ModelGEM.h

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// Copyright 2019-2020 CERN and copyright holders of ALICE O2.
// See https://alice-o2.web.cern.ch/copyright for details of the copyright holders.
// All rights not expressly granted are reserved.
//
// This software is distributed under the terms of the GNU General Public
// License v3 (GPL Version 3), copied verbatim in the file "COPYING".
//
// In applying this license CERN does not waive the privileges and immunities
// granted to it by virtue of its status as an Intergovernmental Organization
// or submit itself to any jurisdiction.
 
 
// ================================================================================
// How are the electron efficiencies obtained?
// ================================================================================
// Within the scope of two PhD thesis models have been derived in order to
// describe the collection as well as the extraction efficiencies for GEM
// foils. In the following you can find a brief sketch about the procedure behind this.
// Details can be found in the following two papers which emerged out of this
// research:
//   [1] Paper Jonathan,
//   [2] Paper Viktor.
//
// Simulations / Measurements [1]:
// For different GEM geometries (standard, medium, large pitch) the electric potentials
// and fieldmaps were obtained by numerical calculations in Ansys. The fieldmaps were
// then used in Garfield++ in order to simulate the drift of the charge carriers
// and the amplification processes. In order to obtain the efficiencies a fixed
// amount of electrons has been randomely distributed above the GEM for the simulations.
// The efficiencies were thereupon derived by counting where the initial electrons and
// electrons from the amplification region ended, e.g. Copper top / bottom, anode etc.
// Indeed the simulated efficiencies are in a good agreement to measurements. See [1] for
// more details.
//
// Calculations [2]:
// In oder to get an analytic understanding of the efficiencies a simplified and
// two-dimensional model has been investigated. Simplified means: No differentian
// between an inner and an outer diameter, no Polyimide layer, no gas/no diffusion
// and two-dimensional cut of the hexagonal 3D GEM structure.
// The resulting equations are in a good agreement to the results from the simulations
// in terms of limits, offsets and curves for different pitches (in case of no diffusion).
// Nevertheless differences can be found due to the simplifications in the model.
// By introducing three fit parameter (s1, s2 and s3) the calculations can be tuned
// in a way to describe the simulated datapoints. The resulting equations
// describe the efficiencies in a full region and for different GEM geometries.
//
// The results from the fitted equations are implemented in this class.
 
// ================================================================================
// Remarks for naming of the variables:
// ================================================================================
//
// mFitElecEffNumberHoles (in PhD/paper: N)
//   Describes the number of holes for the 2D model calculations. The number
//   of holes is given by 2N-1, i.e. mFitElecEffNumberHoles=2 refers to 3 GEM holes (one
//   central GEM hole and two GEM holes at the outside).
//
// mFitElecEffThickness (in PhD/paper: d) [unit: micrometers]
//   Thickness of the GEM foil which
//
// mFitElecEffPitch (in PhD/paper: p) [unit: micrometers]
//   Pitch of the GEM foil.
//
// mFitElecEffHoleDiameter (in PhD/paper: L) [unit: micrometers]
//   Hole diameter for the GEM hole. There is no differentiation between an inner
//   and an outer hole diameter for the 2D model calculations.
//
// mFitElecEffWidth (in PhD/paper: w) [unit: micrometers]
//   Describes the width for a unit cell (pitch) + 2x the distance to the end of the
//   GEM electrodes. This variable can be expressed in terms of the pitch and the hole
//   diameter according to w=2p-L. It is only used for internal calculations and no
//   definition is required by the user.
//
// mFitElecEffDistancePrevStage (in PhD/paper: g1) [unit: micrometers]
//   Here g1/2 describes the distance from the center of the GEM foil to the cathode
//   or the previous amplification stage.
//
// mFitElecEffDistanceNextStage (in PhD/paper: g2) [unit: micrometers]
//   Here g2/2 describes the distance from the center of the GEM foil to the anode
//   or the next amplification stage.
//
// mGeometryTuneEta1 (in PhD/paper: s1) [unitless]
//   This is a fit parameter which has been used in order to scale eta1 for the fit
//   of the calculations to the simulations.
//
// mGeometryTuneEta2 (in PhD/paper: s2) [unitless]
//   This is a fit parameter which has been used in order to scale eta2 for the fit
//   of the calculations to the simulations.
//
// mGeometryTuneDiffusion (in PhD/paper: s3) [unitless]
//   This is a fit parameter which has been used in order to tune the equations to
//   describe diffusion.
 
#ifndef ALICEO2_TPC_ModelGEM_H_
#define ALICEO2_TPC_ModelGEM_H_
 
#include <array>
 
namespace o2
{
namespace tpc
{
 
 
class ModelGEM
{
 public:
  ModelGEM();
 
  ~ModelGEM() = default;
 
  float getElectronCollectionEfficiency(float elecFieldAbove, float gemPotential, int geom);
 
  float getElectronExtractionEfficiency(float elecFieldBelow, float gemPotential, int geom);
 
  float getAbsoluteGain(float gemPotential, int geom);
 
  void setAbsGainScalingFactor(float absGainScaling) { mAbsGainScaling = absGainScaling; };
 
  float getSingleGainFluctuation(float gemPotential, int geom);
 
  void setStackProperties(const std::array<int, 4>& geometry, const std::array<float, 5>& distance, const std::array<float, 4>& potential, const std::array<float, 5>& electricField);
 
  float getStackEnergyResolution();
 
  float getStackEffectiveGain();
 
  void setAttachment(float attachment) { mAttachment = attachment; };
 
 private:
  float getParameterC1(int geom);
 
  float getParameterC2(int geom);
 
  float getParameterC3(int geom);
 
  float getParameterC4(int geom);
 
  float getParameterC5(int geom);
 
  float getParameterC6();
 
  float getParameterC7(float eta1, float eta2, int geom);
 
  float getParameterC8(float eta1, float eta2, int geom);
 
  float getParameterC9(float eta1, float eta2, int geom);
 
  float getParameterC7Bar(float eta1, float eta2, int geom);
 
  float getParameterC8Bar(float eta1, float eta2, int geom);
 
  float getParameterC9Bar(float eta1, float eta2, int geom);
 
  float getParameterC7BarFromX(float intXStart, float intXEnd, int geom);
 
  float getParameterC8BarFromX(float intXStart, float intXEnd, int geom);
 
  float getParameterC9BarFromX(float intXStart, float intXEnd, int geom);
 
  float getLambdaCathode(int geom);
 
  float getLambdaCathodef2(int geom);
 
  float getLambdaCathodeF2(int n, int geom);
 
  float getMu1Cathode(int geom);
 
  float getMu1Cathodef2(int geom);
 
  float getMu1CathodeF2(int n, int geom);
 
  float getMu2Cathode(int geom);
 
  float getMu2Cathodef2(int geom);
 
  float getMu2CathodeF2(int n, int geom);
 
  float getMu2Top(float intXStart, float intXEnd, int geom);
 
  float getMu2Topf2(float intXStart, float intXEnd);
 
  float getMu2TopfTaylorTerm0(int geom);
 
  float getMu2TopfTaylorTerm2(int geom);
 
  float getMu2TopF2(int n, float intXStart, float intXEnd, int geom);
 
  float getMu2TopFTaylorTerm0(int n, int geom);
 
  float getMu2TopFTaylorTerm2(int n, int geom);
 
  float getIntXEndBot(float eta1, float eta2, int geom);
 
  float getIntXEndTop(float eta1, float eta2, int geom);
 
  float getEta1Kink1(float eta2, int geom);
 
  float getEta1Kink2(float eta2, int geom);
 
  float getEta2Kink1(float eta1, int geom);
 
  float getEta2Kink2(float eta1, int geom);
 
  float getHtop0(int geom);
 
  float getHtop2(int geom);
 
  void flipDistanceNextPrevStage();
 
  const int mFitElecEffNumberHoles = 200;      
  const float mFitElecEffThickness = 50.0;     
  const float mFitElecEffHoleDiameter = 60.0;  
  float mFitElecEffDistancePrevStage = 2110.0; 
  float mFitElecEffDistanceNextStage = 2110.0; 
 
  const std::array<float, 3> mFitElecEffPitch; 
  const std::array<float, 3> mFitElecEffWidth; 
 
  const float mFitElecEffFieldAbove = 2000.0;                                                  
  const float mFitElecEffFieldBelow = 0.0;                                                     
  const float mFitElecEffPotentialGEM = 300.0;                                                 
  const float mFitElecEffFieldGEM = mFitElecEffPotentialGEM / (mFitElecEffThickness * 0.0001); 
 
  const std::array<float, 3> mFitElecEffTuneEta1;      
  const std::array<float, 3> mFitElecEffTuneEta2;      
  const std::array<float, 3> mFitElecEffTuneDiffusion; 
 
  const std::array<float, 3> mFitAbsGainConstant; 
  const std::array<float, 3> mFitAbsGainSlope;    
  float mAbsGainScaling;                          
 
  const std::array<float, 3> mFitSingleGainF0; 
  const std::array<float, 3> mFitSingleGainU0; 
  const std::array<float, 3> mFitSingleGainQ;  
 
  std::array<float, 3> mParamC1;
  std::array<float, 3> mParamC2;
  std::array<float, 3> mParamC3;
  std::array<float, 3> mParamC4;
  std::array<float, 3> mParamC5;
  std::array<float, 3> mParamC6;
 
  std::array<int, 4> mGeometry;        
  std::array<float, 5> mDistance;      
  std::array<float, 4> mPotential;     
  std::array<float, 5> mElectricField; 
 
  float mStackEffectiveGain;
 
  int mStackEnergyCalculated;
 
  float mAttachment;
 
  const float Pi = 3.1415926;
 
  // Energy of incident photons (eV)
  const float PhotonEnergy = 5900.0;
 
  // Mean energy to create electron-ion pair in gas (here NeCO2N2, in eV)
  const float Wi = 37.3;
 
  // Fano factor for NeCO2N2 90-10-5 (Please check this!)
  const float Fano = 0.13;
};
} // namespace tpc
} // namespace o2
 
#endif // ALICEO2_TPC_ModelGEM_H_