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 \page ExampleReverseMC01 Example ReverseMC01 
 
 This example illustrates the use of Reverse Monte Carlo in Geant4.
 
 ## Author
 
 This example code and the adjoint classes in the G4 toolkit  have been developed by L.Desorgher (SpaceIT GmbH)
 under the ESA contract 21435/08/NL/AT. For any (reasonable) question  you may contact the author 
 at the following email address : desorgher@spaceit.ch 
 
 
 
 ## Abstract
 
 This is the README file for the first G4 example illustrating the use of the Reverse Monte Carlo (RMC) mode in a Geant4 
 application. The  Reverse Monte Carlo method is also known as the Adjoint Monte Carlo (AMC) method  and 
 in this document we will alternate both Reverse and Adjoint terms.
 
 ## Other documentation
 
 See also the section 3.7.3 Adjoint/Reverse Monte carlo in the 
 Geant4 User guide for application developers.
 
 
 ## Definition of Reverse/Adjoint Monte Carlo
 
 When the sensitive part of a detector is small compared  to its entire size and to the size  of the
 external extended primary particle source,  a lot of computing time is spent during a normal Monte Carlo run 
 in the simulation of  particle showers that are not contributing to the detector signal.  
 In such particular case the Reverse Monte Carlo (RMC) method, also known as the 
 Adjoint Monte Carlo method, can be used. 
 In this method  particles are generated  in or on the external surface of the sensitive  volume 
 of the instrument and then are tracked backward in the geometry till they reach  the source surface, 
 or exceed an energy threshold. During the reverse tracking reverse reactions are applied to the particles.
 
 
 
 ## The Reverse Monte Carlo mode in Geant4 (since G4.9.3 release)
 
 (See also the section 3.7.3 Adjoint/Reverse Monte carlo in the 
 Geant4 User guide for application developers.)
 
 Different G4Adjoint classes have been implemented into the Geant4 
 toolkit to run an adjoint/reverse simulation in a Geant4 application.
 In this implementation an adjoint run is divided in a succession 
 of alternative adjoint and forward tracking  of adjoint and normal particles.
 One Geant4 event treats one of this tracking phase.
 
 
 ### Reverse tracking phase
 
 Adjoint particles (adjoint_e-, adjoint_gamma,...) are generated one by one on the so called
 adjoint source with random position, energy (1/E distribution) and direction. The adjoint
 source is the external surface of a user defined volume or of a user defined sphere. The 
 adjoint source should contain one or several sensitive volumes and should be small 
 compared to the entire geometry. The user can set the minimum and maximum energy of the 
 adjoint source. After its generation the adjoint primary particle is tracked backward in
 the geometry till a user defined external surface (spherical or boundary of a volume) 
 or is killed before if it reaches a user defined upper energy limit that represents the
 maximum energy of the external source. During the reverse tracking, reverse processes take 
 place where the adjoint particle being tracked can be either scattered or transformed in 
 another type of adjoint particle. During the reverse tracking the 
 G4AdjointSimulationManager replaces the user defined primary, run, stepping, ... actions, 
 by its own actions. 
 
 ### Forward tracking phase:
 
 When an adjoint particle reaches the external surface its weight, type,  position, 
 and direction are registered and a  normal primary particle with a type equivalent 
 to the last generated adjoint primary is generated with the same energy, 
 position but opposite direction  and is  tracked in the forward direction 
 in the sensitive region as in a forward MC simulation. 
 During this forward tracking phase the  event, stacking, stepping, tracking actions defined 
 by the user for its general forward application are used. 
 By this clear separation between adjoint and forward tracking phases, the code of the 
 user developed for a forward simulation should be only slightly 
 modified to adapt it for an adjoint simulation. Indeed  the computation of the signal 
 is done by the same user actions or analysis classes that the one used in the forward 
 simulation mode.  Before the G4.10.0 release the reverse and forward tracking mode 
 took place  in separated  events. Since the G4.10.0 release, 
 in order to preapre to  the migration of the 
 ReverseMC to the G4 Multiple Threading mode, the reverse and forward tracking
 phase of corresponding adjoint and forward primaries have been merged in the same 
 event.
 
 
 ### Reverse Processes
 
 During the reverse tracking phase reverse processes act on the adjoint particles.
 The Reverse processes that  are available at the moment in Geant4 are the:
         - Reverse discrete  Ionization for e-, proton and ions
         - Continuous gain of energy by ionization and bremsstrahlung for e- and by ionization for protons and ions
         - Reverse discrete e- bremsstrahlung  
         - Reverse photoelectric effect 
         - Reverse Compton scattering
         - Approximated multiple scattering (MS) (see section 5.3)
                 
 
 It is important to note that the electromagnetic reverse processes are cut dependent 
 as their equivalent forward processes. The implementation of the reverse processes is
  based on the forward processes
 implemented in the G4 standard electromagnetic package.              
 
 
 ### Remark on Nb of adjoint particle types and Nb of G4 events considered in an adjoint simulation
 
 The list of type of adjoint and forward particles that are generated on the adjoint source
 and considered in the simulation is a function of the adjoint processes declared in the 
 physics list. For example if only the e- and gamma electromagnetic processes are considered
 , only adjoint e- and adjoint gamma will be considered as primaries. In this case an 
 adjoint event will be divided in two G4 events. The first event will  consist 
 into  the coupled  reverse and forward  tracking of an adjoint e- and its equivalent 
 forward e-, while the second events will process the reverse and forward trackings
 of corresponsing adjoint and forward primary gamms. In this case a 
 run of 100 adjoint events will consist into 200 Geant4 events. If the proton ionization is
 also considered adjoint and forward protons  are also generated as primaries 
 and 300 Geant4 events are processed for 100 adjoint events.
 
 ### Modifications to bring in a existing G4 application to use the Reverse MC method
 
 (for more details see also the section 3.7.3 Adjoint/Reverse Monte carlo in the 
 Geant4 User guide for application developers.)
 
 Due the clear separation  between the reverse and forward  tracking  phase  only few modifications are needed 
 to an existing  Geant4 application in order to adapt it for the use of the reverse simulation mode.
 Except in the physics list where all the reverse processes and their forward equivalent 
 have to be declared, the principal code modifications  are needed only in the analysis phase at the end 
 of the forward tracking where computed signals have to be multiplied by the weight 
 of the last reverse tracks and then normalized to different user defined spectra and angular distribution representing 
 the external source.
 The weight of the adjoint tracks is computed by the G4Adjoint classes and the user needs
 only to multiply them to the primary differential, directional spectrum of its choice. 
 The adjoint weight a the end  of tracks can be also registered if needed in answer matrices.
  
 More precisely, in order to be able to use the Reverse MC method in his simulation, the user should modify 
 its code as such:
   
   - Adapt its physics list to use Reverse Processes for adjoint particles. An example of such physics list is provided in an extended 
           example. 
   - Create an instance of    G4AdjointSimManager somewhere in the main() code.
   
   - Modify the analysis part of the code to normalize the signal computed during the forward phase to the weight of the last adjoint particle
          that reaches the external surface. This is done by using the following method of G4AdjointSimManager:
             - G4int GetIDOfLastAdjParticleReachingExtSource()                                
             - G4ThreeVector GetPositionAtEndOfLastAdjointTrack(){ return last_pos;}
             - G4ThreeVector GetDirectionAtEndOfLastAdjointTrack(){ return last_direction;}
             - G4double GetEkinAtEndOfLastAdjointTrack(){ return last_ekin;} 
             - G4double GetEkinNucAtEndOfLastAdjointTrack(){ return last_ekin_nuc;}
             - G4double GetWeightAtEndOfLastAdjointTrack(){return last_weight;}
             - G4double GetCosthAtEndOfLastAdjointTrack(){return last_cos_th;}
             - G4String GetFwdParticleNameAtEndOfLastAdjointTrack(){return last_fwd_part_name;}
             - G4int GetFwdParticlePDGEncodingAtEndOfLastAdjointTrack(){return last_fwd_part_PDGEncoding;}
             - G4int GetFwdParticleIndexAtEndOfLastAdjointTrack().
 
      In order to have a code working for both forward and adjoint simulation mode, the extra code needed in user actions for the adjoint
      simulation mode can be separated to the code needed only for the normal forward  simulation by using the following method:
            - G4bool GetAdjointSimMode() that return true if   an adjoint simulation is running and false if not!
 
 
 
 ## exampleRMC01
 
 The example RMC01 illustrates how to modify a G4 application in order to use 
 both forward and reverse MC modes in the same code.
            
         
 ### Geometry
  
 The following simple geometry is considered:
    - sensitive Silicon cylinder at the center of an Aluminum spherical shielding with 10 cm  Radius.
    - two 0.5mm thick Tantalum plates set horizontally above and below the Sensitive Cylinder 
 
 The free parameters of the geometry that can bes set by the user are:
    - the thickness of the Aluminum shielding  
    - the height of the sensitive Si cylinder
    - the radius of the sensitive Si cylinder
       
  
 
 ### Physics
 
 The physical processes considered  are:
         - Reverse and forward discrete  Ionization for e- and  proton   
         - Continuous gain and loss of energy by ionization and bremsstrahlung for e- and by ionization for protons 
         - Reverse and forward discrete e- bremsstrahlung  
         - Reverse and forward photoelectric effect 
         - Reverse and forward Compton scattering
         - Reverse and forward Multiple scattering
 
 These processes are implemented in the class G4AdjointPhysicsList distributed with the example. The G4AdjointPhysicsMessenger allows the user
 to switch on/off some processes for testing purpose. By default all processes cited above are considered except the proton ionization that
 has to be specifically switch on in the macro file by the user.
 
 
 
 ### Analysis and output of the code
 
 The example computes the energy deposited in the sensitive Si cylinder and the current of e-, protons, and gamma 
 entering this cylinder.
 The Hits are registered in the sensitive detector class RMC01SD that is a typical G4 sensitive detector class 
 used in a forward simulation and is not modified at all
 for the adjoint simulation mode. 
 The analysis of the registered hits during forward events is done by the RMCO1AnalysisManager.
 That is the class that illustrates how to adapt an analysis code of a fwd simulation in order to use it also for 
 an adjoint simulation.
 In this class during a forward simulation the  method EndOfEventForForwardSimulation is used at the end of an event 
 while during an adjoint simulation at the end of fwd tracking event the method EndOfEventForAdjointSimulation is called.
 By looking at the source of RMCO1AnalysisManager and more particularly to its method EndOfEventForAdjointSimulation the user will
 learn how to adapt its G4 analysis code for an adjoint simulation.
 
 The outputs of an adjoint simulation are:
 
  - The total energy deposited and particle current entering the sensitive cylinder normalized 
   automatically to a user defined primary spectrum(exponential or power law) .These results are stored in the files:
    - Adj_Edep_vs_EkinPrim.txt                            
    - Adj_ElectronCurrent.txt
    - Adj_GammaCurrent.txt
    - Adj_ProtonCurrent.txt
    - ConvergenceOfAdjointSimulationResults.txt: 
                          The total normalized edep and its relative error registered every 5000 adjoint events
          
          
  - The answer matrix of the energy deposited and particles current on the sensitive cylinder in function of primary energy of e-, gamma and
  protons. These results are stored in the files Adj********_Answer.txt
                         
                  
         
 The outputs of a forward simulation are:         
   - The mean energy deposited and particle current entering the sensitive cylinder per event.
    These results are stored in the files:
    - Fwd_Edep_vs_EkinPrim.txt                            
    - Fwd_ElectronCurrent.txt
    - Fwd_GammaCurrent.txt
    - Fwd_ProtonCurrent.txt
           
  
 
 ### Run macrofiles
 
 The following example run macro files are distributed with the code:
   - run_adjoint_simulation_electron.mac and  run_adjoint_simulation_proton.mac for adjoint simulations 
 
   - run_forward_simulation_electron.mac  and run_forward_simulation_proton.mac for forward simulations
         
 
 ### Comparison of adjoint and forward simulation results
 
 It is the responsibility of the user to select in the macro file the same external spectrum 
 for both the forward and adjoint simulations  and to normalize the per event results of the forward simulation 
 to the fluence considered in the adjoint  simulation. 
 
 For the macro files that are provided  with the examples it consists into multiplying  the forward results by pi*100.
 This normalization factor is explained by the following:
         
   - For the forward simulation the results are given  per number of events. It corresponds  
     to a normalization to a  fluence of 1 particle emanating from the external source. 
 
   - In run_fwd_simulation.mac the source is set on a sphere of 10 cm radius (see /gps commands in
     macrofile).Therefore the omnidirectional  fluence for the fwd simulation  is 1./(pi*R^2) with R=10cm. 
 
   - The adjoint results  are normalized to a fluence of 1/cm2.
     (See command /RMC01/analysis/SetExponentialSpectrumForAdjointSim in macrofile)
 
   - In conclusion to compare the adjoint and forward results, the forward results should
                         be multiplied by pi*R^2/cm2= pi*100.
 
 
 
 ## Control of the adjoint simulation and the RMC01 code by G4 macro UI commands
 
 Different G4 macro UI commands are provided to control the RMC01 example and the adjoint simulation.
 Some macro commands are provided within the geant4 toolkit and appears in a G4 application when the singleton 
 class G4AdjointSimManager is called somewhere in the code, the other macro commands are 
 declared in the code  distributed within the example.
 
 
 ### G4UI commands in the directory /adjoint
 
 The macro command directory  /adjoint appears in a user application when the singleton 
 class G4AdjointSimManager is called somewhere in the code. 
 It allows to control the adjoint source, the external source and start an adjoint simulation.
 
 The command to start an adjoint  run is:
 
 - /adjoint/start_run nb \n
         Start an adjoint simulation with a number of events given by nb. It is important to note that the total number of events in the sense of G4 
         will be nb*2*nb_primary_considered (see  3.4.)
         
 
 The commands to control the adjoint source are:
 
 - /adjoint/DefineSphericalAdjSource R X Y Z unit_length \n
         The adjoint source is set on a sphere with radius R and centered on position (X,Y,Z) 
                                  
 - /adjoint/DefineSphericalAdjSourceCenteredOnAVolume phys_vol_name R unit_length \n
         The external source is set on a sphere with radius R and with its center position located at the center of the 
         the physical volume specified by the name phys_vol_name.
 - /adjoint/DefineAdjSourceOnExtSurfaceOfAVolume phys_vol_name \n
 The external surface is set as the external boundary of a the physical volume with name phys_vol_name
                         
 - /adjoint/SetAdjSourceEmin  Emin energy_unit \n
  Set the minimum  energy of the external source
                 
 - /adjoint/SetAdjSourceEmax  Emax energy_unit \n
  Set the maximum  energy of the external source
                         
 - /adjoint/ConsiderAsPrimary  particle_name \n
  The type  of particle specified by  "particle_name" will be added in the list of primary adjoint particles. 
  The list of candidates depends on the reverse physics processes considered in the simulation. At the most the 
  potential candidates are (e-, gamma, proton , ion). For this example only e-, gamma, proton
  can be chosen. As the proton ionization is not considered by default, the default list of particles is
  [e-,gamma]. To have also the proton as candidate the proton ionization should 
  be switch on (/adjoint_physics/UseProtonIonisation true).
 
 - /adjoint/NeglectAsPrimary  particle_name \n
 
  The type  of particle specified by  "particle_name" will be removed from the list of primary adjoint particles. 
  The list of candidates depends on the reverse physics processes considered in the simulation. At the most the 
  potential candidates are (e-, gamma, proton , ion). For this example only e-, gamma, proton
  can be chosen. As the proton ionization is not considered by default, the default list of particles is
  [e-,gamma].To have also the proton as candidate the proton ionization should 
  be switch on (/adjoint_physics/UseProtonIonisation true). 
                 
 
 The commands to control the external source are:
 
 - /adjoint/DefineSphericalExtSource R X Y Z unit_length:\n
 The external source is set on a sphere with radius R and centered on position (X,Y,Z) 
                                  
 - /adjoint/DefineSphericalExtSourceCenteredOnAVolume phys_vol_name R unit_length\n
 The external source is set on a sphere with radius R and with its center position located at the center of the 
 the physical volume specified by the name phys_vol_name.
 
 - /adjoint/DefineExtSourceOnExtSurfaceOfAVolume phys_vol_name \n
 The external surface is set as the external boundary of a the physical volume with name phys_vol_name
 
 - /adjoint/SetExtSourceEmax  Emax energy_unit \n
 Set the maximum  energy of the external source. An adjoint track will be stop when a an adjoint particle get an energy higher than this maximum energy.
         
 
 
 ### G4UI commands in the directory /adjoint_physics
 
 These commands allow to control the electromagnetic processes that will be considered in the simulation.
 
 The processes that can be used are:
 - Reverse and forward e- continuous and discrete  Ionization. Always switch on
 - Reverse and forward e- Bremsstrahlung. Switch on by default
 - Reverse and forward Compton scattering. Switch on by default
 - Reverse and forward photo electric effect. Switch on by default
 - Reverse and forward photo electric effect. Switch on by default
 - Reverse and forward multiple scattering. Switch on by default
 - Reverse and forward proton continuous and discrete  Ionization. Switch off by default 
 - Forward e-e+ pair production. Switch off by default. 
          
 
 The commands that can be used to switch on of these processes are:
 
 - /adjoint_physics/UseProtonIonisation true/false \n
    Switch on/off the reverse and forward proton ionization. Off by default. 
 
 - /adjoint_physics/UseBremsstrahlung true/false \n
    Switch on/off the reverse and forward e- bremsstrahlung. On by default.      
 
 - /adjoint_physics/UseCompton true/false \n
    Switch on/off the Compton scattering. On by default. 
 
 
 - /adjoint_physics/UseMS true/false \n
    Switch on/off the multiple scattering. On by default.
    
 
 - /adjoint_physics/UseEgainElossFluctuation true/false  \n
    Switch on/off the fluctuation in the continuous energy loss/gain.   On by default. Only for test purpose.    
 
 - /adjoint_physics/UsePEEffect true/false \n
    Switch on/off the photo electric effect. On by default.      
 
 
 - /adjoint_physics/UseGammaConversion true/false \n
    Switch on/off the forward e-e+ pair production from gamma. Off by default. When On all the e+
    electromagnetic physics is considered.
    
    
 The user can also fix the maximum energy Emax and minimum energy Emin of the adjoint physical processes used 
 in the simulation. The adjoint process will be applied to particles within the energy range [Emin, Emax] 
 and will produce adjoint secondary only in this energy range. It is recommended to fix Emin to the minimum
 energy  of the adjoint source and fix Emax to the maximum energy of the external source.  
 The commands controlling Emin and Emax are:
 
 - /adjoint_physics/SetEminForAdjointModels Emin Energy_unit \n
 Set the minimum energy of the adjoint processes/models.
         
 - /adjoint_physics/SetEmaxForAdjointModels Emin Energy_unit \n
 Set the maximum energy of the adjoint processes/models.
  
    
 ### G4UI commands in the directory /RMC01
 
 
 Commands/RMC01/geometry/  to control the geometry:
 
 - /RMC01/geometry/SetSensitiveVolumeHeight H length_unit \n
 Set the height H of the Si sensitive cylinder.
         
 
 - /RMC01/geometry/SetSensitiveVolumeRadius R length_unit \n
 Set the radius R of the Si sensitive cylinder.  
 
 - /RMC01/geometry/SetShieldingThickness    D length_unit \n
 Set the thickness D of the aluminum shielding.
    
 Commands /RMC01/analysis/ to control the primary spectrum used for the normalization of the 
 adjoint simulation results and fix the expected precision of the computed Edep:
 
 - /RMC01/analysis/SetPowerLawPrimSpectrumForAdjointSim particle_name F F_unit alpha Emin Emax E_unit \n
         Set the primary spectrum to which the adjoint simulation results will be normalised to a power law
         spectrum E^(-alpha) of particle defined by    particle_name, with an omnidirectional fluence F, and
         energy range [Emin,Emax]. The fluence unit candidates for F_unit  are [1/cm2, 1/m2, cm-2, m-2]. 
          
    
 - /RMC01/analysis/SetExponentialSpectrumForAdjointSim particle_name F F_unit E0 Emin Emax E_unit \n
         Set the primary spectrum to which the adjoint simulation results will be normalised to an exponential
         spectrum exp(-E/E0) of particle defined by    particle_name, with an omnidirectional fluence F, and
         energy range [Emin,Emax]. The fluence unit candidates for F_unit  are [1/cm2, 1/m2, cm-2, m-2]. 
                 
 
  
 - /RMC01/analysis/SetExpectedPrecisionOfResults precision \n
         Set the expected precision in % for the computed energy deposited in the sensitive volume 
         for both the forward and adjoint simulation case. When the relative statistical error 
         of the  computed energy deposited reach this precision the run is aborted and the results are registered.
         Otherwise the run continue till the nb of events specified by the user are processed. By default the precision is set
         to 0. meaning that the run will not be aborted in this case. 
           
         
 
 
 
 
 ## Known issues
 
 ### Rare too high weight in the adjoint simulation
 
 In rare cases an adjoint track may get a much too high weight when  reaching the external source.
 While this happen not often it may corrupt the simulation results significantly. The reason  of this high weight is 
 the joint use at low e- and gamma  energy of both  the photoelectric and bremsstrahlung processes.
 Unfortunately we still need some investigations to remove this problem  at the level of physical processes. 
 However  this problem can be solved  at the level of event action in the user code by adding a test on the adjoint 
 weight. Such test has been implemented in the example RMC01. 
 In this implementation  an event is rejected when the relative error of the computed  normalised edep 
 increase during one event by more than 50% when the precision  is already below 10%.
  
 
 ### Limitation of the reverse bremsstrahlung
 
 The difference between the differential cross sections used in the adjoint and forward bremsstrahlung 
  models is the source of a higher flux of >100 keV gamma in the reverse simulation compared to the forward simulation.
 The adjoint processes/models should make use of the direct differential cross section to sample
  the adjoint  secondaries and compute the adjoint cross section.
 The differential cross section used in G4AdjointeBremstrahlungModel  is obtained by the numerical derivation
 over the cut energy of the direct cross section provided  by G4eBremsstrahlungModel. 
 This would be a correct procedure if the  distribution of secondary in   G4eBremsstrahlungModel  
 would match this differential cross section. Unfortunately it is not the case as independent  parameterization are used 
  in   G4eBremsstrahlungModel  for both the cross sections and the sample of secondary. (It means that in the forward case 
  if one would integrate the effective differential cross section considered  in the simulation we would not find back 
  the used cross section). 
  In the future we plan to correct this problem by using an extra weight correction factor after the occurrence of a reverse
  bremsstrahlung. This weight factor should be the ratio between the differential CS used in the adjoint simulation and the 
 one effectively used in the forward processes. As it is impossible to have access to the forward differential CS 
  in G4eBremsstrahlungModel we  are investigating the feasibility to use  the differential CS considered in  
  G4Penelope models. 
    
 
 ### Limitation of the reverse multiple scattering
 
 For the reverse multiple scattering we are using the same models than for the forward case.
 This approximation makes that the discrepancy between the adjoint and forward 
 simulation cases can get to a level of ~ 10-15% relative differences in the test cases that we have considered. 
 In the future we plan to improve   the adjoint multiple scattering models  by forcing the computation of 
 multiple scattering effect at the end of an adjoint step.

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