectPosition) {
            const double tau = distToLastStop / euclidean_norm(driftPerTimeStep) * itsBunch_m->getdT();
            if (localNum > 0) {
                stashedR.create(localNum);
                stashedR = itsBunch_m->R;
                stashedRefPartR = itsBunch_m->RefPartR_m;
 
                for (size_t i = 0; i < localNum; ++ i) {
                    itsBunch_m->R[i] += tau * (Physics::c * itsBunch_m->P[i] / Util::getGamma(itsBunch_m->P[i]) -
                                               driftPerTimeStep / itsBunch_m->getdT());
                }
            }
 
            driftPerTimeStep = itsBunch_m->toLabTrafo_m.rotateTo(driftPerTimeStep);
            itsBunch_m->RefPartR_m = itsBunch_m->RefPartR_m + tau * driftPerTimeStep / itsBunch_m->getdT();
            CoordinateSystemTrafo update(tau * driftPerTimeStep / itsBunch_m->getdT(),
                                         Quaternion(1.0, 0.0, 0.0, 0.0));
            itsBunch_m->toLabTrafo_m = itsBunch_m->toLabTrafo_m * update.inverted();
 
            itsBunch_m->set_sPos(stepSizes_m.getFinalZStop());
 
            itsBunch_m->calcBeamParameters();
        }
        if (!statDump && !driftToCorrectPosition) itsBunch_m->calcBeamParameters();
 
        msg << *itsBunch_m << endl;
        itsDataSink_m->dumpH5(itsBunch_m, FDext);
 
        if (driftToCorrectPosition) {
            if (localNum > 0) {
                itsBunch_m->R = stashedR;
                stashedR.destroy(localNum, 0);
            }
 
            itsBunch_m->RefPartR_m = stashedRefPartR;
            itsBunch_m->set_sPos(pathLength_m);
 
            itsBunch_m->calcBeamParameters();
        }
 
        msg << level2 << "* Wrote beam phase space." << endl;
    }
}
 
void ParallelTTracker::updateReference(const BorisPusher &pusher) {
    updateReferenceParticle(pusher);
    updateRefToLabCSTrafo();
}
 
void ParallelTTracker::updateReferenceParticle(const BorisPusher &pusher) {
    const double direction = back_track? -1: 1;
    const double dt = direction * std::min(itsBunch_m->getT(),
                                           direction * itsBunch_m->getdT());
    const double scaleFactor = Physics::c * dt;
    Vector_t Ef(0.0), Bf(0.0);
 
    itsBunch_m->RefPartR_m /= scaleFactor;
    pusher.push(itsBunch_m->RefPartR_m, itsBunch_m->RefPartP_m, dt);
    itsBunch_m->RefPartR_m *= scaleFactor;
 
    IndexMap::value_t elements = itsOpalBeamline_m.getElements(itsBunch_m->RefPartR_m);
    IndexMap::value_t::const_iterator it = elements.begin();
    const IndexMap::value_t::const_iterator end = elements.end();
 
    for (; it != end; ++ it) {
        const CoordinateSystemTrafo &refToLocalCSTrafo = itsOpalBeamline_m.getCSTrafoLab2Local((*it));
 
        Vector_t localR = refToLocalCSTrafo.transformTo(itsBunch_m->RefPartR_m);
        Vector_t localP = refToLocalCSTrafo.rotateTo(itsBunch_m->RefPartP_m);
        Vector_t localE(0.0), localB(0.0);
 
        if ((*it)->applyToReferenceParticle(localR,
                                            localP,
                                            itsBunch_m->getT() - 0.5 * dt,
                                            localE,
                                            localB)) {
            *gmsg << level1 << "The reference particle hit an element" << endl;
            globalEOL_m = true;
        }
 
        Ef += refToLocalCSTrafo.rotateFrom(localE);
        Bf += refToLocalCSTrafo.rotateFrom(localB);
    }
 
    pusher.kick(itsBunch_m->RefPartR_m, itsBunch_m->RefPartP_m, Ef, Bf, dt);
 
    itsBunch_m->RefPartR_m /= scaleFactor;
    pusher.push(itsBunch_m->RefPartR_m, itsBunch_m->RefPartP_m, dt);
    itsBunch_m->RefPartR_m *= scaleFactor;
}
 
void ParallelTTracker::transformBunch(const CoordinateSystemTrafo &trafo) {
    const unsigned int localNum = itsBunch_m->getLocalNum();
    for (unsigned int i = 0; i < localNum; ++i) {
        itsBunch_m->R[i] = trafo.transformTo(itsBunch_m->R[i]);
        itsBunch_m->P[i] = trafo.rotateTo(itsBunch_m->P[i]);
        itsBunch_m->Ef[i] = trafo.rotateTo(itsBunch_m->Ef[i]);
        itsBunch_m->Bf[i] = trafo.rotateTo(itsBunch_m->Bf[i]);
    }
}
 
void ParallelTTracker::updateRefToLabCSTrafo() {
    Vector_t R = itsBunch_m->toLabTrafo_m.transformFrom(itsBunch_m->RefPartR_m);
    Vector_t P = itsBunch_m->toLabTrafo_m.rotateFrom(itsBunch_m->RefPartP_m);
 
    pathLength_m += std::copysign(1, itsBunch_m->getdT()) * euclidean_norm(R);
 
    CoordinateSystemTrafo update(R, getQuaternion(P, Vector_t(0, 0, 1)));
 
    transformBunch(update);
 
    itsBunch_m->toLabTrafo_m = itsBunch_m->toLabTrafo_m * update.inverted();
}
 
void ParallelTTracker::applyFractionalStep(const BorisPusher &pusher, double tau) {
    double t = itsBunch_m->getT();
    t += tau;
    itsBunch_m->setT(t);
 
    // the push method below pushes for half a time step. Hence the ref particle
    // should be pushed for 2 * tau
    itsBunch_m->RefPartR_m /= (Physics::c * 2 * tau);
    pusher.push(itsBunch_m->RefPartR_m, itsBunch_m->RefPartP_m, tau);
    itsBunch_m->RefPartR_m *= (Physics::c * 2 * tau);
 
    pathLength_m = zstart_m;
 
    Vector_t R = itsBunch_m->toLabTrafo_m.transformFrom(itsBunch_m->RefPartR_m);
    Vector_t P = itsBunch_m->toLabTrafo_m.rotateFrom(itsBunch_m->RefPartP_m);
    CoordinateSystemTrafo update(R, getQuaternion(P, Vector_t(0, 0, 1)));
    itsBunch_m->toLabTrafo_m = itsBunch_m->toLabTrafo_m * update.inverted();
}
 
void ParallelTTracker::findStartPosition(const BorisPusher &pusher) {
 
    StepSizeConfig stepSizesCopy(stepSizes_m);
    if (back_track) {
        stepSizesCopy.shiftZStopLeft(zstart_m);
    }
 
    double t = 0.0;
    itsBunch_m->setT(t);
 
    dtCurrentTrack_m = stepSizesCopy.getdT();
    selectDT();
 
    if ((back_track && itsOpalBeamline_m.containsSource()) ||
        Util::getKineticEnergy(itsBunch_m->RefPartP_m, itsBunch_m->getM()) < 1e-3) {
        double gamma = 0.1 / itsBunch_m->getM() + 1.0;
        double beta = sqrt(1.0 - 1.0 / std::pow(gamma, 2));
        itsBunch_m->RefPartP_m = itsBunch_m->toLabTrafo_m.rotateTo(beta * gamma * Vector_t(0, 0, 1));
    }
 
    while (true) {
        autophaseCavities(pusher);
 
        t += itsBunch_m->getdT();
        itsBunch_m->setT(t);
 
        Vector_t oldR = itsBunch_m->RefPartR_m;
        updateReferenceParticle(pusher);
        pathLength_m += euclidean_norm(itsBunch_m->RefPartR_m - oldR);
 
        double speed = euclidean_norm(itsBunch_m->RefPartP_m * Physics::c / Util::getGamma(itsBunch_m->RefPartP_m));
 
        if (pathLength_m > stepSizesCopy.getZStop()) {
            ++ stepSizesCopy;
 
            if (stepSizesCopy.reachedEnd()) {
                -- stepSizesCopy;
                double tau = (stepSizesCopy.getZStop() - pathLength_m) / speed;
                applyFractionalStep(pusher, tau);
 
                break;
            }
 
            dtCurrentTrack_m = stepSizesCopy.getdT();
            selectDT();
        }
 
        if (std::abs(pathLength_m - zstart_m) <=  0.5 * itsBunch_m->getdT() * speed) {
            double tau = (zstart_m - pathLength_m) / speed;
            applyFractionalStep(pusher, tau);
 
            break;
        }
    }
 
    changeDT();
}
 
void ParallelTTracker::autophaseCavities(const BorisPusher &pusher) {
 
    double t = itsBunch_m->getT();
    Vector_t nextR = itsBunch_m->RefPartR_m / (Physics::c * itsBunch_m->getdT());
    pusher.push(nextR, itsBunch_m->RefPartP_m, itsBunch_m->getdT());
    nextR *= Physics::c * itsBunch_m->getdT();
 
    auto elementSet = itsOpalBeamline_m.getElements(nextR);
    for (auto element: elementSet) {
        if (element->getType() == ElementType::TRAVELINGWAVE) {
            const TravelingWave *TWelement = static_cast<const TravelingWave *>(element.get());
            if (!TWelement->getAutophaseVeto()) {
                CavityAutophaser ap(itsReference, element);
                ap.getPhaseAtMaxEnergy(itsOpalBeamline_m.transformToLocalCS(element, itsBunch_m->RefPartR_m),
                                       itsOpalBeamline_m.rotateToLocalCS(element, itsBunch_m->RefPartP_m),
                                       t, itsBunch_m->getdT());
            }
 
        } else if (element->getType() == ElementType::RFCAVITY) {
            const RFCavity *RFelement = static_cast<const RFCavity *>(element.get());
            if (!RFelement->getAutophaseVeto()) {
                CavityAutophaser ap(itsReference, element);
                ap.getPhaseAtMaxEnergy(itsOpalBeamline_m.transformToLocalCS(element, itsBunch_m->RefPartR_m),
                                       itsOpalBeamline_m.rotateToLocalCS(element, itsBunch_m->RefPartP_m),
                                       t, itsBunch_m->getdT());
            }
        }
    }
}
 
struct DistributionInfo {
    unsigned int who;
    unsigned int whom;
    unsigned int howMany;
};
 
void ParallelTTracker::evenlyDistributeParticles() {
    const int numNodes = Ippl::getNodes();
    if (itsBunch_m->hasFieldSolver() || numNodes == 1) return;
 
    long onAverage = itsBunch_m->getTotalNum() / Ippl::getNodes();
    if (itsBunch_m->getTotalNum() % Ippl::getNodes() > 0.5 * Ippl::getNodes())
        ++ onAverage;
 
    std::vector<long> localParticles(numNodes, 0);
    localParticles[Ippl::myNode()] = itsBunch_m->getLocalNum() - onAverage;
    allreduce(&(localParticles[0]),
              numNodes,
              std::plus<long>());
 
    std::vector<DistributionInfo> send;
    std::vector<DistributionInfo> receive;
 
    for (int i = 0; i < Ippl::getNodes(); ++ i) {
        if (localParticles[i] <= 0) continue;
 
        for (int j = 0; j < Ippl::getNodes(); ++ j) {
            if (j == i || localParticles[j] >= 0) continue;
 
            long numParts = std::min(localParticles[i], -localParticles[j]);
            localParticles[i] -= numParts;
            localParticles[j] += numParts;
 
            if (i == Ippl::myNode() || j == Ippl::myNode()) {
                DistributionInfo request;
                request.who = i;
                request.whom = j;
                request.howMany = numParts;
 
                if (i == Ippl::myNode()) {
                    send.push_back(request);
                } else {
                    receive.push_back(request);
                }
            }
 
            if (localParticles[i] == 0) break;
        }
    }
 
    std::vector<MPI_Request> requests;
    const long sizeSingleParticle = 9 * sizeof(double) + sizeof(short) + sizeof(int) + sizeof(PID_t::Return_t);
    long idx = itsBunch_m->getLocalNum() - 1;
    int tag = Ippl::Comm->next_tag(P_SPATIAL_TRANSFER_TAG, P_LAYOUT_CYCLE);
 
    std::vector<char> send_msgbuf;
 
    if (!send.empty()) {
        const char *buffer;
 
        unsigned int totalSend = 0, startIndex = 0;
        for (DistributionInfo &request: send) {
            totalSend += request.howMany;
        }
        send_msgbuf.reserve(totalSend * sizeSingleParticle);
 
        for (DistributionInfo &request: send) {
            size_t sizePrior = send_msgbuf.size();
            for (long i = 0; i < request.howMany; ++ i, -- idx) {
                buffer = reinterpret_cast<const char*>(&(itsBunch_m->R[idx](0)));
                send_msgbuf.insert(send_msgbuf.end(), buffer, buffer + 3 * sizeof(double));
                buffer = reinterpret_cast<const char*>(&(itsBunch_m->P[idx](0)));
                send_msgbuf.insert(send_msgbuf.end(), buffer, buffer + 3 * sizeof(double));
                buffer = reinterpret_cast<const char*>(&(itsBunch_m->Q[idx]));
                send_msgbuf.insert(send_msgbuf.end(), buffer, buffer + sizeof(double));
                buffer = reinterpret_cast<const char*>(&(itsBunch_m->M[idx]));
                send_msgbuf.insert(send_msgbuf.end(), buffer, buffer + sizeof(double));
                buffer = reinterpret_cast<const char*>(&(itsBunch_m->dt[idx]));
                send_msgbuf.insert(send_msgbuf.end(), buffer, buffer + sizeof(double));
                buffer = reinterpret_cast<const char*>(&(itsBunch_m->POrigin[idx]));
                send_msgbuf.insert(send_msgbuf.end(), buffer, buffer + sizeof(ParticleOrigin));
                buffer = reinterpret_cast<const char*>(&(itsBunch_m->TriID[idx]));
                send_msgbuf.insert(send_msgbuf.end(), buffer, buffer + sizeof(int));
                buffer = reinterpret_cast<const char*>(&(itsBunch_m->ID[idx]));
                send_msgbuf.insert(send_msgbuf.end(), buffer, buffer + sizeof(PID_t::Return_t));
            }
 
            size_t sendSizeThis = send_msgbuf.size() - sizePrior;
            MPI_Request req = Ippl::Comm->raw_isend(&(send_msgbuf[startIndex]),
                                                    sendSizeThis,
                                                    request.whom,
                                                    tag);
 
            requests.push_back(req);
 
            startIndex += sendSizeThis;
        }
 
        itsBunch_m->destroy(totalSend, idx + 1, true);
    }
 
    for (unsigned int i = 0; i < receive.size(); ++ i) {
        int node = Communicate::COMM_ANY_NODE;
        char *recvbuf;
        const int bufsize = Ippl::Comm->raw_probe_receive(recvbuf, node, tag);
 
        int j = 0;
 
        while (j < bufsize) {
            ++ idx;
            itsBunch_m->create(1);
            {
                const double *buffer = reinterpret_cast<const double*>(recvbuf + j);
                itsBunch_m->R[idx] = Vector_t(buffer[0], buffer[1], buffer[2]);
                itsBunch_m->P[idx] = Vector_t(buffer[3], buffer[4], buffer[5]);
                itsBunch_m->Q[idx] = buffer[6];
                itsBunch_m->M[idx] = buffer[7];
                itsBunch_m->dt[idx] = buffer[8];
            }
            j += 9 * sizeof(double);
 
            {
                const ParticleOrigin *buffer = reinterpret_cast<const ParticleOrigin*>(recvbuf + j);
                itsBunch_m->POrigin[idx] = buffer[0];
            }
            j += sizeof(ParticleOrigin);
 
            {
                const int *buffer = reinterpret_cast<const int*>(recvbuf + j);
                itsBunch_m->TriID[idx] = buffer[0];
            }
            j += sizeof(int);
 
            {
                const PID_t::Return_t *buffer = reinterpret_cast<const PID_t::Return_t*>(recvbuf + j);
                itsBunch_m->ID[idx] = buffer[0];
            }
            j += sizeof(PID_t::Return_t);
        }
 
        delete[] recvbuf;
    }
 
    if (!requests.empty()) {
        MPI_Waitall(requests.size(), &(requests[0]), MPI_STATUSES_IGNORE);
    }
}