1 | \section{Conversion from range cut to kinetic energy cut} |
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2 | |
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3 | In Geant4 charged particles are tracked to the end of their range. |
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4 | The differential cross section of $\delta$-electron productions |
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5 | and bremsstrahlung grow rapidly when secondary energy decrease. If all |
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6 | secondary particles will be tracked the CPU performance of any Monte Carlo code |
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7 | will be pure. The traditional solution is to use cuts. The specific of |
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8 | Geant4 \cite{cuts.G4} is that user provides value of cut in term |
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9 | of {\it cut in range}, which is unique for defined {\it G4Region} |
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10 | or for the complete geometry. |
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11 | |
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12 | Range is used, rather than energy, as a more natural concept for designing a |
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13 | coherent policy for different particles and materials. Definition of |
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14 | the certain value of the {\it cut in range} means the requirement for precision |
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15 | of spatial radioactive dose deposition. This conception is more |
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16 | strict for a simulation code and provides less handles for user to modify |
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17 | final results. At the same time, it ensures that simulation validated in |
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18 | one geometry is valid also for the other geometries. |
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19 | |
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20 | The value of cut is defined for electrons, positrons, gamma and protons. |
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21 | At the beginning of initialization of Geant4 physics the conversion from unique |
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22 | {\it cut in range} to cuts in kinetic energy for each {\it G4MaterialCutsCouple} |
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23 | \cite{cuts.Region} is performed. At that moment no energy loss or range table |
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24 | is created, so computation should be performed using original formulas. |
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25 | For electrons and positrons ionization above $10 keV$ |
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26 | a simplified Berger-Seltzer energy loss formula |
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27 | (\ref{eion.de}) is used, in which the density correction term is omitted. |
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28 | The contribution of the bremsstrahlung is added using empirical |
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29 | parameterized formula. |
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30 | For $T < 10 keV$ the linear dependence of ionization losses on |
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31 | electron velocity is assumed, bremsstrahlung contribution is neglected. |
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32 | Using these simplified formulas that energy loss vector for each {\it G4Element} |
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33 | is built. From this vector the range vector for the given material is constructed. |
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34 | The stopping range is defined as |
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35 | \begin{equation} |
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36 | R(T)= \int_0^T \frac{1}{(dE/dx)} \, dE . |
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37 | \end{equation} |
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38 | The integration has been done analytically for the low energy part and |
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39 | numerically above an energy limit $1 \; keV$. Using this table for each {\it cut in range} |
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40 | the corresponding kinetic energy can be found out. If obtained $cut in energy$ |
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41 | cannot be below |
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42 | the parameter $lowlimit$ (default $1 \; keV$) and above $highlimit$ (default $10 \; GeV$). |
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43 | If in specific application lower cut is required, |
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44 | then the allowed energy cut needs to be extended:\\ |
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45 | \\ |
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46 | {\it \footnotesize G4ProductionCutsTable::GetProductionCutsTable()$\to$SetEnergyRange(lowlimit,highlimit);} |
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47 | or via UI commands |
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48 | $$/cuts/setMinCutEnergy\;\; 100\;\; eV$$ |
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49 | $$/cuts/setMaxCutEnergy\;\; 100\;\; TeV$$ |
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50 | In contrary to electrons, gammas has no range, so some approximation should |
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51 | be used for range to energy conversion. |
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52 | An approximate empirical formula is used to compute the {\em absorption |
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53 | cross section} of a photon in an element $\sigma_{abs}$. Here, the {\em absorption cross |
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54 | section} means the sum of the cross sections of the gamma conversion, Compton |
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55 | scattering and photoelectric effect. These processes are the ``destructive'' |
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56 | processes for photons: they destroy the photon or decrease its energy. |
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57 | The coherent or Rayleigh scattering changes the direction of the gamma |
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58 | only; its cross section is not included in the {\em absorption cross section}. |
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59 | |
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60 | The {\tt AbsorptionLength} $L_{abs}$ vector is calculated for every material as : |
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61 | \begin{equation} |
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62 | L_{abs} = 5/\sigma_{abs}. |
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63 | \end{equation} |
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64 | The factor 5 comes from the requirement that the probability of having |
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65 | no 'destructive' interaction should be small, hence |
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66 | \begin{equation} |
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67 | \exp(-\mbox{$L_{abs} \sigma_{abs}$}) = \exp(-5) = 6.7 \times 10^{-3}. |
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68 | \end{equation} |
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69 | The photon cross section for a material has a minimum at a certain |
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70 | energy $E_{min}$. Correspondingly $L_{abs}$ |
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71 | has a maximum at $E = E_{min}$, |
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72 | the value of the maximal $L_{abs}$ is the biggest "meaningful" |
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73 | cut in absorption length. If the cut given by the user is bigger than this |
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74 | maximum, a warning is printed and the cut in kinetic energy is set to the |
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75 | {\it highlimit}. |
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76 | |
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77 | The cut for proton is introduced with Geant4 v9.3. The main goal |
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78 | of this cut is to limit production of all recoil ions including protons |
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79 | in elastic scattering |
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80 | processes. A simple linear conversion formula is used to compute energy threshold from the value |
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81 | of cut in range, in particular, the cut in range $1~mm$ corresponds |
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82 | to the production threshold $100 keV$. |
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83 | |
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84 | The conversion from range to energy can be studied using {\it G4EmCalculator} |
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85 | class. This class allows access or recalculation of energy loss, ranges and |
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86 | other values. It can be instantiated and at any place of user code |
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87 | and can be used after initialisation of Physics Lists:\\ |
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88 | \\ |
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89 | {\it G4EmCalculator calc;\\ |
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90 | calc.ComputeEnergyCutFromRangeCut(range, particle, material);}\\ |
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91 | \\ |
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92 | here particle and material may be string names or corresponding const pointers |
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93 | to {\it G4ParticleDefinition} and {\it G4Material}. |
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94 | |
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95 | \subsection{Status of this document} |
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96 | \ 9.10.98 created by L. Urb\'an. \\ |
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97 | 27.07.01 minor revision M.Maire \\ |
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98 | 17.08.04 moved to common to all charged particles (mma) \\ |
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99 | 04.12.04 minor re-wording by D.H. Wright \\ |
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100 | 18.05.07 rewritten by V. Ivanchenko \\ |
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101 | 11.12.08 minor revision by V. Ivanchenko, Geant4 v9.2 \\ |
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102 | 11.12.09 minor revision by V. Ivanchenko, Geant4 v9.3 \\ |
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103 | |
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104 | \begin{latexonly} |
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105 | |
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106 | \begin{thebibliography}{99} |
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107 | |
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108 | \bibitem{cuts.G4} |
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109 | Geant4 Collaboration (S.~Agostinelli et al.), |
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110 | {\em Nucl. Instr. Meth. A506 (2003) 250.} |
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111 | \bibitem{cuts.Region} |
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112 | J.~Allison et al., {\em IEEE Trans. Nucl. Sci., 53 (2006) 270.} |
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113 | \end{thebibliography} |
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114 | |
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115 | \end{latexonly} |
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116 | |
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117 | \begin{htmlonly} |
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118 | |
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119 | \subsection{Bibliography} |
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120 | |
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121 | \begin{enumerate} |
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122 | \item Geant4 Collaboration (S.~Agostinelli et al.), |
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123 | {\em Nucl. Instr. Meth. A506 (2003) 250.} |
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124 | \item J.~Allison et al., {\em IEEE Trans. Nucl. Sci., 53 (2006) 270.} |
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125 | \end{enumerate} |
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126 | |
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127 | \end{htmlonly} |
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128 | |
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129 | |
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