Examples¶
This page shows some examples of a Grasshopper GDML input file.
Example Alpha Particle Energy Loss¶
The world volume consists of Air at 1e-4 atm of pressure. The first red disk is Air at 1 atm and the second red disk is the detector volume made of G4_Si.
Example Beta Particles in Water Transmission¶
The world volume consists of Air at 1e-4 atm of pressure. The first red disk is G4_WATER and the second red disk is the detector volume made of G4_Si.
Example Hand Calculations for 20 Situations¶
5 particles, 2 shields, 2 energies
| ID | Particle | Shield | Energy |
|---|---|---|---|
| 01 | Proton | Water 1cm | 1 MeV |
| 02 | Proton | Water 1cm | 10 MeV |
| 03 | Proton | G4_Fe 1cm | 1 MeV |
| 04 | Proton | G4_Fe 1cm | 10 MeV |
| 05 | Neutron | Water 1cm | 1 MeV |
| 06 | Neutron | Water 1cm | 10 MeV |
| 07 | Neutron | G4_Fe 1cm | 1 MeV |
| 08 | Neutron | G4_Fe 1cm | 10 MeV |
| 09 | Electron | 0.5 Air 1cm | 1 MeV |
| 10 | Electron | 0.5 Air 1cm | 10 MeV |
| 11 | Electron | 1.0 Air 1cm | 1 MeV |
| 12 | Electron | 1.0 Air 1cm | 10 MeV |
| 13 | Alpha | 0.5 Air 1cm | 1 MeV |
| 14 | Alpha | 0.5 Air 1cm | 10 MeV |
| 15 | Alpha | 1.0 Air 1cm | 1 MeV |
| 16 | Alpha | 1.0 Air 1cm | 10 MeV |
| 17 | Gamma | Water 1cm | 1 MeV |
| 18 | Gamma | Water 1cm | 10 MeV |
| 19 | Gamma | G4_Fe 1cm | 1 MeV |
| 20 | Gamma | G4_Fe 1cm | 10 MeV |
Equations used¶
Transmission (Differential Cross Section):
\(I = I_0 e^{-\Sigma(E) x}\)
Use tables,
Parameters:
- c: speed of light
- \(\epsilon_0\): Vacuum permittivity
- beta: the ratio of v to c
- e: electron charge
- m_e: electron mass
| ID | Particle | Shield* | Energy | Stopping Power | Transmission |
|---|---|---|---|---|---|
| 01 | Proton | Water 1cm | 100 MeV | 7.289e0 cm2/g | 6.8e-4 |
| 02 | Proton | Water 1cm | 1 GeV | 2.211e0 cm2/g | 1.1e-1 |
| 03 | Proton | G4_Fe 1cm | 100 MeV | 0.05043 cm2/g | 6.7e-1 |
| 04 | Proton | G4_Fe 1cm | 1 GeV | 0.00157 cm2/g | 9.88e-1 |
| 05 | Neutron | Water 1cm | 1 MeV | ||
| 06 | Neutron | Water 1cm | 10 MeV | ||
| 07 | Neutron | G4_Fe 1cm | 1 MeV | ||
| 08 | Neutron | G4_Fe 1cm | 10 MeV | ||
| 09 | Electron | 0.5 Air 1cm | 100 MeV | 2.41e0 cm2/g | 9.97e-1 |
| 10 | Electron | 0.5 Air 1cm | 1 GeV | 1.46e1 cm2/g | 9.82e-1 |
| 11 | Electron | 1.0 Air 1cm | 100 MeV | 4.82e0 cm2/g | 9.94e-1 |
| 12 | Electron | 1.0 Air 1cm | 1 GeV | 2.91e1 cm2/g | 9.65e-1 |
| 13 | Alpha | 0.5 Air 1cm | 1 MeV | 9.62e2 cm2/g | 3.08e-1 |
| 14 | Alpha | 0.5 Air 1cm | 10 MeV | 2.32e2 cm2/g | 7.53e-1 |
| 15 | Alpha | 1.0 Air 1cm | 1 MeV | 1.92e3 cm2/g | 9.47e-2 |
| 16 | Alpha | 1.0 Air 1cm | 10 MeV | 4.64e2 cm2/g | 5.67e-1 |
| 17 | Gamma | Water 1cm | 1 MeV | ||
| 18 | Gamma | Water 1cm | 10 MeV | ||
| 19 | Gamma | G4_Fe 1cm | 1 MeV | ||
| 20 | Gamma | G4_Fe 1cm | 10 MeV |
- water is liquid state
Additionally the following formula could be used but is unnecessary for these high level estimates.
Energy Loss (Bethe Block Formula)
\(- <\dfrac{dE}{dx}> = \dfrac{4 \pi}{m_e c^2} \dfrac{n z^2}{\beta^2} (\dfrac{e^2}{4 \pi \epsilon_0})^2 [ln(\dfrac{2 m_e c^2 \beta^2}{I(1 - \beta^2)}) - \beta^2]\)