CSRIGFWakeFunction.cpp

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//
// Class CSRIGFWakeFunction
//
// Copyright (c) 2008 - 2020, Paul Scherrer Institut, Villigen PSI, Switzerland
// All rights reserved
//
// This file is part of OPAL.
//
// OPAL is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// You should have received a copy of the GNU General Public License
// along with OPAL. If not, see <https://www.gnu.org/licenses/>.
//
#include "Solvers/CSRIGFWakeFunction.h"
 
#include "AbsBeamline/RBend.h"
#include "AbsBeamline/SBend.h"
#include "AbstractObjects/OpalData.h"
#include "Algorithms/PartBunchBase.h"
#include "Filters/Filter.h"
#include "Filters/SavitzkyGolay.h"
#include "Physics/Physics.h"
#include "Physics/Units.h"
#include "Solvers/RootFinderForCSR.h"
#include "Utilities/Options.h"
#include "Utilities/Util.h"
 
#include <cmath>
#include <fstream>
#include <iostream>
 
CSRIGFWakeFunction::CSRIGFWakeFunction(const std::string& name, std::vector<Filter*> filters, const unsigned int& N):
    WakeFunction(name, N),
    filters_m(filters.begin(), filters.end()),
    lineDensity_m(),
    dlineDensitydz_m(),
    bendRadius_m(0.0),
    totalBendAngle_m(0.0)
{
    if (filters_m.size() == 0) {
        defaultFilter_m.reset(new SavitzkyGolayFilter(7, 3, 3, 3));
        filters_m.push_back(defaultFilter_m.get());
    }
 
    diffOp_m = filters_m.back();
}
 
void CSRIGFWakeFunction::apply(PartBunchBase<double, 3>* bunch) {
    Inform msg("CSRWake ");
 
    std::pair<double, double> meshInfo;
    calculateLineDensity(bunch, meshInfo);
    const double &meshOrigin = meshInfo.first;
    const double &meshSpacing = meshInfo.second;
    const unsigned int numOfSlices = lineDensity_m.size();
 
    if (Ez_m.size() < numOfSlices) {
        Ez_m.resize(numOfSlices, 0.0);
        Chi_m.resize(numOfSlices, 0.0);
        Grn_m.resize(numOfSlices, 0.0);
        Psi_m.resize(numOfSlices, 0.0);
    }
 
    for (unsigned int i = 0; i < numOfSlices; ++i) {
        Ez_m[i] = 0.0;
    }
 
    Vector_t smin, smax;
    bunch->get_bounds(smin, smax);
    double minPathLength = smin(2) + bunch->get_sPos() - FieldBegin_m;
    for (unsigned int i = 1; i < numOfSlices; i++) {
        double pathLengthOfSlice = minPathLength + i * meshSpacing;
        double angleOfSlice = pathLengthOfSlice/bendRadius_m;
        if (angleOfSlice > 0.0 && angleOfSlice <= totalBendAngle_m){
            calculateGreenFunction(bunch, meshSpacing);
        }
        // convolute with line density
        calculateContributionInside(i, angleOfSlice, meshSpacing);
        calculateContributionAfter(i, angleOfSlice, meshSpacing);
        Ez_m[i] /= 4 * Physics::pi * Physics::epsilon_0;
    }
 
    // calculate the wake field seen by the particles
    for (unsigned int i = 0; i < bunch->getLocalNum(); ++i) {
        const Vector_t &R = bunch->R[i];
        unsigned int indexz = (unsigned int)floor((R(2) - meshOrigin) / meshSpacing);
        double leverz = (R(2) - meshOrigin) / meshSpacing - indexz;
        PAssert_LT(indexz + 1, numOfSlices);
 
        bunch->Ef[i](2) += (1. - leverz) * Ez_m[indexz] + leverz * Ez_m[indexz + 1];
    }
 
    if (Options::csrDump) {
        static std::string oldBendName;
        static unsigned long counter = 0;
 
        if (oldBendName != bendName_m) counter = 0;
 
        const int every = 1;
        bool print_criterion = (counter + 1) % every == 0;
        if (print_criterion) {
            static unsigned int file_number = 0;
            if (counter == 0) file_number = 0;
            double spos = bunch->get_sPos();
            if (Ippl::myNode() == 0) {
                std::stringstream filename_str;
                filename_str << bendName_m << "-CSRWake" << std::setw(5) << std::setfill('0') << file_number << ".txt";
 
                std::string fname = Util::combineFilePath({
                    OpalData::getInstance()->getAuxiliaryOutputDirectory(),
                    filename_str.str()
                });
 
                std::ofstream csr(fname);
                csr << spos << ", " << FieldBegin_m << ", " << smin(2) << ", " << smax(2) << ", " << meshSpacing*64 << std::endl;
                for (unsigned int i = 0; i < lineDensity_m.size(); ++ i) {
                    csr << i *meshSpacing << "\t"
                        << Ez_m[i] << "\t"
                        << lineDensity_m[i] << std::endl;
                }
                csr.close();
                msg << "** wrote " << fname << endl;
            }
            ++ file_number;
        }
        ++ counter;
        oldBendName = bendName_m;
    }
}
 
void CSRIGFWakeFunction::initialize(const ElementBase* ref) {
    if (ref->getType() == ElementType::RBEND ||
       ref->getType() == ElementType::SBEND) {
 
        const Bend2D *bend = static_cast<const Bend2D *>(ref);
        double End;
 
        bendRadius_m = bend->getBendRadius();
        bend->getDimensions(Begin_m, End);
        Length_m = bend->getEffectiveLength();
        FieldBegin_m = bend->getEffectiveCenter() - Length_m / 2.0;
        totalBendAngle_m = std::abs(bend->getBendAngle());
        bendName_m = bend->getName();
    }
}
 
void CSRIGFWakeFunction::calculateLineDensity(PartBunchBase<double, 3>* bunch,
                                              std::pair<double, double>& meshInfo) {
    bunch->calcLineDensity(nBins_m, lineDensity_m, meshInfo);
 
    // the following is only needed for after dipole
    std::vector<Filter *>::const_iterator fit;
    for (fit = filters_m.begin(); fit != filters_m.end(); ++ fit) {
        (*fit)->apply(lineDensity_m);
    }
    dlineDensitydz_m.assign(lineDensity_m.begin(), lineDensity_m.end());
    diffOp_m->calc_derivative(dlineDensitydz_m, meshInfo.second);
}
 
void CSRIGFWakeFunction::calculateGreenFunction(PartBunchBase<double, 3>* bunch,
                                                double meshSpacing) {
    unsigned int numOfSlices = lineDensity_m.size();
    double gamma = bunch->get_meanKineticEnergy() / (bunch->getM() * Units::eV2MeV)+1.0;
    double xmu_const = 3.0 * gamma * gamma * gamma / (2.0 * bendRadius_m);
    double chi_const = 9.0 / 16.0 * (6.0 - std::log(27.0 / 4.0));
 
    for (unsigned int i = 0; i < numOfSlices; ++i) {
        Chi_m[i] = 0.0;
        double z = i * meshSpacing;
        double xmu = xmu_const * z;
        double b = std::sqrt(xmu * xmu + 1.0) + xmu;
        if (xmu < 1e-3)
            Chi_m[i] = chi_const + 0.5 * std::pow(xmu, 2) - 7.0 / 54.0 * std::pow(xmu, 4) + 140.0 / 2187.0 * std::pow(xmu, 6);
        else
            Chi_m[i] = 9.0 / 16.0 * (3.0 * (-2.0 * xmu * std::pow(b, 1.0/3.0) + std::pow(b, 2.0/3.0) + std::pow(b, 4.0/3.0)) +
                                     std::log(std::pow((1 - std::pow(b, 2.0 / 3.0)) / xmu, 2) / (1 + std::pow(b, 2.0 / 3.0) + std::pow(b, 4.0 / 3.0))));
    }
    double grn_const = -16.0/(27.0 * gamma * gamma * meshSpacing);
    Grn_m[0] = grn_const * (Chi_m[1] - Chi_m[0]);
    Grn_m[numOfSlices - 1] = 0.0;
    for (unsigned int i = 1; i < numOfSlices - 1; ++i) {
        Grn_m[i] = grn_const * (Chi_m[i + 1] - 2.0 * Chi_m[i] + Chi_m[i - 1]);
    }
}
 
void CSRIGFWakeFunction::calculateContributionInside(size_t sliceNumber,
                                                     double angleOfSlice,
                                                     double /*meshSpacing*/) {
    if (angleOfSlice > totalBendAngle_m || angleOfSlice < 0.0) return;
    int startSliceNum = 0;
    for (int j = sliceNumber; j >= startSliceNum; j--)
        Ez_m[sliceNumber] += lineDensity_m[j] * Grn_m[sliceNumber - j];
}
 
void CSRIGFWakeFunction::calculateContributionAfter(size_t sliceNumber,
                                                    double angleOfSlice,
                                                    double meshSpacing) {
    if (angleOfSlice <= totalBendAngle_m) return;
 
    double Ds_max = bendRadius_m * std::pow(totalBendAngle_m, 3) / 24. * (4. - 3.* totalBendAngle_m / angleOfSlice);
 
    // First do contribution from particles whose retarded position is
    // prior to the bend.
    double Ds_max2 = bendRadius_m * std::pow(totalBendAngle_m, 2) / 6. * (3. * angleOfSlice - 2. * totalBendAngle_m);
    int j = 0;
    double frac = 0.0;
    if (Ds_max2 / meshSpacing < sliceNumber) {
        j = sliceNumber - static_cast<int>(std::floor(Ds_max2 / meshSpacing));
        frac = Ds_max2 / meshSpacing - (sliceNumber - j);
        Ez_m[sliceNumber] -= (frac * lineDensity_m[j - 1] + (1. - frac) * lineDensity_m[j]) / (2. * angleOfSlice - totalBendAngle_m);
    }
 
    // Now do delta function contribution for particles whose retarded position
    // is in the bend.
    if (Ds_max / meshSpacing < sliceNumber) {
        j = sliceNumber - static_cast<int>(std::floor(Ds_max / meshSpacing));
        frac = Ds_max / meshSpacing - (sliceNumber - j);
        Ez_m[sliceNumber] += (frac * lineDensity_m[j - 1] + (1.0 - frac) * lineDensity_m[j]) / (2. * angleOfSlice - totalBendAngle_m);
    }
 
    // Now do integral contribution for particles whose retarded position is in
    // the bend.
 
    double angleOverlap = angleOfSlice - totalBendAngle_m;
    int k = sliceNumber;
    if (Ds_max / meshSpacing < sliceNumber) {
        k = j;
        Psi_m[k] = calcPsi(Psi_m[k], angleOverlap, meshSpacing * (k + frac));
        if (Psi_m[k] > 0 && Psi_m[k] < totalBendAngle_m)
            Ez_m[sliceNumber] += 0.5 * (frac * dlineDensitydz_m[sliceNumber - k - 1] + (1.0 - frac) * dlineDensitydz_m[sliceNumber - k]) / (Psi_m[k] + 2.0 * angleOverlap);
    } else {
        Psi_m[0] = calcPsi(Psi_m[0], angleOverlap, meshSpacing * sliceNumber);
        if (Psi_m[0] > 0 && Psi_m[0] < totalBendAngle_m)
            Ez_m[sliceNumber] += 0.5 * dlineDensitydz_m[0] / (Psi_m[0] + 2.0 * angleOverlap);
    }
 
    // Do rest of integral.
    for (unsigned int l = sliceNumber - k + 1; l < sliceNumber; ++ l) {
        Psi_m[l] = calcPsi(Psi_m[l], angleOverlap, meshSpacing * (sliceNumber - l));
        if (Psi_m[l] > 0 && Psi_m[l] < totalBendAngle_m)
            Ez_m[sliceNumber] += dlineDensitydz_m[l] / (Psi_m[l] + 2.0 * angleOverlap);
    }
 
    // We don't go right to the end as there is a singularity in the numerical integral that we don't quite know
    // how to deal with properly yet. This introduces a very slight error in the calculation (fractions of a percent).
    Psi_m[sliceNumber] = calcPsi(Psi_m[sliceNumber], angleOverlap, meshSpacing / 4.0);
    if (Psi_m[sliceNumber] > 0 && Psi_m[sliceNumber] < totalBendAngle_m)
        Ez_m[sliceNumber] += 0.5 * dlineDensitydz_m[sliceNumber] / (Psi_m[sliceNumber] + 2.0 * angleOverlap);
 
    double prefactor = -4 / bendRadius_m;
    Ez_m[sliceNumber] *= prefactor;
}
 
double CSRIGFWakeFunction::calcPsi(const double& psiInitial, const double& x, const double& Ds) const {
    const int Nmax = 100;
    const double eps = 1e-10;
    double psi = std::pow(24. * Ds / bendRadius_m, 1. / 3.);
    if (psiInitial != 0.0) psi = psiInitial;
 
    for (int i = 0; i < Nmax; ++i) {
        double residual = bendRadius_m * psi * psi * psi * (psi + 4. * x) - 24. * Ds * psi - 24. * Ds * x;
        if (std::abs(residual) < eps)
            return psi;
        psi -= residual / (4. * bendRadius_m * psi * psi * psi + 12. * x * bendRadius_m * psi * psi - 24. * Ds);
    }
    RootFinderForCSR rootFinder(bendRadius_m, 4 * x * bendRadius_m, -24 * Ds, -24 * Ds * x);
    if (rootFinder.hasPositiveRealRoots()) {
        return rootFinder.searchRoot(eps);
    }
 
    ERRORMSG("In CSRWakeFunction::calcPsi(): exceed maximum number of iterations!" << endl);
    return psi;
}
 
WakeType CSRIGFWakeFunction::getType() const {
    return WakeType::CSRIGFWakeFunction;
}