# Optimization of Transmission X-ray Target for Intense Pulsed Electron Beam Accelerators
## 2 Materials and Methods
### X-ray Conversion Simulation  
For the simulation of electron stopping in matter and photon generation, the Monte Carlo code FLUKA (FLUKtuierende KAskade) [28,29] released by the Conseil European pour la Recherche Nucleaire (CERN) was used. First used for electron accelerator shielding, FLUKA has developed into a general-purpose particle transportation simulation software for over 60 particles and is widely used for radiation shielding [30, 31, 32], dosimetry [33,34], detector design [35, 36, 37], X-ray generation [38, 39, 40], and medical physics [28,41]. To deal with bremsstrahlung, the latest version of FLUKA adopts improved Seltzer and Berger differential cross-sections for the transport algorithm on charged particles and photons, and can handle electron and photon transportation with energy down to 1 keV, obtaining good accuracy for primary electrons with a single scattering algorithm. The graphical user interface Flair [42] further enables fast editing of FLUKA input, visualization of geometry, monitoring of program running, post-processing, and demonstration of simulation results, making FLUKA more easy to use compared with other MC programs. In the MC simulation, the IPEB was simplified as a pencil beam with a radius of 3.5 cm, emitted from \(z=-1\) cm (1 cm of accelerating gap) with the beam center along the \(z\)-axis in the positive direction. The energy spectrum of the IPEB was sampled with the distribution in Figure 2 and compiled into the FLUKA simulation via a Fortran script. The targets in the simulation had a radius of 5 cm with their rear surfaces on the xoy plane with the surface center on the point (0, 0, 0). The xoy plane divided the whole space into two parts, with the \(z<0\) part in the vacuum and the other half in the air, making the rear surface of the target align on the plane of the vacuum-air boundary (Figure 3). The targets were divided into two groups; the first was tungsten and molybdenum targets for the evaluation of X-ray conversion with thicknesses from 0 to CSDA (Continuous Slowing Down Approximation) range estimated with the NIST (National Institute of Standards and Technology) ESTAR database [43]. The CSDA range of tungsten and molybdenum was taken as 155 and 248 \(\upmu\)m, taking their density of 19.26 and 10.28 g/cm\({}^{3}\), respectively. For the analysis of the combination of a conversion layer (tungsten or molybdenum) and a membrane (titanium) X-ray window, tests were made from the thinnest conversion layer at maximum photon emission with a thick titanium window to the thickest conversion layer with a thinnest titanium window of 50 \(\upmu\)m. The use of tungsten was for the verification of the maximum achievable X-ray output, and molybdenum, for its moderate price, also served as a candidate for the X-ray conversion layer. Although beryllium is widely used in X-ray windows, due to its toxicity, the use of beryllium for X-ray windows with a radius of several cm for possible applications such as food and environmental irradiation brings inferiority in safety and maintenance compared with using titanium. For simplicity in modeling, the conversion layer and the titanium window were separated by a plane into  
Figure 2: The normalized energy spectrum of the IPEBs deduced from the diode input voltage. a cylinder. As it is complicated to estimate the CSDA range in a two-layer structure with ESTAR, tungsten and molybdenum targets with the thickness of ESTAR CSDA range were tested with FLUKA and the same criteria, i.e., decreasing the electron fluence by seven orders, were adopted to determine dual-layer target thicknesses. For the tally of the spatial distribution of photon fluence and dose equivalent, considering the model symmetry, the results on the roz plane with a binning resolution of 1 mm in an area of 20 \(\times\) 40 cm\({}^{2}\) were scored. In FLUKA, the dose equivalent was calculated by taking the results from photon fluence and spectrum, with conversion coefficients from ICRP74 [44] and Pelliccioni data [45].