Distribution.cpp 193 KB
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// ------------------------------------------------------------------------
// $RCSfile: Distribution.cpp,v $
// ------------------------------------------------------------------------
// $Revision: 1.3.4.1 $
// ------------------------------------------------------------------------
// Copyright: see Copyright.readme
// ------------------------------------------------------------------------
//
// Class: Distribution
//   The class for the OPAL Distribution command.
//
// ------------------------------------------------------------------------
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#include "Distribution/Distribution.h"
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#include "Distribution/SigmaGenerator.h"
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#include "AbsBeamline/SpecificElementVisitor.h"
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#include <cmath>
#include <cfloat>
#include <iomanip>
#include <iostream>
#include <string>
#include <vector>
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#include <numeric>
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#include "AbstractObjects/Expressions.h"
#include "Attributes/Attributes.h"
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#include "Utilities/OpalOptions.h"
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#include "Utilities/Options.h"
#include "halton1d_sequence.hh"
#include "AbstractObjects/OpalData.h"
#include "Algorithms/PartBunch.h"
#include "Algorithms/PartBins.h"
#include "Algorithms/bet/EnvelopeBunch.h"
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#include "Structure/Beam.h"
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#include "Structure/BoundaryGeometry.h"
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#include "Algorithms/PartBinsCyc.h"
#include "BasicActions/Option.h"
#include "Distribution/LaserProfile.h"
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#include "Elements/OpalBeamline.h"
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#include "AbstractObjects/BeamSequence.h"
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#include <gsl/gsl_cdf.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_sf_erf.h>
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#include <gsl/gsl_linalg.h>
#include <gsl/gsl_blas.h>
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#include "MagneticField.h"

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extern Inform *gmsg;

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#define DISTDBG1
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#define noDISTDBG2
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//
// Class Distribution
// ------------------------------------------------------------------------

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namespace AttributesT
{
    enum AttributesT {
                      DISTRIBUTION,
                      FNAME,
                      WRITETOFILE,
                      WEIGHT,
                      INPUTMOUNITS,
                      EMITTED,
                      EMISSIONSTEPS,
                      EMISSIONMODEL,
                      EKIN,
                      ELASER,
                      W,
                      FE,
                      CATHTEMP,
                      NBIN,
                      XMULT,
                      YMULT,
                      ZMULT,
                      TMULT,
                      PXMULT,
                      PYMULT,
                      PZMULT,
                      OFFSETX,
                      OFFSETY,
                      OFFSETZ,
                      OFFSETT,
                      OFFSETPX,
                      OFFSETPY,
                      OFFSETPZ,
                      SIGMAX,
                      SIGMAY,
                      SIGMAR,
                      SIGMAZ,
                      SIGMAT,
                      TPULSEFWHM,
                      TRISE,
                      TFALL,
                      SIGMAPX,
                      SIGMAPY,
                      SIGMAPZ,
                      MX,
                      MY,
                      MZ,
                      MT,
                      CUTOFFX,
                      CUTOFFY,
                      CUTOFFR,
                      CUTOFFLONG,
                      CUTOFFPX,
                      CUTOFFPY,
                      CUTOFFPZ,
                      FTOSCAMPLITUDE,
                      FTOSCPERIODS,
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                      R,                          // the correlation matrix (a la transport)
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                      CORRX,
                      CORRY,
                      CORRZ,
                      CORRT,
                      R51,
                      R52,
                      R61,
                      R62,
                      LASERPROFFN,
                      IMAGENAME,
                      INTENSITYCUT,
                      NPDARKCUR,
                      INWARDMARGIN,
                      EINITHR,
                      FNA,
                      FNB,
                      FNY,
                      FNVYZERO,
                      FNVYSECOND,
                      FNPHIW,
                      FNBETA,
                      FNFIELDTHR,
                      FNMAXEMI,
                      SECONDARYFLAG,
                      NEMISSIONMODE,
                      VSEYZERO,                   // sey_0 in Vaughn's model.
                      VEZERO,                     // Energy related to sey_0 in Vaughan's model.
                      VSEYMAX,                    // sey max in Vaughan's model.
                      VEMAX,                      // Emax in Vaughan's model.
                      VKENERGY,                   // Fitting parameter denotes the roughness of
                                                  // surface for impact energy in Vaughn's model.
                      VKTHETA,                    // Fitting parameter denotes the roughness of
                                                  // surface for impact angle in Vaughn's model.
                      VVTHERMAL,                  // Thermal velocity of Maxwellian distribution
                                                  // of secondaries in Vaughan's model.
                      VW,
                      SURFMATERIAL,               // Add material type, currently 0 for copper
                                                  // and 1 for stainless steel.
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		      EX,                         // below is for the matched distribution
		      EY,
		      ET,
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		      MAGSYM,                     // number of sector magnets
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                      LINE,
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		      FMAPFN,
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		      RESIDUUM,
		      MAXSTEPSCO,
		      MAXSTEPSSI,
		      ORDERMAPS,
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		      E2,
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                      SIZE
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    };
}

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namespace LegacyAttributesT
{
    enum LegacyAttributesT {
    // DESCRIPTION OF THE DISTRIBUTION:
    DEBIN,
    SBIN,
    TEMISSION,
    SIGLASER,
    AG,
    SIGMAPT,
    TRANSVCUTOFF,
    CUTOFF,
    Z,
    T,
    PT,
    ALPHAX,
    ALPHAY,
    BETAX,
    BETAY,
    DX,
    DDX,
    DY,
    DDY,
    SIZE
};
}

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Distribution::Distribution():
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    Definition(AttributesT::SIZE + LegacyAttributesT::SIZE, "DISTRIBUTION",
               "The DISTRIBUTION statement defines data for the 6D particle distribution."),
    distrTypeT_m(DistrTypeT::NODIST),
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    numberOfDistributions_m(1),
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    emitting_m(false),
    scan_m(false),
    emissionModel_m(EmissionModelT::NONE),
    tEmission_m(0.0),
    tBin_m(0.0),
    currentEmissionTime_m(0.0),
    currentEnergyBin_m(0.0),
    currentSampleBin_m(0.0),
    numberOfEnergyBins_m(0),
    numberOfSampleBins_m(0),
    energyBins_m(NULL),
    energyBinHist_m(NULL),
    randGenEmit_m(NULL),
    pTotThermal_m(0.0),
    cathodeWorkFunc_m(0.0),
    laserEnergy_m(0.0),
    cathodeFermiEnergy_m(0.0),
    cathodeTemp_m(0.0),
    emitEnergyUpperLimit_m(0.0),
    inputMoUnits_m(InputMomentumUnitsT::NONE),
    sigmaTRise_m(0.0),
    sigmaTFall_m(0.0),
    tPulseLengthFWHM_m(0.0),
    laserProfileFileName_m(""),
    laserImageName_m(""),
    laserIntensityCut_m(0.0),
    laserProfile_m(NULL),
    darkCurrentParts_m(0),
    darkInwardMargin_m(0.0),
    eInitThreshold_m(0.0),
    workFunction_m(0.0),
    fieldEnhancement_m(0.0),
    fieldThrFN_m(0.0),
    maxFN_m(0),
    paraFNA_m(0.0),
    paraFNB_m(0.0),
    paraFNY_m(0.0),
    paraFNVYSe_m(0.0),
    paraFNVYZe_m(0.0),
    secondaryFlag_m(0),
    ppVw_m(0.0),
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    vVThermal_m(0.0),
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    referencePz_m(0.0),
    referenceZ_m(0.0),
    avrgpz_m(0.0),
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    I_m(0.0),
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    E_m(0.0),
    bega_m(0.0),
    M_m(0.0)
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{
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    SetAttributes();

    Distribution *defaultDistribution = clone("UNNAMED_Distribution");
    defaultDistribution->builtin = true;
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    try {
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        OpalData::getInstance()->define(defaultDistribution);
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    } catch(...) {
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        delete defaultDistribution;
    }

    SetFieldEmissionParameters();
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}
/**
 *
 *
 * @param name
 * @param parent
 */
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Distribution::Distribution(const std::string &name, Distribution *parent):
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    Definition(name, parent),
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    distT_m(parent->distT_m),
    distrTypeT_m(DistrTypeT::NODIST),
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    numberOfDistributions_m(parent->numberOfDistributions_m),
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    emitting_m(parent->emitting_m),
    scan_m(parent->scan_m),
    particleRefData_m(parent->particleRefData_m),
    addedDistributions_m(parent->addedDistributions_m),
    particlesPerDist_m(parent->particlesPerDist_m),
    emissionModel_m(parent->emissionModel_m),
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    tEmission_m(parent->tEmission_m),
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    tBin_m(parent->tBin_m),
    currentEmissionTime_m(parent->currentEmissionTime_m),
    currentEnergyBin_m(parent->currentEmissionTime_m),
    currentSampleBin_m(parent->currentSampleBin_m),
    numberOfEnergyBins_m(parent->numberOfEnergyBins_m),
    numberOfSampleBins_m(parent->numberOfSampleBins_m),
    energyBins_m(NULL),
    energyBinHist_m(NULL),
    randGenEmit_m(parent->randGenEmit_m),
    pTotThermal_m(parent->pTotThermal_m),
    cathodeWorkFunc_m(parent->cathodeWorkFunc_m),
    laserEnergy_m(parent->laserEnergy_m),
    cathodeFermiEnergy_m(parent->cathodeFermiEnergy_m),
    cathodeTemp_m(parent->cathodeTemp_m),
    emitEnergyUpperLimit_m(parent->emitEnergyUpperLimit_m),
    xDist_m(parent->xDist_m),
    pxDist_m(parent->pxDist_m),
    yDist_m(parent->yDist_m),
    pyDist_m(parent->pyDist_m),
    tOrZDist_m(parent->tOrZDist_m),
    pzDist_m(parent->pzDist_m),
    xWrite_m(parent->xWrite_m),
    pxWrite_m(parent->pxWrite_m),
    yWrite_m(parent->yWrite_m),
    pyWrite_m(parent->pyWrite_m),
    tOrZWrite_m(parent->tOrZWrite_m),
    pzWrite_m(parent->pzWrite_m),
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    avrgpz_m(parent->avrgpz_m),
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    inputMoUnits_m(parent->inputMoUnits_m),
    sigmaTRise_m(parent->sigmaTRise_m),
    sigmaTFall_m(parent->sigmaTFall_m),
    tPulseLengthFWHM_m(parent->tPulseLengthFWHM_m),
    sigmaR_m(parent->sigmaR_m),
    sigmaP_m(parent->sigmaP_m),
    cutoffR_m(parent->cutoffR_m),
    cutoffP_m(parent->cutoffP_m),
    distCorr_m(parent->distCorr_m),
    laserProfileFileName_m(parent->laserProfileFileName_m),
    laserImageName_m(parent->laserImageName_m),
    laserIntensityCut_m(parent->laserIntensityCut_m),
    laserProfile_m(NULL),
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    darkCurrentParts_m(parent->darkCurrentParts_m),
    darkInwardMargin_m(parent->darkInwardMargin_m),
    eInitThreshold_m(parent->eInitThreshold_m),
    workFunction_m(parent->workFunction_m),
    fieldEnhancement_m(parent->fieldEnhancement_m),
    fieldThrFN_m(parent->fieldThrFN_m),
    maxFN_m(parent->maxFN_m),
    paraFNA_m(parent-> paraFNA_m),
    paraFNB_m(parent-> paraFNB_m),
    paraFNY_m(parent-> paraFNY_m),
    paraFNVYSe_m(parent-> paraFNVYSe_m),
    paraFNVYZe_m(parent-> paraFNVYZe_m),
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    secondaryFlag_m(parent->secondaryFlag_m),
    ppVw_m(parent->ppVw_m),
    vVThermal_m(parent->vVThermal_m),
    tRise_m(parent->tRise_m),
    tFall_m(parent->tFall_m),
    sigmaRise_m(parent->sigmaRise_m),
    sigmaFall_m(parent->sigmaFall_m),
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    cutoff_m(parent->cutoff_m),
    I_m(parent->I_m),
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    E_m(parent->E_m),
    bega_m(parent->bega_m),
    M_m(parent->M_m)
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{
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}

Distribution::~Distribution() {

    if((Ippl::getNodes() == 1) && (os_m.is_open()))
        os_m.close();

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    if (energyBins_m != NULL) {
        delete energyBins_m;
        energyBins_m = NULL;
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    }

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    if (energyBinHist_m != NULL) {
        gsl_histogram_free(energyBinHist_m);
        energyBinHist_m = NULL;
    }

    if (randGenEmit_m != NULL) {
        delete randGenEmit_m;
        randGenEmit_m = NULL;
    }

    if(laserProfile_m) {
        delete laserProfile_m;
        laserProfile_m = NULL;
    }
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}
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/*
void Distribution::printSigma(SigmaGenerator<double,unsigned int>::matrix_type& M, Inform& out) {
  for(int i=0; i<M.size1(); ++i) {
    for(int j=0; j<M.size2(); ++j) {
      *gmsg  << M(i,j) << " ";
    }
    *gmsg << endl;
  }
}
*/
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/**
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 * At the moment only write the header into the file dist.dat
 * PartBunch will then append (very uggly)
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 * @param
 * @param
 * @param
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 */
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void Distribution::WriteToFile() {
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  /*
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    if(Ippl::getNodes() == 1) {
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        if(os_m.is_open()) {
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            ;
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        } else {
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            *gmsg << " Write distribution to file data/dist.dat" << endl;
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            std::string file("data/dist.dat");
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            os_m.open(file.c_str());
            if(os_m.bad()) {
                *gmsg << "Unable to open output file " <<  file << endl;
            }
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            os_m << "# x y ti px py pz "  << std::endl;
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            os_m.close();
        }
    }
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  */
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}

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/// Distribution can only be replaced by another distribution.
bool Distribution::canReplaceBy(Object *object) {
    return dynamic_cast<Distribution *>(object) != 0;
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}

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Distribution *Distribution::clone(const std::string &name) {
    return new Distribution(name, this);
}
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void Distribution::execute() {
}
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void Distribution::update() {
}
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void Distribution::Create(size_t &numberOfParticles, double massIneV) {
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    SetFieldEmissionParameters();
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    switch (distrTypeT_m) {
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    case DistrTypeT::MATCHEDGAUSS:
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        CreateMatchedGaussDistribution(numberOfParticles, massIneV);
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        break;
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    case DistrTypeT::FROMFILE:
        CreateDistributionFromFile(numberOfParticles, massIneV);
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        break;
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    case DistrTypeT::GAUSS:
        CreateDistributionGauss(numberOfParticles, massIneV);
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        break;
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    case DistrTypeT::BINOMIAL:
        CreateDistributionBinomial(numberOfParticles, massIneV);
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        break;
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    case DistrTypeT::FLATTOP:
        CreateDistributionFlattop(numberOfParticles, massIneV);
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        break;
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    case DistrTypeT::GUNGAUSSFLATTOPTH:
        CreateDistributionFlattop(numberOfParticles, massIneV);
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        break;
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    case DistrTypeT::ASTRAFLATTOPTH:
        CreateDistributionFlattop(numberOfParticles, massIneV);
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        break;
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    default:
        INFOMSG("Distribution unknown." << endl;);
        break;
    }
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    // AAA Scale and shift coordinates according to distribution input.
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    ScaleDistCoordinates();
    ShiftDistCoordinates(massIneV);
}
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void  Distribution::CreatePriPart(PartBunch *beam, BoundaryGeometry &bg) {
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    if(Options::ppdebug) {  // This is Parallel Plate Benchmark.
        int pc = 0;
        size_t lowMark = beam->getLocalNum();
        double vw = this->GetVw();
        double vt = this->GetvVThermal();
        double f_max = vw / vt * exp(-0.5);
        double test_a = vt / vw;
        double test_asq = test_a * test_a;
        size_t count = 0;
        size_t N_mean = static_cast<size_t>(floor(bg.getN() / Ippl::getNodes()));
        size_t N_extra = static_cast<size_t>(bg.getN() - N_mean * Ippl::getNodes());
        if(Ippl::myNode() == 0)
            N_mean += N_extra;
        if(bg.getN() != 0) {
            for(size_t i = 0; i < bg.getN(); i++) {
                if(pc == Ippl::myNode()) {
                    if(count < N_mean) {
                        /*==============Parallel Plate Benchmark=====================================*/
                        double test_s = 1;
                        double f_x = 0;
                        double test_x = 0;
                        while(test_s > f_x) {
                            test_s = IpplRandom();
                            test_s *= f_max;
                            test_x = IpplRandom();
                            test_x *= 10 * test_a; //range for normalized emission speed(0,10*test_a);
                            f_x = test_x / test_asq * exp(-test_x * test_x / 2 / test_asq);
                        }
                        double v_emi = test_x * vw;
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                        double betaemit = v_emi / Physics::c;
                        double betagamma = betaemit / sqrt(1 - betaemit * betaemit);
                        /*============================================================================ */
                        beam->create(1);
                        if(pc != 0) {
                            beam->R[lowMark + count] = bg.getCooridinate(Ippl::myNode() * N_mean + count + N_extra);
                            beam->P[lowMark + count] = betagamma * bg.getMomenta(Ippl::myNode() * N_mean + count);
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                        } else {
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                            beam->R[lowMark + count] = bg.getCooridinate(count);
                            beam->P[lowMark + count] = betagamma * bg.getMomenta(count);
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                        }
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                        beam->Bin[lowMark + count] = 0;
                        beam->PType[lowMark + count] = 0; // create primary particle bunch;
                        beam->TriID[lowMark + count] = 0;
                        beam->Q[lowMark + count] = beam->getChargePerParticle();
                        beam->LastSection[lowMark + count] = 0;
                        beam->Ef[lowMark + count] = Vector_t(0.0);
                        beam->Bf[lowMark + count] = Vector_t(0.0);
                        beam->dt[lowMark + count] = beam->getdT();
                        count ++;
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                    }
                }
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                pc++;
                if(pc == Ippl::getNodes())
                    pc = 0;
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            }
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            bg.clearCooridinateArray();
            bg.clearMomentaArray();
            beam->boundp();
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        }
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        *gmsg << *beam << endl;
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    } else {// Normal procedure to create primary particles
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        int pc = 0;
        size_t lowMark = beam->getLocalNum();
        size_t count = 0;
        size_t N_mean = static_cast<size_t>(floor(bg.getN() / Ippl::getNodes()));
        size_t N_extra = static_cast<size_t>(bg.getN() - N_mean * Ippl::getNodes());
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        if(Ippl::myNode() == 0)
            N_mean += N_extra;
        if(bg.getN() != 0) {
            for(size_t i = 0; i < bg.getN(); i++) {
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                if(pc == Ippl::myNode()) {
                    if(count < N_mean) {
                        beam->create(1);
                        if(pc != 0)
                            beam->R[lowMark + count] = bg.getCooridinate(Ippl::myNode() * N_mean + count + N_extra); // node 0 will emit the particle with coordinate ID from 0 to N_mean+N_extra, so other nodes should shift to node_number*N_mean+N_extra
                        else
                            beam->R[lowMark + count] = bg.getCooridinate(count); // for node0 the particle number N_mean =  N_mean + N_extra
                        beam->P[lowMark + count] = Vector_t(0.0);
                        beam->Bin[lowMark + count] = 0;
                        beam->PType[lowMark + count] = 0; // create primary particle bunch.
                        beam->TriID[lowMark + count] = 0;
                        beam->Q[lowMark + count] = beam->getChargePerParticle();
                        beam->LastSection[lowMark + count] = 0;
                        beam->Ef[lowMark + count] = Vector_t(0.0);
                        beam->Bf[lowMark + count] = Vector_t(0.0);
                        beam->dt[lowMark + count] = beam->getdT();
                        count++;
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                    }
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                }
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                pc++;
                if(pc == Ippl::getNodes())
                    pc = 0;
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            }
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        }
        bg.clearCooridinateArray();
        beam->boundp();//fixme if bg.getN()==0?
    }
    *gmsg << *beam << endl;
}
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void Distribution::DoRestartOpalT(PartBunch &beam, size_t Np, int restartStep) {
    h5_file_t *H5file;
    h5_int64_t rc;
    std::string fn;
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    IpplTimings::startTimer(beam.distrReload_m);
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    //        beam.setTEmission(Attributes::getReal(itsAttr[AttributesT::SIZE + LegacyAttributesT::TEMISSION]));
    fn = OpalData::getInstance()->getInputBasename() + std::string(".h5");
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#ifdef PARALLEL_IO
    H5file = H5OpenFile(fn.c_str(), H5_O_RDONLY, Ippl::getComm());
#else
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    H5file = H5OpenFile(fn.c_str(), H5_O_RDONLY, 0);
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#endif

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    if(H5file == (void*)H5_ERR) {
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	throw OpalException("Distribution::DoRestartOpalT",
                            "could not open file '" + fn + "'");
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    }

    if(restartStep == -1) {
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        restartStep = H5GetNumSteps(H5file) - 1 ;
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        OpalData::getInstance()->setRestartStep(restartStep);
    } else {
        if(restartStep != H5GetNumSteps(H5file) - 1 && !OpalData::getInstance()->hasRestartFile()) {
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            throw OpalException("Distribution::DoRestartOpalT",
                                "can't append to the file '" + fn + "'");
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        }
    }

    rc = H5SetStep(H5file, restartStep);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    int N = (int)H5PartGetNumParticles(H5file);

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    int numberOfParticlesPerNode = (int) floor((double) N / Ippl::getNodes());
    long long starti = Ippl::myNode() * numberOfParticlesPerNode;
    long long endi = starti + numberOfParticlesPerNode - 1;

    // In case we miss some particles we add them at the end on the last core
    if(Ippl::myNode() == (Ippl::getNodes() - 1)) {
        if(Ippl::getNodes()*numberOfParticlesPerNode < N)
            endi += (N - (Ippl::getNodes() * numberOfParticlesPerNode));
    }
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    rc = H5PartSetView(H5file, starti, endi);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    N = (int)H5PartGetNumParticles(H5file);
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    assert(N >= 0);
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    double actualT;
    rc = H5ReadStepAttribFloat64(H5file, "TIME", &actualT);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    beam.setT(actualT);
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    double dPhiGlobal;
    rc = H5ReadFileAttribFloat64(H5file, "dPhiGlobal", &dPhiGlobal);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    OpalData::getInstance()->setGlobalPhaseShift(dPhiGlobal);

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    h5_int64_t ltstep;
    rc = H5ReadStepAttribInt64(H5file, "LocalTrackStep", &ltstep);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    beam.setLocalTrackStep((long long)ltstep);

    h5_int64_t gtstep;
    rc = H5ReadStepAttribInt64(H5file, "GlobalTrackStep", &gtstep);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    beam.setGlobalTrackStep((long long)gtstep);
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    std::unique_ptr<char[]> varray(new char[(N)*sizeof(double)]);
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    h5_float64_t *farray = reinterpret_cast<h5_float64_t *>(varray.get());
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    h5_int64_t *larray = reinterpret_cast<h5_int64_t *>(varray.get());
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    beam.create(N);

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    rc = H5PartReadDataFloat64(H5file, "x", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n) {
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        beam.R[n](0) = farray[n];
        beam.Bin[n] = 0; // not initialized
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    }
    rc = H5PartReadDataFloat64(H5file, "y", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
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        beam.R[n](1) = farray[n];
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    rc = H5PartReadDataFloat64(H5file, "z", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
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        beam.R[n](2) = farray[n];
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    rc = H5PartReadDataFloat64(H5file, "px", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
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        beam.P[n](0) = farray[n];
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    rc = H5PartReadDataFloat64(H5file, "py", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
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        beam.P[n](1) = farray[n];
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    rc = H5PartReadDataFloat64(H5file, "pz", farray);
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    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
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        beam.P[n](2) = farray[n];
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    rc = H5PartReadDataFloat64(H5file, "q", farray);
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    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
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        beam.Q[n] = farray[n];
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    rc = H5PartReadDataInt64(H5file, "lastsection", larray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
        beam.LastSection[n] = (short) larray[n];

    Ippl::Comm->barrier();
    rc = H5CloseFile(H5file);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
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    beam.boundp();

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    IpplTimings::stopTimer(beam.distrReload_m);

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    *gmsg << "Total number of particles in the h5 file = " << N << " NPerBunch= " << beam.getTotalNum()
          << " Global step " << gtstep << " Local step " << ltstep << endl
          << " restart step= " << restartStep << " time of restart = " << actualT
          << " phishift= " << OpalData::getInstance()->getGlobalPhaseShift() << endl;
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}

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void Distribution::DoRestartOpalCycl(PartBunch &beam, size_t Np, int restartStep, const int specifiedNumBunch) {
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    h5_int64_t rc;
    IpplTimings::startTimer(beam.distrReload_m);
    *gmsg << "---------------- Start reading hdf5 file----------------" << endl;
    h5_file_t *H5file;

    std::string fn = OpalData::getInstance()->getInputBasename() + std::string(".h5");

#ifdef PARALLEL_IO
    H5file = H5OpenFile(fn.c_str(), H5_O_RDONLY, Ippl::getComm());
#else
    H5file = H5OpenFile(fn.c_str(), H5_O_RDONLY, 0);
#endif

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    if(H5file == (void*)H5_ERR) {
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        throw OpalException("Distribution::DoRestartOpalCycl",
                            "could not open file '" + fn + "'");
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    }

    if(restartStep == -1) {
        restartStep = H5GetNumSteps(H5file) - 1;
        OpalData::getInstance()->setRestartStep(restartStep);
    } else {
        if(restartStep != H5GetNumSteps(H5file) - 1 && !OpalData::getInstance()->hasRestartFile()) {
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            throw OpalException("Distribution::DoRestartOpalCycl",
                                "can't append to the file '" + fn + "'");
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        }
    }

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    *gmsg << "Restart from hdf5 format file " << fn
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          << ", read phase space data of DumpStep " << (int)restartStep << endl;
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    rc = H5SetStep(H5file, restartStep);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    const int globalN = (int)H5PartGetNumParticles(H5file);

    *gmsg << "total number of particles = " << globalN << endl;

    int numberOfParticlesPerNode = (int) floor((double) globalN / Ippl::getNodes());
    long long starti = Ippl::myNode() * numberOfParticlesPerNode;
    long long endi = 0;

    if(Ippl::myNode() == Ippl::getNodes() - 1)
        endi = -1;
    else
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        endi = starti + numberOfParticlesPerNode - 1;
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    rc = H5PartSetView(H5file, starti, endi);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    const int localN = (int)H5PartGetNumParticles(H5file);
    assert(localN >= 0);

    h5_int64_t ltstep;
    rc = H5ReadStepAttribInt64(H5file, "LocalTrackStep", &ltstep);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    beam.setLocalTrackStep((long long)ltstep);

    h5_int64_t gtstep;
    rc = H5ReadStepAttribInt64(H5file, "GlobalTrackStep", &gtstep);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    beam.setGlobalTrackStep((long long)gtstep);

    char opalFlavour[128];
    rc = H5ReadStepAttribString(H5file, "OPAL_flavour", opalFlavour);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

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    rc = H5ReadStepAttribFloat64(H5file, "REFPR",&referencePr_m);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

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    referencePt_m = 0.0;
    rc = H5ReadStepAttribFloat64(H5file, "REFPT",&referencePt_m);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

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    referencePz_m = 0.0;
    rc = H5ReadStepAttribFloat64(H5file, "REFPZ",&referencePz_m);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

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    rc = H5ReadStepAttribFloat64(H5file, "REFR",&referenceR_m);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

    rc = H5ReadStepAttribFloat64(H5file, "REFTHETA",&referenceTheta_m);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

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    referenceZ_m = 0.0;
    rc = H5ReadStepAttribFloat64(H5file, "REFZ",&referenceZ_m);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

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    double meanE;
    rc = H5ReadStepAttribFloat64(H5file, "ENERGY", &meanE);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

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    double pathLength;;
    rc = H5ReadStepAttribFloat64(H5file, "SPOS", &pathLength);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

    beam.setLPath(pathLength);

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    *gmsg << "* Restart Energy = " << meanE << " (MeV), Path lenght = " << pathLength << " (m)" <<  endl;

    // beam.getM() in eV, meanE in MeV had to change 1e3 to 1e6 -DW
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    double ga = 1 + meanE / beam.getM() * 1.0e6;
    double be = sqrt(1.0 - (1.0 / (ga * ga)));
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    bega_m = be * ga;
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    *gmsg << "* Gamma = " << ga << ", Beta = " << be << endl;
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    std::unique_ptr<char[]> varray(new char[(localN)*sizeof(double)]);
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    double *farray = reinterpret_cast<double *>(varray.get());
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    h5_int64_t *larray = reinterpret_cast<h5_int64_t *>(varray.get());

    beam.create(localN);

    if(strcmp(opalFlavour, "opal-t") == 0) {
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        *gmsg << "Restart from hdf5 file generated by OPAL-t" << endl;

        // force the initial time to zero
        beam.setT(0.0);
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	beam.setLocalTrackStep((long long) 0 );
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        rc = H5PartReadDataFloat64(H5file, "x", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.R[n](0) = -farray[n];

        rc = H5PartReadDataFloat64(H5file, "y", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.R[n](2) = farray[n];

        rc = H5PartReadDataFloat64(H5file, "z", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.R[n](1) = farray[n];

        rc = H5PartReadDataFloat64(H5file, "px", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.P[n](0) = -farray[n];

        rc = H5PartReadDataFloat64(H5file, "py", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.P[n](2) = farray[n];

        rc = H5PartReadDataFloat64(H5file, "pz", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.P[n](1) = farray[n];

        rc = H5PartReadDataInt64(H5file, "id", larray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.ID[n] = larray[n];

    } else {
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        *gmsg << "Restart from hdf5 file generated by OPAL-cycl" << endl;

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        rc = H5ReadStepAttribFloat64(H5file, "AZIMUTH", &phi_m);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

        rc = H5ReadStepAttribFloat64(H5file, "ELEVATION", &psi_m);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

        h5_int64_t localDump = 0;
        previousH5Local_m = false;
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        rc = H5ReadStepAttribInt64(H5file, "LOCAL", &localDump);
        if(rc != H5_SUCCESS) {

            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

            throw OpalException("Error during restart for Cyclotron Tracker:",
                                "You are trying to restart from a legacy file that doesn't contain\
  information on local/global frame. We are working on legacy support, but for now you have to use\
  OPAL 1.3.0!");

        } else {
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            if (localDump == 1) previousH5Local_m = true;
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        }

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        double actualT;
        rc = H5ReadStepAttribFloat64(H5file, "TIME", &actualT);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        beam.setT(actualT);

        h5_int64_t SteptoLastInj;
        rc = H5ReadStepAttribInt64(H5file, "SteptoLastInj", &SteptoLastInj);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        beam.setSteptoLastInj((int)SteptoLastInj);
        *gmsg << "Tracking Step since last bunch injection is " << SteptoLastInj << endl;

        h5_int64_t numBunch;
        rc = H5ReadStepAttribInt64(H5file, "NumBunch", &numBunch);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        beam.setNumBunch((int)numBunch);
        *gmsg << numBunch << " Bunches(bins) exist in this file" << endl;

        rc = H5PartReadDataFloat64(H5file, "x", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.R[n](0) = farray[n];

        rc = H5PartReadDataFloat64(H5file, "y", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.R[n](1) = farray[n];

        rc = H5PartReadDataFloat64(H5file, "z", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.R[n](2) = farray[n];

        rc = H5PartReadDataFloat64(H5file, "px", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.P[n](0) = farray[n];

        rc = H5PartReadDataFloat64(H5file, "py", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.P[n](1) = farray[n];

        rc = H5PartReadDataFloat64(H5file, "pz", farray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.P[n](2) = farray[n];

        rc = H5PartReadDataInt64(H5file, "id", larray);
        if(rc != H5_SUCCESS)
            ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
        for(unsigned long int n = 0; n < (unsigned int) localN; ++n)
            beam.ID[n] = larray[n];

        // only for multi-bunch mode
        if(specifiedNumBunch > 1) {
            // the allowed maximal bin number is set to 1000
            beam.setPBins(new PartBinsCyc(1000, numBunch));
        }
    }

    Ippl::Comm->barrier();
    rc = H5CloseFile(H5file);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    beam.boundp();
    beam.Q = beam.getChargePerParticle();

    if(strcmp(opalFlavour, "opal-t") == 0) {
        Vector_t meanR(0.0, 0.0, 0.0);
        Vector_t meanP(0.0, 0.0, 0.0);
        unsigned long int newLocalN = beam.getLocalNum();
        for(unsigned int i = 0; i < newLocalN; ++i) {
            for(int d = 0; d < 3; ++d) {
                meanR(d) += beam.R[i](d);
                meanP(d) += beam.P[i](d);
            }
        }
        reduce(meanR, meanR, OpAddAssign());
        meanR /= Vector_t(globalN);
        reduce(meanP, meanP, OpAddAssign());
        meanP /= Vector_t(globalN);
        *gmsg << "Rmean = " << meanR << "[m], Pmean=" << meanP << endl;

        for(unsigned int i = 0; i < newLocalN; ++i) {
            beam.R[i] -= meanR;
            beam.P[i] -= meanP;
        }
    }

    *gmsg << "----------------Finish reading hdf5 file----------------" << endl;
    IpplTimings::stopTimer(beam.distrReload_m);
}

void Distribution::DoRestartOpalE(EnvelopeBunch &beam, size_t Np, int restartStep) {
    h5_file_t *H5file;
    h5_int64_t rc;
    std::string fn;

    IpplTimings::startTimer(beam.distrReload_m);

    if(OpalData::getInstance()->hasRestartFile()) {
        fn = OpalData::getInstance()->getRestartFileName();
        *gmsg << "Restart from a specified file:" << fn << endl;

    } else {
        fn = OpalData::getInstance()->getInputBasename() + std::string(".h5");
    }

#ifdef PARALLEL_IO
    H5file = H5OpenFile(fn.c_str(), H5_O_RDONLY, Ippl::getComm());
#else
    H5file = H5PartOpenFile(fn.c_str(), H5_O_RDONLY, 0);
#endif

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    if(H5file == (void*)H5_ERR) {
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	throw OpalException("Distribution::DoRestartOpalE",
                            "could not open file '" + fn + "'");
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    }

    if(restartStep == -1) {
        restartStep = H5GetNumSteps(H5file) - 1;
        OpalData::getInstance()->setRestartStep(restartStep);
    } else {
        if(restartStep != H5GetNumSteps(H5file) - 1 && !OpalData::getInstance()->hasRestartFile()) {
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            throw OpalException("Distribution::DoRestartOpalE",
                                "can't append to the file '" + fn + "'");
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        }
    }

    rc = H5SetStep(H5file, restartStep);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    int N = (int)H5PartGetNumParticles(H5file);

    h5_int64_t totalSteps = H5GetNumSteps(H5file);
    *gmsg << "total number of slices = " << N << " total steps " << totalSteps << endl;

    beam.distributeSlices(N);
    beam.createBunch();
    long long starti = beam.mySliceStartOffset();
    long long endi = beam.mySliceEndOffset();

    rc = H5PartSetView(H5file, starti, endi);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    N = (int)H5PartGetNumParticles(H5file);
    assert(N >= 0 && (unsigned int) N != beam.numMySlices());

    double actualT;
    rc = H5ReadStepAttribFloat64(H5file, "TIME", &actualT);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);

    beam.setT(actualT);
    double dPhiGlobal;
    rc = H5ReadFileAttribFloat64(H5file, "dPhiGlobal", &dPhiGlobal);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    OpalData::getInstance()->setGlobalPhaseShift(dPhiGlobal);

    h5_int64_t ltstep;
    rc = H5ReadStepAttribInt64(H5file, "LocalTrackStep", &ltstep);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    beam.setLocalTrackStep((long long)ltstep);

    h5_int64_t gtstep;
    rc = H5ReadStepAttribInt64(H5file, "GlobalTrackStep", &gtstep);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    beam.setGlobalTrackStep((long long)gtstep);

    std::unique_ptr<char[]> varray(new char[(N)*sizeof(double)]);
    double *farray = reinterpret_cast<double *>(varray.get());
    h5_int64_t *larray = reinterpret_cast<h5_int64_t *>(varray.get());

    rc = H5PartReadDataFloat64(H5file, "x", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n) {
        beam.setX(n, farray[n]);
    }
    rc = H5PartReadDataFloat64(H5file, "y", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
        beam.setY(n, farray[n]);

    rc = H5PartReadDataFloat64(H5file, "z", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
        beam.setZ(n, farray[n]);

    rc = H5PartReadDataFloat64(H5file, "px", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
        beam.setPx(n, farray[n]);

    rc = H5PartReadDataFloat64(H5file, "py", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
        beam.setPy(n, farray[n]);

    rc = H5PartReadDataFloat64(H5file, "beta", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
        beam.setBeta(n, farray[n]);

    rc = H5PartReadDataFloat64(H5file, "X0", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
        beam.setX0(n, farray[n]);

    rc = H5PartReadDataFloat64(H5file, "pX0", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
        beam.setPx0(n, farray[n]);

    rc = H5PartReadDataFloat64(H5file, "Y0", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
        beam.setY0(n, farray[n]);

    rc = H5PartReadDataFloat64(H5file, "pY0", farray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0; n < (unsigned int) N; ++n)
        beam.setPy0(n, farray[n]);

    rc = H5PartReadDataInt64(H5file, "lastsection", larray);
    if(rc != H5_SUCCESS)
        ERRORMSG("H5 rc= " << rc << " in " << __FILE__ << " @ line " << __LINE__ << endl);
    for(unsigned long int n = 0</