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.

Table of Contents:
-----------------

1.Definition of Reverse/Adjoint Monte Carlo

2.The Reverse Monte Carlo mode in Geant4 (since G4.9.3 release)
2.1. Reverse tracking phase
2.2. Forward tracking phase
2.3. Reverse processes
2.4. Remark on Nb of adjoint particle types and G4 events considered in an adjoint simulation
2.5. Modifications to bring in a existing G4 application to use the Reverse MC method

3.exampleRMC01
3.1. Geometry
3.2. Physics
3.3. Analysis and output of the code
3.4. Run macrofiles
3.5. Comparison of adjoint and forward simulation results. Normalization!

4.Control of the adjoint simulation and the RMC01 code by G4 macro UI commands
4.1. G4UI commands in the directory /adjoint
4.2. G4UI commands in the directory /adjoint_physics
4.3. G4UI commands in the directory /RMC01

5. Known issues
5.1. Rare too high weight in the adjoint simulation
5.2. Limitation of the reverse bremsstrahlung
5.3.Limitation of the reverse multiple scattering

1. 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.

2. 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 the reverse tracking of an adjoint primary particle
and its secondaries, and the forward tracking of a primary particle euqivalent
to the adjoint primary as well as its secondaries.

2.1. 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.

2.2. 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 prepare 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.

2.3. 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)

For the gamma reverse physics an adjoint gamma reverse forced interaction process has been implemented
since GEANT4.10.3. THis process splits a new created gamma in two tracks.
The first tracks is used to force a free flight of the adjoint gamma through the geometry.
The second track is used to force a reverse bremsstrahlung or a reverse compton at some random
position along the free flight track.

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.

2.4. 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 gammas. 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.

2.5. 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 reverse tracks that have reached the external surface of the simulatrion
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 adjoint particle that reached the external surface during the last tracking phase.
This is done by using the following method of G4AdjointSimManager.
size_t GetNbOfAdointTracksReachingTheExternalSurface()
G4int GetIDOfLastAdjParticleReachingExtSource(size_t i)
G4ThreeVector GetPositionAtEndOfLastAdjointTrack(size_t i)
G4ThreeVector GetDirectionAtEndOfLastAdjointTrack(size_t i)
G4double GetEkinAtEndOfLastAdjointTrack(size_t i)
G4double GetEkinNucAtEndOfLastAdjointTrack(size_t i)
G4double GetWeightAtEndOfLastAdjointTrack(size_t i)
G4double GetCosthAtEndOfLastAdjointTrack(size_t i)
G4String GetFwdParticleNameAtEndOfLastAdjointTrack(size_t i)
G4int GetFwdParticlePDGEncodingAtEndOfLastAdjointTrack(size_t i)
G4int GetFwdParticleIndexAtEndOfLastAdjointTrack(size_t i).
Since the version Geant4.10.3 several adjoint tracks can arrive on the external surface during the same events.
It is therefore important to loop over alll these tracks when normalizing the weights at the end of the event.
The method GetNbOfAdointTracksReachingTheExternalSurface() returns the number of adjoint tracks that reached the
external surface. Ine the other methods the input parameter i allows to get the information of the ith track.

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!

3. 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.

3.1. 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

3.2. 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.

3.3. 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
-ConvergenceOfAdjointSimulationResults.txt: The total normalized edep and its relative error registered every 5000 adjoint events

3.4. 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

3.5. 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.

4. 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.

4.1. G4UI commands in the directory /adjoint
-----------------------------------------------
The macro commands in the 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
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
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
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
The external surface is set as the external boundary of a the physical volume with name phys_vol_name

-/adjoint/SetAdjSourceEmin Emin energy_unit
Set the minimum energy of the external source

-/adjoint/SetAdjSourceEmax Emax energy_unit
Set the maximum energy of the external source

-/adjoint/ConsiderAsPrimary particle_name
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
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:
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
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
The external surface is set as the external boundary of a the physical volume with name phys_vol_name

-/adjoint/SetExtSourceEmax Emax energy_unit
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.

4.2. 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.
If switch all the e+ electromagnetic physics is considered.

The commands that can be used to switch on of these processes are:

/adjoint_physics/UseProtonIonisation true/false
-Switch on/off the reverse and forward proton ionization. Off by default.

/adjoint_physics/UseBremsstrahlung true/false
-Switch on/off the reverse and forward e- bremsstrahlung. On by default.

/adjoint_physics/UseCompton true/false
-Switch on/off the Compton scattering. On by default.

/adjoint_physics/UseMS true/false
-Switch on/off the multiple scattering. On by default.

/adjoint_physics/UseEgainElossFluctuation true/false
-Switch on/off the fluctuation in the continuous energy loss/gain. On by default. Only for test purpose.

/adjoint_physics/UsePEEffect true/false
-Switch on/off the photo electric effect. On by default.

/adjoint_physics/UseGammaConversion true/false
-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
-Set the minimum energy of the adjoint processes/models.

/adjoint_physics/SetEmaxForAdjointModels Emin Energy_unit
-Set the maximum energy of the adjoint processes/models.

4.3. G4UI commands in the directory /RMC01
----------------------------------------------

Commands/RMC01/geometry/ to control the geometry:

/RMC01/geometry/SetSensitiveVolumeHeight H length_unit
Set the height H of the Si sensitive cylinder.

/RMC01/geometry/SetSensitiveVolumeRadius R length_unit
Set the radius R of the Si sensitive cylinder.

/RMC01/geometry/SetShieldingThickness D length_unit
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
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
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
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.

5. Known issues
--------------------------------
--------------------------------

5.1 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%.

5.2 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.

5.3 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.