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 \page Examplefield01 Example field01
 
   Example that enables investigation of the accuracy and performance of the
   tracking in a magnetic field.
 
    The key Geant4 capabilities demonstrated in this example are:
    - creating a uniform magnetic field interactively using the field
      messenger,
    - choosing the type of Runge Kutta stepper used for integration of the
      motion of charged particles in the magnetic field,
    - controlling the thresholds that determine which looping particles are
      killed by G4Transportation.
 
   Some of these capabilities are available via interactive commands,
   implemented in F01FieldMessenger.
 
   The magnetic field is defined in the F01DetectorConstruction::ConstructSDandField() 
   method in the F01DetectorConstruction class using the G4FieldBuilder class.
 
   The interactive commands, under the /field directory, are created with
   the instantiation of G4FieldBuilder in the F03DetectorConstruction constructor,
 
 ## Choosing the type of stepper
 
   The basic capabilities of choosing the stepper type are demonstrated in the
   field.in macro file:
 
 ```
 /field/stepperType  TsitourasRK45   ##  Choose a stepper type   ( Tsitouras )
 /field/stepperType  RK547FEq1       ##  Choose an FSAL stepper  ( FEqRK1 )
 /field/setMinimumStep 0.1 mm        ##  Smaller steps always succeed
 /field/update                       ##  Initialise using parameters above
                                     ##  if they were changed after initialization
 ```
 
   In addition it is possible to choose to use a new type of stepper, known
   as 'First Same as Last' or FSAL, which in each step obtains the field value
   at the step endpoint and evaluates the 'right hand size' of the equation
   for the next integration step.  This reduces the number of calls to the field
   evaluation, which can be one the most computationally expensive methods,
   while providing similar accuracy.
 
   There are several potential choices of the stepper type. Here are some suggestions:
 ```
      ===========================================================================
      Number  Name of Stepper      Comments
      ===========================================================================
      Recommended - default since Geant4 10.4:
 
        DormandPrince745        : Uses a pair 4th & 5th order formulae (like other 4/5
                                  well-known and very efficient embedded method
                                  methods); their difference is the error estimate.
                                  Highly recommended in literature, including
                                  Hairer & Wanner, & Numerical Recipes
                                  Used in several established RK code (e.g. DOPRI5)
      ===========================================================================
      Good choices for reasonably smooth fields:
 
        BogackiShampine45       : more efficient embedded 4/5 pair
                                  Used in many applications, including
                                  RKSUITE suite.
 
        TsitourasRK45.          : potentially the most efficient embedded 4/5
                                  pair - found in expanded search of parameter space.
 
        DormandPrinceRK56.      : higher order embedded method from authors of DoPri5.
                                  Uses a pair 5th & 6th order formulae.
 
        DormandPrinceRK78.      : higher order embedded method from authors of DoPri5.
                                  Uses a pair 7th & 8th order formulae.
 
        NystromRK4              : a specialised Nystrom method for magnetic fields.
                                  Reuses the field value at the mid-point of the step,
                                  and also provides an analytical estimation of the
                                  integration error based on numerical evaluation of
                                  fourth order variation in the equation for
                                  magnetic field.
      ===========================================================================
      The new 'First Same as Last' (FSAL) steppers can be chosen in addition:
         RKFEq1                 : FSAL stepper with improved equilibrium properties.
                                  When kinks or other anomalies are encountered,
                                  and at the start of integration when the best
                                  step size is not known, this type of stepper
                                  converges faster and more smoothly to good
                                  step sizes.
      ===========================================================================
      The old default and old first alternative -
 
         ClassicalRK4           : original Runge-Kutta method, very robust but slower )
                                ( obtains error estimate by doing 2 half steps )
                                  Good baseline for comparison - long experience of use.
                                  May be good alternative for less smooth fields.
 
         CashKarpRKF45          : The oldest 'embedded' RK method in Geant4 -
                                  also fairly robust.
                                  Faster than  ClassicalRK4 for smoother fields,
                                  as it does not need two half steps to estimate error.
                                  Available since Geant4 1.0
 
      ===========================================================================
      Other potential choices for non-smooth fields (with kinks, abrupt changes):
 
         SimpleHeum             : low   order, with error obtained from half-steps
         BogackiShampine23      : lower order embedded method  (new in 10.3-beta)
      ===========================================================================
 ```
 
 ## Controlling the killing of looping particles
 
 Occasionally tracks 'looping' in a strong magnetic field, making little
 progress even over hundreds of integration steps.  This is due to a
 combination of a strong magnetic field and a thin material (gas or vacuum)
 in which the size of a physics step is substantially larger than the radius
 of curvature of the track.
 
 Since the amount of CPU time which can be consumed by one or few such tracks
 is very large, it is important to limit the number of integration steps
 spent on these tracks.  The module for propagation in field in Geant4
 flags tracks which take more than a certain number (default 1,000) integration
 steps without reaching the requested end of the step size, which was
 determined by the physics and geometry.
 
 The Geant4 G4Transportation and G4CoupledTransportation processes are tasked
 to select which of the looping tracks are killed and which survive. To
 balance the potential significant cost of integrating looping particles,
 three thresholds exist
 
 - **The 'Warning' Energy**: a track with energy below this value that is found to
 loop is killed silently (no warning.)
 Above the 'Warning Energy', if a track is selected for killing a warning is
 generated.
 
 - **The 'Important' Energy**: the threshold energy above which a track will survive
 for multiple steps if found looping.
 
 - Number of 'tracking' steps. They will be only be killed only if they still
 loop after than.
 **The number of 'trials'**: the number of steps that 'important' tracks survive.
 
 Note that currently only stable particles are killed. ( Refinements to enable
 toggling whether unstable particles can be killed are in development. )
 
 This example demonstrate choosing different values for these parametes
 in the main() method of field01.cc using one of two techniques.
 
 ### i) Using G4PhysicsListHelper
 
 The first method is new in Geant4 release 10.5, and uses the G4PhysicsListHelper
 which has methods to choose a pre-selected set of parameter values. The choices
 are between a set each of low and high thresholds.  Either one can be enabled
 by calling correspondingly
 ```cpp
 G4PhysicsListHelper::GetPhysicsListHelper()->UseLowLooperThresholds();
 ```
 or
 ```cpp
 G4PhysicsListHelper::GetPhysicsListHelper()->UseHighLooperThresholds();
 ```
 
 These methods must be called before the physics is constructed - i.e. typically
 before RunManager's Initialise() method is called.
 This works only if either
   - a modular physics lists is used, or if
   - the G4ModularPhysicsList and its AddTransporation method are used to create and register a common transportation process for all particles (one for each thread).
 
 ### ii) Fine grained control (available in Geant4 versions since 7.0)
 
 Fine grained control of the Transportation's parameters for looping particles
 is also possible.
 
 This is demonstrated in the F01RunAction::ChangeLooperParameters() method,
 which is called by the BeginOfRunAction.  There the appropriate
 Transportation object for the electron is obtained, and its parameters
 (if valid) are used to overwrite the thresholds in the G4Transportation class.
 
 For example, to ensure that only looping particles with energy 10 keV are
 killed silently we change the value of the 'Warning' Energy:
 ```cpp
 runAction->SetWarningEnergy( 10.0 * CLHEP::keV );
 ```
 [ This is passed along to the registered G4Transportation or
 G4CoupledTransportation object by the F01RunAction's ChangeLooperParameters.]
 
 As a result the killing of any (stable) looping track with energy over 10 keV
 will generate a warning.
 
 A second configurable energy threshold enables tracks above it to survive a
 chosen number of 'tracking' steps.  They will be only be killed only if they
 still loop after than number of tracking steps.  F01RunAction's methods are
 used to configure these parameters:
 ```cpp
 runAction->SetImportantEnergy( 0.1  * CLHEP::MeV );
 runAction->SetNumberOfTrials( 30 );
 ```
 which the run action passes to the G4Transportation or
 G4CoupledTransportation object registered for the electron.
 
 Note that for all pre-configured and modular physics lists share a single
 Transportation process for all types of particles.  So the parameters for
 killing loopers will be shared by all particle types in this case.
 
 ## Background Information
 
 ### GEOMETRY DEFINITION
 
  The "Absorber" is a solid made of a given material.
 
  Three parameters define the absorber :
  - the material of the absorber,
  - the thickness of an absorber,
  - the transverse size of the absorber (the input face is a square).
 
  The volume "World" contains the "Absorber".
  In this test the parameters of the "World" can be changed , too.
 
  In addition a transverse uniform magnetic field can be applied.
 
  The default geometry is constructed in F01DetectorConstruction class,
  but all the parameters can be changed via
  the commands defined in the F01DetectorMessenger class.
 
 ### AN EVENT : THE PRIMARY GENERATOR
 
  The primary kinematic consists of a single particle (electron, Ekin = 0.5 GeV)
  which hits the
  absorber perpendicular to the input face. The type of the particle
  and its energy are set in the F01PrimaryGeneratorAction class, and can
  be changed via the G4 build-in commands of G4ParticleGun class (see
  the macros provided with this example).
 
  It is also possible to change the position of the primary particle vertex
  or activate its randomization via the commands defined in  the
  F01PrimaryGeneratorMessenger class.
 
  A RUN is a set of events.
 
 ### DETECTOR RESPONSE
 
   The spatial distribution of charged particles transported in magnetic
   field is envistigated.
   A HIT is a record, event per event , of all the
   informations needed to simulate and analyse the detector response.
 
   In this example a F01CalorHit is defined as a set of 2 informations:
   - the total energy deposit in the absorber,
   - the total tracklength of all charged particles in the absorber,
 
   Therefore  the absorber is declared
   'sensitive detector' (SD), see F01CalorimeterSD, which means they can contribute to the hit.
 
 ### PHYSICS LIST
 
  The particle's type and the physic processes which will be available
  in this example are set in the FTFP_BERT physics list. This physics list
  requires data files for electromagnetic and hadronic processes.
  See more on installation of the datasets in Geant4 Installation Guide,
 
 ### HOW TO START ?
 
   - Execute field01 in 'batch' mode from macro file e.g.
 ```
 % ./field01 field01.in
 ```
 
   - Execute field01 in 'interactive' mode with visualization e.g.
 ```
 % ./field01
 ....
 Idle> /run/beamOn 1
 ....
 ```

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