ParallelCyclotronTracker.cpp 152 KB
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// ------------------------------------------------------------------------
// $RCSfile: ParallelCyclotronTracker.cpp,v $
// ------------------------------------------------------------------------
// $Revision: 1.1 $initialLocalNum_m
// ------------------------------------------------------------------------
// Copyright: see Copyright.readme
// ------------------------------------------------------------------------
//
// Class: ParallelCyclotronTracker
//   The class for tracking particles with 3D space charge in Cyclotrons and FFAG's
//
// ------------------------------------------------------------------------
//
// $Date: 2007/10/17 04:00:08 $
// $Author: adelmann, yang $
//
// ------------------------------------------------------------------------
#include <cfloat>
#include <iostream>
#include <fstream>
#include <vector>
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#include "AbstractObjects/OpalData.h"
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#include "Algorithms/ParallelCyclotronTracker.h"

#include "AbsBeamline/Collimator.h"
#include "AbsBeamline/Corrector.h"
#include "AbsBeamline/Cyclotron.h"
#include "AbsBeamline/Diagnostic.h"
#include "AbsBeamline/Drift.h"
#include "AbsBeamline/ElementBase.h"
#include "AbsBeamline/Lambertson.h"
#include "AbsBeamline/Marker.h"
#include "AbsBeamline/Monitor.h"
#include "AbsBeamline/Multipole.h"
#include "AbsBeamline/Probe.h"
#include "AbsBeamline/RBend.h"
#include "AbsBeamline/RFCavity.h"
#include "AbsBeamline/RFQuadrupole.h"
#include "AbsBeamline/SBend.h"
#include "AbsBeamline/Separator.h"
#include "AbsBeamline/Septum.h"
#include "AbsBeamline/Solenoid.h"
#include "AbsBeamline/CyclotronValley.h"
#include "AbsBeamline/Stripper.h"

#include "BeamlineGeometry/Euclid3D.h"
#include "BeamlineGeometry/PlanarArcGeometry.h"
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#include "BeamlineGeometry/RBendGeometry.h"
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#include "Beamlines/Beamline.h"

#include "Fields/BMultipoleField.h"
#include "FixedAlgebra/FTps.h"
#include "FixedAlgebra/FTpsMath.h"
#include "FixedAlgebra/FVps.h"

#include "Physics/Physics.h"

#include "Utilities/NumToStr.h"
#include "Utilities/OpalException.h"


#include "Ctunes.h"
#include "Ctunes.cc"
#include <cassert>


#include <hdf5.h>
#include "H5hut.h"

class Beamline;
class PartData;
using Physics::c;
using Physics::m_p; // GeV
using Physics::PMASS;
using Physics::PCHARGE;
using Physics::pi;
using Physics::q_e;

const double c_mmtns = c * 1.0e-6; // m/s --> mm/ns
const double mass_coeff = 1.0e18 * q_e / c / c; // from GeV/c^2 to basic unit: GV*C*s^2/m^2

#define PSdim 6

extern Inform *gmsg;

// typedef FVector<double, PSdim> Vector;

/**
 * Constructor ParallelCyclotronTracker
 *
 * @param beamline
 * @param reference
 * @param revBeam
 * @param revTrack
 */
ParallelCyclotronTracker::ParallelCyclotronTracker(const Beamline &beamline,
        const PartData &reference,
        bool revBeam, bool revTrack):
    Tracker(beamline, reference, revBeam, revTrack),
    sphys(NULL),
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    eta_m(0.01),
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    myNode_m(Ippl::myNode()),
    initialLocalNum_m(0),
    initialTotalNum_m(0) {
    itsBeamline = dynamic_cast<Beamline *>(beamline.clone());
}

/**
 * Constructor ParallelCyclotronTracker
 *
 * @param beamline
 * @param bunch
 * @param ds
 * @param reference
 * @param revBeam
 * @param revTrack
 * @param maxSTEPS
 * @param timeIntegrator
 */
ParallelCyclotronTracker::ParallelCyclotronTracker(const Beamline &beamline,
                                                   PartBunch &bunch,
                                                   DataSink &ds,
                                                   const PartData &reference,
                                                   bool revBeam, bool revTrack,
                                                   int maxSTEPS, int timeIntegrator):
    Tracker(beamline, reference, revBeam, revTrack),
    sphys(NULL),
    maxSteps_m(maxSTEPS),
    timeIntegrator_m(timeIntegrator),
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    eta_m(0.01),
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    myNode_m(Ippl::myNode()),
    initialLocalNum_m(bunch.getLocalNum()),
    initialTotalNum_m(bunch.getTotalNum()) {
    itsBeamline = dynamic_cast<Beamline *>(beamline.clone());
    itsBunch = &bunch;
    itsDataSink = &ds;
    //  scaleFactor_m = itsBunch->getdT() * c;
    scaleFactor_m = 1;
    multiBunchMode_m = 0;

    IntegrationTimer_m = IpplTimings::getTimer("Integration");
    TransformTimer_m   = IpplTimings::getTimer("Frametransform");
    DumpTimer_m        = IpplTimings::getTimer("Dump");
    BinRepartTimer_m   = IpplTimings::getTimer("Binaryrepart");
}

/**
 * Destructor ParallelCyclotronTracker
 *
 */
ParallelCyclotronTracker::~ParallelCyclotronTracker() {
    for(list<Component *>::iterator compindex = myElements.begin(); compindex != myElements.end(); compindex++) {
        delete(*compindex);
    }
    for(beamline_list::iterator fdindex = FieldDimensions.begin(); fdindex != FieldDimensions.end(); fdindex++) {
        delete(*fdindex);
    }
    delete itsBeamline;
}

/**
 *
 *
 * @param fn Base file name
 */
void ParallelCyclotronTracker::openFiles(string SfileName) {

    string  SfileName2 = SfileName + string("-Angle0.dat");

    outfTheta0_m.precision(8);
    outfTheta0_m.setf(ios::scientific, ios::floatfield);

    outfTheta0_m.open(SfileName2.c_str());
    outfTheta0_m << "#  r [mm]          p_r[rad]       theta [mm]          p_theta[rad]        z [mm]          p_z[rad]"
                 << endl;

    SfileName2 = SfileName + string("-Angle1.dat");

    outfTheta1_m.precision(8);
    outfTheta1_m.setf(ios::scientific, ios::floatfield);

    outfTheta1_m.open(SfileName2.c_str());
    outfTheta1_m << "#  r [mm]          p_r[rad]       theta [mm]          p_theta[rad]        z [mm]          p_z[rad]"
                 << endl;

    SfileName2 = SfileName + string("-Angle2.dat");

    outfTheta2_m.precision(8);
    outfTheta2_m.setf(ios::scientific, ios::floatfield);

    outfTheta2_m.open(SfileName2.c_str());
    outfTheta2_m << "#  r [mm]          p_r[rad]       theta [mm]          p_theta[rad]        z [mm]          p_z[rad]"
                 << endl;

    // for single Particle Mode, output after each turn, to define matched initial phase ellipse.

    SfileName2 = SfileName + string("-afterEachTurn.dat");

    outfThetaEachTurn_m.precision(8);
    outfThetaEachTurn_m.setf(ios::scientific, ios::floatfield);

    outfThetaEachTurn_m.open(SfileName2.c_str());
    outfThetaEachTurn_m << "# r [mm]          p_r[rad]       theta [mm]          p_theta[rad]        z [mm]          p_z[rad]" << endl;

}

/**
 * Close all files related to
 * special output in the Cyclotron
 * mode.
 */
void ParallelCyclotronTracker::closeFiles() {

    outfTheta0_m.close();
    outfTheta1_m.close();
    outfTheta2_m.close();
    outfThetaEachTurn_m.close();
}



/**
 *
 *
 * @param cycl
 */
void ParallelCyclotronTracker::visitCyclotron(const Cyclotron &cycl) {

    *gmsg << "* --------- Cyclotron ------------------------------" << endl;

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    Cyclotron *elptr = dynamic_cast<Cyclotron *>(cycl.clone());
    myElements.push_back(elptr);
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    double ri = elptr->getRinit();
    *gmsg << "* RINIT= " << ri << " [mm]" << endl;
    referenceR = ri;

    double pri = elptr->getPRinit();
    //msg << "PRINIT= " << pri << " [CU]" << endl;
    referencePr = pri;

    double phii = elptr->getPHIinit();
    *gmsg << "* PHIINIT= " << phii << " [deg]" << endl;
    referenceTheta = phii;
    if(referenceTheta <= -180.0 || referenceTheta > 180.0) {
        throw OpalException("Error in ParallelCyclotronTracker::visitCyclotron", "PHIINIT is out of [-180, 180)!");
    }

    referencePz = 0.0;
    referencePtot =  itsReference.getGamma() * itsReference.getBeta();
    referencePt = sqrt(referencePtot * referencePtot - referencePr * referencePr);
    if(referencePtot < 0.0) referencePt *= -1.0;

    sinRefTheta_m = sin(phii / 180.0 * pi);
    cosRefTheta_m = cos(phii / 180.0 * pi);

    *gmsg << "* Initial gamma = " << itsReference.getGamma() << endl;

    *gmsg << "* Initial beta = " << itsReference.getBeta() << endl;

    *gmsg << "* Total reference momentum   = " << referencePtot * 1000.0 << " [MCU]" << endl;

    *gmsg << "* Reference azimuthal momentum  = " << referencePt * 1000.0 << " [MCU]" << endl;

    *gmsg << "* Reference radial momentum     = " << referencePr * 1000.0 << " [MCU]" << endl;

    double sym = elptr->getSymmetry();
    *gmsg << "* " << sym << " fold field symmerty " << endl;

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    // ckr: this just returned the default value as defined in Component.h
    // double rff = elptr->getRfFrequ();
    // *gmsg << "* Rf frequency= " << rff << " [MHz]" << endl;
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    string fmfn = elptr->getFieldMapFN();
    *gmsg << "* Field map file name= " << fmfn << " " << endl;

    string type = elptr->getType();
    *gmsg << "* Type of cyclotron= " << type << " " << endl;

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    bool Sflag = elptr->getSuperpose();
    *gmsg << "* Electric field map are superpoesed ?  " << Sflag << " " << endl;


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    double h = elptr->getCyclHarm();
    *gmsg << "* Harmonic number h= " << h << " " << endl;

    /**
     * To ease the initialise() function, set a integral parameter fieldflag internally.
     * Its value is  by the option "TYPE" of the element  "CYCLOTRON"
     * fieldflag = 1, readin PSI format measured field file (default)
     * fieldflag = 2, readin carbon cyclotron field file created by Jianjun Yang, TYPE=CARBONCYCL
     * fieldflag = 3, readin ANSYS format file for CYCIAE-100 created by Jianjun Yang, TYPE=CYCIAE
     * fieldflag = 4, readin AVFEQ format file for Riken cyclotrons
     * fieldflag = 5, readin FFAG format file for MSU/FNAL FFAG
     * fieldflag = 6, readin both median plane B field map and 3D E field map of RF cavity for compact cyclotron
     */
    int  fieldflag;
    if(type == string("CARBONCYCL")) {
        fieldflag = 2;
    } else if(type == string("CYCIAE")) {
        fieldflag = 3;
    } else if(type == string("AVFEQ")) {
        fieldflag = 4;
    } else if(type == string("FFAG")) {
        fieldflag = 5;
    } else if(type == string("BANDRF")) {
        fieldflag = 6;
    } else
        fieldflag = 1;

    // read field map on the  middle plane of cyclotron.
    // currently scalefactor is set to 1.0
    elptr->initialise(itsBunch, fieldflag, 1.0);

    double BcParameter[8];
    for(int i = 0; i < 8; i++) BcParameter[i] = 0.0;
    string ElementType = "CYCLOTRON";
    BcParameter[0] = elptr->getRmin();
    BcParameter[1] = elptr->getRmax();

    // store inner radius and outer radius of cyclotron field map in the list
    buildupFieldList(BcParameter, ElementType, elptr);

}

/**
 * Not implemented and most probable never used
 *
 */
void ParallelCyclotronTracker::visitBeamBeam(const BeamBeam &) {
    *gmsg << "In BeamBeam tracker is missing " << endl;
}

/**
 *
 *
 * @param coll
 */
void ParallelCyclotronTracker::visitCollimator(const Collimator &coll) {

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    *gmsg << "* --------- Collimator -----------------------------" << endl;
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    Collimator* elptr = dynamic_cast<Collimator *>(coll.clone());
    myElements.push_back(elptr);
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    double xstart = elptr->getXStart();
    *gmsg << "Xstart= " << xstart << " [mm]" << endl;
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    double xend = elptr->getXEnd();
    *gmsg << "Xend= " << xend << " [mm]" << endl;
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    double ystart = elptr->getYStart();
    *gmsg << "Ystart= " << ystart << " [mm]" << endl;
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    double yend = elptr->getYEnd();
    *gmsg << "Yend= " <<yend << " [mm]" << endl;
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    double width = elptr->getWidth();
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    *gmsg << "Width= " << width << " [mm]" << endl;
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    elptr->initialise(itsBunch, 1.0);

    double BcParameter[8];
    for(int i = 0; i < 8; i++)
        BcParameter[i] = 0.0;
    string ElementType = "CCOLLIMATOR";
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    BcParameter[0] = xstart ;
    BcParameter[1] = xend;
    BcParameter[2] = ystart ;
    BcParameter[3] = yend;
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    BcParameter[4] = width ;
    buildupFieldList(BcParameter, ElementType, elptr);
}

/**
 *
 *
 * @param corr
 */
void ParallelCyclotronTracker::visitCorrector(const Corrector &corr) {
    *gmsg << "In Corrector; L= " << corr.getElementLength() << endl;
    myElements.push_back(dynamic_cast<Corrector *>(corr.clone()));
}

/**
 *
 *
 * @param diag
 */
void ParallelCyclotronTracker::visitDiagnostic(const Diagnostic &diag) {
    *gmsg << "In Diagnostic; L= " << diag.getElementLength() << endl;
    myElements.push_back(dynamic_cast<Diagnostic *>(diag.clone()));
}

/**
 *
 *
 * @param drift
 */
void ParallelCyclotronTracker::visitDrift(const Drift &drift) {
    *gmsg << "In drift L= " << drift.getElementLength() << endl;
    myElements.push_back(dynamic_cast<Drift *>(drift.clone()));
}

/**
 *
 *
 * @param lamb
 */
void ParallelCyclotronTracker::visitLambertson(const Lambertson &lamb) {
    *gmsg << "In Lambertson; L= " << lamb.getElementLength() << endl;
    myElements.push_back(dynamic_cast<Lambertson *>(lamb.clone()));
}

/**
 *
 *
 * @param marker
 */
void ParallelCyclotronTracker::visitMarker(const Marker &marker) {
    //   *gmsg << "In Marker; L= " << marker.getElementLength() << endl;
    myElements.push_back(dynamic_cast<Marker *>(marker.clone()));
    // Do nothing.
}

/**
 *
 *
 * @param corr
 */
void ParallelCyclotronTracker::visitMonitor(const Monitor &corr) {
    //   *gmsg << "In Monitor; L= " << corr.getElementLength() << endl;
    myElements.push_back(dynamic_cast<Monitor *>(corr.clone()));
    //   applyDrift(flip_s * corr.getElementLength());
}

/**
 *
 *
 * @param mult
 */
void ParallelCyclotronTracker::visitMultipole(const Multipole &mult) {
    *gmsg << "In Multipole; L= " << mult.getElementLength() << " however the element is missing " << endl;
    myElements.push_back(dynamic_cast<Multipole *>(mult.clone()));
}

/**
 *
 *
 * @param prob
 */
void ParallelCyclotronTracker::visitProbe(const Probe &prob) {

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    *gmsg << "* -----------  Probe -------------------------------" << endl;
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    Probe *elptr = dynamic_cast<Probe *>(prob.clone());
    myElements.push_back(elptr);
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    double xstart = elptr->getXstart();
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    *gmsg << "XStart= " << xstart << " [mm]" << endl;
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    double xend = elptr->getXend();
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    *gmsg << "XEnd= " << xend << " [mm]" << endl;
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    double ystart = elptr->getYstart();
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    *gmsg << "YStart= " << ystart << " [mm]" << endl;
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    double yend = elptr->getYend();
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    *gmsg << "YEnd= " << yend << " [mm]" << endl;
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    double width = elptr->getWidth();
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    *gmsg << "Width= " << width << " [mm]" << endl;
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    // initialise, do nothing
    elptr->initialise(itsBunch, 1.0);

    double BcParameter[8];
    for(int i = 0; i < 8; i++)
        BcParameter[i] = 0.0;
    string ElementType = "PROBE";
    BcParameter[0] = xstart ;
    BcParameter[1] = xend;
    BcParameter[2] = ystart ;
    BcParameter[3] = yend;
    BcParameter[4] = width ;

    // store probe parameters in the list
    buildupFieldList(BcParameter, ElementType, elptr);
}

/**
 *
 *
 * @param bend
 */
void ParallelCyclotronTracker::visitRBend(const RBend &bend) {
    *gmsg << "In RBend; L= " << bend.getElementLength() << " however the element is missing " << endl;
    myElements.push_back(dynamic_cast<RBend *>(bend.clone()));
}

/**
 *
 *
 * @param as
 */
void ParallelCyclotronTracker::visitRFCavity(const RFCavity &as) {

    *gmsg << "* --------- RFCavity ------------------------------" << endl;
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    RFCavity *elptr = dynamic_cast<RFCavity *>(as.clone());
    myElements.push_back(elptr);
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    if((elptr->getComponentType() != "SINGLEGAP") && (elptr->getComponentType() != "DOUBLEGAP")) {
        *gmsg << (elptr->getComponentType()) << endl;
        throw OpalException("ParallelCyclotronTracker::visitRFCavity",
                            "The ParallelCyclotronTracker can only play with cyclotron type RF system currently ...");
    }

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    double rmin = elptr->getRmin();
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    *gmsg << "* Minimal radius of cavity= " << rmin << " [mm]" << endl;

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    double rmax = elptr->getRmax();
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    *gmsg << "* Maximal radius of cavity= " << rmax << " [mm]" << endl;

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    double rff = elptr->getCycFrequency();
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    *gmsg << "* RF frequency (2*pi*f)= " << rff << " [rad/s]" << endl;

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    string fmfn = elptr->getFieldMapFN();
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    *gmsg << "* RF Field map file name= " << fmfn << endl;

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    double angle = elptr->getAzimuth();
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    *gmsg << "* Cavity azimuth position= " << angle << " [deg] " << endl;

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    double gap = elptr->getGapWidth();
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    *gmsg << "* Cavity gap width= " << gap << " [mm] " << endl;

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    double pdis = elptr->getPerpenDistance();
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    *gmsg << "* Cavity Shift distance= " << pdis << " [mm] " << endl;


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    double phi0 = elptr->getPhi0();
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    *gmsg << "* Initial RF phase (t=0)= " << phi0 << " [deg] " << endl;

    // read cavity voltage profile data from file.
    elptr->initialise(itsBunch, 1.0);

    double BcParameter[8];
    for(int i = 0; i < 8; i++)
        BcParameter[i] = 0.0;
    string ElementType = "CAVITY";
    BcParameter[0] = rmin;
    BcParameter[1] = rmax;
    BcParameter[2] = pdis;
    BcParameter[3] = angle;

    buildupFieldList(BcParameter, ElementType, elptr);
}

/**
 *
 *
 * @param rfq
 */
void ParallelCyclotronTracker::visitRFQuadrupole(const RFQuadrupole &rfq) {
    *gmsg << "In RFQuadrupole; L= " << rfq.getElementLength() << " however the element is missing " << endl;
    myElements.push_back(dynamic_cast<RFQuadrupole *>(rfq.clone()));
}

/**
 *
 *
 * @param bend
 */
void ParallelCyclotronTracker::visitSBend(const SBend &bend) {
    *gmsg << "In SBend; L= " << bend.getElementLength() << " however the element is missing " << endl;
    myElements.push_back(dynamic_cast<SBend *>(bend.clone()));
}

/**
 *
 *
 * @param sep
 */
void ParallelCyclotronTracker::visitSeparator(const Separator &sep) {
    *gmsg << "In Seapator L= " << sep.getElementLength() << " however the element is missing " << endl;
    myElements.push_back(dynamic_cast<Separator *>(sep.clone()));
}

/**
 *
 *
 * @param sept
 */
void ParallelCyclotronTracker::visitSeptum(const Septum &sept) {
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    *gmsg << "* -----------  Septum -------------------------------" << endl;
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    Septum *elptr = dynamic_cast<Septum *>(sept.clone());
    myElements.push_back(elptr);
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    double xstart = elptr->getXstart();
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    *gmsg << "XStart= " << xstart << " [mm]" << endl;
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    double xend = elptr->getXend();
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    *gmsg << "XEnd= " << xend << " [mm]" << endl;
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    double ystart = elptr->getYstart();
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    *gmsg << "YStart= " << ystart << " [mm]" << endl;
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    double yend = elptr->getYend();
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    *gmsg << "YEnd= " << yend << " [mm]" << endl;
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    double width = elptr->getWidth();
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    *gmsg << "Width= " << width << " [mm]" << endl;
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    // initialise, do nothing
    elptr->initialise(itsBunch, 1.0);

    double BcParameter[8];
    for(int i = 0; i < 8; i++)
        BcParameter[i] = 0.0;
    string ElementType = "SEPTUM";
    BcParameter[0] = xstart ;
    BcParameter[1] = xend;
    BcParameter[2] = ystart ;
    BcParameter[3] = yend;
    BcParameter[4] = width ;

    // store septum parameters in the list
    buildupFieldList(BcParameter, ElementType, elptr);
}

/**
 *
 *
 * @param solenoid
 */
void ParallelCyclotronTracker::visitSolenoid(const Solenoid &solenoid) {
    myElements.push_back(dynamic_cast<Solenoid *>(solenoid.clone()));
    Component *elptr = *(--myElements.end());
    if(!elptr->hasAttribute("ELEMEDGE")) {
        *gmsg << "Solenoid: no position of the element given!" << endl;
        return;
    }
}

/**
 *
 *
 * @param pplate
 */
void ParallelCyclotronTracker::visitParallelPlate(const ParallelPlate &pplate) {//do nothing

    //*gmsg << "ParallelPlate: not in use in ParallelCyclotronTracker!" << endl;

    //buildupFieldList(startField, endField, elptr);

}

/**
 *
 *
 * @param cv
 */
void ParallelCyclotronTracker::visitCyclotronValley(const CyclotronValley &cv) {
    // Do nothing here.
}
/**
 * not used
 *
 * @param angle
 * @param curve
 * @param field
 * @param scale
 */
void ParallelCyclotronTracker::applyEntranceFringe(double angle, double curve,
        const BMultipoleField &field, double scale) {

}

/**
 *
 *
 * @param stripper
 */

void ParallelCyclotronTracker::visitStripper(const Stripper &stripper) {

    *gmsg << "* ---------Stripper------------------------------" << endl;

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    Stripper *elptr = dynamic_cast<Stripper *>(stripper.clone());
    myElements.push_back(elptr);

    double xstart = elptr->getXstart();
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    *gmsg << "XStart= " << xstart << " [mm]" << endl;

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    double xend = elptr->getXend();
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    *gmsg << "XEnd= " << xend << " [mm]" << endl;

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    double ystart = elptr->getYstart();
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    *gmsg << "YStart= " << ystart << " [mm]" << endl;

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    double yend = elptr->getYend();
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    *gmsg << "YEnd= " << yend << " [mm]" << endl;

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    double width = elptr->getWidth();
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    *gmsg << "Width= " << width << " [mm]" << endl;

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    double opcharge = elptr->getOPCharge();
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    *gmsg << "Charge of outcome particle = +e * " << opcharge << endl;

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    double opmass = elptr->getOPMass();
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    *gmsg << "Mass of the outcome particle = " << opmass << " [GeV/c^2]" << endl;

    elptr->initialise(itsBunch, 1.0);

    double BcParameter[8];
    for(int i = 0; i < 8; i++)
        BcParameter[i] = 0.0;
    string ElementType = "STRIPPER";
    BcParameter[0] = xstart ;
    BcParameter[1] = xend;
    BcParameter[2] = ystart ;
    BcParameter[3] = yend;
    BcParameter[4] = width ;
    BcParameter[5] = opcharge;
    BcParameter[6] = opmass;

    buildupFieldList(BcParameter, ElementType, elptr);
}


void ParallelCyclotronTracker::applyExitFringe(double angle, double curve,
        const BMultipoleField &field, double scale) {

}


/**
 *
 *
 * @param BcParameter
 * @param ElementType
 * @param elptr
 */
void ParallelCyclotronTracker::buildupFieldList(double BcParameter[], string ElementType, Component *elptr) {
    beamline_list::iterator sindex;

    type_pair *localpair = new type_pair();
    localpair->first = ElementType;

    for(int i = 0; i < 8; i++)
        *(((localpair->second).first) + i) = *(BcParameter + i);

    (localpair->second).second = elptr;

    // always put cyclotron as the first element in the list.
    if(ElementType == "CYCLOTRON") {
        sindex = FieldDimensions.begin();
    } else {
        sindex = FieldDimensions.end();
    }
    FieldDimensions.insert(sindex, localpair);

    // FixMe: so why not free up the memory?
    // free memory
    //  if(localpair)
    //    free(localpair);
}

/**
 *
 *
 * @param bl
 */
void ParallelCyclotronTracker::visitBeamline(const Beamline &bl) {
    itsBeamline->iterate(*dynamic_cast<BeamlineVisitor *>(this), false);
}

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void ParallelCyclotronTracker::checkNumPart(std::string s) {
    int nlp = itsBunch->getLocalNum();
    int minnlp = 0;
    int maxnlp = 111111;
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    reduce(nlp, minnlp, OpMinAssign());
    reduce(nlp, maxnlp, OpMaxAssign());
    *gmsg << s << " min local particle number " << minnlp << " max local particle number: " << maxnlp << endl;
}

/**
 *
 *
 */
void ParallelCyclotronTracker::execute() {

    /*
      Initialize common variables and structures
      for the integrators
    */

    step_m = 0;
    restartStep0_m = 0;

    // record how many bunches has already been injected. ONLY FOR MPM
    BunchCount_m = itsBunch->getNumBunch();

    // For the time being, we set bin number equal to bunch number. FixMe: not used
    BinCount_m = BunchCount_m;

    itsBeamline->accept(*this);

    // display the selected elements
    *gmsg << "-----------------------------" << endl;
    *gmsg << "The selected Beam line elements are :" << endl;
    for(beamline_list::iterator sindex = FieldDimensions.begin(); sindex != FieldDimensions.end(); sindex++)
        *gmsg << ((*sindex)->first) << endl;
    *gmsg << "-----------------------------" << endl;

    // external field arrays for dumping
    for(int k = 0; k < 2; k++)
        FDext_m[k] = Vector_t(0.0, 0.0, 0.0);
    extE_m = Vector_t(0.0, 0.0, 0.0);
    extB_m = Vector_t(0.0, 0.0, 0.0);

    if(timeIntegrator_m == 0) {
        *gmsg << "* 4th order Runge-Kutta integrator" << endl;
        Tracker_RK4();
    } else if(timeIntegrator_m == 1) {
        *gmsg << "* 2nd order Leap-Frog integrator" << endl;
        Tracker_LF();
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    } else if(timeIntegrator_m == 2) {
        *gmsg << "* Multiple time stepping (MTS) integrator" << endl;
        Tracker_MTS();
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    } else {
        *gmsg << "ERROR: Invalid name of TIMEINTEGRATOR in Track command" << endl;
        exit(1);
    }

    *gmsg << "-----------------------------" << endl;
    *gmsg << "Finalize i.e. write data and close files :" << endl;
    for(beamline_list::iterator sindex = FieldDimensions.begin(); sindex != FieldDimensions.end(); sindex++) {
        (((*sindex)->second).second)->finalise();
    }
    *gmsg << "-----------------------------" << endl;
}

/**
   In general the two tracker have much code in common.
   This is a great source of errors.
   Need to avoid this

*/



/**
 *
 *
 */
void ParallelCyclotronTracker::Tracker_LF() {

    Inform *gmsgAll;
    gmsgAll = new  Inform("CycTracker LF", INFORM_ALL_NODES);

    BorisPusher pusher;

    // time steps interval between bunches for multi-bunch simulation.
    const int stepsPerTurn = itsBunch->getStepsPerTurn();

    beamline_list::iterator sindex = FieldDimensions.begin();
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    Cyclotron *elptr = dynamic_cast<Cyclotron *>(((*sindex)->second).second);
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    if (elptr == NULL)
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        throw OpalException("ParallelCyclotronTracker::Tracker_LF()",
                            "The first item in the FieldDimensions list does not seem to be a cyclotron element");

    const double harm = elptr-> getCyclHarm();
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    // load time
    const double dt = itsBunch->getdT() * 1.0e9 * harm; //[s]-->[ns]

    // find the injection time interval
    if(numBunch_m > 1) {
        *gmsg << "Time interval between neighbour bunches is set to " << stepsPerTurn *dt << "[ns]" << endl;
    }

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    initTrackOrbitFile();
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    int SteptoLastInj = itsBunch->getSteptoLastInj();

    // get data from h5 file for restart run
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    if(OpalData::getInstance()->inRestartRun()) {
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        restartStep0_m = itsBunch->getLocalTrackStep();
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        step_m = restartStep0_m;
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        if (numBunch_m > 1) itsBunch->resetPartBinID2(eta_m);
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        *gmsg << "* Restart at integration step " << restartStep0_m << endl;
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    }

    if(OpalData::getInstance()->hasBunchAllocated() && Options::scan) {
        lastDumpedStep_m = 0;
        itsBunch->setT(0.0);
    }

    *gmsg << "* Beginning of this run is at t= " << itsBunch->getT() * 1e9 << " [ns]" << endl;
    *gmsg << "* The time step is set to dt= " << dt << " [ns]" << endl;

    // for single Particle Mode, output at zero degree.
    if(initialTotalNum_m == 1)
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        openFiles(OpalData::getInstance()->getInputBasename());
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    double const initialReferenceTheta = referenceTheta / 180.0 * pi;
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    initDistInGlobalFrame();
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    //  read in some control parameters
    const int SinglePartDumpFreq = Options::sptDumpFreq;
    const int resetBinFreq = Options::rebinFreq;
    const int scSolveFreq = Options::scSolveFreq;
    const bool doDumpAfterEachTurn = Options::psDumpEachTurn;


    int boundpDestroyFreq = 10; // todo: is it better treat as a control parameter

    // prepare for dump after each turn
    double oldReferenceTheta = initialReferenceTheta;

    *gmsg << "single particle trajectory dump frequency is set to " << SinglePartDumpFreq << endl;
    *gmsg << "particles repartition frequency is set to " << Options::repartFreq << endl;
    if(numBunch_m > 1)
        *gmsg << "particles energy bin ID reset frequency is set to " << resetBinFreq << endl;

    // if initialTotalNum_m = 2, trigger SEO mode
    // prepare for transverse tuning calculation
    vector<double> Ttime, Tdeltr, Tdeltz;
    // prepare for transverse tuning calculation
    vector<int> TturnNumber;
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    turnnumber_m = 1;
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    // flag to determine when to transit from single-bunch to multi-bunches mode
    bool flagTransition = false;
    // step point determining the next time point of check for transition
    int stepsNextCheck = step_m + itsBunch->getStepsPerTurn();

    const  double deltaTheta = pi / (stepsPerTurn);
    // record at which angle the space charge are solved
    double angleSpaceChargeSolve = 0.0;

    if(initialTotalNum_m == 1) {
        *gmsg << "* *---------------------------- SINGLE PARTICLE MODE------ ----------------------------*** " << endl;
        *gmsg << "* Instruction: when the total particle number equal to 1, single particle mode is triggered automatically," << endl
              << "* The initial distribution file must be specified which should contain only one line for the single particle " << endl
              << "* *------------NOTE: SINGLE PARTICLE MODE ONLY WORKS SERIALLY ON SINGLE NODE ------------------*** " << endl;
        if(Ippl::getNodes() != 1)
            throw OpalException("Error in ParallelCyclotronTracker::execute", "SINGLE PARTICLE MODE ONLY WORKS SERIALLY ON SINGLE NODE!");

    } else if(initialTotalNum_m == 2) {
        *gmsg << "* *------------------------ STATIC EQUILIBRIUM ORBIT MODE ----------------------------*** " << endl;
        *gmsg << "* Instruction: when the total particle number equal to 2, SEO mode is triggered automatically." << endl
              << "* This mode does NOT include any RF cavities. The initial distribution file must be specified" << endl
              << "* In the file the first line is for reference particle and the second line is for offcenter particle." << endl
              << "* The tunes are calculated by FFT routines based on these two particles. " << endl
              << "* *------------NOTE: SEO MODE ONLY WORKS SERIALLY ON SINGLE NODE ------------------*** " << endl;
        if(Ippl::getNodes() != 1)
            throw OpalException("Error in ParallelCyclotronTracker::execute", "SEO MODE ONLY WORKS SERIALLY ON SINGLE NODE!");
    }

    // *****************II***************
    // main integration loop
    // *****************II***************
    *gmsg << "---------------------------- Start tracking ----------------------------" << endl;
    for(; step_m < maxSteps_m; step_m++) {
        bool dumpEachTurn = false;
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        if(step_m % SinglePartDumpFreq == 0) {
            singleParticleDump();
        }
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        Ippl::Comm->barrier();

        // Push for first half step
        itsBunch->R *= Vector_t(0.001);
        push(0.5 * dt * 1e-9);
        itsBunch->R *= Vector_t(1000.0);

        // bunch injection
        if(numBunch_m > 1) {

            if((BunchCount_m == 1) && (multiBunchMode_m == 2) && (!flagTransition)) {
                if(step_m == stepsNextCheck) {
                    // under 3 conditions, following code will be execute
                    // to check the distance between two neighborring bunches
                    // 1.multi-bunch mode, AUTO sub-mode
                    // 2.After each revolution
                    // 3.only one bunch exists

                    *gmsg << "checking for automatically injecting new bunch ..." << endl;

                    itsBunch->R /= Vector_t(1000.0); // mm --> m
                    itsBunch->calcBeamParameters_cycl();
                    itsBunch->R *= Vector_t(1000.0); // m --> mm

                    Vector_t Rmean = itsBunch->get_centroid() * 1000.0; // m --> mm

                    RThisTurn_m = sqrt(pow(Rmean[0], 2.0) + pow(Rmean[1], 2.0));

                    Vector_t Rrms = itsBunch->get_rrms() * 1000.0; // m --> mm

                    double XYrms =  sqrt(pow(Rrms[0], 2.0) + pow(Rrms[1], 2.0));


                    // if the distance between two neighbour bunch is less than CoeffDBunches_m times of its 2D rms size
                    // start multi-bunch simulation, fill current phase space to initialR and initialP arrays

                    if((RThisTurn_m - RLastTurn_m) < CoeffDBunches_m * XYrms) {
                        // since next turn, start multi-bunches
                        saveOneBunch();
                        flagTransition = true;

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                        *gmsg << "*** Save beam distribution at turn #" << turnnumber_m << " ***" << endl;
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                        *gmsg << "*** After one revolution, Multi-Bunch Mode will be invorked ***" << endl;

                    }

                    stepsNextCheck += stepsPerTurn;

                    *gmsg << "RLastTurn = " << RLastTurn_m << " [mm]" << endl;
                    *gmsg << "RThisTurn = " << RThisTurn_m << " [mm]" << endl;
                    *gmsg << "    XYrms = " << XYrms    << " [mm]" << endl;

                    RLastTurn_m = RThisTurn_m;
                }
            } else if(SteptoLastInj == stepsPerTurn - 1) {
                if(BunchCount_m < numBunch_m) {

                    // under 4 conditions, following code will be execute
                    // to read new bunch from hdf5 format file for FORCE or AUTO mode
                    // 1.multi-bunch mode
                    // 2.after each revolution
                    // 3.existing bunches is less than the specified bunches
                    // 4.FORCE mode, or AUTO mode with flagTransition = true
                    // Note: restart from 1 < BunchCount < numBunch_m must be avoided.
                    *gmsg << "step " << step_m << ", inject a new bunch... ... ..." << endl;
                    BunchCount_m++;

                    // read initial distribution from h5 file
                    if(multiBunchMode_m == 1) {
                        readOneBunch(BunchCount_m - 1);
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                        itsBunch->resetPartBinID2(eta_m);
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                    } else if(multiBunchMode_m == 2) {

                        if(OpalData::getInstance()->inRestartRun())
                            readOneBunchFromFile(BunchCount_m - 1);
                        else
                            readOneBunch(BunchCount_m - 1);

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                        itsBunch->resetPartBinID2(eta_m);
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                    }

                    SteptoLastInj = 0;

                    itsBunch->setNumBunch(BunchCount_m);

                    stepsNextCheck += stepsPerTurn;

                    // update  after injection
                    itsBunch->boundp();

                    Ippl::Comm->barrier();
                    *gmsg << BunchCount_m << "'th bunch injected, total particle number = " << itsBunch->getTotalNum() << endl;
                }
            } else if(BunchCount_m == numBunch_m) {
                // After this, numBunch_m is wrong but useless
                numBunch_m--;

            } else {
                SteptoLastInj++;
            }
        }

        // calculate self fields Space Charge effects are included only when total macropaticles number is NOT LESS THAN 1000.
        if(itsBunch->hasFieldSolver() && initialTotalNum_m >= 1000) {
            if(step_m % scSolveFreq == 0) {
                //    *gmsg << "Calculate space charge at step " << step_m<<endl;
                // Firstly reset E and B to zero before fill new space charge field data for each track step
                itsBunch->Bf = Vector_t(0.0);
                itsBunch->Ef = Vector_t(0.0);

                Vector_t const meanR = calcMeanR();
                if((itsBunch->weHaveBins()) && BunchCount_m > 1) {
                    IpplTimings::startTimer(TransformTimer_m);
                    double const binsPhi = itsBunch->calcMeanPhi() - 0.5 * pi;
                    angleSpaceChargeSolve = binsPhi;
                    globalToLocal(itsBunch->R, binsPhi, meanR);

                    //scale coordinates
                    itsBunch->R /= Vector_t(1000.0); // mm --> m

                    if((step_m + 1) % boundpDestroyFreq == 0)
                        itsBunch->boundp_destroy();
                    else
                        itsBunch->boundp();

                    IpplTimings::stopTimer(TransformTimer_m);

                    // calcualte gamma for each energy bin
                    itsBunch->calcGammas_cycl();

                    repartition();
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                    // calculate space charge field for each energy bin
                    for(int b = 0; b < itsBunch->getLastemittedBin() ; b++) {

                        if(itsBunch->pbin_m->getTotalNumPerBin(b) >= 1000) {
                            //if(itsBunch->getNumPartInBin(b) >= 1000) {
                            itsBunch->setBinCharge(b, itsBunch->getChargePerParticle());
                            //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%//
                            itsBunch->computeSelfFields_cycl(b);
                            //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%//
                            INFOMSG("Bin:" << b << ", charge per particle " <<  itsBunch->getChargePerParticle() << endl);
                        } else {
                            INFOMSG("Note: Bin " << b << ": less than 1000 particles, omit space charge fields" << endl);
                        }
                    }

                    itsBunch->Q = itsBunch->getChargePerParticle();

                    IpplTimings::startTimer(TransformTimer_m);

                    //scale coordinates back
                    itsBunch->R *= Vector_t(1000.0); // m --> mm
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                    localToGlobal(itsBunch->R, binsPhi, meanR);
                    localToGlobal(itsBunch->Ef, binsPhi);
                    localToGlobal(itsBunch->Bf, binsPhi);
                } else {
                    Vector_t const meanP = calcMeanP();
                    double const phi = calculateAngle(meanP(0), meanP(1)) - 0.5 * pi;
                    angleSpaceChargeSolve = phi;
                    globalToLocal(itsBunch->R, phi, meanR);

                    //scale coordinates
                    itsBunch->R /= Vector_t(1000.0); // mm --> m

                    if((step_m + 1) % boundpDestroyFreq == 0)
                        itsBunch->boundp_destroy();
                    else
                        itsBunch->boundp();

                    IpplTimings::stopTimer(TransformTimer_m);
                    repartition();
                    //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%//
                    double const meanGamma = sqrt(1.0 + pow(meanP(0), 2.0) + pow(meanP(1), 2.0));
                    itsBunch->computeSelfFields_cycl(meanGamma);
                    //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%//

                    IpplTimings::startTimer(TransformTimer_m);

                    //scale coordinates back
                    itsBunch->R *= Vector_t(1000.0); // m --> mm
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                    localToGlobal(itsBunch->R, phi, meanR);
                    localToGlobal(itsBunch->Ef, phi);
                    localToGlobal(itsBunch->Bf, phi);
                }

                IpplTimings::stopTimer(TransformTimer_m);
            } else {
                Vector_t const meanP = calcMeanP();
                double const phi = calculateAngle(meanP(0), meanP(1)) - 0.5 * pi;
                double const deltaPhi = phi - angleSpaceChargeSolve;
                localToGlobal(itsBunch->Ef, deltaPhi);
                localToGlobal(itsBunch->Bf, deltaPhi);
            }
        } else {
            // if field solver is not available , only update bunch, to transfer particles between nodes if needed,
            // reset parameters such as LocalNum, initialTotalNum_m.
            // INFOMSG("No space charge Effects are included!"<<endl;);
            if((step_m % Options::repartFreq * 100) == 0 && initialTotalNum_m >= 1000) {
                Vector_t const meanR = calcMeanR();
                Vector_t const meanP = calcMeanP();
                double const phi = calculateAngle(meanP(0), meanP(1)) - 0.5 * pi;
                angleSpaceChargeSolve = phi; // we do not solve anything why set this?
                globalToLocal(itsBunch->R, phi, meanR);

                //scale coordinates
                itsBunch->R /= Vector_t(1000.0); // mm --> m

                if((step_m + 1) % boundpDestroyFreq == 0)
                    itsBunch->boundp_destroy();
                else
                    itsBunch->boundp();
                repartition();

                //scale coordinates back
                itsBunch->R *= Vector_t(1000.0); // m --> mm

                localToGlobal(itsBunch->R, phi, meanR);
            }
        }

        //  kick particles for one step
        IpplTimings::startTimer(IntegrationTimer_m);
        for(unsigned int i = 0; i < itsBunch->getLocalNum(); ++i) {
            Vector_t externalE, externalB;
            double partR;

            externalB = Vector_t(0.0, 0.0, 0.0);
            externalE = Vector_t(0.0, 0.0, 0.0);

            partR = sqrt(dot(itsBunch->R[i], itsBunch->R[i]));

            beamline_list::iterator sindex = FieldDimensions.begin();

            if(((((*sindex)->second).first)[0] <= partR) && ((((*sindex)->second).first)[1] >= partR))
                (((*sindex)->second).second)->apply(itsBunch->R[i], Vector_t(0.0), itsBunch->getT() * 1e9, externalE, externalB);

	    externalB = externalB / 10.0; // kgauss -> T

            if(itsBunch->hasFieldSolver()) {
                externalE += itsBunch->Ef[i];
                externalB += itsBunch->Bf[i];
            }
            pusher.kick(itsBunch->R[i], itsBunch->P[i], externalE , externalB, dt * 1.0e-9, itsBunch->M[i] * 1.0e9, itsBunch->Q[i] / q_e);
        }
        IpplTimings::stopTimer(IntegrationTimer_m);

        // Push for second half step
        itsBunch->R *= Vector_t(0.001);
        push(0.5 * dt * 1e-9);
        itsBunch->R *= Vector_t(1000.0);
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	// apply the plugin elements: probe, colilmator, stripper, septum
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	bool flagNeedUpdate=false;
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	flagNeedUpdate = applyPluginElements(dt);
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	if(itsBunch->weHaveBins() && flagNeedUpdate)
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	  itsBunch->resetPartBinID2(eta_m);
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        // recalculate bingamma and reset the BinID for each particles according to its current gamma
        if((itsBunch->weHaveBins()) && BunchCount_m > 1 && step_m % resetBinFreq == 0)
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            itsBunch->resetPartBinID2(eta_m);
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        // dump  data after one push in single particle tracking
        if(initialTotalNum_m == 1) {
            int i = 0;

            // change phase space parameters from local reference frame of bunch (dr,dtheta,dz) to global Cartesian frame (X,Y,Z)
            for(int j = 0; j < 3; j++) {
                variable_m[j]   = itsBunch->R[i](j);  //[x,y,z]  units: [mm]
                variable_m[j+3] = itsBunch->P[i](j);  //[px,py,pz]  units: dimensionless
            }

            double temp_meanTheta = calculateAngle2(variable_m[0], variable_m[1]);//[ -pi ~ pi ]
            if((oldReferenceTheta < initialReferenceTheta - deltaTheta) &&
               (temp_meanTheta >= initialReferenceTheta - deltaTheta)) {
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                ++turnnumber_m;
                *gmsg << "Turn " << turnnumber_m << endl;
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                dumpEachTurn = true;
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                outfThetaEachTurn_m << "#Turn number = " << turnnumber_m << ", Time = " << itsBunch->getT() * 1e9 << " [ns]" << endl;
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                outfThetaEachTurn_m << " " << sqrt(variable_m[0]*variable_m[0] + variable_m[1]*variable_m[1])
                                    << " " << variable_m[3]*cos(temp_meanTheta) + variable_m[4]*sin(temp_meanTheta)
                                    << " " << temp_meanTheta / pi * 180
                                    << " " << -variable_m[3]*sin(temp_meanTheta) + variable_m[4]*cos(temp_meanTheta)
                                    << " " << variable_m[2]
                                    << " " << variable_m[5] << endl;
            }
            // FixMe: should be defined elesewhere !
            // define 3 special azimuthal angles where dump particle's six parameters  at each turn into 3 ASCII files.
            const double azimuth_angle0 = 0.0;
            const double azimuth_angle1 = 22.5 / 180.0 * pi;
            const double azimuth_angle2 = 45.0 / 180.0 * pi;
            if((oldReferenceTheta < azimuth_angle0 - deltaTheta) && (temp_meanTheta >= azimuth_angle0 - deltaTheta)) {
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                outfTheta0_m << "#Turn number = " << turnnumber_m << ", Time = " << itsBunch->getT() * 1e9 << " [ns]" << endl;
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                outfTheta0_m << " " << sqrt(variable_m[0]*variable_m[0] + variable_m[1]*variable_m[1])
                             << " " << variable_m[3]*cos(temp_meanTheta) + variable_m[4]*sin(temp_meanTheta)
                             << " " << temp_meanTheta / pi * 180
                             << " " << -variable_m[3]*sin(temp_meanTheta) + variable_m[4]*cos(temp_meanTheta)
                             << " " << variable_m[2]
                             << " " << variable_m[5] << endl;
            }

            if((oldReferenceTheta < azimuth_angle1 - deltaTheta) && (temp_meanTheta >= azimuth_angle1 - deltaTheta)) {
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                outfTheta1_m << "#Turn number = " << turnnumber_m << ", Time = " << itsBunch->getT() * 1e9 << " [ns]" << endl;
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                outfTheta1_m << " " << sqrt(variable_m[0]*variable_m[0] + variable_m[1]*variable_m[1])
                             << " " << variable_m[3]*cos(temp_meanTheta) + variable_m[4]*sin(temp_meanTheta)
                             << " " << temp_meanTheta / pi * 180
                             << " " << -variable_m[3]*sin(temp_meanTheta) + variable_m[4]*cos(temp_meanTheta)
                             << " " << variable_m[2]
                             << " " << variable_m[5] << endl;
            }

            if((oldReferenceTheta < azimuth_angle2 - deltaTheta) && (temp_meanTheta >= azimuth_angle2 - deltaTheta)) {
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                outfTheta2_m << "#Turn number = " << turnnumber_m << ", Time = " << itsBunch->getT() * 1e9 << " [ns]" << endl;
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                outfTheta2_m << " " << sqrt(variable_m[0]*variable_m[0] + variable_m[1]*variable_m[1])
                             << " " << variable_m[3]*cos(temp_meanTheta) + variable_m[4]*sin(temp_meanTheta)
                             << " " << temp_meanTheta / pi * 180
                             << " " << -variable_m[3]*sin(temp_meanTheta) + variable_m[4]*cos(temp_meanTheta)
                             << " " << variable_m[2]
                             << " " << variable_m[5] << endl;
            }
            oldReferenceTheta = temp_meanTheta;
        }


        // check whether one turn over for multi-bunch tracking.
        if(doDumpAfterEachTurn && initialTotalNum_m > 2) {
            Vector_t const meanR = calcMeanR();

            // in global Cartesian frame, calculate the location in global frame of bunch
            oldReferenceTheta = calculateAngle2(meanR(0), meanR(1));

            // both for single bunch and multi-bunch
            // avoid dump at the first step
            // dumpEachTurn has not been changed in first push
            if((step_m > 10) && ((step_m + 1) % stepsPerTurn) == 0) {
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                ++turnnumber_m;
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                dumpEachTurn = true;
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                *gmsg << "Turn " << turnnumber_m << " total particles " << itsBunch->getTotalNum() << endl;
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            }
        }

        // dump phase space distribution of bunch
        if((((step_m + 1) % Options::psDumpFreq == 0) && initialTotalNum_m != 2) ||
           (doDumpAfterEachTurn && dumpEachTurn && initialTotalNum_m != 2)) {

            IpplTimings::startTimer(DumpTimer_m);

            itsBunch->setSteptoLastInj(SteptoLastInj);

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            itsBunch->setLocalTrackStep((step_m + 1));
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            extE_m = Vector_t(0.0, 0.0, 0.0);
            extB_m = Vector_t(0.0, 0.0, 0.0);

            //--------------------- calculate mean coordinates  of bunch -------------------------------//
            //------------  and calculate the external field at the mass of bunch-----------------------//

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            Vector_t const meanR = calcMeanR();
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            *gmsg << "meanR=( " << meanR(0) << " " << meanR(1) << " " << meanR(2) << " ) [mm] " << endl;

            double meanRadius = sqrt(meanR(0) * meanR(0) + meanR(1) * meanR(1));

            beamline_list::iterator DumpSindex = FieldDimensions.begin();

            if(((((*DumpSindex)->second).first)[0] <= meanRadius) &&
               ((((*DumpSindex)->second).first)[1] >= meanRadius)) {
                (((*DumpSindex)->second).second)->apply(meanR, Vector_t(0.0), itsBunch->getT() * 1e9, extE_m, extB_m);
            }

            FDext_m[0] = extB_m / 10.0; // kgauss -> T
            FDext_m[1] = extE_m;

            //----------------------------dump in global frame-------------------------------------//
            // Note: Don't dump when
            // 1. after one turn
            // in order to sychronize the dump step for multi-bunch and single bunch for compare
            // with each other during post-process phase.
            if(!(Options::psDumpLocalFrame)) {
                itsBunch->R /= Vector_t(1000.0); // mm --> m

                lastDumpedStep_m = itsDataSink->writePhaseSpace_cycl(*itsBunch, FDext_m);

                //  itsDataSink->writeStatData(*itsBunch, FDext_m ,0.0,0.0,0.0);
                itsBunch->R *= Vector_t(1000.0); // m --> mm
                *gmsg << "* Phase space dump " << lastDumpedStep_m << " (global frame) at integration step "
                      << step_m + 1 << " T= " << itsBunch->getT() * 1e9 << " [ns]" << endl;

                //----------------------------dump in local frame-------------------------------------//
            } else {
                Vector_t const meanP = calcMeanP();
                double const phi = calculateAngle(meanP(0), meanP(1)) - 0.5 * pi;
                globalToLocal(itsBunch->R, phi, meanR);
                globalToLocal(itsBunch->P, phi, meanP);
                itsBunch->R /= Vector_t(1000.0); // mm --> m
                lastDumpedStep_m = itsDataSink->writePhaseSpace_cycl(*itsBunch, FDext_m);
                itsDataSink->writeStatData(*itsBunch, FDext_m , 0.0, 0.0, 0.0);
                itsBunch->R *= Vector_t(1000.0); // m --> mm
                localToGlobal(itsBunch->R, phi, meanR);
                localToGlobal(itsBunch->P, phi, meanP);
                *gmsg << "* Phase space dump " << lastDumpedStep_m << " (local frame) at integration step "
                      << step_m + 1 << " T= " << itsBunch->getT() * 1e9 << " [ns]" << endl;

            }
            IpplTimings::stopTimer(DumpTimer_m);
        }
    }

    for(size_t ii = 0; ii < (itsBunch->getLocalNum()); ii++) {
        if(itsBunch->ID[ii] == 0) {
            // FixMe: FinalMomentum2  = dot(itsBunch->P[ii],itsBunch->P[ii]);
            double FinalMomentum2  = pow(itsBunch->P[ii](0), 2.0) +
                                     pow(itsBunch->P[ii](1), 2.0) +
                                     pow(itsBunch->P[ii](2), 2.0);
            double FinalEnergy = (sqrt(1.0 + FinalMomentum2) - 1.0) * itsBunch->getM() * 1.0e-6;
            *gmsgAll << "* Final energy of reference particle = " << FinalEnergy << " [MeV]" << endl;
            *gmsgAll << "* Total phase space dump number including the initial distribution) = " << lastDumpedStep_m + 1 << endl;
            *gmsgAll << "* One can restart simulation from the last dump step ( -restart " << lastDumpedStep_m << " )" << endl;
        }
    }

    Ippl::Comm->barrier();

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    if(myNode_m == 0) outfTrackOrbit_m.close();
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    if(initialTotalNum_m == 1)
        closeFiles();

    *gmsg << *itsBunch << endl;

    // free memory
    if(gmsgAll)
        free(gmsgAll);

}

void ParallelCyclotronTracker::Tracker_RK4() {

    Inform *gmsgAll;
    gmsgAll = new  Inform("CycTracker RK4", INFORM_ALL_NODES);
    // time steps interval between bunches for multi-bunch simulation.
    const int stepsPerTurn = itsBunch->getStepsPerTurn();
    // record how many bunches has already been injected. ONLY FOR MPM
    BunchCount_m = itsBunch->getNumBunch();
    // decide how many energy bins. ONLY FOR MPM
    BinCount_m = BunchCount_m;
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    beamline_list::iterator sindex = FieldDimensions.begin();
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    Cyclotron *elptr = dynamic_cast<Cyclotron *>(((*sindex)->second).second);
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    if (elptr == NULL)
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        throw OpalException("ParallelCyclotronTracker::Tracker_LF()",
                            "The first item in the FieldDimensions list does not seem to be a cyclotron element");
    const double harm = elptr-> getCyclHarm();
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    // load time
    double t  = itsBunch->getT() * 1.0e9;
    const double dt = itsBunch->getdT() * 1.0e9 * harm; //[s]-->[ns]

    // find the injection time interval
    if(numBunch_m > 1) {
        *gmsg << "Time interval between neighbour bunches is set to " << stepsPerTurn *dt << "[ns]" << endl;
    }

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    initTrackOrbitFile();
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    // get data from h5 file for restart run
    if(OpalData::getInstance()->inRestartRun()) {
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        restartStep0_m = itsBunch->getLocalTrackStep();
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        step_m = restartStep0_m;
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        if (numBunch_m > 1) itsBunch->resetPartBinID2(eta_m);
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        *gmsg << "* Restart at integration step " << restartStep0_m << endl;
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    }

    if(OpalData::getInstance()->hasBunchAllocated() && Options::scan) {
        lastDumpedStep_m = 0;
        t = 0.0;
    }

    *gmsg << "* Beginning of this run is at t= " << t << " [ns]" << endl;
    *gmsg << "* The time step is set to dt= " << dt << " [ns]" << endl;

    // for single Particle Mode, output at zero degree.
    if(initialTotalNum_m == 1)
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        openFiles(OpalData::getInstance()->getInputBasename());
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    initDistInGlobalFrame();
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    //  read in some control parameters
    const int SinglePartDumpFreq = Options::sptDumpFreq;
    const int resetBinFreq = Options::rebinFreq;
    const int scSolveFreq = Options::scSolveFreq;
    const bool doDumpAfterEachTurn = Options::psDumpEachTurn;

    int boundpDestroyFreq = 10; // todo: is it better treat as a control parameter

    // prepare for dump after each turn
    const double initialReferenceTheta = referenceTheta / 180.0 * pi;
    double oldReferenceTheta = initialReferenceTheta;

    *gmsg << "* Single particle trajectory dump frequency is set to " << SinglePartDumpFreq << endl;
    *gmsg << "* The frequency to solve space charge fields is set to " << scSolveFreq << endl;
    *gmsg << "* The repartition frequency is set to " << Options::repartFreq << endl;

    if(numBunch_m > 1)
        *gmsg << "* The particles energy bin reset frequency is set to " << resetBinFreq << endl;

    // if initialTotalNum_m = 2, trigger SEO mode and prepare for transverse tuning calculation
    vector<double> Ttime, Tdeltr, Tdeltz;
    vector<int> TturnNumber;
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    turnnumber_m = 1;
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