Foil Diffuser Investigation with GEANT4
FFoil Diffuser Investigation with GEANT4
Joseph M. Fabritius II, Konstantin Borozdin, Peter WalstromNovember 14, 2018
Abstract
An investigation into the appropriate materials for use as a diffuser foil in electron radiog-raphy was undertaken in GEANT4. Simulations were run using various refractory materials todetermine a material of appropriate Z number such that energy loss is minimal. The plottedresults of angular spread and energy spread are shown. It is concluded that higher Z numbermaterials such as tungsten, tantalum, platinum or uranium could be used as diffuser materials.Also, an investigation into the handling of bremsstrahlung, multiple coulomb scattering, andionization in GEANT4 was performed.
In deciding on the best material for a diffuser foil for increasing the angular spread of the acceleratorbeam in electron radiography, one must take into account four physical phenomena:1. Multiple Coulomb scattering (the desired effect, which increases the angular spread of thebeam). This is mostly due to elastic scattering from nuclei and is approximately describedby the Particle Data Group (PDG) formula 27.14.2. Ionization energy loss and straggling (the part of the energy loss not due to bremsstrahlung)3. Energy loss due to bremsstrahlung4. Melting temperatureChoosing a diffuser foil for electron radiography experiments requires the material must be bothrefractory, that is resistant to melting or deformation under high temperatures, and to also havea low energy spread so that the effects of chromatic blur are lessened. Chromatic blurring effectscan be directly seen in the energy loss of the beam through the material. By choosing a materialwith less energy loss an appropriate diffuser material can be found. To accomplish this task severalelements were chosen from the Particle Data Group table on atomic properties of materials. Thosematerials that were found to have a melting point of over 1400 K were chosen for investigation:carbon (graphite), silicon, iron, tantalum, tungsten, platinum, and uranium.1 a r X i v : . [ phy s i c s . acc - ph ] D ec he optimal material Z was found by first choosing the foil thickness of each refractory materialso that a specified angular spread, θ rms , was achieved. A desired angular spread of 0.2 mRadwas chosen as the reference of comparison between diffuser materials. The diffuser thickness wascalculated using the multiple scattering distribution equation: θ rms = 13 . βcp z (cid:114) xX (cid:20) . xX (cid:21) (1)where βc is the electron speed, z is the particle charge number, x is the thickness of the material,and X is the radiation length of the material. The main material dependence is in the factor (cid:113) xX ,where x is the thickness in g/cm and X is the radiation length, also in g/cm . The above equationwas taken from the PDG journal( pg 290, 27.14) on Multiple scattering through small angles.The simulations for investigating the foil materials were run in GEANT4 using the same codefor previous electron radiography investigations. A pencil beam of 12 GeV electrons was fired at aslab of material with a detector situated just beyond the object for capturing deflected electrons.Secondary particles were ignored in the detector for these simulations. The geometry is shown inthe figure below. Figure 1:
The test simulation geometry. Figure is not to scale.
Using Equation (1), the initial material thicknesses were used for preliminary simulations. Withthese initial simulations the angular distribution of the beam through the diffuser was plotted inROOT to verify the spread was 0.2 mRad. The thickness of the material slab was then incrementallyadjusted until the resulting angular spread was 0.2 ± For each diffuser material, a histogram of the energy loss of the electron beam through the materialwas created. When compared along the same energy range it can be seen that for the lower Zmaterials there is a much larger energy loss, evident in the RMS values shown in the plots below.The peak of the histogram can be seen to decrease as Z number decreases.
Figure 2:
Energy loss histograms plotted for the lower Z materials. The energy scale was focused on the range of11994 MeV to 12000 MeV, with 500 bins. igure 3: Energy loss histograms plotted for the higher Z materials. The energy scale was focused on the range of11994 MeV to 12000 MeV, with 500 bins.
Higher Z materials evidently have less energy loss, and will thus make for better diffusers inelectron radiography as the chromatic blur effects will be lessened than with lower Z. To examinea better comparison of the higher Z materials the energy histograms were replotted in a smallerinterval to focus on the peak area. From the newer energy plots it is apparent that the peaksand RMS values are close enough that there is no appreciable difference and the choice of diffusermaterial will depend on other criteria, such as availability of material in foil form, or secondaryparticle creation. Further investigative studies will be required.4 igure 4:
Energy loss histograms plotted for the higher Z materials. The energy scale was focused on the range of11999 MeV to 12000 MeV, with 500 bins.
Apart from the refractory nature of the material, the three other processes are important in ourinvestigation. The Multiple Coulomb scattering effect is described by Equation (1) above.The deterministic part of the ionization energy loss dEdx ion. (in units of MeV-cm /g) has a some-what more complicated material dependence, including some dependence on the mean ionizationpotential of the material, but the main factor is trend is that dEdx ion. increases as ZA increases. Thisdependence is illustrated by Fig. 5, which is a plot of the minimum dEdx for various elements vs. ZA . Random ionization energy straggling, which is added to the deterministic energy loss, giving aLandau distribution for thin objects, also increases as ZA increases.Bremsstrahlung energy loss is small compared to ionization energy loss for thin foils. In thethick limit, where an electron emits a substantial number of “hard” photons, total bremsstrahlung5nergy loss is proportional to beam energy, i.e. dEdx ≈ E X , where E is the incident energy. However,for typical diffuser foils, we are in the “thin” limit, where the probability of a “hard” bremsstrahlungevent is low (the definition of a hard event is somewhat arbitrary, but it can be taken to be emissionof a photon with an energy of 0.1% of the incident electron energy). Figure 5:
Miniumum ionization dEdx in MeV-cm /g vs. ZA for various materials. The materials in order of increasing ZA are U, W, Be, Cu, Al, and C. The outlier is Be. Using the MCS mean-angle formula and ignoring the log factor, we can write for the foil thick-nesss x foil required to get a certain mean MCS angle θ , x foil = C ( E ) X θ , where C ( E ) is approx-imately material-independent and contains the dependence on the electron energy. On the otherhand, the ionization energy loss distribution for a particular foil thickness x scales roughly as ZA ,so the ionization energy loss in a foil of a particular material with a thickness that gives a specifiedmean scattering angle θ is ∆ E ion ∼ ZA X θ . Since both ZA and X decrease with increasing atomicweight, this favors high-Z diffuser materials, provided that their melting temperature is high.To investigate the dominant effect in electron deflection within the GEANT4 code a simplescheme was developed. Using the same simulation set-up as the diffuser investigation, a simplifiedPhysics List was written that only included the processes G4eBremsstrahlung and G4eMultipleScattering.Simulations consisted of firing 1 million electrons at a 168 µ m slab of tantalum. Three separatesimulations were run with only bremsstrahlung, only multiple Coulomb Scattering, and both pro-cesses active. Histograms of the angular spread were plotted and are presented below. It is obviousfrom the plots that angular deflection is dominated by multiple Coulomb scattering, with electronbremsstrahlung only contributing a small amount to the deflection of the electron as it travelsthrough the tantalum. 6 igure 6: Histograms of angular distribution.
TOP : Both the G4eBremsstrahlung and G4eMultipleScatteringprocesses were active for this simulation.
BOTTOM LEFT : Only the G4eMultipleScattering process was activefor this simulation.
BOTTOM RIGHT : Only the G4eBremsstrahlung process was active for this simulation.
After investigating the angular spread effects of the physical processes in the GEANT4 code wealso wanted to confirm the energy loss effects of those processes. The prior manufactured physicslist was modified to include the G4eIonisation process and simulations were run with all threeprocesses, and with only G4eIonisation active. The results, shown in the figure below, confirmthat the energy loss of the electrons through the tantalum sample is dominated by the ionizationprocess. 7 igure 7:
Histograms of energy loss.
TOP : Only G4eBremsstrahlung active, the majority of electrons( 67.5%) didnot lose energy and passed right through the foil.
BOTTOM : Only G4eIonisation active. This is the dominanteffect on energy loss, as seen when compared to the energy loss diagrams using a full physics list.
We were also curious about the angular dependence of the energy loss from bremsstrahlung inGEANT4. Histograms were created by plotting logarithmic angle versus logarithm of total energyand subtracting the electrons final energy at the detector. The final plot shows there is a correlationbetween energy loss and angle, so another simulation was run using 12 MeV electrons instead of 12GeV electrons to see how the correlation would change or if the relation was a static product of arandom distribution. Both plots are presented below, and it can be seen that the relation becomes8teeper for higher energy particles.
Figure 8:
Histogram of angle distribution versus energy loss for 12 GeV electron beam incident on 168 µ m tantalumslab. Figure 9:
Histogram of angle distribution versus energy loss for 12 MeV electron beam incident on 168 µ m tantalumslab.m tantalumslab.