1 | \chapter{Electromagnetic Fields} |
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2 | |
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3 | \section{Creating a New Type of Field} |
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4 | {\sc Geant4} currently handles magnetic and electric fields and, |
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5 | in future releases, will handle combined electromagnetic |
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6 | fields. Fields due to other forces, not yet included in |
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7 | {\sc Geant4}, can be provided by describing the new field and the |
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8 | force it exerts on a particle passing through it. For the |
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9 | time being, all fields must be time-independent. This |
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10 | restriction may be lifted in the future. |
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11 | |
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12 | In order to accommodate a new type of field, two classes must |
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13 | be created: a field type and a class that determines the force. |
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14 | The {\sc Geant4} system must then be informed of the new field. |
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15 | |
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16 | \paragraph{A new Field class} |
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17 | A new type of Field class may be created by inheriting from |
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18 | G4Field |
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19 | \begin{verbatim} |
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20 | class NewField : public G4Field |
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21 | { |
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22 | public: |
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23 | void GetFieldValue( const double Point[3], |
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24 | double *pField )=0; |
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25 | } |
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26 | \end{verbatim} |
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27 | and deciding how many components your field will have, and what |
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28 | each component represents. For example, three components are |
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29 | required to describe a vector field while only one component is |
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30 | required to describe a scalar field. |
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31 | |
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32 | If you want your field to be a combination of different fields, |
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33 | you must choose your convention for which field goes first, |
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34 | which second etc. For example, to define an electromagnetic field we |
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35 | follow the convention that components 0,1 and 2 refer to the magnetic |
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36 | field and components 3, 4 and 5 refer to the electric field. |
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37 | |
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38 | By leaving the GetFieldValue method pure virtual, you force |
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39 | those users who want to describe their field to create a |
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40 | class that implements it for their detector's instance of |
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41 | this field. So documenting what each component means is required, |
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42 | to give them the necessary information. |
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43 | |
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44 | For example someone can describe DetectorAbc's field by creating |
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45 | a class DetectorAbcField, that derives from your NewField |
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46 | \begin{verbatim} |
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47 | class DetectorAbcField : public NewField |
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48 | { |
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49 | public: |
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50 | void MyFieldGradient::GetFieldValue( const double Point[3], |
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51 | double *pField ); |
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52 | } |
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53 | \end{verbatim} |
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54 | |
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55 | They then implement the function GetFieldValue |
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56 | \begin{verbatim} |
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57 | void MyFieldGradient::GetFieldValue( const double Point[3], |
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58 | double *pField ) |
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59 | { |
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60 | // We expect pField to point to pField[9]; |
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61 | // This & the order of the components of pField is your own |
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62 | // convention |
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63 | |
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64 | // We calculate the value of pField at Point ... |
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65 | } |
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66 | \end{verbatim} |
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67 | |
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68 | \paragraph{A new Equation of Motion for the new Field} |
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69 | Once you have created a new type of field, you must create an |
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70 | Equation of Motion for this Field. This is required in order to |
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71 | obtain the force that a particle feels. |
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72 | |
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73 | To do this you must inherit from G4Mag\_EqRhs and create your own |
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74 | equation of motion that understands your field. In it |
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75 | you must implement the virtual function EvaluateRhsGivenB. Given |
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76 | the value of the field, this function calculates the |
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77 | value of the generalised force. This is the only function that |
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78 | a subclass must define. |
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79 | \begin{verbatim} |
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80 | virtual void EvaluateRhsGivenB( const G4double y[], |
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81 | const G4double B[3], |
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82 | G4double dydx[] ) const = 0; |
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83 | \end{verbatim} |
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84 | |
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85 | In particular, the derivative vector dydx is a vector with six |
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86 | components. The first three are the derivative of the position |
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87 | with respect to the curve length. Thus they should set equal to |
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88 | the normalised velocity, which is components 3, 4 and 5 of y. |
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89 | \begin{verbatim} |
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90 | (dydx[0], dydx[1], dydx[2]) = (y[3], y[4], y[5]) |
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91 | \end{verbatim} |
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92 | |
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93 | The next three components are the derivatives of the velocity |
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94 | vector with respect to the path length. So you should write the |
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95 | "force" components for |
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96 | \begin{verbatim} |
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97 | dydx[3], dydx[4] and dydx[5] |
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98 | \end{verbatim} |
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99 | |
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100 | for your field. |
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101 | |
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102 | \paragraph{Get a G4FieldManager to use your field} |
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103 | In order to inform the {\sc Geant4} system that you want it to use |
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104 | your field as the global field, you must do the following steps: |
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105 | |
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106 | \begin{enumerate} |
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107 | \item Create a Stepper of your choice: |
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108 | \begin{verbatim} |
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109 | |
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110 | yourStepper = new G4ClassicalRK( yourEquationOfMotion ); |
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111 | // or if your field is not smooth eg |
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112 | // new G4ImplicitEuler( yourEquationOfMotion ); |
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113 | \end{verbatim} |
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114 | \item Create a chord finder that uses your Field and Stepper. You |
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115 | must also give it a minimum step size, below which it |
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116 | does not make sense to attempt to integrate: |
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117 | \begin{verbatim} |
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118 | yourChordFinder= new G4ChordFinder( yourField, |
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119 | yourMininumStep, // say 0.01*mm |
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120 | yourStepper ); |
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121 | \end{verbatim} |
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122 | \item Next create a G4FieldManager and give it that chord finder, |
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123 | \begin{verbatim} |
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124 | yourFieldManager= new G4FieldManager(); |
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125 | yourFieldManager.SetChordFinder(yourChordFinder); |
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126 | \end{verbatim} |
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127 | \item Finally we tell the Geometry that this FieldManager is |
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128 | responsible for creating a field for the detector. |
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129 | \begin{verbatim} |
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130 | G4TransportationManager::GetTransportationManager() |
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131 | -> SetFieldManager( yourFieldManager ); |
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132 | \end{verbatim} |
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133 | \end{enumerate} |
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134 | |
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135 | \paragraph{Changes for non-electromagnetic fields} |
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136 | If the field you are interested in simulating is not electromagnetic, |
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137 | another minor modification may be required. The |
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138 | transportation currently chooses whether to propagate a particle |
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139 | in a field or rectilinearly based on whether the particle is |
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140 | charged or not. If your field affects non-charged particles, you |
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141 | must inherit from the G4Transportation and re-implement the |
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142 | part of GetAlongStepPhysicalInteractionLength that decides whether |
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143 | the particles is affected by your force. |
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144 | |
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145 | In particular the relevant section of code does the following: |
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146 | \begin{verbatim} |
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147 | // Does the particle have an (EM) field force exerting upon it? |
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148 | // |
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149 | if( (particleCharge!=0.0) ){ |
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150 | |
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151 | fieldExertsForce= this->DoesGlobalFieldExist(); |
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152 | // Future: will/can also check whether current volume's field is Zero or |
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153 | // set by the user (in the logical volume) to be zero. |
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154 | } |
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155 | \end{verbatim} |
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156 | and you want it to ask whether it feels your force. If, for the sake |
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157 | of an example, you wanted to see the effects of gravity on a |
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158 | heavy hypothetical particle, you could say |
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159 | |
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160 | \begin{verbatim} |
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161 | |
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162 | // Does the particle have my field's force exerted on it? |
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163 | // |
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164 | if (particle->GetName() == "VeryHeavyWIMP") { |
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165 | fieldExertsForce= this->DoesGlobalFieldExist(); // For gravity |
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166 | } |
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167 | \end{verbatim} |
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168 | |
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169 | After doing all these steps, you will be able to see the effects of |
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170 | your force on a particle's motion. |
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171 | |
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172 | \section{Status of this chapter} |
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173 | |
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174 | 10.06.02 partially re-written by D.H. Wright \\ |
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175 | 14.11.02 spell check by P. Arce \\ |
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176 | |
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177 | |
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178 | |
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179 | |
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180 | |
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181 | |
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