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8 | </script></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">5.8. |
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9 | Track Error Propagation |
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10 | </th></tr><tr><td width="20%" align="left"><a accesskey="p" href="ch05s07.html"><img src="AllResources/IconsGIF/prev.gif" alt="Prev"></a> </td><th width="60%" align="center">Chapter 5. |
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11 | Tracking and Physics |
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12 | </th><td width="20%" align="right"> <a accesskey="n" href="ch06.html"><img src="AllResources/IconsGIF/next.gif" alt="Next"></a></td></tr></table><hr></div><div class="sect1" lang="en"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="sect.G4Error"></a>5.8. |
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13 | Track Error Propagation |
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14 | </h2></div></div></div><p> |
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15 | The error propagation package serves to propagate one particle together with its error from a given trajectory state until a user-defined target is reached (a surface, a volume, a given track length,...). |
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16 | </p><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.G4Error.Physics"></a>5.8.1. |
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17 | Physics |
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18 | </h3></div></div></div><p> |
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19 | The error propagator package computes the average trajectory that a particle would follow. |
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20 | This means that the physics list must have the following characteristics: |
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21 | </p><div class="itemizedlist"><ul type="disc"><li> No multiple scattering </li><li> No random fluctuations for energy loss </li><li> No creation of secondary tracks </li><li> No hadronic processes </li></ul></div><p> |
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22 | It has also to be taken into account that when the propagation is done backwards (in the direction opposed to the one the original track traveled) the energy loss has to be changed into an energy gain. |
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23 | </p><p> |
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24 | All this is done in the <code class="literal">G4ErrorPhysicsList</code> class, that is automatically set by <code class="literal">G4ErrorPropagatorManager</code> as the GEANT4 physics list. |
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25 | It sets <code class="literal">G4ErrorEnergyLoss</code> as unique electromagnetic process. This process uses the GEANT4 class <code class="literal">G4EnergyLossForExtrapolator</code> to compute the average energy loss for forwards or backwards propagation. |
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26 | To avoid getting too different energy loss calculation when the propagation is done forwards (when the energy at the beginning of the step is used) or backwards (when the energy at the end of the step is used, always smaller than at the beginning) <code class="literal">G4ErrorEnergyLoss</code> computes once the energy loss and then replaces the original energy loss by subtracting/adding half of this value (what is approximately the same as computing the energy loss with the energy at the middle of the step). |
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27 | In this way, a better calculation of the energy loss is obtained with a minimal impact on the total CPU time. |
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28 | </p><p> |
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29 | The user may use his/her own physics list instead of <code class="literal">G4ErrorPhysicsList</code>. As it is not needed to define a physics list when running this package, the user may have not realized that somewhere else in his/her application it has been defined; therefore a warning will be sent to advert the user that he is using a physics list different to <code class="literal">G4ErrorPhysicsList</code>. If a new physics list is used, it should also initialize the <code class="literal">G4ErrorMessenger</code> with the classes that serve to limit the step: |
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30 | |
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31 | </p><div class="informalexample"><pre class="programlisting"> |
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32 | G4ErrorEnergyLoss* eLossProcess = new G4ErrorEnergyLoss; |
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33 | G4ErrorStepLengthLimitProcess* stepLengthLimitProcess = new G4ErrorStepLengthLimitProcess; |
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34 | G4ErrorMagFieldLimitProcess* magFieldLimitProcess = new G4ErrorMagFieldLimitProcess; |
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35 | new G4ErrorMessenger( stepLengthLimitProcess, magFieldLimitProcess, eLossProcess ); |
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36 | </pre></div><p> |
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37 | |
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38 | </p><p> |
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39 | To ease the use of this package in the reconstruction code, the physics list, whether <code class="literal">G4ErrorPhysicsList</code> or the user's one, will be automatically initialized before starting the track propagation if it has not been done by the user. |
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40 | </p></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.G4Error.TrajState"></a>5.8.2. |
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41 | Trajectory state |
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42 | </h3></div></div></div><p> |
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43 | The user has to provide the particle trajectory state at the initial point. |
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44 | To do this it has to create an object of one of the children classes of <code class="literal">G4ErrorTrajState</code>, providing: |
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45 | </p><div class="itemizedlist"><ul type="disc"><li> Particle type </li><li> Position </li><li> Momentum </li><li> Trajectory error matrix </li></ul></div><div class="informalexample"><pre class="programlisting"> |
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46 | G4ErrorTrajState( const G4String& partType, |
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47 | const G4Point3D& pos, |
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48 | const G4Vector3D& mom, |
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49 | const G4ErrorTrajErr& errmat = G4ErrorTrajErr(5,0) ); |
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50 | </pre></div><p> |
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51 | A particle trajectory is characterized by five independent variables as a function of one parameter (e.g. the path length). |
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52 | Among the five variables, one is related to the curvature (to the absolute value of the momentum), two are related to the direction of the particle and the other two are related to the spatial location. |
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53 | </p><p> |
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54 | There are two possible representations of these five parameters in the error propagator package: as a free trajectory state, class <code class="literal">G4ErrorTrajStateFree</code>, or as a trajectory state on a surface, class <code class="literal">G4ErrorTrajStateonSurface</code>. |
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55 | </p><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.G4Error.TrajState.FreTrajState"></a>5.8.2.1. |
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56 | Free trajectory state |
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57 | </h4></div></div></div> |
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58 | |
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59 | In the free trajectory state representation the five trajectory parameters are |
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60 | |
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61 | <div class="itemizedlist"><ul type="disc"><li> G4double fInvP </li><li> G4double fLambda </li><li> G4double fPhi </li><li> G4double fYPerp </li><li> G4double fZPerp </li></ul></div><p> |
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62 | where <code class="literal">fInvP</code> is the inverse of the momentum. |
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63 | <code class="literal">fLambda</code> and <code class="literal">fPhi</code> are the dip and azimuthal angles related to the momentum components in the following way: |
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64 | </p><code class="literal"> |
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65 | p_x = p cos(lambda) cos(phi) |
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66 | p_y = p cos(lambda) sin(phi) |
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67 | p_z = p sin(lambda) |
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68 | </code><p> |
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69 | that is, <code class="literal">lambda = 90 - theta</code>, where <code class="literal">theta</code> is the usual angle with respect to the Z axis. |
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70 | </p><p> |
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71 | <code class="literal">fYperp</code> and <code class="literal">fZperp</code> are the coordinates of the trajectory in a local orthonormal reference frame with the X axis along the particle direction, the Y axis being parallel to the X-Y plane (obtained by the vectorial product of the global Z axis and the momentum). |
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72 | </p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.G4Error.TrajState.SurfaceTrajState"></a>5.8.2.2. |
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73 | Trajectory state on a surface |
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74 | </h4></div></div></div><p> |
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75 | In the trajectory state on a surface representation the five trajectory parameters are |
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76 | </p><div class="itemizedlist"><ul type="disc"><li> G4double fInvP </li><li> G4double fPV </li><li> G4double fPW </li><li> G4double fV </li><li> G4double fW </li></ul></div><p> |
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77 | where <code class="literal">fInvP</code> is the inverse of the momentum; |
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78 | <code class="literal">fPV</code> and <code class="literal">fPW</code> are the momentum components in an orthonormal coordinate system with axis U, V and W; |
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79 | <code class="literal">fV</code> and <code class="literal">fW</code> are the position components on this coordinate system. |
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80 | </p> |
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81 | |
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82 | For this representation the user has to provide the plane where the parameters are calculated. |
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83 | This can be done by providing two vectors, V and W, contained in the plane: |
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84 | |
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85 | <div class="informalexample"><pre class="programlisting"> |
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86 | G4ErrorSurfaceTrajState( const G4String& partType, |
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87 | const G4Point3D& pos, |
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88 | const G4Vector3D& mom, |
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89 | const G4Vector3D& vecV, |
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90 | const G4Vector3D& vecW, |
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91 | const G4ErrorTrajErr& errmat = G4ErrorTrajErr(5,0) ); |
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92 | </pre></div> |
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93 | |
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94 | or by providing a plane |
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95 | |
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96 | <div class="informalexample"><pre class="programlisting"> |
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97 | G4ErrorSurfaceTrajState( const G4String& partType, |
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98 | const G4Point3D& pos, |
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99 | const G4Vector3D& mom, |
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100 | const G4Plane3D& plane, |
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101 | const G4ErrorTrajErr& errmat = G4ErrorTrajErr(5,0) ); |
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102 | </pre></div> |
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103 | |
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104 | In this second case the vector V is calculated as the vector in the plane perpendicular to the global vector X (if the plane normal is equal to X, Z is used instead) and W is calculated as the vector in the plane perpendicular to V. |
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105 | |
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106 | </div></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.G4Error.Err"></a>5.8.3. |
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107 | Trajectory state error |
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108 | </h3></div></div></div><p> |
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109 | The 5X5 error matrix should also be provided at the creation of the trajectory state as a <code class="literal">G4ErrorTrajErr</code> object. |
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110 | If it is not provided a default object will be created filled with null values. |
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111 | </p><p> |
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112 | Currently the <code class="literal">G4ErrorTrajErr</code> is a <code class="literal">G4ErrorSymMatrix</code>, a simplified version of <code class="literal">CLHEP HepSymMatrix</code>. |
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113 | </p><p> |
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114 | The error matrix is given in units of GeV and cm. Therefore you should do the conversion if your code is using other units. |
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115 | </p></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.G4Error.Target"></a>5.8.4. |
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116 | Targets |
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117 | </h3></div></div></div><p> |
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118 | The user has to define up to where the propagation must be done: the target. |
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119 | The target can be a surface <code class="literal">G4ErrorSurfaceTarget</code>, which is not part of the GEANT4 geometry. |
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120 | It can also be the surface of a GEANT4 volume <code class="literal">G4ErrorGeomVolumeTarget</code>, so that the particle will be stopped when it enters this volume. |
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121 | Or it can be that the particle is stopped when a certain track length is reached, by implementing a <code class="literal">G4ErrorTrackLengthTarget</code>. |
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122 | </p><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.G4Error.Target.SurfaceTarget"></a>5.8.4.1. |
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123 | Surface target |
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124 | </h4></div></div></div> |
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125 | |
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126 | When the user chooses a <code class="literal">G4ErrorSurfaceTarget</code> as target, the track is propagated until the surface is reached. |
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127 | This surface is not part of GEANT4 geometry, but usually traverses many GEANT4 volumes. |
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128 | The class <code class="literal">G4ErrorNavigator</code> takes care of the double navigation: for each step the step length is calculated as the minimum of the step length in the full geometry (up to a GEANT4 volume surface) and the distance to the user-defined surface. |
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129 | To do it, <code class="literal">G4ErrorNavigator</code> inherits from <code class="literal">G4Navigator</code> and overwrites the methods <code class="literal">ComputeStep()</code> and <code class="literal">ComputeSafety()</code>. |
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130 | |
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131 | Two types of surface are currently supported (more types could be easily implemented at user request): plane and cylindrical. |
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132 | |
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133 | <div class="sect4" lang="en"><div class="titlepage"><div><div><h5 class="title"><a name="sect.G4Error.Target.SurfaceTarget.PlaneSurfaceTarget"></a>5.8.4.1.1. |
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134 | Plane surface target |
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135 | </h5></div></div></div><code class="literal">G4ErrorPlaneSurfaceTarget</code> implements an infinite plane surface. |
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136 | The surface can be given as the four coefficients of the plane equation <code class="literal">ax+by+cz+d = 0</code>: |
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137 | |
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138 | <div class="informalexample"><pre class="programlisting"> |
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139 | G4ErrorPlaneSurfaceTarget(G4double a=0, |
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140 | G4double b=0, |
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141 | G4double c=0, |
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142 | G4double d=0); |
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143 | </pre></div> |
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144 | |
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145 | or as the normal to the plane and a point contained in it: |
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146 | |
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147 | <div class="informalexample"><pre class="programlisting"> |
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148 | G4ErrorPlaneSurfaceTarget(const G4Normal3D &n, |
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149 | const G4Point3D &p); |
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150 | </pre></div> |
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151 | |
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152 | or as three points contained in it: |
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153 | |
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154 | <div class="informalexample"><pre class="programlisting"> |
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155 | G4ErrorPlaneSurfaceTarget(const G4Point3D &p1, |
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156 | const G4Point3D &p2, |
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157 | const G4Point3D &p3); |
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158 | </pre></div></div><div class="sect4" lang="en"><div class="titlepage"><div><div><h5 class="title"><a name="sect.G4Error.Target.SurfaceTarget.CylSurfaceTarget"></a>5.8.4.1.2. |
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159 | Cylindrical surface target |
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160 | </h5></div></div></div><code class="literal">G4ErrorCylSurfaceTarget</code> implements an infinite-length cylindrical surface (a cylinder without end-caps). |
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161 | The surface can be given as the radius, the translation and the rotation |
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162 | |
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163 | <div class="informalexample"><pre class="programlisting"> |
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164 | G4ErrorCylSurfaceTarget( const G4double& radius, |
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165 | const G4ThreeVector& trans=G4ThreeVector(), |
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166 | const G4RotationMatrix& rotm=G4RotationMatrix() ); |
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167 | </pre></div> |
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168 | |
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169 | or as the radius and the affine transformation |
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170 | |
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171 | <div class="informalexample"><pre class="programlisting"> |
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172 | G4ErrorCylSurfaceTarget( const G4double& radius, |
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173 | const G4AffineTransform& trans ); |
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174 | </pre></div></div></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.G4Error.Target.VolumeTarget"></a>5.8.4.2. |
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175 | Geometry volume target |
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176 | </h4></div></div></div><p> |
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177 | When the user chooses a <code class="literal">G4ErrorGeomVolumeTarget</code> as target, the track is propagated until the surface of a GEANT4 volume is reached. User can choose if the track will be stopped only when the track enters the volume, only when the track exits the volume or in both cases. |
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178 | </p> |
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179 | |
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180 | The object has to be instantiated giving the name of a logical volume existing in the geometry: |
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181 | |
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182 | <div class="informalexample"><pre class="programlisting"> |
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183 | G4ErrorGeomVolumeTarget( const G4String& name ); |
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184 | </pre></div></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.G4Error.Target.TrkLenTarget"></a>5.8.4.3. |
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185 | Track Length target |
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186 | </h4></div></div></div><p> |
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187 | When the user chooses a <code class="literal">G4ErrorTrackLengthTarget</code> as target, the track is propagated until the given track length is reached. |
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188 | </p> |
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189 | |
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190 | The object has to be instantiated giving the value of the track length: |
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191 | <div class="informalexample"><pre class="programlisting"> |
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192 | G4ErrorTrackLengthTarget(const G4double maxTrkLength ); |
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193 | </pre></div><p> |
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194 | It is implemented as a <code class="literal">G4VDiscreteProcess</code> and it limits the step in <code class="literal">PostStepGetPhysicalInteractionLength</code>. |
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195 | To ease its use, the process is registered to all particles in the constructor. |
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196 | </p></div></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.G4Error.Propagation"></a>5.8.5. |
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197 | Managing the track propagation |
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198 | </h3></div></div></div><p> |
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199 | The user needs to propagate just one track, so there is no need of run and events. neither of <code class="literal">G4VPrimaryGeneratorAction</code>. |
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200 | |
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201 | <code class="literal">G4ErrorPropagator</code> creates a track from the information given in the <code class="literal">G4ErrorTrajState</code> and manages the step propagation. |
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202 | The propagation is done by the standard GEANT4 methods, invoking <code class="literal">G4SteppingManager::Stepping() </code> to propagate each step. |
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203 | </p><p> |
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204 | After one step is propagated, <code class="literal">G4ErrorPropagator</code> takes cares of propagating the track errors for this step, what is done by <code class="literal">G4ErrorTrajStateFree::PropagateError()</code>. |
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205 | The equations of error propagation are only implemented in the representation of <code class="literal">G4ErrorTrajStateFree</code>. |
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206 | Therefore if the user has provided instead a <code class="literal">G4ErrorTrajStateOnSurface</code> object, it will be transformed into a <code class="literal">G4ErrorTrajStateFree</code> at the beginning of tracking, and at the end it is converted back into <code class="literal">G4ErrorTrajStateOnSurface</code> on the target surface (on the normal plane to the surface at the final point). |
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207 | </p><p> |
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208 | The user <code class="literal">G4VUserTrackingAction::PreUserTrackingAction( const G4Track* )</code> and <code class="literal">G4VUserTrackingAction::PreUserTrackingAction( const G4Track* )</code> are also invoked at the beginning and at the end of the track propagation. |
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209 | </p><p> |
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210 | <code class="literal">G4ErrorPropagator</code> stops the tracking when one of the three conditions is true: |
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211 | |
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212 | </p><div class="itemizedlist"><ul type="disc"><li> Energy is exhausted </li><li> World boundary is reached </li><li> User-defined target is reached </li></ul></div><p> |
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213 | |
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214 | In case the defined target is not reached, <code class="literal">G4ErrorPropagator::Propagate()</code> returns a negative value. |
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215 | </p><p> |
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216 | The propagation of a trajectory state until a user defined target can be done by invoking the method of <code class="literal">G4ErrorPropagatorManager</code> |
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217 | </p><div class="informalexample"><pre class="programlisting"> |
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218 | G4int Propagate( G4ErrorTrajState* currentTS, const G4ErrorTarget* target, |
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219 | G4ErrorMode mode = G4ErrorMode_PropForwards ); |
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220 | </pre></div><p> |
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221 | </p> |
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222 | |
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223 | You can get the pointer to the only instance of <code class="literal">G4ErrorPropagatorManager</code> with |
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224 | |
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225 | <div class="informalexample"><pre class="programlisting"> |
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226 | G4ErrorPropagatorManager* g4emgr = G4ErrorPropagatorManager::GetErrorPropagatorManager(); |
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227 | </pre></div> |
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228 | |
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229 | Another possibility is to invoke the propagation step by step, returning control to the user after each step. This can be done with the method |
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230 | |
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231 | <div class="informalexample"><pre class="programlisting"> |
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232 | G4int PropagateOneStep( G4ErrorTrajState* currentTS, |
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233 | G4ErrorMode mode = G4ErrorMode_PropForwards ); |
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234 | </pre></div> |
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235 | |
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236 | In this case you should register the target first with the command |
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237 | |
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238 | <div class="informalexample"><pre class="programlisting"> |
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239 | G4ErrorPropagatorData::GetG4ErrorPropagatorData()->SetTarget( theG4eTarget ); |
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240 | </pre></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.G4Error.Propagation.ErrorPropagation"></a>5.8.5.1. |
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241 | Error propagation |
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242 | </h4></div></div></div> |
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243 | |
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244 | As in the GEANT3-based GEANE package, the error propagation is based on the equations of the European Muon Collaboration, that take into account: |
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245 | |
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246 | <div class="itemizedlist"><ul type="disc"><li> Error from curved trajectory in magnetic field </li><li> Error from multiple scattering </li><li> Error from ionization </li></ul></div><p> |
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247 | The formulas assume propagation along an helix. |
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248 | This means that it is necessary to make steps small enough to assure magnetic field constantness and not too big energy loss. |
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249 | </p></div></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.G4Error.StepLimits"></a>5.8.6. |
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250 | Limiting the step |
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251 | </h3></div></div></div> |
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252 | |
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253 | There are three ways to limit the step. |
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254 | The first one is by using a fixed length value. This can be set by invoking the user command : |
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255 | |
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256 | <div class="informalexample"><pre class="programlisting"> |
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257 | G4UImanager::GetUIpointer()->ApplyCommand("/geant4e/limits/stepLength MY_VALUE MY_UNIT"); |
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258 | </pre></div> |
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259 | |
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260 | The second one is by setting the maximum percentage of energy loss in the step (or energy gain is propagation is backwards). |
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261 | This can be set by invoking the user command : |
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262 | |
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263 | <div class="informalexample"><pre class="programlisting"> |
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264 | G4UImanager::GetUIpointer()->ApplyCommand("/geant4e/limits/energyLoss MY_VALUE"); |
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265 | </pre></div> |
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266 | |
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267 | The last one is by setting the maximum difference between the value of the magnetic field at the beginning and at the end of the step. Indeed what is limited is the curvature, or exactly the value of the magnetic field divided by the value of the momentum transversal to the field. |
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268 | This can be set by invoking the user command : |
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269 | |
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270 | <div class="informalexample"><pre class="programlisting"> |
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271 | G4UImanager::GetUIpointer()->ApplyCommand("/geant4e/limits/magField MY_VALUE"); |
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272 | </pre></div> |
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273 | |
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274 | The classes that limit the step are implemented as GEANT4 processes. Therefore, the invocation of the above-mentioned commands should only be done after the initialization (for example after <code class="literal">G4ErrorPropagatorManager::InitGeant4e()</code>. |
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275 | |
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276 | </div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="ch05s07.html"><img src="AllResources/IconsGIF/prev.gif" alt="Prev"></a> </td><td width="20%" align="center"><a accesskey="u" href="ch05.html"><img src="AllResources/IconsGIF/up.gif" alt="Up"></a></td><td width="40%" align="right"> <a accesskey="n" href="ch06.html"><img src="AllResources/IconsGIF/next.gif" alt="Next"></a></td></tr><tr><td width="40%" align="left" valign="top">5.7. |
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277 | User Limits |
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278 | </td><td width="20%" align="center"><a accesskey="h" href="index.html"><img src="AllResources/IconsGIF/home.gif" alt="Home"></a></td><td width="40%" align="right" valign="top"> Chapter 6. |
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279 | User Actions |
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280 | </td></tr></table></div></body></html> |
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