TRestAxionField.cxx

/*************************************************************************
 * This file is part of the REST software framework.                     *
 *                                                                       *
 * Copyright (C) 2016 GIFNA/TREX (University of Zaragoza)                *
 * For more information see http://gifna.unizar.es/trex                  *
 *                                                                       *
 * REST 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.                                   *
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 * REST is distributed in the hope that it will be useful,               *
 * but WITHOUT ANY WARRANTY; without even the implied warranty of        *
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the          *
 * GNU General Public License for more details.                          *
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 * You should have a copy of the GNU General Public License along with   *
 * REST in $REST_PATH/LICENSE.                                           *
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 *************************************************************************/
 
#include "TRestAxionField.h"
 
#include <TComplex.h>
#include <TVectorD.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_integration.h>
 
#include <numeric>
 
#include "TH1F.h"
 
using namespace std;
 
ClassImp(TRestAxionField);
 
TRestAxionField::TRestAxionField() { Initialize(); }
 
TRestAxionField::~TRestAxionField() {}
 
void TRestAxionField::Initialize() {
    fBufferGas = NULL;
 
}
 
double TRestAxionField::BL(Double_t Bmag, Double_t Lcoh) {
    Double_t lengthInMeters = Lcoh * units("m");
 
    Double_t tm =
        REST_Physics::lightSpeed / REST_Physics::naturalElectron * units("GeV") / units("eV");  // eV --> GeV
    Double_t sol = lengthInMeters * Bmag * tm;
    sol = sol * 1.0e-10;
 
    return sol;
}
 
double TRestAxionField::BLHalfSquared(Double_t Bmag, Double_t Lcoh)  // (BL/2)**2
{
    Double_t lengthInMeters = Lcoh * units("m");
 
    Double_t tm =
        REST_Physics::lightSpeed / REST_Physics::naturalElectron * units("GeV") / units("eV");  // eV --> GeV
    Double_t sol = lengthInMeters * Bmag * tm / 2;
    sol = sol * sol * 1.0e-20;
 
    return sol;
}
 
Double_t TRestAxionField::GammaTransmissionProbability(Double_t ma, Double_t mg, Double_t absLength) {
    Double_t cohLength = fLcoh * units("m");  // Default REST units are mm;
 
    Double_t photonMass = mg;
 
    if (mg == 0 && fBufferGas) photonMass = fBufferGas->GetPhotonMass(fEa);
 
    RESTDebug << "+--------------------------------------------------------------------------+" << RESTendl;
    RESTDebug << " TRestAxionField::GammaTransmissionProbability. Parameter summary" << RESTendl;
    RESTDebug << " Photon mass : " << photonMass << " eV" << RESTendl;
    RESTDebug << " Axion mass : " << ma << " eV" << RESTendl;
    RESTDebug << " Axion energy : " << fEa << " keV" << RESTendl;
    RESTDebug << " Lcoh : " << fLcoh << " mm" << RESTendl;
    RESTDebug << " Bmag : " << fBmag << " T" << RESTendl;
    RESTDebug << "+--------------------------------------------------------------------------+" << RESTendl;
 
    if (ma == 0.0 && photonMass == 0.0) return BLHalfSquared(fBmag, fLcoh);
 
    Double_t q = (ma * ma - photonMass * photonMass) / 2. / (fEa * units("eV"));
    Double_t l = cohLength * REST_Physics::PhMeterIneV;
    Double_t phi = q * l;
 
    Double_t Gamma = absLength;
    if (absLength == 0 && fBufferGas) Gamma = fBufferGas->GetPhotonAbsorptionLength(fEa);  // cm-1
    Double_t GammaL = Gamma * cohLength * units("cm") / units("m");                        // m --> cm
 
    if (fDebug) {
        std::cout << "+------------------------+" << std::endl;
        std::cout << " Intermediate calculations" << std::endl;
        std::cout << " q : " << q << " eV" << std::endl;
        std::cout << " l : " << l << " eV-1" << std::endl;
        std::cout << " phi : " << phi << std::endl;
        std::cout << "Gamma : " << Gamma << std::endl;
        std::cout << "GammaL : " << GammaL << std::endl;
        std::cout << "+------------------------+" << std::endl;
    }
 
    Double_t MFactor = phi * phi + GammaL * GammaL / 4.0;
    MFactor = 1.0 / MFactor;
 
    if (fDebug) {
        std::cout << "Mfactor : " << MFactor << std::endl;
        std::cout << "(BL/2)^2 : " << BLHalfSquared(fBmag, fLcoh) << std::endl;
        std::cout << "cos(phi) : " << cos(phi) << std::endl;
        std::cout << "Exp(-GammaL) : " << exp(-GammaL) << std::endl;
    }
 
    double sol = (double)(MFactor * BLHalfSquared(fBmag, fLcoh) *
                          (1 + exp(-GammaL) - 2 * exp(-GammaL / 2) * cos(phi)));
 
    if (fDebug) std::cout << "Axion-photon transmission probability : " << sol << std::endl;
 
    return sol;
}
 
Double_t TRestAxionField::GammaTransmissionProbability(Double_t Bmag, Double_t Lcoh, Double_t Ea, Double_t ma,
                                                       Double_t mg, Double_t absLength) {
    fBmag = Bmag;
    fLcoh = Lcoh;
    fEa = Ea;
 
    return GammaTransmissionProbability(ma, mg, absLength);
}
 
Double_t TRestAxionField::GammaTransmissionProbability(std::vector<Double_t> Bmag, Double_t deltaL,
                                                       Double_t Ea, Double_t ma, Double_t mg,
                                                       Double_t absLength) {
    // Default REST units are mm. We express cohLength in m.
    Double_t Lcoh = (Bmag.size() - 1) * deltaL;  // in mm
    Double_t cohLength = Lcoh * units("m");      // in m
 
    Double_t photonMass = mg;
 
    if (mg == 0 && fBufferGas) photonMass = fBufferGas->GetPhotonMass(Ea);
 
    Double_t fieldAverage = 0;
    if (Bmag.size() > 0) fieldAverage = std::accumulate(Bmag.begin(), Bmag.end(), 0.0) / Bmag.size();
 
    if (fDebug) {
        std::cout << "+--------------------------------------------------------------------------+"
                  << std::endl;
        std::cout << " TRestAxionField::GammaTransmissionProbability. Parameter summary" << std::endl;
        std::cout << " Photon mass : " << photonMass << " eV" << std::endl;
        std::cout << " Axion mass : " << ma << " eV" << std::endl;
        std::cout << " Axion energy : " << Ea << " keV" << std::endl;
        std::cout << " Lcoh : " << cohLength << " m" << std::endl;
        std::cout << " Bmag average : " << fieldAverage << " T" << std::endl;
        std::cout << "+--------------------------------------------------------------------------+"
                  << std::endl;
    }
 
    // In vacuum
    if (ma == 0.0 && photonMass == 0.0) return BLHalfSquared(fieldAverage, Lcoh);
 
    Double_t q = (ma * ma - photonMass * photonMass) / 2. / (Ea * units("eV"));
    Double_t l = cohLength * REST_Physics::PhMeterIneV;
    Double_t phi = q * l;
 
    Double_t Gamma = absLength;
    if (absLength == 0 && fBufferGas) Gamma = fBufferGas->GetPhotonAbsorptionLength(Ea);  // cm-1
    Double_t GammaL = Gamma * cohLength * units("cm") / units("m");                       // m --> cm
 
    if (fDebug) {
        std::cout << "+------------------------+" << std::endl;
        std::cout << " Intermediate calculations" << std::endl;
        std::cout << " q : " << q << " eV" << std::endl;
        std::cout << " l : " << l << " eV-1" << std::endl;
        std::cout << " phi : " << phi << std::endl;
        std::cout << "Gamma : " << Gamma << std::endl;
        std::cout << "GammaL : " << GammaL << std::endl;
        std::cout << "+------------------------+" << std::endl;
    }
 
    Double_t MFactor = phi * phi + GammaL * GammaL / 4.0;
    MFactor = 1.0 / MFactor;
 
    if (fDebug) {
        std::cout << "Mfactor : " << MFactor << std::endl;
        std::cout << "(BL/2)^2 : " << BLHalfSquared(fieldAverage, Lcoh) << std::endl;
        std::cout << "cos(phi) : " << cos(phi) << std::endl;
        std::cout << "Exp(-GammaL) : " << exp(-GammaL) << std::endl;
    }
 
    Double_t deltaIneV = deltaL * units("m") * REST_Physics::PhMeterIneV;
    TComplex sum(0, 0);
    for (unsigned int n = 0; n < Bmag.size() - 1; n++) {
        Double_t Bmiddle = 0.5 * (Bmag[n] + Bmag[n + 1]);
 
        Double_t lStepIneV = ((double)n + 0.5) * deltaIneV;
        Double_t lStepInCm = ((double)n + 0.5) * deltaL * units("cm");
 
        TComplex qCgC(0.5 * Gamma * lStepInCm, -q * lStepIneV);
        qCgC = TComplex::Exp(qCgC);
 
        TComplex integrand = Bmiddle * deltaL * qCgC;  // The integrand is in T by mm
 
        sum += integrand;
    }
 
    Double_t sol = exp(-GammaL) * sum.Rho2() * BLHalfSquared(1, 1);
    // Now T and mm have been recalculated in natural units using BLHalfSquared(1,1).
 
    if (fDebug) std::cout << "Axion-photon transmission probability : " << sol << std::endl;
 
    return (Double_t)sol;
}
 
std::pair<Double_t, Double_t> TRestAxionField::GammaTransmissionFieldMapProbability(Double_t Ea, Double_t ma,
                                                                                    Double_t accuracy,
                                                                                    Int_t num_intervals,
                                                                                    Int_t qawo_levels) {
    gsl_set_error_handler_off();
 
    if (!fMagneticField) {
        RESTError << "TRestAxionField::GammaTransmissionFieldMapProbability requires a magnetic field map!"
                  << RESTendl;
        RESTError << "Use TRestAxionField::AssignMagneticField method to assign one" << RESTendl;
        return {0.0, 0.0};
    }
 
    if (fMagneticField->GetTrackLength() <= 0) return {0.0, 0.0};
 
    double photonMass = 0;  // Vacuum
    if (fBufferGas) photonMass = fBufferGas->GetPhotonMass(Ea);
 
    if (fDebug) {
        std::cout << "+--------------------------------------------------------------------------+"
                  << std::endl;
        std::cout << " TRestAxionField::GammaTransmissionProbability. Parameter summary" << std::endl;
        std::cout << " Photon mass : " << photonMass << " eV" << std::endl;
        std::cout << " Axion mass : " << ma << " eV" << std::endl;
        std::cout << " Axion energy : " << Ea << " keV" << std::endl;
        std::cout << "+--------------------------------------------------------------------------+"
                  << std::endl;
    }
 
    double q = (ma * ma - photonMass * photonMass) / 2. / (Ea * units("eV"));
    q = q * REST_Physics::PhMeterIneV * units("m") / units("mm");  // mm-1
 
    double Gamma = 0;
    if (fBufferGas) Gamma = fBufferGas->GetPhotonAbsorptionLength(Ea) * units("cm") / units("mm");  // mm-1
 
    if (fDebug) {
        std::cout << "+------------------------+" << std::endl;
        std::cout << " Intermediate calculations" << std::endl;
        std::cout << " q : " << q << " eV" << std::endl;
        std::cout << "Gamma : " << Gamma << std::endl;
        std::cout << "+------------------------+" << std::endl;
    }
 
    if (q == 0)
        return ComputeResonanceIntegral(Gamma, accuracy, num_intervals);
    else
        return ComputeOffResonanceIntegral(q, Gamma, accuracy, num_intervals, qawo_levels);
 
    return {0.0, 0.0};
}
 
std::pair<Double_t, Double_t> TRestAxionField::ComputeResonanceIntegral(Double_t Gamma, Double_t accuracy,
                                                                        Int_t num_intervals) {
    double reprob, rerr;
 
    std::pair<TRestAxionMagneticField*, double> params = {fMagneticField, Gamma};
 
    gsl_integration_workspace* workspace = gsl_integration_workspace_alloc(num_intervals);
 
    gsl_function F;
    F.function = &Integrand;
    F.params = &params;
 
    auto start = std::chrono::system_clock::now();
 
    int status = gsl_integration_qag(&F, 0, fMagneticField->GetTrackLength(), accuracy, accuracy,
                                     num_intervals, GSL_INTEG_GAUSS61, workspace, &reprob, &rerr);
 
    if (status > 0) return {0, status};
 
    auto end = std::chrono::system_clock::now();
    auto seconds = std::chrono::duration_cast<std::chrono::milliseconds>(end - start);
 
    double GammaL = Gamma * fMagneticField->GetTrackLength();
    double C = exp(-GammaL) * BLHalfSquared(1, 1);
 
    double prob = C * reprob * reprob;
    double proberr = 2 * C * reprob * rerr;
 
    if (fDebug) {
        std::cout << " ---- TRestAxionField::ComputeResonanceIntegral (QAG) ----" << std::endl;
        std::cout << "Gamma: " << Gamma << " mm-1" << std::endl;
        std::cout << "accuracy: " << accuracy << std::endl;
        std::cout << "num_intervals: " << num_intervals << std::endl;
        std::cout << " -------" << std::endl;
        std::cout << "Probability: " << prob << std::endl;
        std::cout << "Probability error: " << proberr << std::endl;
        std::cout << "Computing time: " << seconds.count() << std::endl;
        std::cout << " -------" << std::endl;
    }
 
    std::pair<Double_t, Double_t> sol = {prob, proberr};
    return sol;
}
 
std::pair<Double_t, Double_t> TRestAxionField::ComputeOffResonanceIntegral(Double_t q, Double_t Gamma,
                                                                           Double_t accuracy,
                                                                           Int_t num_intervals,
                                                                           Int_t qawo_levels) {
    double reprob, rerr;
    double improb, imerr;
 
    std::pair<TRestAxionMagneticField*, double> params = {fMagneticField, Gamma};
 
    gsl_integration_workspace* workspace = gsl_integration_workspace_alloc(num_intervals);
 
    gsl_function F;
    F.function = &Integrand;
    F.params = &params;
 
    auto start = std::chrono::system_clock::now();
 
    gsl_integration_qawo_table* wf =
        gsl_integration_qawo_table_alloc(q, fMagneticField->GetTrackLength(), GSL_INTEG_COSINE, qawo_levels);
    int status =
        gsl_integration_qawo(&F, 0, accuracy, accuracy, num_intervals, workspace, wf, &reprob, &rerr);
    if (status > 0) {
        gsl_integration_qawo_table_free(wf);
        return {0, status};
    }
 
    gsl_integration_qawo_table_set(wf, q, fMagneticField->GetTrackLength(), GSL_INTEG_SINE);
    status = gsl_integration_qawo(&F, 0, accuracy, accuracy, num_intervals, workspace, wf, &improb, &imerr);
    if (status > 0) {
        gsl_integration_qawo_table_free(wf);
        return {0, status};
    }
 
    auto end = std::chrono::system_clock::now();
    auto seconds = std::chrono::duration_cast<std::chrono::milliseconds>(end - start);
 
    double GammaL = Gamma * fMagneticField->GetTrackLength();
    double C = exp(-GammaL) * BLHalfSquared(1, 1);
 
    double prob = C * (reprob * reprob + improb * improb);
    double proberr = 2 * C * TMath::Sqrt(reprob * reprob * rerr * rerr + improb * improb * imerr * imerr);
 
    if (fDebug) {
        std::cout << " ---- TRestAxionField::ComputeOffResonanceIntegral (QAWO) ----" << std::endl;
        std::cout << "Gamma: " << Gamma << " mm-1" << std::endl;
        std::cout << "q: " << q << "mm-1" << std::endl;
        std::cout << "accuracy: " << accuracy << std::endl;
        std::cout << "num_intervals: " << num_intervals << std::endl;
        std::cout << "qawo_levels: " << qawo_levels << std::endl;
        std::cout << " -------" << std::endl;
        std::cout << "Probability: " << prob << std::endl;
        std::cout << "Probability error: " << proberr << std::endl;
        std::cout << "Computing time: " << seconds.count() << std::endl;
        std::cout << " -------" << std::endl;
    }
 
    std::pair<Double_t, Double_t> sol = {prob, proberr};
    return sol;
}
 
Double_t TRestAxionField::AxionAbsorptionProbability(Double_t ma, Double_t mg, Double_t absLength) {
    Double_t cohLength = fLcoh * units("m");  // Default REST units are mm;
 
    Double_t photonMass = mg;
    if (mg == 0 && fBufferGas) photonMass = fBufferGas->GetPhotonMass(fEa);
 
    if (fDebug) {
        RESTDebug << "+--------------------------------------------------------------------------+"
                  << RESTendl;
        RESTDebug << " TRestAxionField::AxionAbsorptionProbability. Parameter summary" << RESTendl;
        RESTDebug << " Photon mass : " << photonMass << " eV" << RESTendl;
        RESTDebug << " Axion mass : " << ma << " eV" << RESTendl;
        RESTDebug << " Axion energy : " << fEa << " keV" << RESTendl;
        RESTDebug << " Lcoh : " << fLcoh << " mm" << RESTendl;
        RESTDebug << " Bmag : " << fBmag << " T" << RESTendl;
        RESTDebug << "+--------------------------------------------------------------------------+"
                  << RESTendl;
    }
 
    if (ma == 0.0 && photonMass == 0.0) return BLHalfSquared(fBmag, fLcoh);
 
    Double_t q = (ma * ma - photonMass * photonMass) / 2. / (fEa * units("eV"));
    Double_t l = cohLength * REST_Physics::PhMeterIneV;
    Double_t phi = q * l;
 
    Double_t Gamma = absLength;
    if (absLength == 0 && fBufferGas) Gamma = fBufferGas->GetPhotonAbsorptionLength(fEa);  // cm-1
    Double_t GammaL = Gamma * cohLength * units("cm") / units("m");
 
    if (fDebug) {
        RESTDebug << "+------------------------+" << RESTendl;
        RESTDebug << " Intermediate calculations" << RESTendl;
        RESTDebug << " q : " << q << " eV" << RESTendl;
        RESTDebug << " l : " << l << " eV-1" << RESTendl;
        RESTDebug << " phi : " << phi << RESTendl;
        RESTDebug << "Gamma : " << Gamma << RESTendl;
        RESTDebug << "GammaL : " << GammaL << RESTendl;
        RESTDebug << "+------------------------+" << RESTendl;
    }
 
    Double_t MFactor = phi * phi + GammaL * GammaL / 4.0;
    MFactor = 1.0 / MFactor;
 
    if (fDebug) {
        RESTDebug << "Mfactor : " << MFactor << RESTendl;
        RESTDebug << "(BL/2)^2 : " << BLHalfSquared(fBmag, fLcoh) << RESTendl;
        RESTDebug << "cos(phi) : " << cos(phi) << RESTendl;
        RESTDebug << "Exp(-GammaL) : " << exp(-GammaL) << RESTendl;
    }
 
    double sol = (double)(MFactor * BLHalfSquared(fBmag, fLcoh) * GammaL);
 
    if (fDebug) RESTDebug << "Axion-photon absorption probability : " << sol << RESTendl;
 
    return sol;
}
 
Double_t TRestAxionField::AxionAbsorptionProbability(Double_t Bmag, Double_t Lcoh, Double_t Ea, Double_t ma,
                                                     Double_t mg, Double_t absLength) {
    fBmag = Bmag;
    fLcoh = Lcoh;
    fEa = Ea;
 
    return AxionAbsorptionProbability(ma, mg, absLength);
}
 
Double_t TRestAxionField::GammaTransmissionFWHM(Double_t step) {
    Double_t maxMass = 10;  // 10eV is the maximum mass (exit condition)
 
    Double_t resonanceMass = 0;
    if (fBufferGas) resonanceMass = fBufferGas->GetPhotonMass(fEa);
 
    Double_t scanMass = resonanceMass;
    Double_t Pmax = GammaTransmissionProbability(resonanceMass);
    while (Pmax / 2 < GammaTransmissionProbability(scanMass)) {
        scanMass += step;
        if (scanMass > maxMass) {
            RESTError << "TRestAxionField::GammaTransmissionProbability. Something went wrong when "
                         "calculating FWHM"
                      << RESTendl;
            return maxMass;
        }
    }
 
    Double_t fwhm = scanMass - resonanceMass;
    if (fwhm <= 0) {
        RESTError << "TRestAxionField::GammaTransmissionProbability. Problem calculating FWHM!" << RESTendl;
        fwhm = step;
    }
    return 2 * fwhm;
}
 
std::vector<std::pair<Double_t, Double_t>> TRestAxionField::GetMassDensityScanning(std::string gasName,
                                                                                   double maMax,
                                                                                   double rampDown) {
    std::vector<std::pair<Double_t, Double_t>> massDensityPairs;
 
    // Storing the gas pointer, if there was one
    TRestAxionBufferGas* previousGas = nullptr;
    if (fBufferGas) {
        previousGas = fBufferGas;
        fBufferGas = nullptr;
    }
 
    // We are in vacuum now
    double firstMass = GammaTransmissionFWHM() / 2;
 
    TRestAxionBufferGas gas;
    gas.SetGasDensity(gasName, 0);
    AssignBufferGas(&gas);  // We are in gas now
 
    Double_t ma = firstMass;
    Double_t density = gas.GetDensityForMass(firstMass, fEa);
 
    massDensityPairs.push_back(std::make_pair(ma, density));
 
    while (ma < maMax) {
        Double_t factor = TMath::Exp(-ma * rampDown) + 1;
        gas.SetGasDensity(gasName, density);
 
        ma += GammaTransmissionFWHM() / factor;
        density = gas.GetDensityForMass(ma);
 
        massDensityPairs.push_back(std::make_pair(ma, density));
    }
 
    // Recovering back the gas that was defined before calling this method
    fBufferGas = previousGas;
 
    return massDensityPairs;
}