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. Author manuscript; available in PMC: 2021 Apr 7.
Published in final edited form as: Biomed Phys Eng Express. 2019 Jan 24;5(2):025030. doi: 10.1088/2057-1976/aae55f

Design and numerical simulations of W-diamond transmission target for distributed x-ray sources

Praneeth Kandlakunta 1, Allan Thomas 1, Yuewen Tan 1, Rao Khan 1, Tiezhi Zhang 1
PMCID: PMC8026105  NIHMSID: NIHMS1644009  PMID: 33833868

Abstract

Distributed x-ray sources enable novel designs of x-ray imaging systems. However, the x-ray power of such sources is limited by the focal spot power density of the fixed anode. To further improve x-ray output, we have designed and evaluated a diamond-W transmission target for multi-pixel x-ray sources. The target features a thin layer of tungsten deposited on a diamond substrate. The thickness of tungsten layer was optimized for maximum fluence through Monte Carlo simulations. Finite element thermal simulations were performed to evaluate focal spot temperature in the target under different power loadings and dwell duration. The results showed that the optimal thickness of the tungsten layer in the W-diamond transmission target is linearly proportional to the electron energy. A 5–6 μm tungsten thickness is suitable for the kVps ranges from 60 kVp to 140 kVp. A W-diamond transmission target produces up to 20% more x-ray fluence than a traditional W reflection target in the beam center depending on the kVp settings. The x-ray spectrum of the transmission target shows less characteristic x-rays than that of reflection target. The thermal performance of W-diamond targets for peak power is significantly better than that of reflection targets. The maximum focal spot power densities of W-diamond transmission and W reflection targets are both strongly dependent on the dwell duration. For longer pulse durations, the W-diamond target allows as much as a four-fold increase in power and an eight-fold increase in power density in comparison to a traditional W reflection target for the same temperature spikes. The stability of the W-diamond bond needs to be tested experimentally. Nevertheless, the W-diamond transmission target is an appealing target that can significantly simplify the design and improve the performance of distributed x-ray sources.

Keywords: distributed x-ray source, x-ray target material, novel x-ray imaging system

1. Introduction

X-ray imaging is a most common medical imaging modality in radiology, as well as image guided intervention and radiotherapy. The x-ray production in an x-ray tube predominantly takes place through the Bremsstrahlung interaction process, which is highly inefficient. Most of electrons’ kinetic energy is converted to heat, which is deposited in the focal spot, transferred to the anode body and eventually dissipated to the environment. The power of modern x-ray tubes may be as high as 100 kW. Thus heat management is crucially important in x-ray tube design. Figure 1 illustrates the three important steps of heat transfer from the target to the outside environment in an x-ray tube. The heat is conducted from the focal spot to the anode body via thermal conduction and then transferred to the tube housing by both conduction and radiation. Tungsten is the preferred target material in x-ray tubes due to its desirable properties such as high atomic number for Bremsstrahlung production and a high melting point (3422 °C). As a large amount of energy is deposited into a small focal spot volume, traditional x-ray tubes employ a rotating anode to spread the energy to a larger area. High power x-ray tubes have to use a large focal spot size in order to avoid local melting of the target material, thereby sacrificing the image resolution. Besides limiting the image resolution, x-ray tube focal spot power density also limits imaging speed, particularly for stationary anode tubes. Various methods and designs have been explored to overcome some of these limits to current x-ray sources and imaging systems. A MetalJet x-ray source has been developed which uses a high-speed liquid metal as an x-ray target to achieve high x-ray flux (Hemberg et al 2003).

Figure 1.

Figure 1.

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The three key heat transfer steps in an x-ray tube.

Spatially distributed multi-pixel x-ray source (McCollough and Morin 1994, Schmidt et al 2004, Speidel et al 2006, Walker et al 2017, Zhang et al 2005) is an emerging x-ray source technology that may enable the design of novel imaging systems with improved image quality, higher imaging speed and reduced imaging exposure. A tetrahedron beam computed tomography (TBCT) system based on a linear array x-ray source has been proposed to overcome the image quality problems of current cone beam CT systems (Zhang et al 2009). A TBCT benchtop system has been developed with a multi-pixel field emission x-ray (MPFEX) source (Xu et al 2011). Fixed-gantry digital tomosynthesis has also been proposed which does not require any mechanical movement (Maltz et al 2009). An inverse geometry CT system based on a multi-pixel x-ray source has been proposed as well (De Man et al 2007). We recently developed a multi-pixel thermionic emission x-ray (MPTEX) source using oxide cathodes (Kandlakunta et al 2017).

Unlike conventional x-ray tubes with a single focal spot, the total heat of a distributed x-ray source is distributed to a plurality of focal spot positions in distributed x-ray sources. Despite this feature, the total area of the focal spots is still limited. Focal spot power density is still the limiting factor for maximum tube power of distributed x-ray sources. A distributed x–ray source operates in pulse-mode—the x-ray pixels are activated sequentially with a short dwell duration. Oosterkamp described the power limitation of the x-ray target in pulse-mode (Oosterkamp 1948) as,

P=ΔTA2πλρct, (1)

where P is the electron beam power deposited in the focal spot, ΔT is the temperature rise, A is the focal spot area, t is the dwell duration, λ, ρ and c are respectively the thermal conductivity, density, and specific heat of the target material. The maximum power allowed is inversely proportional to the square root of dwell duration.

For rotating anodes, the dwell duration decreases with an increase in anode rotational speed. Although not entirely impossible, development of a multi-pixel x-ray source with a rotating anode is extremely challenging due to its elongated anode geometry. Distributed x-ray sources may reduce dwell duration t by increasing the scanning speed; however, the x-ray detector speed limits the maximum practical source scanning speed. For rotating anode x-ray sources, the x-ray focal spot remains in the same position, thus the detector integration time is independent of the anode rotation speed. For distributed x-ray sources, the data of each x-ray pulse (pixel) must be differentiated as it represents sampling at different spatial positions. Modern CT detectors can be read out at roughly 10 000–20 000 samples per second (ANALOG DEVICES, Detection Technology, Precision Measurement Technologies, Speidel et al 2015). It limits the minimum dwell duration to about 50 μs for distributed x-ray sources when CT detector is used. The flat panel imager has a much lower read out speed, thus will impose a severe constraint on the power of distributed x-ray sources.

An alternative approach to increase the focal spot power density is to enhance the thermal performance of the x-ray target material. According to equation (1), the power of an x-ray source is proportional to the square root of the thermal conductivity of the target material. Diamond has the highest thermal conductivity (2200 W mK−1) among all known materials (Olson et al 1993, Onn et al 1992, Slack 1973, Wei et al 1993). Since the low atomic number carbon atoms of diamond are inefficient in x-ray production, a thin layer of tungsten can be deposited on the diamond substrate to improve x-ray production efficiency. Alternatively, one can grow diamond on a tungsten substrate.

Because the tungsten layer is very thin and diamond is almost transparent to x-ray, the W-diamond can be used as transmission target instead of reflective target. There are several advantages of transmission target for distributed x-ray sources: (1) A transmission target can simplify the geometry design as the x-ray beam comes out of the tube on the opposite side of the cathodes. On the other hand, the x-ray beam from reflection targets comes out between the cathode and the anode where space is usually very limited, in turn limiting the maximum field size; (2) As electrons strike the target, there is a significant amount of electrons scattered back to the vacuum after bombarding the target. These back-scattered electrons may add a long tail to the focal spot when they return and strike the target again. In the transmission target design, the x-rays generated by back-scattered electrons are largely absorbed by the anode body; (3) Transmission targets produce a desirable symmetric x-ray fluence profile with maximum fluence at the center of the field, whereas reflection targets procure asymmetric intensity due to the ‘heel-effect’; (4) Transmission target has symmetric focal spot shapes across the field with smaller spot size in the field center. The reflection targets have asymmetric projected focal spot sizes with smaller spot at the edge of the field.

Despite these advantages, a transmission target is difficult to be utilized in high power tubes due to its limited mechanical strength that prohibits its use on rotating anode. Distributed x-ray sources employ fixed anodes thereby transmission target is a possible option. For example, the Scanning Beam Digital x-ray (SBDX) source employed transmission target with a thin layer of tungsten integrated with a beryllium plate (Speidel et al 2006). In this study, we designed and optimized a W-diamond transmission target design using Monte Carlo (MC) and finite element thermal simulations.

2. Methods and materials

2.1. Design of W-diamond transmission target

The transmission target consists of a thin tungsten film deposited on a ~2 mm thick diamond substrate brazed on a copper or graphite base. Its high thermal conductivity supports fast heat removal from the target and its low atomic number results in negligible attenuation of x-ray produced in the W layer. Figure 2(a) illustrates the cross-sectional view of the transmission target geometry corresponding to a single x-ray source pixel in a distributed x-ray source array. For comparison, a reflection target is also shown in Figure 2(b). The copper base of the transmission target not only allows fast heat removal from the target, but it also provides collimation to produce cone or fan-shaped beams. With primary collimation close to the target, it is possible to develop a multi-pixel x-ray source with fine pixel spacing.

Figure 2.

Figure 2.

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Schematic of the cross-section of (a) W-diamond transmission target made of a thin tungsten layer deposited on a diamond substrate brazed on a copper base, (b) conventional reflection target made of a thick tungsten slab embedded in copper base.

2.2. Monte Carlo (MC) simulations of energy deposition

Electrons impinging on the target at the focal spot gradually lose their energy at various depths in the target. To accurately model the energy deposition for thermal analysis, we performed MC radiation transport simulations using the Geant4 simulation toolkit (Allison et al 2006, Amako et al 2005). Energy depositions of 80 keV, 100 keV and 120 keV electrons were obtained as a function of depth in tungsten target.

2.3. Monte Carlo simulation of x-ray fluence and spectrum

The MC model of the x-ray source with a transmission target consists of a monoenergetic electron beam striking the W-diamond composite target in a 1 × 1 mm2 focal spot area perpendicularly. The x-ray fluence was recorded in a detector positioned at a distance of 3 cm from the focal spot. The geometrical setup of the Geant4 MC model is shown in Figure 3(a). MC simulations were performed for different thicknesses of the tungsten target, while the thickness of diamond was kept at 2 mm.

Figure 3.

Figure 3.

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Geometries used in the MC models to simulate (a) W-diamond transmission target and (b) conventional reflection W target (the fluence detector is tilted to account for the anode angle. A 3 mm filter was placed in front of the detector to mimic filtration by the vacuum envelope of a physical x-ray tube.

For comparison, a reflection target was also modeled by MC simulation. Figure 3(b) shows the Geant4 MC model of the reflection target. The x-ray fluence is scored for a 15° anode angle 3 cm away from the focal spot. Due to the anode angle, the cross-section of the electron beam and the physical focal spot size change to a 1 × 2 mm2 area so that reflection target will have about the same projected focal spot as the transmission target. For both reflection and transmission target models, a 3 mm aluminum (Al) layer was used as a low-energy x-ray absorber to filter out low energy x-ray photons that will not exit the vacuum chamber of a physical x-ray tube.

The x-ray fluence generated by the transmission target is expected to increase with the thickness of tungsten until all electrons are stopped. On the other hand, the self-absorption of the tungsten target also increases with the thickness of tungsten. Thus, the x-ray fluence of the transmission target will reach a maximum at a particular thickness for a given electron beam energy. MC simulations were performed for electron energies in the range of 40–140 keV and x-ray fluences for different thicknesses of the tungsten target were calculated. On the other hand, the thickness of the reflection target has no effect on x-ray fluence, therefore only a 5 mm thick W target was modeled. X-ray spectra of the transmission target were compared with that of the reflection target. Additionally, angular fluence profiles from the transmission and reflection targets were also determined for both models. Fluence profiles were generated for the W-diamond transmission target with various tungsten thicknesses.

2.4. Finite element transient thermal simulation of target temperature

To evaluate the focal spot power density limitation, finite element thermal simulations were performed to study the focal spot temperature and heat dissipation rate. Finite element models of the W-diamond transmission target and W reflection target were built using COMSOL Multiphysics Finite Element Analysis (FEA) software (COMSOL, Inc. Burlington, MA, USA). The FEA model of the W-diamond target comprises a 5 μm tungsten target and 2 mm thick diamond substrate on a copper base as shown in Figure 2(a). The focal spot was modeled as a multilayer heating element with the powers as a function of depth generated by the MC simulation. A focal spot area of 1 × 1 mm2 was assumed in all the simulations of the transmission target. Only one-fourth of the actual volume was modeled to take advantage of the symmetry in the target geometry and reduce computation time.

The temperature dependence of tungsten’s thermal conductivity and specific heat (Bergman and Incropera 2011) were included in the material model. The temperature of the top and bottom surfaces of the copper base were kept constant at 373 K as the boundary condition assuming the tube is water cooled. The focus of the thermal simulations was evaluating only the peak power, which is limited by the focal spot power density. The boundary condition is supposed to have a negligible effect on the maximum temperature of focal spot due to the large distance of the small focal spot from the boundary. Thus, the determination of maximum x-ray power allowable for a given pulse duration is not affected. Transient thermal simulations were performed with different incident electron beam energies as the pulse-width varied from 50 μs to 3 ms. The resulting transient temperature distributions of the x-ray focal spot at different pulse widths and powers were calculated. The maximum allowed tube power keeping the target temperature spikes under 3000 °C for a given pulse duration were determined.

A spatially distributed x-ray source may employ large number of electron emitters, from ten’s to hundred’s or even higher, to generate the same number of focal spots on an elongated target. The number of focal spots determines the target duty-cycle. For a distributed source with for example, 50 focal spots, each cathode has 1/50 = 2% duty cycle.

3. Results

3.1. Energy deposition in the target

The penetration of 80, 100 and 120 keV electrons and their energy deposition as a function of depth in tungsten were modeled using MC simulations. The results are shown in figure 4. The maximum range of 120 keV electrons in tungsten is less than 8 μm, which is about half of their continuously slowing down approximation (CSDA) range. Furthermore, as shown in figure 4 (right), most of the electron energy is deposited within the first few microns of the tungsten target material.

Figure 4.

Figure 4.

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Left: The trajectories of 120 keV electrons in a 10 μm tungsten target. Right: Geant4MC results of energy deposition as a function of depth for 80, 100 and 120 keV electrons.

3.2. Characteristics of x-ray beam produced by W-diamond transmission target

Figure 5 plots x-ray fluence (a) and energy fluence (b) produced by a W-diamond transmission target as a function of tungsten thickness. As expected, x-ray fluence first increases to a maximum point and then decreases owing to self-absorption by the tungsten target material. The energy fluence follows the same trend. Figure 6 shows the thickness of tungsten that produces maximum x-ray fluence for different energies. The optimal thickness increases almost linearly with electron energy. Our simulation results are comparable to the results reported in literature (Nasseri 2016).

Figure 5.

Figure 5.

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(a) Transmission x-ray fluence from the W-diamond target as a function of tungsten thickness recorded for different electron beam energies, (b) Energy fluence of transmission x-rays from the W-diamond target as a function of tungsten thickness recorded for a 120 keV electron beam energy.

Figure 6.

Figure 6.

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Optimal thickness of the W layer for a W-diamond transmission target as a function of electron beam energy.

An x-ray system may employ different accelerating voltage (kVp) settings in clinical imaging based on the size of the subjects. The kVp setting used for imaging humans usually ranges from 60–140 kVp. If we define 100% efficiency when the x-ray fluence is maximized for a specific energy, the efficiency will reduce when the energy is changed. The normalized efficiencies of 1–11 μm tungsten targets for transmission fluence were evaluated at different electron energies and the results are plotted in figure 7. A tungsten thickness of 5–6 μm appears to be acceptable for the energy range within 60–140 keV, for which the x-ray fluence remains above 80% of its maximum value.

Figure 7.

Figure 7.

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Normalized efficiency of the transmission target of tungsten thicknesses from 1 to 11 μm for transmission fluence at different electron beam energies. Fluence efficiency is defined as the ratio of x-ray fluence at a given thickness to the maximized fluence (at optimal thickness) for a specific electron energy.

Figure 8 compares the photon spectra produced by bombarding 120 keV electrons on a 5 μm W-diamond transmission target and a 5 mm thick reflection target. Both x-ray beams are filtered by a 3 mm aluminum filter. The results indicate that the Bremsstrahlung component of the transmission target is about 20% higher than that of the reflection target. However, the characteristic x-ray peaks of the transmission target are significantly lower when compared to the reflection target. The lower characteristic x-ray component can be attributed to the energy threshold of characteristic x-ray production. Characteristic x-rays are generated only in the first few microns of tungsten, after which the electrons do not have sufficient energy for characteristic x-ray production. Thus, although the total numbers of characteristic x-ray photons are the same in transmission and reflection targets, they are absorbed more in the transmission target since they must pass through more tungsten layers to contribute to the x-ray fluence. Nevertheless, the total integral fluence of high energy x-rays is still higher for the transmission target, even with the additional 2 mm diamond filter.

Figure 8.

Figure 8.

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X-ray spectra of 5 μm thick W-diamond transmission and 5 mm thick W reflection targets. Both targets are bombarded with 120 keV electrons and filtered by a 3 mm aluminum layer.

Figure 9 plots the angular distribution of the x-ray fluence relative to the target surface. Overall, the fluence is more uniform for the reflection target, as expected. However, the fluence of the reflection target at its central axis cannot be utilized. X-ray tubes with a reflection target usually have a small anode angle; therefore, only the fluence at large angles (close to 90 degree in Figure 9) can be utilized. Such a fluence distribution exhibits the classical heel effect. The transmission target, on the other hand, can utilize the photons along the central axis where the fluence is maximal. Although the flat region of its fluence is smaller compared with the reflection target, this would not impose a problem for x-ray imaging as only a small angular window is used in x-ray systems. The results indicate that for a 120 kVp beam the W-diamond transmission target with a 5–6 μm W layer can produce ~20% higher fluence than a reflection target with the same tube power.

Figure 9.

Figure 9.

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Angular dependent x-ray fluence profiles from W-diamond transmission targets with different W thicknesses and a W reflection target for a 120 keV electron beam.

3.3. Transient thermal simulations

In transient thermal analysis, the focal spot was modeled as laminated heating elements. The power of each heating element layer was assigned as a function of depth based on the MC results of section 3.1. The finite element contains only 1/4th of the anode to take advantage of the symmetry of the geometry. Figure 10 shows (a) schematic drawing of the transmission target model used in the COMSOL simulations (b) the temperature distribution of the transmission target by a 3 ms pulse with a power of 11 kW (120 kV and 91.7 mA) and (c) the temperature distribution for the same settings in the x-y plane of the target. The maximum temperature is observed at the center of the focal spot as expected. The temperature decreases quickly outside the focal spot and the gradient is very slow in the copper base.

Figure 10.

Figure 10.

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(a) Schematic drawing of the transmission target model used in COMSOL simulations. The FEA model contains only ¼ of transmission target to take advantage of the symmetry (b) Temperature distribution near the focal spot on the W-diamond transmission target surface for a 3 ms, 11 kW beam calculated using COMSOL (c) Temperature distribution in the x-y plane of the target for a 3 ms, 11 kW beam.

Figures 11 (a) and (b) show the temperature history of the focal spots for W-diamond transmission and W reflection targets, respectively. The focal spot size of the transmission target and reflection target are 1 × 1 mm2 and 1 × 2 mm2, respectively. The electron beam powers used are 11 kW for the transmission target and 1.9 kW for the reflection target—recall that these powers were chosen based on limiting the maximum temperature for the focal spot to 3000 °C. For the transmission target, the focal spot temperature rises very fast from 20 °C to 2500 °C during the first 0.5 ms, but later slowly reaches 3000 °C in 3 ms resulting in a plateau. This plateau in the temperature curve results from the equilibrium state of heat transfer. When the temperature gradient is high enough, the heat deposition may equal the heat removal so that temperature does not increase any further.

Figure 11.

Figure 11.

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Variation of the maximum focal spot temperatures with time during a 3 ms pulse (2% duty cycle) of (a) 11 kW electron beam power for the W-diamond transmission target and (b) 1.9 kW electron beam power for the W reflection target.

When the electron beam is turned off, the temperature drops rapidly to 280 °C in 5 ms. At the end of the 150 ms pulse cycle (assuming a 2% duty cycle i.e. pulse repetition rate of 6.67 Hz), that is, before the start of next pulse, the temperature drops to 67 °C. This indicates that pulse mode operation of the tube will enable faster dissipation of heat with a low duty cycle. Therefore, the beam power allowable during the pulse duration may be kept significantly high for short pulse widths. For the reflection target, the temperature curve rises almost continuously and does not result in a plateau like that seen with the W-diamond transmission target. The focal spot temperature also decreases rapidly within 150 ms.

To keep the W-diamond target temperature spike under 3000 °C, the maximum powers allowed for different pulse widths were obtained and plotted in figure 12. The maximum power is greatly affected by the pulse width. When the pulse width increased from 50 μs to 3 ms, the maximum power is reduced from 22 kW to 11 kW for the transmission target. Hence, in order to achieve high tube output, x-ray sources with a stationary anode must run with short pulse widths. The simulation also predicts that more than 22 kW peak power may be achievable for pulse widths smaller than 50 μs. For comparison, the same study was also performed for a 5 mm thick W reflection target with a focal spot size of 1 × 2 mm2. The reflection target exhibits a similar trend. However, the maximum beam power loading is only 14 kW for 50 μs dwell duration compared with 22 kW for the W-diamond target. The difference in maximum powers between the two target types is even larger for longer pulses. When the pulse width is longer than 1 ms, the maximum power of the W-diamond transmission target can be four times higher than the reflection target. Figure 12 also plots the maximum power given by equation (1), which agrees with the FEA results for the reflection target. The slight differences between the results may be due to the nonlinear thermal conductivity and specific heat used in the simulation model.

Figure 12.

Figure 12.

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Maximum tube power calculated as a function of pulse width for the W-diamond transmission target and a conventional W reflection target. Analytical calculations (equation (1)) for the reflection target are also included for comparison.

4. Discussion

In this study, we have demonstrated the advantages and characteristics of W-diamond transmission target for distributed x-ray sources. There are many approaches to develop W-diamond targets. Chemical vapor deposition (CVD) techniques have been used to grow diamond on various substrates. CVD has shown to achieve diamond thicknesses on the order of few mm with a high growth rate (Tallaire et al 2006, Yan et al 2002). The temperature of the substrate for growing diamond is kept above 700 °C to enhance the growth of diamond crystals while suppressing the growth of graphite. Apart from silicon, molybdenum and tungsten are widely used as substrate materials where a localized carbide layer of a few nm can be formed. Diamond crystals can be grown on diamond and non-diamond substrates like copper, gold, silicon or tungsten by chemical transport in a closed system. Substrates made up of carbides such as SiC, WC and TiC are particularly suitable for diamond deposition (May 2000).

In this work, we optimized W-diamond transmission target via thorough MC and transient FEA thermal simulations. The results indicate that a 5–6 μm thick tungsten layer will have the optimal x-ray production efficiency for the energy range within 60–140 kVp. Additionally, the W-diamond transmission target may produce ~20% more x-ray fluence in central axis for the same power compared with a traditional W reflection target. The maximum power that keeps the focal spot temperature below the melting point is strongly dependent on the pulse duration. For pulse widths of a few ms, the power allowed by the W-diamond transmission target can be about four times higher than the traditional W reflection target. Thus, the composite transmission target design may allow significant improvement in the output of multi-pixel x-ray sources. As an example, the power density limit of the 1 mm × 1 mm focal spot for the transmission target when the source operates with 50 μs pulses is as high as 22 kW mm−2. And even though the physical focal spot size of the reflection target is larger than the projected focal spot due to the anode angle, the transmission target can still achieve up to four times higher power despite its focal spot area only being half that of the reflection target.

The simulation study is based on an ideal situation where the thermal resistances between the W-diamond and diamond-anode body are ignored. The high temperature gradient may cause stress in the W film. W and diamond both have low thermal expansion coefficients, and the focal spot size is very small. Thus W-diamond targets obtained by PVD or CVD techniques may have sufficient adherence to maintain its integrality duration operation. The durability of the W-diamond target needs to be investigated experimentally.

Graphitization may happen in vacuum when diamond temperatures is higher than 2100 °C. However, the diamond-graphite phase transition usually took at least several seconds or minutes (Davies and Evans 1972). A TBCT as well as other imaging system with distributed x-ray sources operates in pulse-mode. The transient thermal simulation indicates that the duration that diamond temperature above 1000 °C is less than 3 ms, which may be too short for graphitization. This expectation should be validated experimentally too.

Besides phase stability, the mechanical strength between the W film and diamond substrate needs to be tested experimentally. The temperature spikes of the focal spots may cause thermal stress in the W-diamond bond. Moreover, the local heating with a short duration can induce acoustic vibrations, which could expand a small crack in the substrate into a fatal damage, especially in the case of high-repetition rate. This is similar to a rotating anode, where the same tungsten target is heated up with very high repetition rate. A fixed anode of distributed x-ray source does not suffer the same high centrifugal force as a rotating anode. We are currently performing experimental study to test the stability of W-diamond target.

MC simulations showed that transmission targets produce less characteristic x-rays than the reflection target. We attribute this effect to the energy threshold of characteristic x-ray production. The characteristic x-rays are generated within the first couple of microns of the tungsten target and are attenuated by the tungsten layers afterward. This result suggests that transmission target may not be optimal for the x-ray sources that characteristic x-rays are important for, for example the x-ray source for mammography systems.

5. Conclusion

MC and finite element thermal simulations were performed to optimize a W-diamond transmission target and evaluate its performance. The results showed that the optimal thickness of the tungsten layer in the W-diamond transmission target is linearly proportional to the electron energy, which agrees with the study of Nasseri et al for W-Be target (Nasseri 2016). A 5–6 μm tungsten thickness is suitable for the kVps ranges from 60–140 kVp. A W-diamond transmission target produces at least the same or 20% more x-ray fluence than a traditional W reflection target in the beam center depending on the kVp settings. The thermal performance of W-diamond target is significantly better than reflection target. The maximum focal spot power densities of W-diamond transmission and W reflection targets are both strongly dependent on the dwell duration. For longer pulse durations, the W-diamond target allows as much as a four-fold increase in power and an eight-fold increase in power density in comparison to a traditional W reflection target for the same temperature spikes. Despite the favorable performance given by this simulation study, the mechanical and metallurgical satiability of W-diamond target should be investigated experimentally.

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