Characterization of Heavy Ion Beams at the Heavy Ion Medical Accelerator in Chiba Using a Li-drifted 5-mm Silicon Detector

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1 University of Tennessee, Knoxville Trace: Tennessee Research and Creative Exchange Nuclear Engineering Reports Fall 2012 Characterization of Heavy Ion Beams at the Heavy Ion Medical Accelerator in Chiba Using a Li-drifted 5-mm Silicon Detector Alexander Lang University of Tennessee, Knoxville Follow this and additional works at: Part of the Nuclear Commons Recommended Citation Lang, Alexander, "Characterization of Heavy Ion Beams at the Heavy Ion Medical Accelerator in Chiba Using a Li-drifted 5-mm Silicon Detector" (2012). Nuclear Engineering Reports. This Report is brought to you for free and open access by Trace: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Nuclear Engineering Reports by an authorized administrator of Trace: Tennessee Research and Creative Exchange. For more information, please contact trace@utk.edu.

2 Characterization of Heavy Ion Beams at the Heavy Ion Medical Accelerator in Chiba using a Li-drifted 5-mm Silicon Detector. Alexander Lang

3 Abstract Measurements were taken at the Heavy Ion Medical Accelerator in Chiba, Japan (HIMAC) to characterize accelerator beams to assist in the study of various tissue equivalent proportional counters (TEPCs) designed by Colorado State University (CSU), Oklahoma State University (OSU), and the National Aeronautics and Space Administration (NASA). There were four beams that were part of the HIMAC experiment: 290 MeV/nucleon carbon 150 MeV/nucleon helium 500 MeV/nucleon argon 500 MeV/nucleon iron For the first time ever, a single, 5-mm lithium drifted silicon detector was used to characterize the beam and measure the spectrum of particles striking the TEPCs. If successful, this new methodology can greatly simplify previously used methods and reduce the amount of beam time needed to characterize the beam. Data from the detector was used to yield information on the particle s species (atomic number) and energy. The data analysis was more complex than the standard analysis performed on Sidetector data due to several complications that became evident during the experiments. The 5mm Silicon detector used to analyze the beams was discovered to have suffered radiation damage from previous experiments. On the night of the Helium run, there was limited time to perform the TEPC measurements, so silicon detector measurements of the beam were not taken. The data for the Argon beam was corrupted, and all information that was taken was lost. In spite of these difficulties, useful data was extracted from the carbon and iron runs. To model energy deposited in the damaged silicon detector by the ion beam and its fragments, a Gumbel distribution was used to fit the pulse height spectrum from each ion. Elements of the iron spectrum were identifiable down to carbon. A peak in the energy spectrum that did not correspond to any element was identified as the energy deposited directly into the damaged region of the detector by the iron beam. The carbon spectrum was identifiable down to helium and was analyzed similarly to the iron spectrum, only with slight adjustments. Due to the nature of the response of TEPCs, the beams were characterized by their track-averaged linear energy transfer (LET).The iron beam had an average track-averaged LET of /- 28 MeV/cm with / % of the beam composed of fragmented particles. The carbon beam had an average track-averaged LET of / MeV/cm with /- 3.39% of the beam composed of fragmented particles. Page 1

4 Table of Contents Abstract... 1 Introduction... 4 TEPC environment... 4 Background... 7 The Experimental Setup... 8 Analysis Energy Loss of Iron Beam and Its Fragments Choosing a Distribution Fitting the Fe Spectrum using the Gumbel Distribution Fe Incomplete Depletion Fitting the Gumbel Spectrum Comparison with Zeitlin s experiment Carbon Analysis Conclusion and Future Work Works Cited Appendix B: Data taken from HIMAC Appendix C: Stopping Power Calculations MATLAB codes Iron Beam Calculations and Results Page 2

5 Figure 1 Energy spectra of galactic protons, helium ions, carbon ions, and iron ions respectively (from top to bottom) at solar minimum (Nation Council on Radiation Protection and Measurements)... 5 Figure 2 Relative Abundance of even numbered galactic cosmic ray nuclei compared to their weighted stopping power (Nation Council on Radiation Protection and Measurements)... 6 Figure 3 Map of HIMAC. Biology room (the circled room) is the room where experiments took place Figure 4 Box Diagram of Silicon detector setup... 9 Figure 5 Pictures of the detector system. Upper left is the Silicon detector, upper right is the pre-amp box, bottom left is the pre-amp power supply, and bottom right is the Bias supply and amplifier (the 2 white boxes) for the silicon detector Figure 6 Raw data received from the Iron and Carbon beam Figure 7 Comparison of Fe data from HIMAC to a previous Fe beam experiment Figure 8 Average Energy of the Iron beam. Measurements were taken by the employees of HIMAC while tuning the beam Figure 9 LET of each ion at the face of the Silicon Detector Figure 10 Fitting distributions to the iron peak Figure 11 Initial calibration of the Gumbel spectrum Figure 12 Calibration of the iron spectrum Figure 13 Gumbel Spectrum compared to raw data Figure 14 Cross-sectional area of the face of the detector Figure 15 Illustration of energy deposited in damaged region of the detector Figure 16 the Gumbel spectrum with the incomplete depletion of iron particles added Figure 17 Gumbel Spectrum after Chi-Square fitting Figure 18 Error of the Gumbel Distribution Figure 19 The Complete Gumbel Spectrum Figure 20 Spread of Thin Beam through beam line using PHITS. Model records track of Fe particles using only coulomb interaction Figure 21 Spread of Broad Beam through beam line using PHITS. Model records track of Fe particles using only coulomb interaction Figure 22 LET of tissue equivalent material for the Carbon Beam at the detector's location Figure 23 Conversion of channel to Tissue Equivalent LET for the Carbon Beam Figure 24 Gumbel Spectrum using only single elements Figure 25 Carbon Spectrum with simultaneous interactions of products of Carbon fragmentation Figure 26 Gumbel Spectrum using iron beam information about the damaged portion of the detector. 31 Figure 27 The completed Carbon Gumbel Spectrum Page 3

6 Introduction TEPC environment The radiation environment in open space is characterized by galactic cosmic rays (GCRs) and solar particle events (SPEs). GCRs are isotropic throughout open space and come from sources outside our solar system. Their intensity is influenced by solar activity and its effect on the interplanetary magnetic field, which has an 11 year solar cycle. From 100 MeV to 10 GeV per nucleon, GCRs consist of 87 % protons, 12 % Helium ions, and one percent heavier ions (Nation Council on Radiation Protection and Measurements Report 98). SPEs are large emissions of charged particles. These events occur sporadically, more often during the active period of the solar cycle, but do not occur for every solar flare. SPE s major contributions are protons and helium, and the duration of the SPE can vary. The differential energy flux of some galactic particles at solar minimum can be seen in Figure 1. Page 4

7 Figure 1 Energy spectra of galactic protons, helium ions, carbon ions, and iron ions respectively (from top to bottom) at solar minimum (Nation Council on Radiation Protection and Measurements) NASA, CSU, and OSU are working on new designs for TEPCs to be used in future missions in space. These counters are designed to determine the dose received in lunar and other open space environments. Since the LET is proportional to the square of the atomic number, the small abundance of heavier ions makes a significant contribution to the dose and dose equivalent compared to the galactic protons, as shown in Figure 2. As a result, these TEPCs must be able to respond to a wide range of particles and their associated LETs. Page 5

8 Figure 2 Relative Abundance of even numbered galactic cosmic ray nuclei compared to their weighted stopping power (Nation Council on Radiation Protection and Measurements) Because heavier ions make a significant contribution to the LET in open space environment, the detectors were tested with four heavy ion beams at HIMAC: 290 MeV/nucleon Carbon 150 MeV/nucleon Helium 500 MeV/nucleon Argon 500 MeV/nucleon Iron The heavy ion beams are created at HIMAC using a synchrotron that accelerates charged particles through guiding magnetic fields. The beam line can be seen in Figure 3, and the circled room is where experiments took place. The beam goes through multiple materials before reaching the TEPC detectors, resulting in many nuclear fragmentation events that change the beam s characteristics. Because of these events, the beam is not a single ion at a single energy when reaching the location of the TEPCs, but is made up of many different ions. As a result, the TEPC detectors cannot be adequately characterized without knowing the characteristics of the beam at the detectors location. The purpose of this experiment is to characterize the beam so that the TEPC detectors can be adequately evaluated. Page 6

9 Figure 3 Map of HIMAC. Biology room (the circled room) is the room where experiments took place. Background As a heavy charge particle transverse through material it is dominantly subjected to coulomb interactions. This interaction is described by the electronic stopping power, which gives the average energy loss of the heavy ion per unit distance travelled through a given material. Stopping power has a relationship between the charged ion and the medium that ion goes through. It is proportional to the atomic number squared of the ion and inversely proportional to the velocity of that ion. Also, it is proportional to electron density of the medium and inversely proportional to its molar mass. It should also be noted that stopping power is very weakly dependent on the average excitation energy of the medium. Page 7

10 The physical property is accurate within a few percent as long as (Particle Data Group). By evaluating this equation through small increments of the beam line, the average energy of each ion at the beginning of the detector and the exit of the detector can be calculated. Using this information, the energy deposited in the detector can be found. By knowing the energy of the ion, the stopping power can be characterized in any material of interest (e.g. tissue). Energetic ions have a probability of interaction with the atomic nuclei of materials. Assuming every ion-nucleus interaction results in fragmentation, the fraction of the beam that undergoes fragmentation is described by the exponential distribution. φ ni σ i φ 0 is the fraction of the beam that does not interact is the number of targets per unit volume in the i th material o n i = N a M ρ m N a is Avogadro s number Ρ is mass density M m is molar mass is the charge-changing cross section of ion-nucleus interaction in the i th material ti thickness of the i th material A silicon detector was used to take measurements of the ion beam at the TEPC detector site. Silicon is a semiconducting material. It takes about 3.6eV of energy to bring an electron from the valence band of silicon into the conduction band. When this occurs in a silicon detector a free electron and a hole is made. The hole is the gap in the electron orbital that formally held the free electron in the silicon atom. When an electric field is applied to the silicon detector, the hole will travel along the field while the electron will travel in the opposite direction. Increasing the electric field will cause the velocity of these particles to increase slowly. Eventually, a saturation velocity is reached which the velocity becomes independent of the increasing electric field (Knoll, p.356). The collection of charge from free electrons will be proportional to the energy deposited in the detector. The current produced by a silicon detector can be integrated to find out the energy deposited by the interaction of a charge ion. The Experimental Setup Page 8

11 The experiments at HIMAC were done in two rooms in the Biology section of the facility. The beam room is where the accelerator beam enters and the detectors were setup, and the lab room was where the data acquisition and beam control systems were setup, so we could observe incoming data and adjust the parameters of the detector systems. Pre-Amp Power Supply CSU MCA Detector Detector Guard Ring Pre-amp Amplifier HV Beam Room Data Acquisition Room Figure 4 Box Diagram of Silicon detector setup Figure 4 shows the schematic diagram of silicon detector system setup with the type of equipment in Table 1. Photos of the experimental setup can be seen in Figure 5. Table 1 Equipment used for Silicon Detectors Equipment Model High-Voltage Power Supply LBL dual-bias supply Model 21x821 Pre-Amp Power Supply 14x5181 Pre-Amplifier 4 channel switchable Gain P.A. Amplifier Dual Shaping amp 21x588 P-1 The detector is set so that the face of the detector is perpendicular at the central axis of the beam. The distance between the entrance of the beam into the beam room and the detector is around 3 meters. The beam itself goes through multiple mediums before entering the room. Table 2 Material along the beam line Page 9 Order of Material Beam Line Transverses through Medium Thickness (cm) Lead 0.4 Air Kapton 0.006

12 Air 31.4 Aluminum Acetate 0.04 Aluminum Air A guard ring is attached to the outside of the detector to keep the electric field uniform throughout the entire detector. Aluminum foil is wrapped around the detector as a makeshift light seal to reduce noise from photon excitation. Both the detector and the guard ring require voltage, but information produced by the guard ring was not needed. The high voltage supply box had some issues with the lower unit voltage supply, so a T-adapter was applied to the working high-voltage unit so that both the detector and the guard ring were insured a bias. The pre-amp has two switches that adjust the maximum deposited energy that can be handled by the circuitry. There are three options: 0.1GeV, 1GeV, and 10GeV. In actuality, the pre-amp was able to read up to 3GeV per event in the 1GeV setting. By approximating the beam energy at the detector site, the appropriate setting can be made on the preamp box before the beam runs begin. All the beams had the 1GeV setting except for the Helium beam, which had the 0.1GeV setting. During the beginning of the beam run, the voltage was set high enough for complete depletion of the silicon detector. The range of CSU s MCA is 0-5 V, so the amplifier was adjusted so that the peak of the primary beam ion was around 3V by viewing the amplifier s output through an oscilloscope. As stated previously, data was only obtained from two of the four beams. Page 10 Figure 5 Pictures of the detector system. Upper left is the Silicon detector, upper right is the preamp box, bottom left is the pre-amp power supply, and bottom right is the Bias supply and amplifier (the 2 white boxes) for the silicon detector.

13 Analysis From the experiments at HIMAC, data was obtained from the carbon and iron beams. Since the iron beam has more ion species from fragmentation than the carbon beam, there is more information about the behavior of the detector to observe in its spectra. The techniques used to analyze the data were first done with the spectra from the iron beam, and then applied to the spectra of the carbon data. Because the fragments detected along the beam line all move at roughly the same velocity as the primary beam ion, the peaks in the spectrum identify each element that deposited energy into the detector. For the iron beam, the peaks are identifiable down to carbon. Lower Z elements were washed out because of the prevalence of multi-particle events hitting the detector. The peaks after the iron peak are pile-up events (Knoll, p. 586) which is when two or more ions deposit energy into the silicon detector at almost the same time. For the carbon beam, the carbon and alpha ions are easier to identify than other elements. This is because the fragmentation of the carbon nucleus has a high probability of producing alpha particles, as opposed to other reaction channels. Page 11

14 Figure 6 Raw data received from the Iron and Carbon beam The spectra in Figure 6 show worse resolution than what the detector should be producing. After some investigation, the defect was traced back to the detector, and that the cause is most likely an area of incomplete depletion within the silicon wafer. This detector has a history of being used for highenergy and high-intensity charge particle beams and has most likely succumbed to radiation damage. The iron spectrum from HIMAC is compared to data from a similar experiment using similar electronics and similar detectors to get a visual of the damage and identities of peaks corresponding to particles from fragmentation of the beam, as seen in Figure 7(Zeitlin, Heavy fragment production cross sections from 1.05 GeV/nucleon 56 Fe in C, Al, Cu, Pb, and CH 2 targets ). Page 12

15 Figure 7 Comparison of Fe data from HIMAC to a previous Fe beam experiment The previous Fe data is normalized to the HIMAC data by matching the location of the iron peaks. The previous data went through a multi-detector analysis and was directly at the entrance of the beam line minimizing energy straggling from coulomb interactions. The peaks produced from that experiment will be narrower than the peaks from this experiment. The manganese peak is almost completely absorbed in the iron peak. All the peaks in the HIMAC data closely match the location of peaks in the previous data; however, there is an additional peak between the chromium and vanadium peaks. Most importantly, the comparison shows that even though the detector is damaged, it still is functional enough to retrieve information needed to characterize the accelerator beams. Energy Loss of Iron Beam and Its Fragments Since the ion beam passes through a large distance and through multiple materials between extraction from the synchrotron and target location, it would be inaccurate to assume that the iron beam s energy is 500MeV/nucleon at the detector site. Knowing the material in the beam line, stopping Page 13

16 power calculations through small increments of each material was done to get a better approximation of the iron beam s energy at the detector. These calculations were done using an energy-loss code written in MATLAB, and the results match very close to Bragg peak measurements that were taken at HIMAC while tuning the beam (Figure 8Error! Bookmark not defined.). Figure 8 Average Energy of the Iron beam. Measurements were taken by the employees of HIMAC while tuning the beam. Table 3 Exiting energy per nucleon of iron beam through materials of a given thickness in the beam line Material Thickness (cm) Exiting Energy/nucleon of Iron (MeV/A) Lead Air Kapton Air Aluminum Air Acetate Aluminum Air Silicon Characterization of the fragments of the iron beam is more difficult since fragmentation can occur anywhere along the beam line. Page 14

17 Table 4 Information of targets for interaction with the iron beam Target Material Molar Mass (g/mol) Mass density (g/cc) n x t (particles/cm 2 ) Fractional amount Lead e Air e e Aluminum e Acetate e Kapton e e-4 The amount of particles along the beam line is predominately air and lead. The charge changing crosssection for iron beam is almost twice as much for lead than air (assuming the charge changing crosssection of air is similar to CH 2); therefore, the lead target has the highest chance of interaction (Zeitlin, Heavy fragment production cross sections from 1.05 GeV/nucleon 56 Fe in C, Al, Cu, Pb, and CH 2 targets ). The model is simplified by assuming all fragmentations occur at the center of the lead target. Assuming that the particles produced from fragmentation has the same energy per nucleon as iron, stopping power calculations were done for those particles to the detector. Because stopping power can be used to compute the LET in any medium, the LET in tissue is used to characterize the beam at the TEPC location. Figure 9 LET of each ion at the face of the Silicon Detector Page 15

18 Choosing a Distribution In an ideal measurement, a Gaussian distribution provides good fits to the ion peaks, but since the detector is not fully depleted, a new distribution needs to be found to fit the skewness of the peaks. Using the Chi-Square test, a variety of distributions can be compared to see which has the best fit. O i is the observed data point E i is the data point from your experiment Figure 10 Fitting distributions to the iron peak. The Gumbel distribution was the best fitting distribution of the distributions attempted. The Gumbel distribution is also known as the double exponential distribution which has a probability density function (pdf) (Weisstein, mathworld--a Wolfram Web Resource): Page 16

19 For this distribution, mu is the mode of the distribution, Beta is the shaping parameter of the distribution, and sigma is the standard deviation. When fitting the spectrum of each ion, the standard deviation is assumed to be constant; thus, Beta is a fixed parameter. The information given by the stopping power calculations gives the expected value of the beam and its fragments at the sight. The expected value of a Gumbel peak is calculated by Where γ is Euler-Mascheroni constant and is approximately (Weisstein). Fitting the Fe Spectrum using the Gumbel Distribution There is now enough information to calibrate the spectrum in terms of LET in tissue. Initially, the calibration of the peak was assumed to have the mean of the iron peak be the iron s LET in tissue and channel zero as the pedestal. Seen in Figure 10, most of the peaks fit using this calibration, but there are some adjustments needed to be made in the calibration for lower Z elements. Figure 11 Initial calibration of the Gumbel spectrum. Page 17

20 Using Figure 7 and Figure 10, some of the peaks under iron can be distinguished, starting with titanium. Knowing their LET in tissue and using the properties of the Gumbel distribution to find the mean knowing the mode of the peak, the calibration can be adjusted, seen in Figure 11. As a result, the spectrum replicating the raw data has a better fit, as seen in Figure 12. The Gumbel spectrum is nearly complete, but there is additional data between the Vanadium and Chromium peak that has not yet been fitted. Figure 12 Calibration of the iron spectrum. Page 18

21 Figure 13 Gumbel Spectrum compared to raw data Fe Incomplete Depletion The damage to the detector is not homogeneous throughout the detector, and the data between the Vanadium and Chromium peak demonstrates this. Since iron is the dominant element in the spectrum, it is assumed that the contribution to this peak is iron ions that hit the damaged region of the silicon detector. This is an important study because it gives detail on how much damage was done to the detector. An assumption is made that the damaged region gives no information on the energy deposited, i.e. no valence electrons from the damage region escapes that region. Since the ion beam is a broad, uniform beam perpendicular to the face of the silicon detector, the fraction of the area damaged is proportional to the iron depositing energy in the damage area relative to the total iron depositing energy into the detector. The average depth of the damage in the silicon detector can also be identified using stopping power behavior of the iron ion beams. Page 19

22 Figure 14 Cross-sectional area of the face of the detector Figure 15 Illustration of energy deposited in damaged region of the detector E 0 is the energy of the iron beam as it enters the detector E F is the energy the iron beam escapes the detector E i is the energy deposited by the iron beam in the damaged area of the detector Δx is the region of the detector that is fully depleted x- Δx is the region of the detector that is damaged ΔA is the area of the detector not damaged A is the total area of the detector When the area of the silicon detector has no damage throughout the 5mm thickness of the detector, iron beam loses MeV over the 5mm: When the iron beam is crossing the damaged area of the silicon detector, it is depositing MeV over the thickness of 5mm. This value is based on the calibration of channel number to energy. Page 20

23 Therefore only 0.92mm (on average) of the 5mm is not depleting in the damaged area of the detector. An initial guess of 5% of the total iron particles that interacted with the detector hit the depleted region. Assuming the Gumbel energy distribution is produced by particles in this region of the detector, it is added to the spectrum. A fitting of the Gumbel function to the spectrum of the data taken is then done to get a better approximation of how much of the iron ions deposited energy in the damaged area of the detector. Figure 16 the Gumbel spectrum with the incomplete depletion of iron particles added Fitting the Gumbel Spectrum The Chi-square method was chosen to fit each individual peak. The fit was done within one standard deviation from the centroid of each peak. This was done so that the Chi-square value was focused on the peak of interest and did not include neighboring peaks. Page 21

24 Figure 17 Gumbel Spectrum after Chi-Square fitting Figure 18 Error of the Gumbel Distribution After the fit is done, the absolute error (Figure 16) can be seen by using a sum of Gumbel Distributions. The majority of the contribution to the errors below the manganese peak is due to the larger dips in between peaks from the Gumbel distribution than the data. However, these underestimated errors are balanced out by the overestimated iron peak. The total error is about 4.5% The area under the peak of the incompletely depleted iron is about 2.7% of the area under the peak of the completely depleted iron. Therefore, we estimate about 97.4% of the face of the detector is not damaged. For the area that is damaged, using our previous assumption of the average depth of the Page 22

25 radiation damage, 81.6% of the portion of the detector depletes completely. The radius of the detector can be evaluated by the following relationship. A1 A0 With the radius of the detector being 2 inches, excluding the guard ring, the radius of the damaged portion of the cylinder is 0.4 cm. Accelerator beams that have been previously used with this detector have been around 1 cm in diameter. The assumption of damage to the detector fits the profile of the beams that most likely caused the damage in the detector. r r Page 23 Figure 19 The Complete Gumbel Spectrum Adding in a peak to account for the iron in the damaged region completes the fitted Gumbel Spectrum. Again, the Gumbel spectrum was only done for peaks that were identifiable. Multi-particle events and noise interferes with the washed out area below the carbon peak, and everything above the iron peak is due to counts from pile-up events. The area under the curve for an element gives the fluence of that particle. The track-averaged LET from the iron beam can be calculated by

26 where is the flux of the i th element is the average LET of the i th element The track-averaged tissue equivalent LET for the iron beam is MeV/cm. Comparison with Zeitlin s experiment Using information from the fitted Gumbel spectrum, the contribution of the number of iron particles to the total number of events in the spectrum can be found, as well as any other individual element down to carbon. The number of events for Z=6 and above in the fitted Gumbel Spectrum contributes for about 95% of the total number of events taken from the iron beam at HIMAC. Table 5 Contribution of each element in the iron beam Element Percent Contribution (%) Fe Mn 3.45 Cr 2.69 V 1.55 Ti 1.59 Sc 1.27 Ca 1.1 K 0.91 Ar 0.76 Cl 0.57 S 0.56 P 0.55 Si 0.68 Al 0.70 Mg 0.68 Na 0.71 Ne 0.58 F 0.49 O 0.26 N 2.2e-5 C 5.2e-8 Assuming that every time an iron particle has a nuclear interaction with a medium, fragmentation occurs. The charge changing cross-sections measured by Zeitlin et al. (Zeitlin, Heavy fragment production cross sections from 1.05 GeV/nucleon 56 Fe in C, Al, Cu, Pb, and CH 2 targets ) can be used to calculate how many interactions occur by the time they reach the silicon detector using Page 24

27 φ/φ 0 is the iron particles that do not interact by the time it reaches the detector n i is the atomic number of particles per cubic centimeter for a medium σ i is the charge changing cross-section for a medium o At such high energies, this cross-section is assumed to be approximately uniform as a function of energy(zeitlin) t i is the thickness of a medium Table 6 Values of mediums used for calculations Medium σ cc (barns) ρ*t (g/cm 2 ) n σ cct Lead Aluminum Air This information resulted with about 85% of the iron element in the beam reaching the detector with a track-averaged LET of the entire iron beam being 1892 LET/cm in tissue. The experiments done in this work were similar to the experiments of Zeitlin et al., except for distance of the detectors from the target material. Also, the beam used in Zeitlin s experiment was narrow (< 1 cm diameter), whereas the beam used in this experiment was much larger than the surface area of the detector (beam diameter 40 cm). In a broad beam, the fragments outside the radius of the detector have a higher chance of scattering into the detector than the iron particles outside the radius of the detector, due to the fact that fragment scattering comes from nuclear interactions, whereas the Fe scattering is due to coulomb scattering. The results from detector measurements will show a higher fraction of iron fragmentation than if the detector was measuring a thin beam. Another important difference is that the target used in Zeitlin s experiment was very thin when compared to the amount of material the beam passed through in this experiment. The objective of Zeitlin s experiment was to obtain charge-changing cross sections, while for this experiment the goal was to characterize the iron beam for TEPC detectors. The silicon detectors for Zeitlin s experiment were practically at the exit of the beam from the target, whereas for this experiment the silicon detector was approximately 6 meters away from the material creating most of the fragments, the lead sheet. Beam broadening from scattering and energy straggling can cause a difference in the expected number of surviving Fe particles in this experiment as compared to the results from Zeitlin et al. Page 25

28 Figure 20 Spread of Thin Beam through beam line using PHITS. Model records track of Fe particles using only coulomb interaction. Page 26

29 Figure 21 Spread of Broad Beam through beam line using PHITS. Model records track of Fe particles using only coulomb interaction. Page 27

30 Carbon Analysis The peak of the carbon spectrum was fit with the Gumbel Distribution; however, the standard deviation for the carbon beam was a different value of the iron detector. Many parameters such as energy straggling, coulomb scattering, and condition of the detector effect the standard deviation of the peak as expected. The detector most likely experienced additional damage from the HIMAC runs previous to the carbon run, as noted by the need to increase the applied voltage to the detector in order to keep the detector s resolution within usable limits. Treatment of the carbon beam to calculate energy loss and tissue equivalent stopping power was treated with the same assumptions as the iron beam. Figure 22 LET of tissue equivalent material for the Carbon Beam at the detector's location. The large peak in Figure 6 is the carbon ions and the left-most peak is the alpha ions. The carbon nucleus is essentially three alpha particles exhibits behavior of alpha-clustering within the nucleus; therefore, helium will be common occurring specie. Using this assumption and that the pedestal is equivalent to no energy deposition (i.e. zero LET), the iterative process of calibrating peaks to the expected LET of the proper specie from the channel number. Page 28

31 Figure 23 Conversion of channel to Tissue Equivalent LET for the Carbon Beam. After performing the fitting and the subsequent making of the Gumbel spectrum, the overall fit still does not look comparable to our carbon beam measurements from HIMAC. Figure 24 Gumbel Spectrum using only single elements. Because the combinations of fragments from carbon fragmentation have fewer outcomes and smaller atomic numbers than the iron beam, multi-particle events will have a significant effect on the Page 29

32 spectrum. For instance, if an iron particle fragments into manganese and a proton, the LET of those two simultaneously depositing energy into the detector will not be distinguishable by manganese depositing energy by itself in the detector. In the case of Carbon fragmenting into beryllium and helium, there will be a distinguishable difference between simultaneous deposition of the two fragments from beryllium by itself. Figure 25 Carbon Spectrum with simultaneous interactions of products of Carbon fragmentation. The left tail of the carbon peak has missing data, but information from carbon ions interacting with the damaged portion of the detector has not been included into the spectrum. At first the information from the iron beam was used to estimate the carbon deposition in the damaged portion of the Silicon detector, but this did not match the carbon data from the HIMAC experiment. Page 30

33 Figure 26 Gumbel Spectrum using iron beam information about the damaged portion of the detector. Because the detector had two other beam runs between the carbon beam and the iron beam, behavior of the detector changed, therefore the behavior of the damaged portion of the detector is going to behave differently. The incomplete depletion of the carbon beam is then fitted into the carbon data spectrum. Figure 27 The completed Carbon Gumbel Spectrum Page 31

34 The Gumbel Spectrum for the carbon beam yields a track-averaged LET of /- 4.8 MeV/cm with /- 3.4% of the beam fragmented particles. Using cross-section information resulting from a similar experiment, the expected track-averaged LET is MeV/cm (Zeitlin, Fragmentation Cross Sections of 290 and 400 MeV/nucleon 12C beams on elemental targets). Again, these experiments differ due to the distance of the detector to the entrance of the beam, beam diameter, and the effects of energy straggling and coulomb scattering of the carbon ions and its fragments, all of which result in giving slightly different results for this HIMAC experiment. Conclusion and Future Work In order to develop a new, improved method for beam characterization for TEPC tests at heavyion facilities, a single, 5-mm Li drifted Si detector was used to measure the track-averaged LET at the TEPC position in the beam. During the experiments at HIMAC, the silicon detector was determined to have suffered radiation damage from its previous use in high intensity beams. By assuming the damage was done by high intensity beams, and by analysis of the data taken at HIMAC, it was found that an area with a 0.4 cm radius of the detector and.92mm in depth behaved as though it was not fully depleting. This assumed damage fits the profile of damage that would be done by an accelerated beam. However, regardless of the damage, the detector was still functional enough to yield data that could be used to determine the track-averaged LET. The iron beam had an average (LET) track length of /- 28 MeV/cm with / % of the beam being fragmented particles. The carbon beam had an average LET track length of /- 4.8 MeV/cm with /- 3.4% of the beam fragmented particles. These results were compared with data taken previously with a multi-si detector spectrometer with the same beams. The results from this series of experiments were consistent with results from the previous experiments, taking into account differences in material thickness, beam diameter, and distance between the target materials and detector locations. For future work, a further analysis of the silicon detector should be done to analyze the damage it has suffered. Attempts to anneal the detector should be done, to try to return the detector to a fully functioning state. This experiment should be repeated with a fully functional lithium-drifted silicon detector and compare the analysis to see how well results improve. Page 32

35 Works Cited Knoll, Glenn F. Radiation Detection and Measurement 3rd Edition. Hoboken, NJ: John Wiley & Sons, Inc., Nation Council on Radiation Protection and Measurements. "Guidance on Radiation Received in Space Activities." NCRP Report No. 98. July 31, Particle Data Group. "Journal of Physics G." Nuclear and Particle Physics (2010): 286. "Review of Particle Physics." Journal of Physics G: Nuclear and Particle Physics (2010): 286. Weisstein, Eric W. Mathworld- A Wolfram Web Resource. n.d < mathworld--a Wolfram Web Resource. n.d < Zeitlin, C. "Fragmentation Cross Sections of 290 and 400 MeV/nucleon 12C beams on elemental targets." Physical review C (2007): Volume 76.. "Heavy fragment production cross sections from 1.05 GeV/nucleon 56Fe in C, Al, Cu, Pb, and CH2 targets." Physical Review C (1997): Volume 56, Number 1. Page 33

36 Appendix B: Data taken from HIMAC Page 34 Channel # Iron Counts Carbon Counts

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41 Appendix C: Stopping Power Calculations MATLAB codes Information needed for MATLAB Page 39

42 Table 7 Information of Targets along the beamline. Element Z Density (g/cm 3 ) Molar Mass (g/mol) Mean Excitation Energy (MeV) Lead Air E-05 Kapton E-05 Aluminum Acetate E-05 Hydrogen E-05 Carbon Nitrogen Oxygen Argon Sulfur Table 8 Ions produced from the iron beam and carbon beam. Z Rest Mass (MeV) Energy (MeV/nucleon) Atomic number Page 40

43 Carbon Beam Code and results clc clear %This is the stopping power calculations of Carbon particles and the %fragmented particles for the HIMAC run in January of 2011 %We are looking at Carbon at 290 MeV/nucleon. The first thick target %the beam hits is 0.4 cm of lead and an assumption of all particle %break ups occur in the center of the lead target. %At 0.2 cm of the energy of the Carbon beam is at MeV/nucleon so %another assumption on top of the assumption of all break up particles %occuring at this point is that all the fragmentation is also at %MeV/nucleon %After traveling through all the material we then look at the energy %deposited in the 5mm Silicon Detector % lead Air Kapton Air Al Air Acetate Al Air % % % -- \ % ----\ % MeV/nucleon % ----/ % -- / % % %thickness(cm) %I fill these up with zeroes so that MATlab doesn't take the time to do it %for each iteration. These values will be the NRG per nucleon after exiting %each material % T1=zeros(1,6); T2=zeros(1,6); T3=zeros(1,6); T4=zeros(1,6); T5=zeros(1,6); T6=zeros(1,6); T7=zeros(1,6); T8=zeros(1,6); T9=zeros(1,6); T10=zeros(1,6); % %T_deposit gives the energy deposited inside the Silicon detector % T_deposit=zeros(1,6); %The two libraries made are for the ions and the targets these ions go Page 41

44 %through % %these libraries are text files. Information about the library is found %in an excel file called "Ion and Target data.xls" % Ion=dlmread('Himac_2011_Carbon_Ion_Data.txt'); Target=dlmread('Himac_2011_Target_Data.txt'); % %This is where the ion is chosen and given the initial conditions needed % to see energy deposited in targets % for j=1:6 %Ion_choice=input('select Ion by lower case atomic symbol between c-fe: '); Ion_choice=j; disp(' ') % z=ion(1,ion_choice); mc2=ion(2,ion_choice); A=Ion(4,Ion_choice); T=A* ; % %The parameters for stopping power are listed here %Stopping power units are in MeV/cm % r0=2.8179e-13; me=.511; Na= e23; %First we go through the 0.2 cm of lead n=1000; for i=1:n y=t/mc2+1; b2=1-1/(y^2); Sc=4*pi*r0^2*me*z^2/b2... *Na*Target(1,1)*Target(2,1)/Target(3,1)... *log(2*me*b2/target(4,1)); T=T-Sc*0.2/n; end T1(j)=T/A; %Now we go through cm of air %Air composition information collected from NIST website %atomic # weight fraction % % % % n=10000; for i=1:n y=t/mc2+1; b2=1-1/(y^2); ScpC=4*pi*r0^2*me*z^2/b2... *Na*Target(1,7)/Target(3,7)... *log(2*me*b2/target(4,7)); ScpN=4*pi*r0^2*me*z^2/b2... *Na*Target(1,8)/Target(3,8)... Page 42

45 *log(2*me*b2/target(4,8)); ScpO=4*pi*r0^2*me*z^2/b2... *Na*Target(1,9)/Target(3,9)... *log(2*me*b2/target(4,9)); ScpAr=4*pi*r0^2*me*z^2/b2... *Na*Target(1,10)/Target(3,10)... *log(2*me*b2/target(4,10)); Sc=( *ScpC *ScpN *ScpO *ScpAr)... *Target(2,2); T=T-Sc*121.5/n; end T2(j)=T/A; %Now we go through.006 cm of Kapton %Kapton composition information collected from the NIST website as Kapton %Polymide Film %Atomic # Weight fraction % % % % n=100; for i=1:n y=t/mc2+1; b2=1-1/(y^2); ScpH=4*pi*r0^2*me*z^2/b2... *Na*Target(1,6)/Target(3,6)... *log(2*me*b2/target(4,6)); ScpC=4*pi*r0^2*me*z^2/b2... *Na*Target(1,7)/Target(3,7)... *log(2*me*b2/target(4,7)); ScpN=4*pi*r0^2*me*z^2/b2... *Na*Target(1,8)/Target(3,8)... *log(2*me*b2/target(4,8)); ScpO=4*pi*r0^2*me*z^2/b2... *Na*Target(1,9)/Target(3,9)... *log(2*me*b2/target(4,9)); Sc=Target(2,3)... *( *ScpH *ScpC *ScpN *ScpO); T=T-Sc*.006/n; end T3(j)=T/A; %Now we go through 31.4 cm of air using the same values as previously n=1000; for i=1:n y=t/mc2+1; b2=1-1/(y^2); ScpC=4*pi*r0^2*me*z^2/b2... *Na*Target(1,7)/Target(3,7)... *log(2*me*b2/target(4,7)); ScpN=4*pi*r0^2*me*z^2/b2... *Na*Target(1,8)/Target(3,8)... *log(2*me*b2/target(4,8)); ScpO=4*pi*r0^2*me*z^2/b2... *Na*Target(1,9)/Target(3,9)... *log(2*me*b2/target(4,9)); ScpAr=4*pi*r0^2*me*z^2/b2... *Na*Target(1,10)/Target(3,10)... *log(2*me*b2/target(4,10)); Sc=( *ScpC *ScpN *ScpO *ScpAr)... *Target(2,2); Page 43

46 T=T-Sc*31.4/n; end T4(j)=T/A; %Now we go through.0496 cm of Aluminum n=1000; for i=1:n y=t/mc2+1; b2=1-1/(y^2); Sc=4*pi*r0^2*me*z^2/b2... *Na*Target(1,4)*Target(2,4)/Target(3,4)... *log(2*me*b2/target(4,4)); T=T-Sc*0.0496/n; end T5(j)=T/A; %Now we go through 160.7cm of air n=10000; for i=1:n y=t/mc2+1; b2=1-1/(y^2); ScpC=4*pi*r0^2*me*z^2/b2... *Na*Target(1,7)/Target(3,7)... *log(2*me*b2/target(4,7)); ScpN=4*pi*r0^2*me*z^2/b2... *Na*Target(1,8)/Target(3,8)... *log(2*me*b2/target(4,8)); ScpO=4*pi*r0^2*me*z^2/b2... *Na*Target(1,9)/Target(3,9)... *log(2*me*b2/target(4,9)); ScpAr=4*pi*r0^2*me*z^2/b2... *Na*Target(1,10)/Target(3,10)... *log(2*me*b2/target(4,10)); Sc=( *ScpC *ScpN *ScpO *ScpAr)... *Target(2,2); T=T-Sc*160.7/n; end T6(j)=T/A; %Now we go through.04 cm of acetate film %Acetate film composition collected from NIST website as Plyvinyl Acetate %Atomic # Weight fraction % % % n=1000; for i=1:n y=t/mc2+1; b2=1-1/(y^2); ScpH=4*pi*r0^2*me*z^2/b2... *Na*Target(1,6)/Target(3,6)... *log(2*me*b2/target(4,6)); ScpC=4*pi*r0^2*me*z^2/b2... *Na*Target(1,7)/Target(3,7)... *log(2*me*b2/target(4,7)); ScpO=4*pi*r0^2*me*z^2/b2... *Na*Target(1,9)/Target(3,9)... *log(2*me*b2/target(4,9)); Sc=Target(2,5)*... ( *ScpH *ScpC *ScpO); T=T-Sc*.04/n; end Page 44

47 T7(j)=T/A; %Now we go through.0045 cm of Aluminum using same values as previously n=1000; for i=1:n y=t/mc2+1; b2=1-1/(y^2); Sc=4*pi*r0^2*me*z^2/b2... *Na*Target(1,4)*Target(2,4)/Target(3,4)... *log(2*me*b2/target(4,4)); T=T-Sc*0.0045/n; end T8(j)=T/A; %Now we go through 334.6cm of air n=10000; for i=1:n y=t/mc2+1; b2=1-1/(y^2); ScpC=4*pi*r0^2*me*z^2/b2... *Na*Target(1,7)/Target(3,7)... *log(2*me*b2/target(4,7)); ScpN=4*pi*r0^2*me*z^2/b2... *Na*Target(1,8)/Target(3,8)... *log(2*me*b2/target(4,8)); ScpO=4*pi*r0^2*me*z^2/b2... *Na*Target(1,9)/Target(3,9)... *log(2*me*b2/target(4,9)); ScpAr=4*pi*r0^2*me*z^2/b2... *Na*Target(1,10)/Target(3,10)... *log(2*me*b2/target(4,10)); Sc=( *ScpC *ScpN *ScpO *ScpAr)... *Target(2,2); T=T-Sc*334.6/n; end T9(j)=T/A; %Finaly we go through 5mm of silicon detector %and find out the energy deposited in it! T0=T; n=1000; for i=1:n y=t/mc2+1; b2=1-1/(y^2); Sc=4*pi*r0^2*me*z^2/b2... *Na*Target(1,11)*Target(2,11)/Target(3,11)... *log(2*me*b2/target(4,11)); T=T-Sc*0.5/n; end T10(j)=T/A; T_deposit(j)=T0-T; end %The result is a table. For each ion, it shows the escape energy/nucleon %for each material in the in our problem. results={'ion','c','b','be','li'...,'he','h';'material',' ',' ',' ',' ',' ',... ' ';... '0.2 lead',t1(1),t1(2),t1(3),t1(4),t1(5),t1(6)... ;... '121.5 air',t2(1),t2(2),t2(3),t2(4),t2(5),t2(6)... ;... Page 45

48 '.006 Kapton',T3(1),T3(2),T3(3),T3(4),T3(5),T3(6)... ;... '31.4 Air',T4(1),T4(2),T4(3),T4(4),T4(5),T4(6)... ;... '.0496 Aluminum',T5(1),T5(2),T5(3),T5(4),T5(5),T5(6)... ;... '160.7 Air',T6(1),T6(2),T6(3),T6(4),T6(5),T6(6)... ;... '.04 Acetate',T7(1),T7(2),T7(3),T7(4),T7(5),T7(6)... ;... '.0045 Aluminum',T8(1),T8(2),T8(3),T8(4),T8(5),T8(6)... ;... '334.6 Air',T9(1),T9(2),T9(3),T9(4),T9(5),T9(6)... ;... '5mm Silicon',T10(1),T10(2),T10(3),T10(4),T10(5),T10(6)... ;... 'Energy Deposit (MeV)',T_deposit(1),T_deposit(2),T_deposit(3)...,T_deposit(4),T_deposit(5),T_deposit(6);}; %I take the table created in MATlab and place it in an excel file to %simplify the viewing of the results % xlswrite('himac_2011_carbon_ion_energy_loss',results,'energy Loss','A1') Table 9 Results from matlab run of the carbon beam. Ion (MeV/nucleon) C B Be Li He H Material 0.2 lead air Kapton Air Aluminum Air Acetate Aluminum Air mm Silicon Energy Lossed in Detector (MeV) Iron Beam Calculations and Results clc clear %This is the stopping power calculations of Iron particles and its breakup %particles for the HIMAC run in January of 2011 %We are looking at Iron at 500 MeV/nucleon. The first thick target the beam %hits is 0.4 cm of lead and an assumption of all particle break ups occur %in the center of the lead target. Page 46