Application
SR-NIEL Treatment in Geant4 (test58)
test58
test58 is the reference example for NIEL and nuclear stopping power calculation in Geant4.
The physical values returned, computed as an average on the number of impinging particles, are:
- Total track lenght:
X0 is the effective lenght of the path traversed by the incoming particle inside the absorber. - Mean Number of Step:
NS is the number of interactions that were produced along the path. - Mean free path:
λ=X0/NS is mean path traversed in between two consecutive interactions. - Interaction Cross Section:
σ=(λ*n)-1 where n is the number density of the target material. - Mean scattering angle:
is the total deflection angle out of the detector. - Total Energy deposited:
is the energy deposited by means of the physics process that are defined in the physic list (ionization, displacement...). - Nuclear Recoil Energy deposited:
is the energy deposited by nuclear recoil per unit lenght (MeV cm-1) - or (MeV cm2 g-1) - . - NIEL:
is the Non Ionizing Energy Loss computed with the selected threshold energy. - Total Number of primary knock-on atoms (PKA):
is the number of displaced atoms. - Mean Kinetic Energy of PKA
- Total Frenkel-pairs concentration:
FP=Edis/(2.5*Th) is the concentration of stable defects, where Edis is the energy that goes into displacement and Th is the selected threshold energy for displacement.
Two examples, with protons and electrons as incident particles are provided.
Protons
One single proton of 10 MeV energy is impinging on a Silicon cube (1x1x1 cm3). The threshold energy for displacement is set to 21 eV. The only physical process selected in the physic list is the single coulomb scattering. The output result is given:
The visualization of the event is also provided. The big external box is the world where the event took place. The internal box is the Silicon absorber (1x1x1 cm3). The impinging proton track is in cyan and the projected direction of the displaced Silicon atoms are in light grey.
Electrons
One single electron of 10 MeV energy is impinging on a Silicon cube (1x1x1 cm3). The threshold energy for displacement is set to 21 eV. The only physical process selected in the physic list is the single coulomb scattering. The output result is given:
The visualization of the event is also provided. The big external box is the world where the event took place. The internal box is the Silicon absorber (1x1x1 cm3). The impinging electron track is in red and the projected direction of the displaced silicon atoms are in light grey.
Geant4 v 10. Patch for SR-Treatment
SR-NIEL and Geant4 for electrons
The screened relativistic treatments for electrons [Geant4: Class G4eSingleScatteringModel (2014)] protons and ions are included in Geant4 simulation code (see also A. Bagulya et al. (2017)). Several tests were carried on to verify consistency of the latest Geant4 version with respect to the SR-NIEL analytical treatment.
Some bugs were spotted and corrected in the next patches that will be distributed in the coming months. The lastest version of the SR-NIEL classes is available in this website.
The following results are obtained with the patch already applied.
Electrons in Silicon
The easiest geometry was used in these tests: Electrons incident on a slice of Silicon. The numer of incident electrons and the thickness of the slice were tuned to get enough statistic with resonable computing time.
Total Cross Section
Total Cross section in Geant4 code and in SR-NIEL were computed and compared for Electrons incident on a Silicon target.
The mean difference is less than 0.1%.
Differential Cross Section
107 Electrons were generated for traversing a slice of silicon 10-2 μm thick and 2.1x105 interaction were produced. The thickness was kept as thin as possible to reduce the multiple scattering effects in the angle distribution Y(θ) and the energy loss of the trasmitted particles. The differential cross section was calculated as:
where Y(θ) is the number of particle deflected between θ and θ+dθ, n0 is number of incident particles, N the number density of silicon atoms, x the thickness of the target slice and ΔΩ the solid angle between θ and θ+dθ.
The calculated differential cross section was compared to the analytical one contained in SR-NIEL code:
Nuclear Stopping Power
Following is the results of Nuclear Stopping Power coming from simulations in Geant4 compared with the SR-NIEL results. A variable number (to obtain ~103 displaced atoms) of protons were generated for traversing a slice of Silicon 10μm thick.
Non Ionizing Energy Loss
Following is the results of the Non Ionizing Energy Loss (NIEL) coming from simulations in Geant4 compared with the SR-NIEL results. A variable number (to obtain ~103 displaced atoms) of electrons were generated for traversing a slice of Silicon 10μm thick. The threshold energy for displacement was set to 21 eV.
References
Geant4: Class G4eSingleScatteringModel (2014) .
Class Description: single scattering interaction of electrons on nuclei (Ref.~Boschini et al. 2012), Software Reference Manual
Source Code Version: Geant4 11 (December 2022) avaliable at the website
https://geant4.web.cern.ch/download/all
See also Sections~8.6--8.6.2 of Physics Reference Manual for version 11.0 available at the website:
https://geant4.web.cern.ch/docs/
A. Bagulya et al. (2017), Recent progress of Geant4 electromagnetic physics for LHC and other applications, CHEP 2016 Conference, San Francisco, October 8-14 2016, to appear in Journal of Physics: Conference Series (JPCS); available for download.
SR-NIEL and Geant4 for protons and ions
The screened relativistic treatments for electrons, protons and ions [Geant4: Class G4IonCoulombScatteringModel (2014)], and only for Coulomb interaction, are included in Geant4 simulation code. Some tests were carried on to verify consistency of the latest version of Geant4 (10.1) with respect to the SR-NIEL analytical treatment.
Some bugs were spotted and corrected in the next patches that will be distributed in the coming months. The lastest version of the SR-NIEL classes is available in this website.
The following results are obtained with the patch already applied.
Protons in Silicon
The easiest geometry was used in these tests: Protons incident on a slice of Silicon. The numer of incident protons and the thickness of the slice were tuned to get enough statistic with resonable computing time.
Total Cross Section (Coulomb Interactions)
Total Cross section in Geant4 code and in SR-NIEL for Coulomb interactions were computed and compared for Protons incident on a Silicon target.
The mean difference is less than 0.1%.
Differential Cross Section (Coulomb Interactions)
107 Protons were generated for traversing a slice of silicon 10 Å thick and 3.8x105 interactions were produced. The thickness was kept as thin as possible to reduce the multiple scattering effects in the angle distribution Y(θ) and the energy loss of the trasmitted particles. The differential cross section was calculated as:
where Y(θ) is the number of particle deflected between θ and θ+dθ, n0 is number of incident particles, N the number density of silicon atoms, x the thickness of the target slice and ΔΩ the solid angle between θ and θ+dθ.
The calculated differential cross section was compared to the analytical one contained in SR-NIEL code for Coulomb interactions:
Nuclear Stopping Power (Coulomb Interactions)
Following is the results of Nuclear Stopping Power coming from simulations in Geant4 compared with the SR-NIEL results for Coulomb interactions. A variable number (to obtain ~105 displaced atoms) of protons were generated for traversing a slice of Silicon 1μm thick.
Non Ionizing Energy Loss (Coulomb Interactions)
Following is the results of the Non Ionizing Energy Loss (NIEL) coming from simulations in Geant4 compared with the SR-NIEL results for Coulomb interactions. A variable number (to obtain ~105 displaced atoms) of protons were generated for traversing a slice of Silicon 1μm thick. The threshold energy for displacement was set to 21 eV.
Protons in SiC
Same tests was performed on a target compound using protons incident on a slice of SiC. The numer of incident protons and the thickness of the slice were tuned to get enough statistic with resonable computing time.
Nuclear Stopping Power (Coulomb Interactions)
Following is the results of Nuclear Stopping Power coming from simulations in Geant4 compared with the SR-NIEL results for Coulomb interactions. A variable number (to obtain ~106 displaced atoms) of protons were generated for traversing a slice of Silicon 1μm thick.
Non Ionizing Energy Loss (Coulomb Interactions)
Following is the results of the Non Ionizing Energy Loss (NIEL) coming from simulations in Geant4 compared with the SR-NIEL results for Coulomb interactions. A variable number (to obtain ~106 displaced atoms) of protons were generated for traversing a slice of Silicon 1μm thick. The threshold energy for displacement was set to 21 eV.
References
Geant4: Class G4IonCoulombScatteringModel~(2014).
Class Description: Single Scattering Model for protons, alpha and heavy Ions (Ref.~Boschini et al. 2011), Software Reference Manual
Source Code Version: Geant4 11 (December 2022) avaliable at the website
https://geant4.web.cern.ch/download/all
See also Sections~8.4--8.4.6 of Physics Reference Manual for version 11 available at the website:
https://geant4.web.cern.ch/docs/