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 \page Examplefield04 Example field04
 
 
  This example shows how to define/use OVERLAPPING field elements
  in Geant4. Fields might be either magnetic, electric or both.
 
  Credit goes to Tom Roberts and Muons Inc. since much of the code
  and ideas were taken at liberty from the (GNU GPL) source of
  G4BEAMLINE release 1.12.
 
  http://g4beamline.muonsinc.com
 
 ## Classes
 
 - main()
 
   See mains() in field04.cc.
   
   The example can be run with the following optional arguments:
   
   ```
   % ./field04 [-m macro ] [-p physicsList] [-r randomSeed] [-s preinit|idle]
   ```
   
   If a macro is provided with the option "-m", the program runs in a batch mode,
   otherwise the program open the interactive session after executing the
   default initialization macro init_vis.mac. The option "-s preinit" can be used
   to start the program without initialization in PreInit phase.
   
   For example:
   to assign the F04PhysicsList:
   ```
   % ./field04 -p QGSP_BERT
   ```
   
   an initial random number seed with:
   ```
   % ./field04 field04.in -r 12345
   ```
   
   to start with a macro file and an initial seed:
   ```
   % ./field04 -m field04.in -r 12345
   ```
 
 - F04DetectorConstruction
 
   The geometry consists of two solenoidal magnets: a "CaptureMgnt"
   followed by a (blue-colored "TransferMgnt". By definition, the
   axis and center of the "CaptureMgnt" coincide with the "World". The
   position of the "TransferMgnt" relative to the downstream end of the
   "CaptureMgnt", as well as its axis angle, both may vary. A cylindrical
   "Target" is positioned inside the "CaptureMgnt". Its axis can vary
   from 0 to 180 deg, and hence also the direction of the incoming
   proton beam wrt the "CaptureMgnt"'s axis. A "Degrader" is located
   inside the "TransferMgnt", its default position being at the
   upstream end of the "TransferMgnt". Finally, also a "TestPlane" is
   located inside the "TransferMgnt", by default at its downstream end.
 
   The "World" consists of a solid cylinder made of a given material.
   (It is the responsibility of the user to make the world
   large enough to contain the rest of the geometry!)
   
   Three parameters define the world :
   - the material of the world,
   - the world radius,
   - the world length.
   
   Example (default values):
   ```
   /field04/SetWorldMat G4_AIR
   /field04/SetWorldR  5.0 m
   /field04/SetWorldZ 50.0 m
   ```
   
   The "Target" is a solid cylinder made of a given material.
   Five parameters define the target:
   - the material of the target,
   - the target radius,
   - the target thickness,
   - the target position inside the "CaptureMgnt",
   - the target axis angle relative to that of the "CaptureMgnt".
   
   Example (default values):
   ```
   /field04/SetTgtMat G4_W
   /field04/SetTgtRad    0.4 cm
   /field04/SetTgtThick 16.0 cm
   /field04/SetTgtPos 0.0 cm
   /field04/SetTgtAng 170
   ```
   
   The "Degrader" is a solid cylinder made of a given material.
   
   Four parameters define the degrader:
   - the material of the degrader,
   - the degrader radius,
   - the degrader thickness,
   - the degrader position relative to the "TransferMgnt" center.
   
   Example (default values):
   ```
   /field04/SetDgrMat G4_Pb
   /field04/SetDgrRad  30.0 cm
   /field04/SetDgrThick 0.1 cm
   /field04/SetDgrPos -7.4 m
   ```
   
   The "CaptureMgnt" is a solenoid (vacuum cylinder). It is either
   a two-sided or a one-sided magnetic bottle with the B field
   varying linearly from the center value B1 to the edge value B2.
   The one-sided F04FocusSolenoid has the open end at +z and focuses
   on the z < 0 side.
   
   Four parameters define the "CaptureMgnt":
   - the magnet radius,
   - the magnet length,
   - the weaker magnetic field at the center B1
   - the stronger magnetic field at the edge B2
   
   Example (default values):
   ```
   /field04/SetCaptureR 0.6 m
   /field04/SetCaptureZ 4.0 m
   /field/SetCaptureB1 2.5 tesla
   /field/SetCaptureB2 5.0 tesla
   ```
   
   The "TransferMgnt" is a solenoid (vacuum cylinder) with a
   constant B-field. When the "TransferMgnt" follows immediately
   the "CaptureMgnt", its relative position is at 0 cm.
   
   Four parameters define the "TransferMgnt":
   - the magnet radius,
   - the magnet length,
   - the magnet field,
   - the magnet relative position
     (its upstream face wrt the downstream face of the "CaptureMgnt".)
   
   Example (default values):
   ```
   /field04/SetTransferR  0.3 m
   /field04/SetTransferZ 15.0 m
   /field/SetTransferB 5.0 tesla
   /field04/SetTransferP 0.0 m
   ```
   The default geometry is constructed in F04DetectorConstruction class,
   but all the parameters can be changed via the commands defined in
   the F04DetectorMessenger class.
   
 - F04Materials
   
   Material definitions are done through the singleton class F04Materials
   which keeps a pointer to the G4NistManager. It has a method
   GetMaterial by name (G4String) which in turn invokes the
   G4NistManager::FindOrBuildMaterial, and/or G4Material::GetMaterial
   methods. It has also a method CreateMaterials which, for materials
   absent from the NIST data base, shows how to create them using the
   G4NistManager::ConstructNewMaterial method.
   
   
 - F04PrimaryGeneratorAction
   
   The primary kinematic consists of a single particle which hits the
   target perpendicular to its upstream face. The type of the particle
   and its energy are set in the F04PrimaryGeneratorAction class, and can
   be changed via the G4 build-in commands of the G4ParticleGun class.
   In addition, there is a fRndmFlag, which once set allows the beam to
   explore randomly the whole cross section of the target. The default
   beam consists of 500 MeV protons, starting at the upstream face of
   the target, directed along dx = dy = 0, dz = 1 wrt the target frame.
   The default direction should NOT be changed! The arguments of the
   x/y/zvertex commands are relative to the target center.
   
   Example:
   ```
   /gun/random on
   #/gun/xvertex 0 mm
   #/gun/yvertex 0 mm
   #/gun/zvertex -100 mm
   ```
   
 - DETECTOR RESPONSE in F04SteppingAction
 
   Information is extracted from the program via F04SteppingAction
   at the TestPlane.
 
 - F04PhysicsList
 
   The F04PhysicsList extends a selected Geant4 physics list.
   The base physics list name is provided by its name in the F04PhysicsList
   constructor.
 
   In addition to processes defined in the base Geant4 physics list,
   there is added the F04StepMax process and the decay of pions can be assigned
   via dedicated commands in F04PhysicsListMessenger.
 
   The command to define maximum step:
   ```
   /exp/phys/stepMax value unit
   ```
 
   The decay of pions can be assigned via (pi -> e nu, pi -> mu nu):
   ```
   /decay/pienu
   /decay/pimunu
   ```
 
   The pienu assignment includes a small fraction of radiative decay:
   e nu gamma (G4PionRadiativeDecayChannel).
 
   The standard/default muon decay chain is modified to be 98.6%
   G4MuonDecayChannelWithSpin and 1.4% G4MuonRadiativeDecayChannelWithSpin
   in F04PhysicsList::ConstructParticle().
 
   The pion decay process G4PolDecay inherits from G4Decay and implements
   the virtual method - empty in the base class - DaughterPolarization
 
   The muon decay process is G4DecayWithSpin
 
   Furthermore, the following commands are also available, but
   may only be used AFTER /run/initialize
 
   ```
   /process/inactivate msc
   /process/activate msc
   ```
 
 ## Overlapping Fields
 
  The F04GlobalField (a singleton) is instantiated in
  F04DetectorConstruction() and assigned to the global field manager
  in UpdateField():
 ```cpp
 fFieldManager = GetGlobalFieldManager();
 fFieldManager->SetDetectorField(this);
 ```
  The F04GlobalField has a std::vector<ElementField*> FieldList
 
  The field from each individual beamline element is given by a
  F04ElementField object. Any number of overlapping F04ElementField
  objects can be added to the F04GlobalField. Any element that
  represents an element with an EM field must add the appropriate
  F04ElementField to the global F04GlobalField object.
 
  Of course, the F04GlobalField has the method GetFieldValue implemented.
 
  Before /run/initialize in the macro file or command, the update
  field command must have been issued if any of the other following
  field commands was employed:
 ```
 /field/update
 ```
 
  Other options are:
 ```
 /field/setStepperType 4
 /field/setMinStep 10 mm
 /field/setDeltaChord 3.0 mm
 /field/setDeltaOneStep 0.01 mm
 /field/setDeltaIntersection 0.1 mm
 /field/setEpsMin 2.5e-7 mm
 /field/setEpsMax 0.05 mm
 ```
  Each field element has a rectilinear bounding box in global
  coordinate space which is checked before a point is verified to
  actually be inside the F04ElementField (IsWithin and IsOutside).
  SetGlobalPoint is called 8 times for the corners of the local
  bounding box, after a local->global coordinate transform.
 
  The F04ElementField is the interface class used by F04GlobalField to
  compute the field value at a given point[].
 
  A beamline element, for example the F04SimpleSolenoid, will derive
  from F04ElementField and implement the computation for the element.
 ```cpp
 simpleSolenoid
   = new F04SimpleSolenoid(B, l, logicTransferMgnt,TransferMgntCenter);
 ```
  Besides the magnetic field and the length of the simple solenoid,
  the constructor needs the knowledge of the G4LogicalVolume for
  the beamline element and where its center is located in the
  'World'.
 
  The F04ElementField has a G4AffineTransform "fGlobal2local" which
  allows the quick computation of coordinate transformations. It can
  only be determined by knowing the element's coordinate origin in
  the global frame and after all of the geometry has been defined.
  For this reason, the object is prepared in two stages, through the
  constructor providing it with the coordinate center and a pointer
  to the G4LogicalVolume. Later the Construct() method is called to
  calculate the fGlobal2local and the bounding box. This can be done
  from the F04RunAction::BeginOfRunAction method, for only then are we
  certain that the geometry has been completely built:
 ```cpp
 FieldList* fields = F04GlobalField::GetObject()->GetFields();
 
 if (fields) {
    if (fields->size()>0) {
       FieldList::iterator i;
       for (i=fields->begin(); i!=fields->end(); ++i)(*i)->Construct();
    }
 }
 ```
  The F04ElementField constructor will also add the derived object into
  F04GlobalField. Finally, its AddFieldValue() will add the field value
  for this element to field[].
 
 ### User Action Classes
 
 - F04RunActionMessenger:
   ```
   /rndm/save freq - to save rndm status in external files
    0 not saved
          >0 saved on: beginOfRun.rndm
    1 saved on:   endOfRun.rndm
    2 saved on: endOfEvent.rndm
   /rndm/read random/run0evt8268.rndm
 ```
 
 - F04RunAction: \n
   BeginOfRunAction: Deal with random number storage,
   initialization etc. Call the Construct() method of
   F04ElementFields in the FieldList of F04GlobalField object.
   EndOfRunAction: random number storage/status printing.
 
 - F04EventActionMessenger:
   ```
   /event/setverbose
   ```
 
 - F04EventAction(F04RunAction* RA): \n
   Customized BeginOfEvent printing
   EndofEvent:
   saveEngingStatus and showEngineStatus according to flag
   in F04RunAction
 
 - F04TrackingAction: \n
   PreUserTrackingAction: Instantiate F04UserTrackInformation
   and set the application TrackStatus.
   PostUserTrackingAction: Retreive F04UserTrackInformation
   and decide to save random number status accordingly.
 
 - F04SteppingActionMessenger: \n
 
 - F04SteppingAction: \n
   UserSteppingAction: Kill primary if/when outside Target
   volume. Diagnostic/histogram filling for particles at a
   TestPlane. Find decay position and when particle
   FIRST reverses z-momentum component via using a
   F04UserTrackInformation object.
 
 - F04StackingAction: \n
   Track only primaries, pi+ or mu+
 
 - F04UserTrackInformation: \n
   Keep an application F04TrackStatus for the track: \n
   undefined, left, right, reverse
 
 - F04SteppingVerbose: \n
   Only print track header and step information for
   pi+ and mu+.
   Note: the information for primary protons is not printed.
 
 - F04Trajectory, F04TrajectoryPoint: \n
   Example of application specific implementations
 
 ## HOW TO START ?
 
  - Execute field04 in 'batch' mode from macro files e.g.
 ```
 % ./field04 -m field04.in
 ```
 
  - Execute field04 in 'interactive' mode with visualization
 ```
 % ./field04
 ....
 Idle> type your commands
 ....
 ```
 
  - Execute field04 in 'interactive' mode without initialization
 ```
 % ./field04 -s preinit
 ....
 Idle> type your commands, then
 Idle> /run/initialize
 Idle> /control/execute vis.mac
 ....
 ```

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