Introduction Temperature modeling using Finite Element Analysis (FEA) is widely used by particle beam-line designers as a useful tool to determine the thermal performance of an irradiated target system. A comparison study was performed between FEA calculated temperatures on platinum with experimental results using direct thermocouple measurements. The aims are to determine the best beam model for future solid target design, determine the maximum target current for different target materials and the temperature tolerance for any modification to our existing solid targetry system. Material and Methods The theoretical temperature of the target sys-tem was determined using SolidWorks 2013 with Flow Simulation Analysis (FSA) module. The FSA module determines the maximum temperature inside the target material given the global conditions (material specification, flow rates, boundary conditions, etc.) for a given target current. The proton beam was modeled as a volumetric heat source inside the target material based on the distribution of energy loss in the material along the beam axis. The method used by Comor, et al1 was used in this study. The method segmented the target material into five individual layers, each layer being 50 m thick. The energy lost per layer was calculated using SRIM3 and converted into the power lost per layer. A thickness of 250 μm of platinum completely stops the impinging proton beam at 11.5 MeV with the highest deposition of power per layer corresponding to the Bragg peak. The target material used in the simulation reflects the physical target disk used for temperature measurements (platinum, dia. 25.0 mm, thickness 2.0 mm) with two K-type thermocouples (dia. 0.5 mm, stainless steel sheath) embedded in the platinum disk. One thermocouple is located in the geometric center, while the other is located at a radial position 8 mm from center. The outer thermocouple is to determine the peripheral temperature near the o-ring seal. Temperature was maintained below the melting point for the material (Viton®, melting point 220 °C) during the irradiation to ensure the integrity of the water cooling system. The solid targetry system used in this study is an in-house built, significantly modified version2 of a published design1. The solid target system is mounted onto an 18/18MeV IBA Cyclotron with dual ion source, on a 300mm beam-line with no internal optics or steering magnets. A graphite collimator reduces the beam to 10mm in diameter and a degrader is used to reduce the proton beam energy to 11.5 MeV, considered suitable for production of radiometal PET isotopes 89Zr and 64Cu. Temperature was measured with and without the 300 mm beam-line to compare the effects of beam divergence on the solid target (FIGS. 1 and 2). The experiment was conducted using both H− ion sources with different ion-to-puller extraction gaps (ion source 1 is 1.55 mm with ion source 2 at 1.90 mm). The setting of the ion-to-puller gap changes the focusing of the accelerated beam inside the cavity. Results and Discussion The segmented beam model was used to calculate the temperature on and within the target, as well as the maximum temperature of the bulk material. The first segment is the leading segment of the material irradiated by the incident proton beam. Results are shown in TABLE 2. Target temperatures were measured experimentally under two different conditions; target attached at the end of a 300mm beam-line and target attached directly to the cyclotron. The temperature was measured experimentally using the platinum disk with 2 thermocouples inside the bulk target material irradiated on the end of a 300mm beam-line. The measured temperature is shown in TABLE 2. The variation between ion source 1 and 2 for the temperature measured in the center was 11–15 %, while the variation on the radial position was 2–6 %. A smaller ion-to-puller extraction distance (ion source 1) reduces the cross-sectional area of the accelerated beam; the consequent high proton current density (10mm diameter collimated beam) increases the temperature inside the bulk material for a fixed target current. The highest observed radial temperature was 93 °C, with target current of 50 μA using ion source 1. This is well below the melting point for the o-ring seal. The temperature measured experimentally using the same platinum disk with no beam-line is shown in TABLE 4. A temperature difference of up to 7 % was measured between ion source 1 and 2 at the exit port without the beam-line, while the maximum variation on the radial position was 3 %. A comparison between the calculated theoretical and measured temperatures is shown in FIGS. 3 to 6. The temperatures calculated by the FEA model underestimate the temperature regardless of target position (with or without the beam-line) and for both ion sources. The temperature difference between the FEA model and the experimental results increases with increasing target currents. As shown in Figure 3, at the target center the FEA model underestimated the temperature by 22–32 % for ion source 1 and 13–22 % for ion source 2. This is consistent with the difference between the two ion sources due to the difference in the ion-to-puller gap size. With the target mounted at the exit port the theoretical and measured temperature for the center of the platinum disk is shown in FIGURE 4. The FEA model underestimates the temperature at the center of the platinum disc by 2–10 % for both ion sources. As shown with the previous experiment, the margin of error increases with increasing target current. Comparison between FIGS. 3 and 4 shows the measured temperature at the center of the platinum disk is significantly lower when the target is attached to exit port of the cyclotron. Localised area of high current density (hot spots) is not registered as higher temperature in the bulk material. True temperature inside the bulk material is highly dependent on the thermal conductivity of the target material and the resolution of the thermocouple. The cross-sectional area of the beam ‘hot-spot’ will be greater due to beam divergence at the end of the beam line compared with the exit port. The ‘hot’ area of the expanded beam becomes a significant portion of the overall collimated beam (collimator dia. 10.0 mm). A more uniform beam profile (less heterogeneity) evenly distributed the area of high current density across the disk surface, effectively increasing the temperature of the bulk material while decreasing the sensitivity required to measure the true temperature. As observed from this comparative study it appears that a more homogeneous current density leads to a higher temperature measurement at the target center. With the solid target at the end of the beam-line, target current lost on the collimator and beam-line was >55%. The effect of beam divergence is clearly observed in TABLE 5. With the target mounted directly at the exit port the current lost was reduced to < 40 %. Although the average proton current density is the same for any set target current, irrespective of target position, the contribution of the peripheral beam to the total target current should not be underestimated. A loss of ~40 μA on the collimator and beam-line places greater reliance on the center of the ‘hot’ beam to maintain the same target current. The temperature at the radial position (FIG. 5) observes the same trend as for the temperature measured in the center. The error increases for higher target currents and the FEA model underestimated the temperature by 19–40 %. The error at this location is due partly to the model’s assumption of a uniform heat source, applied to the material on a single axis (perpendicular to the material surface) and does not account for any scattering or divergence of the incident proton beam. FIGURE 6 shows that the FEA model underestimated the radial temperature by 16–37 %, when the target is connected to the exit port, for reasons discussed previously. Comparison with FIG. 5 (target on the beam-line) shows the same margin of error between the FEA and the experimental results (19–40 %). The temperature difference between the FEA model and measured temperature at the radial position is independent of the beam profile and beam divergence. The FEA model underestimated the temperature at the radial location with or without the beam-line and for both ion sources. The significance difference in temperature between the FEA model and the experimental is due to our model assumption that the maximum radial temperature is on the irradiated surface and not inside the material corresponding to the layer with the maximum energy lost. In addition, the FEA model does not ac-count for the divergence of the proton beam as it travels through the material. Given the temperature at 50 μA target current is > 90 °C (TABLES 3 and 4) we have capped the experi-ment below this point to prevent any damage the o-ring seal. Conclusion The segmented FEA model was inadequate in determining the temperature for the target at the end of a 300mm beam-line (> 30 % difference). A combination of beam divergence and greater uniform coverage of high current density beam resulted in a higher than predicted temperature reading. However, the segmented FEA model provides a good estimation (< 10 % difference) for the observed temperature of the bulk material at the exit port. The simplistic FEA model was unable estimate the temperature at the radial position (~ 40 % difference) regardless of ion source or target position. A comparison between the two ion sources with different ion-to-puller extraction gap, leading to different focusing of the accelerated beam yield minimal temperature difference. Although a 15% difference was observed between the ion sources at the end of the beam-line, a major contributing factor is beam divergence beyond the magnetic field rather than the beam size of the accelerated beam. Further studies are underway to determine the beam profile (quantitatively using radiographic film), quantify the contribution of the peripheral beam to the total beam current by comparing different size collimators and to investigate other FEA models by applying different beam models (heterogeneous and homogeneous beam) and different heat sources (surface vs. volumetric). Currently the RAPID Lab solid targetry is placed at the end of the beam-line for easy loading and unloading, since multiple target irradiations are performed per month2. However, RAPID is presently developing a new solid targetry sys-tem which eliminates the need for a beam-line and will be able to manage a maximum extracted target current of 150 μA.

The increased interest in the use of light ion therapy is due to the high dose conformity to the target and the dense energy deposition along the tracks resulting in increased relative biological effectiveness compared to conventional radiation therapy. In spite of the good clinical experience, fundamental research on the characteristics of the ion beams is still needed in order to be able to fully explore their use. Therefore, a Monte Carlo track structure code, KITrack, simulating the transport of electrons in liquid water, has been developed and used for calculation of parameters of interest for beam characterization. The influence of the choice of the cross sections for the physical processes on the electron tracks has also been explored. As an alternative to Monte Carlo calculations a semi-analytical approach to calculate the radial dose distribution from ions, has been derived and validated. In advanced radiation therapy, accurate characterization of the beams has to be complemented by comprehensive radiobiological models, which relate the dose deposition into the cells to the outcome of the treatment. The second part of the study has therefore explored the influence of heterogeneity in the dose deposition into the cells as well as the heterogeneity in the cells sensitivity to radiation on the probability of controlling the tumor. Analytical expressions for tumor control probability including heterogeneous dose depositions or variation of radiation sensitivity of cells and tumors have been derived and validated with numerical simulations. The more realistic case of a combination of these effects has also been explored through numerical simulations. The MC code KITrack has evolved into an extremely useful tool for beam characterization. The tumor control probability, given by the analytical derived expression, can help improve radiation therapy. A novel anisotropy index has been proposed. It is a measure of the absence of isotropy and provides deeper understanding of the relationship between beam quality and biological effects. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.</p>

Introduction Temperature modeling using Finite Element Analysis (FEA) is widely used by particle beam-line designers as a useful tool to determine the thermal performance of an irradiated target system. A comparison study was performed between FEA calculated temperatures on platinum with experimental results using direct thermocouple measurements. The aims are to determine the best beam model for future solid target design, determine the maximum target current for different target materials and the temperature tolerance for any modification to our existing solid targetry system. Material and Methods The theoretical temperature of the target sys-tem was determined using SolidWorks 2013 with Flow Simulation Analysis (FSA) module. The FSA module determines the maximum temperature inside the target material given the global conditions (material specification, flow rates, boundary conditions, etc.) for a given target current. The proton beam was modeled as a volumetric heat source inside the target material based on the distribution of energy loss in the material along the beam axis. The method used by Comor, et al1 was used in this study. The method segmented the target material into five individual layers, each layer being 50 m thick. The energy lost per layer was calculated using SRIM3 and converted into the power lost per layer. A thickness of 250 μm of platinum completely stops the impinging proton beam at 11.5 MeV with the highest deposition of power per layer corresponding to the Bragg peak. The target material used in the simulation reflects the physical target disk used for temperature measurements (platinum, dia. 25.0 mm, thickness 2.0 mm) with two K-type thermocouples (dia. 0.5 mm, stainless steel sheath) embedded in the platinum disk. One thermocouple is located in the geometric center, while the other is located at a radial position 8 mm from center. The outer thermocouple is to determine the peripheral temperature near the o-ring seal. Temperature was maintained below the melting point for the material (Viton®, melting point 220 °C) during the irradiation to ensure the integrity of the water cooling system. The solid targetry system used in this study is an in-house built, significantly modified version2 of a published design1. The solid target system is mounted onto an 18/18MeV IBA Cyclotron with dual ion source, on a 300mm beam-line with no internal optics or steering magnets. A graphite collimator reduces the beam to 10mm in diameter and a degrader is used to reduce the proton beam energy to 11.5 MeV, considered suitable for production of radiometal PET isotopes 89Zr and 64Cu. Temperature was measured with and without the 300 mm beam-line to compare the effects of beam divergence on the solid target (FIGS. 1 and 2). The experiment was conducted using both H− ion sources with different ion-to-puller extraction gaps (ion source 1 is 1.55 mm with ion source 2 at 1.90 mm). The setting of the ion-to-puller gap changes the focusing of the accelerated beam inside the cavity. Results and Discussion The segmented beam model was used to calculate the temperature on and within the target, as well as the maximum temperature of the bulk material. The first segment is the leading segment of the material irradiated by the incident proton beam. Results are shown in TABLE 2. Target temperatures were measured experimentally under two different conditions; target attached at the end of a 300mm beam-line and target attached directly to the cyclotron. The temperature was measured experimentally using the platinum disk with 2 thermocouples inside the bulk target material irradiated on the end of a 300mm beam-line. The measured temperature is shown in TABLE 2. The variation between ion source 1 and 2 for the temperature measured in the center was 11–15 %, while the variation on the radial position was 2–6 %. A smaller ion-to-puller extraction distance (ion source 1) reduces the cross-sectional area of the accelerated beam; the consequent high proton current density (10mm diameter collimated beam) increases the temperature inside the bulk material for a fixed target current. The highest observed radial temperature was 93 °C, with target current of 50 μA using ion source 1. This is well below the melting point for the o-ring seal. The temperature measured experimentally using the same platinum disk with no beam-line is shown in TABLE 4. A temperature difference of up to 7 % was measured between ion source 1 and 2 at the exit port without the beam-line, while the maximum variation on the radial position was 3 %. A comparison between the calculated theoretical and measured temperatures is shown in FIGS. 3 to 6. The temperatures calculated by the FEA model underestimate the temperature regardless of target position (with or without the beam-line) and for both ion sources. The temperature difference between the FEA model and the experimental results increases with increasing target currents. As shown in Figure 3, at the target center the FEA model underestimated the temperature by 22–32 % for ion source 1 and 13–22 % for ion source 2. This is consistent with the difference between the two ion sources due to the difference in the ion-to-puller gap size. With the target mounted at the exit port the theoretical and measured temperature for the center of the platinum disk is shown in FIGURE 4. The FEA model underestimates the temperature at the center of the platinum disc by 2–10 % for both ion sources. As shown with the previous experiment, the margin of error increases with increasing target current. Comparison between FIGS. 3 and 4 shows the measured temperature at the center of the platinum disk is significantly lower when the target is attached to exit port of the cyclotron. Localised area of high current density (hot spots) is not registered as higher temperature in the bulk material. True temperature inside the bulk material is highly dependent on the thermal conductivity of the target material and the resolution of the thermocouple. The cross-sectional area of the beam ‘hot-spot’ will be greater due to beam divergence at the end of the beam line compared with the exit port. The ‘hot’ area of the expanded beam becomes a significant portion of the overall collimated beam (collimator dia. 10.0 mm). A more uniform beam profile (less heterogeneity) evenly distributed the area of high current density across the disk surface, effectively increasing the temperature of the bulk material while decreasing the sensitivity required to measure the true temperature. As observed from this comparative study it appears that a more homogeneous current density leads to a higher temperature measurement at the target center. With the solid target at the end of the beam-line, target current lost on the collimator and beam-line was >55%. The effect of beam divergence is clearly observed in TABLE 5. With the target mounted directly at the exit port the current lost was reduced to < 40 %. Although the average proton current density is the same for any set target current, irrespective of target position, the contribution of the peripheral beam to the total target current should not be underestimated. A loss of ~40 μA on the collimator and beam-line places greater reliance on the center of the ‘hot’ beam to maintain the same target current. The temperature at the radial position (FIG. 5) observes the same trend as for the temperature measured in the center. The error increases for higher target currents and the FEA model underestimated the temperature by 19–40 %. The error at this location is due partly to the model’s assumption of a uniform heat source, applied to the material on a single axis (perpendicular to the material surface) and does not account for any scattering or divergence of the incident proton beam. FIGURE 6 shows that the FEA model underestimated the radial temperature by 16–37 %, when the target is connected to the exit port, for reasons discussed previously. Comparison with FIG. 5 (target on the beam-line) shows the same margin of error between the FEA and the experimental results (19–40 %). The temperature difference between the FEA model and measured temperature at the radial position is independent of the beam profile and beam divergence. The FEA model underestimated the temperature at the radial location with or without the beam-line and for both ion sources. The significance difference in temperature between the FEA model and the experimental is due to our model assumption that the maximum radial temperature is on the irradiated surface and not inside the material corresponding to the layer with the maximum energy lost. In addition, the FEA model does not ac-count for the divergence of the proton beam as it travels through the material. Given the temperature at 50 μA target current is > 90 °C (TABLES 3 and 4) we have capped the experi-ment below this point to prevent any damage the o-ring seal. Conclusion The segmented FEA model was inadequate in determining the temperature for the target at the end of a 300mm beam-line (> 30 % difference). A combination of beam divergence and greater uniform coverage of high current density beam resulted in a higher than predicted temperature reading. However, the segmented FEA model provides a good estimation (< 10 % difference) for the observed temperature of the bulk material at the exit port. The simplistic FEA model was unable estimate the temperature at the radial position (~ 40 % difference) regardless of ion source or target position. A comparison between the two ion sources with different ion-to-puller extraction gap, leading to different focusing of the accelerated beam yield minimal temperature difference. Although a 15% difference was observed between the ion sources at the end of the beam-line, a major contributing factor is beam divergence beyond the magnetic field rather than the beam size of the accelerated beam. Further studies are underway to determine the beam profile (quantitatively using radiographic film), quantify the contribution of the peripheral beam to the total beam current by comparing different size collimators and to investigate other FEA models by applying different beam models (heterogeneous and homogeneous beam) and different heat sources (surface vs. volumetric). Currently the RAPID Lab solid targetry is placed at the end of the beam-line for easy loading and unloading, since multiple target irradiations are performed per month2. However, RAPID is presently developing a new solid targetry sys-tem which eliminates the need for a beam-line and will be able to manage a maximum extracted target current of 150 μA.