Implementation of Scattering Pinhole Diagnostic for Detection of Fusion Products on CR-39 at High Particle Fluence. David Orozco

Transcription

1 Implementation of Scattering Pinhole Diagnostic for Detection of Fusion Products on CR-39 at High Particle Fluence by David Orozco AMOVEMS MASSACHUSmETr INSiTITE, OF TECHNOLOGY AUR LIBRARIES Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics at the MASSACHUSETTS INSTITUTE, OF TECHNOLOGY June David Orozco, MMXIV. All rights reserved. The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created. Author... Certified by... Accepted by... Signature redacted Department of Physics May 18, 2014 Signature redacted Richard Petrasso Senior Scientist, Plasma Science and Fusion Center Thesis Supervisor Signature redacted. Nergis Malvalvala Senior Thesis Coordinator, Department of Physics

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3 Implementation of Scattering Pinhole Diagnostic for Detection of Fusion Products on CR-39 at High Particle Fluence by David Orozco Submitted to the Department of Physics on May 18, 2014, in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics Abstract Many Inertial Confinement Fusion (ICF) experiments use solid-state nuclear track detector CR-39 as a means to detect different types of nuclear products. Until recently, it was difficult to use CR-39 in experiments with very high yields because particle tracks would overlap. A scattering pinhole has been implemented in order to reduce the fluence on the CR-39. This paper details the design and implementation of a scattering pinhole to detect protons born from D 3 He nuclear reactions: D +3 He = p+(14.7mev) + a(3.7mev). To do so, basic models relating the scattering angle to material thickness and atomic number were developed. The scattering pinhole reduced the fluence on the CR-39 enough to successfully count all the tracks and calculate a product yield. A proton yield of 2.25e10 t 0.17e10 was calculated and falls within half a standard deviation of the proton yield found with the Wedge Range Filter (WRF) spectrometer, the value being 2.19e10. The image on the CR-39 was predicted to be s = 0.957mm t 0.092mm. This correlates with measured size - = 0.873mm, supporting the validity of the models. To further explore the nuclear this nuclear reaction, the design challenges for detecting 3.7MeV alpha particles was also explored. Thesis Supervisor: Richard Petrasso Title: Senior Scientist, Plasma Science and Fusion Center 3

4 Acknowledgments This is the acknowledgements section. You should replace this with your own acknowledgements. 4

5 Contents 1 Introduction 11 2 Background (Theory and Technical Details) Nuclear Fusion Burning in ICF Measurement Techniques Scattering Pinholes Design and Experimental Setup Alpha Exploration Results 29 5 Conclusion General Sources

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7 List of Figures Plasma contained in a toroidal field inside a tokamak 1-2 Indirect Drive Depiction Coulomb Barrier and Strong Interaction Well Binding Energy Curve ICF Burn Depiction Rayleigh-Taylor instability in capsule Overlapping Tracks on CR Scattering Foil Diagram Particles Striking Pinhole Substrate Proton Transmittance through Scattering Foil Scattering Angle vs Scattering Foil Thickness Scattering Angle vs Z of Scattering Foil Alpha Particle Transmittance through Scattering Foil 4-1 Image of proton tracks on the CR Microscope Frame of CR Proton Counts

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9 List of Tables 3.1 Data table displaying the desired area and the actual area, along with the error on the area

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11 Chapter 1 Introduction Fusion of hydrogen and its isotopes has been identified as a possible alternative energy source. Unlike its nuclear counterpart, fission, fusion produces less radioactive byproducts. Hydrogen isotopes, the favored fusion material, has the highest energy density of all the elements[1] and are the most abundant elements in the universe. The process of fusion was first detailed by Atkinson and Houtermans in The process was used to describe how stars are fueled; this won Hans Bethe the 1967 Nobel Prize in Physics. Fusion was quickly employed for military applications and it was Enrico Fermic who, in 1941, proposed a hypothetical method of achieving fusion with a fission reaction. Because of this, much of fusion research was classified and not open to the public. It wasnt until the 1950s that information was openly disclosed. Fusion involves the confinement and control of plasma. Two methods of doing this are magnetic confinement and inertial confinement. Magnetic confinement fusion (MCF) occurs by trapping plasma in magnetic fields as the name suggests. The plasma is then heated up, with the use of radio waves, until fusion occurs. This requires temperatures over ten million degrees Celsius. MCF fusion is predominantly achieved with a Tokamak, a large toroid that confines a plasma within its volume. Tokamaks generate toroidal magnetic fields to confine plasmas as shown in Fig 1-1. One can imagine a whirling star inside a tokamak that has achieved fusion. Inertial Confinement Fusion (ICF) works by imploding a small capsule, approximately 1mm in diameter, of fusionable material. A sudden laser burst causes the 11

12 Poloidal field magnet Toroidal field ma n et Vacuum chamber Figure 1-1: The above shows how magnets are arranged in a tokamak to produce a toroidal field to confine plasma. Image from http / science. howstuffworks.com/fusion - reactor3.htm capsule to rapidly implode (to a size on the order of 50 microns) increasing the density and the temperature of the fuel high enough to achieve fusion[4]. There are two ways of imploding these tiny capsules: directly and indirectly. Direct drive involves aiming the lasers at the capsule and indirect drive involves aiming the lasers at a cylindrical vessel where the capsule awaits as in Fig 1-2. The cylinder then produces X-rays that compress the capsule enough to achieve fusion. Currently there are two large laser facilities in the United States that perform laser driven ICF: the National Ignition Facility (NIF) in Livermore, California and the OMEGA Laser Facility in Rochester, New York. Both facilities work towards better understanding the fusion process to, ultimately, use fusion as an energy source[5]. Fusion, when its applications were first being considered, did not seem like a very difficult achievement. Once physicist began constructing fusion devices, it became more and more apparent that fusion would not be easily accomplished. Plasma dy- 12

13 Figure 1-2: The above a capsule inside a cylinder. The cylinder is hit by a laser pulses and produces X-rays that compress the capsule to achieve fusion. Image from Lawrence Livermore National Laboratory namics are very complicated and there are many instabilities associated with plasmas. Fusion plasmas are composed of many energetic particles that can, and most likely will, damage surrounding objects. The ICF process is quite literally a controlled explosion. To study and understand these plasmas we need to be able to observe and detect many different aspects of the plasmas and their fusion products. Therefore there are limited diagnostic tools that can be used in these facilities to make measurements. Finding effective methods of making measurements is still an active issue. One prominent method of particle detection in ICF involves the use of a plastic, CR-39. CR-39 is a clear plastic made up of long molecular chains. When particles strike the piece of CR-39, they leave conical damage trails. The CR-39 is then etched, increasing the diameter of the damage trails, allowing one to observe the damage trails under the microscope. By counting the number of tracks (done 13

14 by a computer program), one can determine how many particles were produced in the fusion process[7]. By properly applying filters, we know what particles we are observing. This process, though, comes with its own difficulties. Particles are undercounted when so many particles strike the CR-39 that they overlap. Experiments at NIF and OMEGA can yield a very high number of products causing significant track overlap and error in the results. Recently, a method of reducing the fluence on the CR-39 has been developed in order to find the yields by directly measuring fusion products[9]. The method makes use of a pinhole and Rutherford Scattering to deflect a smaller number particles over a greater area on the CR-39. This has been done successfully to measure protons that were created by fusing Deuterons together. The following experiment successfully measure the yield of 14.7MeV protons produced at the OMEGA laser facility. 14

15 Chapter 2 Background (Theory and Technical Details) 2.1 Nuclear Fusion Nuclear fusion is a physical phenomenon that occurs when nuclei get close enough together that their nuclei overcome the Coulomb barrier and fall into the potential well governed by the strong force. The nuclear force is also called the strong force because it is several orders of magnitude larger than the electromagnetic force. Unlike the electromagnetic force, though, the nuclear force does not follow a simple inverse squared law. Instead the nuclear force overwhelms the Coulomb force at scales of approximately 1 femtometer and then drops off exponentially. The nuclear force is detailed in quantum chromodynamics and is easier to think of as a force that takes over at very short length scales as seen in Fig 2-1. The energy of the system, in this case just two nuclei (can be two hydrogen atoms), is E. Classically this reaction cannot occur unless E is greater than the potential peak. But quantum mechanics describes how particles can tunnel through a barrier with a finite probability. By increasing the energy of the system, it is more and more likely that a particle will tunnel past the Coulomb barrier to a bound state due to the Strong Interaction. Once the atoms fuse, there is a change in mass that is accounted for by mass-energy equivalence E = mc 2 : the fusion process does not conserve mass in the Classical sense 15

16 A 6 \ System Energy E E - Coulmb otential U -Interaction Potential Well Due to Strong Figure 2-1: The system energy E is not enough to overcome the Coulomb barrier. Classically this fusion reaction cannot occur unless E is larger than the peak of the potential. But, as described by quantum mechanics, the system can tunnel past the Coulomb potential and achieve fusion. The system then gains energy related to the difference in mass before and after the fusion reaction. and therefore some of that mass is released as kinetic energy. This kinetic energy is carried by the fusion products. For example, fusing deuteron with a triton produces a 14.1MeV neutron and a 3.5MeV alpha particle. If we sum up the mass of the deuteron and triton and compare it to the mass of the neutron and alpha particle we find a mass difference of 17.6MeV/c 2. This unit system uses c = 1 so the energy ends up being 17.6MeV, the sum of the products energy. In facilities such as NIF and OMEGA the focus is on fusion using capsules with different amounts of tritium, deuterium and Helium-3. As nuclei get larger, the energy that is released during fusion tends to fall lower and lower so it is not favorable to pursue higher Z reactions. Beyond Z = 26, fusing atoms together consumes more 16

17 energy than is released in the process. Fig 2-2[1-)] shows energy relates to atomic mass and how fusing low Z atoms releases significantly more energy than breaking apart high Z nuclei. Fe 8 - of Wsoopes are the - MWs lightly bound, yieldfrom nuclear Itssirn u4tu 1C E 6 - N6Ni (momt 1101tY bound) I 26 Fe e 26 have 8.8 Me, V u 4 - yield from bdng energy. nucear fusion Elemorts bewevr than ion can yiel energy by nuclar fission. 2 -Average mass of fision frugroent is aboui Mass Number, A I k Figure 2-2: Binding energy increases quickly to a plateau point (Iron) and then drops down slowly. [ t 01 For the purposes of this paper, the main reactions observed are the following: D +3 He -a o[3.6mev] + p+[14.7mev] (2.1) D + D -+ T[1.01MeV] + p+ [3.02MeV] (2.2) D + D - n[2.45mev] +3 He[O.82MeV] (2.3) Where D represents deuterons, T Tritons, a Helium (alpha particles), p Hydrogen (protons), and n neutrons. The capsule used in these experiments contained deuterium and Helium-3 so it is necessary to consider all the possible products except the neutrons (they do not cause tracks on the CR-39). 17

18 2.2 Burning in ICF As mentioned before, ICF fusion is driven by lasers that are focused on a small capsule containing fuel. This capsule is made up of a plastic ablator that surrounds Deuterium-Tritium (or some other mixture of fusionable material) ice. The center of the capsule is hollow, and contains a gas, also fusionable material. The idea is to compress the capsule, increasing the density of the ice and gas enough so ignition will occur. Ignition in the specific case when fusion initially begins at the center, with the gas, and the burn propagates outward fusing all of the material Fig 2-3. Figure 2-3: The above shows how a capsule burns would ideally burn. In a) laser energy is incident on the capsule; in b) the plastic shell is ablated and momentum is transferred to the capsule, causing an initial propagating wave; c) the radius of the capsule decreases as the density increases; d) the center of the ignites and a burn wave propagates outward. Image made by Benjamin D. Esham Ignition has yet to be achieved due to instabilities that occur in the driving process. Surface imperfections of the capsule and non-uniform laser input cause fuel to burn non-uniformly. A major instability is the Rayleigh-Taylor instability. This instability occurs when hotter, lighter fluid pushes against colder, denser fluid. Fig 2-4[G] shows how the material on the inside moves outward, past areas in the sphere that cannot contain the plasma.. These issues prevent all the material from being fused therefore more energy is put into the process than is taken out. One method to help deal with laser-induced instabilities is the indirect drive method mentioned earlier. Direct drive shines many lasers on the ablator, and these lasers do not heat uniformly. Each laser essentially creates a small hotspot on the shell therefore creating an instability. Indirect drive instead aims the lasers at a gold 18

19 0. 5Oneec 60 c C I0 80 D I atence(pm) Figure 2-4: The above image shows the Rayleigh-Taylor instability in a pusher experiment[g]. The hot gas in the center has been heated up and escapes through regions of the capsules that are less dense. cylinder (hohlraum) that surrounds the capsule. When the lasers strike the gold, they become x-ray sources that shine on the capsule more uniformly. This eliminates the instabilities due to lasers, but now an instability is created due to the lasers. Indirect drive produces an overall instability that deforms the capsule, while direct drive causes many, small instabilities. To combat the instabilities in indirect drive, physicists are designing curved hohlraum. Therefore it is very important that effective diagnostics are developed so physicists can understand the instabilities that occur in the fusion process in order to improve the ICF fusion process overall to achieve ignition. 19

20 2.3 Measurement Techniques The efficiency of the nuclear reactions are determined by the products and their yields. In general, a lot of knowledge has been gained by observing fusion reactions. This has placed considerable significance in developing methods of detecting the nuclear products. CR-39 solid-state-track detectors have become a prevalent form of measuring charged particles. It is a type of plastic made up of long, molecular chains that can be broken by incoming particles. By etching CR-39 in NaOH, the tracks become visible under a microscope and circular-appearing tracks can be counted by a computer-driven scanning microscope. Extensive work has been done in understanding CR-39 response; track diameter depends on etch time, particle species, particle energy, and even time left out at ambient temperature[7][8]. Longer etch times create larger tracks; different particles lose energy at different rates and rate of energy loss is dependent on energy (it is routinely used to measure protons with energies ranging from 0.5 to 8MeV); and CR-39 tracks are more likely to deform at higher temperatures. Sngl tracks counted Overlapping tracks not counted Figure 2-5: The tracks in frame a) are well separated and can all be individually counted. Tracks in frame b) are so close together that they overlap and are not counted by the computer-driven scanning microscope[9). If too many particles strike the piece of CR-39, holes will begin to overlap and 20

21 the number of holes will not be undercounted. The left image of Fig 2-5[9] shows a frame of the microscope. This frame shows how the holes are spread out enough so they can be counted successfully (yellow dots). The right image on the other hand contains many holes and the red tracks are overlapping holes that the computer interprets as noise. Therefore inferred yield from these results end up being much smaller than actual yield. The fluence (tracks per cm 2 ) at which this becomes a serious problem, for the purpose of this experiment, is approximately 10 6 cm- 2. The amount of particles created in these experiments is on the order of 10" where the length scale, distance from the implosion to the detector, is approximately 20cm to 30cm. A quick calculation over the surface area of a sphere shows that these experiments fall right into this regime where it becomes difficult to effectively resolve the particle tracks. It is unpractical to reduce the fluence on the CR-39 by simply increasing the length scale. This would require alteration of the physical system. Furthermore, the yield for such experiments is only increasing due to the continual successes made in the field. This would cause a constant issue with building larger facilities for increasing yields. Hence, a new method of reducing the fluence on the CR-39 within the current size constraints is essential. 2.4 Scattering Pinholes A method has been developed in order to efficiently use CR-39 to observe the fusion products in high yield conditions. The method is depicted in Fig 2-6. A pinhole is used to limit the number of particles that enter the detector. Placed behind the detector is a foil that scatters the incoming particles. The scattering phenomenon is well known as Rutherford scattering. Incoming particles will take a random walk through the material and when they exit they will fly off in different directions. If the travel length after the pinhole is long enough, the particles will be sufficiently spaced that they will not overlap. The fluence reduction factor can be determined by the geometry of the system and the scattering angle of the foil. So if we have a fluence F on the front of the detector, the reduction factor RF is determined by 21

22 Pinhole with Diameter d L Pinhole Substrate CR-39 Source Scattering Foil Figure 2-6: The above shows the basic arrangement of the scattering pinhole. The number of incoming particles is limited by the area of the pinhole and the particles are dispersed by the scattering pinhole. The particles enter the foil and are spread by Rutherford scattering as shown in the zoomed in cartoon. The particles leave the foil with an average angle 9 and spread over a larger area on the CR-39. 4L 2 (tan 0)2 RF= (2.4 Where L is the distance from the source to pinhole, d the diameter of the pinhole, and 9 the scattering angle. With this value, the fluence on the CR-39 is given by Ff = F/RF- 22

23 Chapter 3 Design and Experimental Setup In order to detect the protons in reaction (1) the fluence on the CR-39 was reduced from the fluence on the pinhole. The experiment occurred at OMEGA and the physical size of the detector package constrains the distance at which the scattering pinhole apparatus is placed. From this, the design options are: material to use as the pinhole substrate; material to use as the scattering foil; thickness of materials; and diameter of the pinhole. Fig 3-1 depicts how the pinhole substrate from Fig 2-6 works in more detail. It is the main form of eliminating the incoming noise and what limits the number of particles that strike the CR-39. Fig 3-2 shows how the scattering foil also filters out unwanted particles and only allows the 14.7MeV protons through. The foil will not only scatter the protons but reduce their energies. CR-39 is most efficient at detecting particles with an energy range between 0.5MeV and 8MeV[7] so it is important that the foil is also thick enough to lower the energy of the protons enough. With the use of TRIM [t 2], a software simulation package, a relationship between the thickness of a material and the average angle 6 was determined for various materials Fig 3-3. These curves are specific to 14.7MeV protons. The effect of atomic number is also another important relation Fig 3-4. From these sets of graphs it is quite likely that 0 (x Z vthickness. In order to stop the 14.8MeV protons, 750pm of Tantalum was used as the pinhole substrate, and, to gain a good scattering angle, 406pm of Copper was used as the 23

24 14.7MeV D3He-p - 3.6MeV D3He-a- Not to Scale 1.01MeV DD-T MeV DD-p MeV DD-He - Figure 3-1: The above shows how the pinhole substrate is meant to stop all the incoming particles. The image shows relative stopping length. 14.7MeV D3He-p 0.5-8MeV 3.6MeV D3He-a 1.01MeV DD-T MeV DD-p 0.82 MeV DD-He - Figure 3-2: protons but foil with an The above shows how the scattering foil not only scatters the D 3 He also filters out other particles. It is important that the protons leave the energy between 0.5MeV and 8MeV[7]. 24

25 ) scattering foil. Copper has Z=29, compared to the Nickels Z=28, and was used instead for convenience. This foil gives a scattering angle of approximately 7'. The simulations also showed that the protons would exit the copper foil with an energy of 6MeV. This energy is low enough to cause noticeable tracks in the CR-39[7]. To achieve a reduction factor of approximately 50, the diameter d of the pinhole was chosen to be 3 00ptm. The distance from the CR-39 to the front of the camera is constrained at 8.9mm. Therefore a spacer of 7.8mm was 3D printed out of ABS (a common plastic) in order to constrain the scattering foil onto the pinhole by pressure caused by spring-loaded encasement. This gives an expected reduction factor of 53 based on equation (4), with L = 7.8mm, 0 ~ 7', and d = 0.3mm. The pinhole was machined with microdrills. Burrs on the edges of the hole make the aperture imperfect, and noncircular. To account for this, pictures were taken of the holes under a microscope with 40x magnification. The images were then downloaded into a computer aided design (CAD) program. The program allowed the image to be scaled properly, cropped, and processed to find the results in Table 1. Desired Actual Uncertainty Area (mm 2 ) Area (mm 2 ) (mm Table 3.1: Data table displaying the desired area and the actual area, along with the error on the area. The error was determined by extremizing cropping choices and is the error on the actual area. The actual reduction factor was approximately 36. Though this is not the desired value, its enough to bring down the fluence sufficiently to read the tracks with 100% detection efficiency. The materials were packaged together and placed inside the vacuum chamber at the OMEGA laser facility The experiment shot number is contained Deuterium and Helium-3. The capsule 25

26 Average Scattering Angle as a function of Thickness for Various Material (I) 0 L.. 0) 0 Q Be -Al Ni -Ta U 4-' 0 -c I Thickness (microns Average Scattering Angle as a function of Thickness for Be(4) I A. I (0 0 1~ 0) 0 (U 4-' 0 -c H 1[* 0.5F Thickness (microns Figure 3-3: The top graph shows how the average scattering angle 9 changes as a function of the material thickness for various materials for 14.7MeV protons. By taking a closer look at the relationship for Beryllium it seems like 9 oc A/Thickness. 26

27 15F I- 0> T = 20pm -T = 40pm T = 8pm -T = 16pm T = 320pm Average Scattering Angle as function of Atomic Number for Various Thicknesses r LI I Atomic Number (Z) Figure 3-4: The above show how the scattering angle is also affected by atomic number (Z). It is quite likely that there is a linear relation between the two. 14.7MeV D3He-p t",14mev 3.6MeV D3He-a 1.01MeV DD-T 3.02MeV DD-p 0.82 MeV DD-He Figure 3-5: The D 3 He alpha particles from reaction (1) have an energy similar to the DD protons from reaction (2). The energy gap between Tritons and the alphas is also rather small. The above shows an ideal situation where only the D3He alphas and the DD protons get through at an energy that can be detected by the CR

28 3.1 Alpha Exploration Fig 3-5 depicts an ideal situation for a scattering foil that would allow the detection of alpha particles. The challenge here is the alpha particles that have an energy very close to the energy of other particles that are created in the fusion process. With the 14.7 MeV protons it was simple enough to filter all other particles because of the difference in energies. It needs to be made sure that the 1.01 Tritons from reaction (2) and 0.8 Helium atoms from reaction (3) are successfully filtered out. Filtering out the DD protons might not be achievable; alphas, for a given energy, are stopped with less material than protons but in this case the protons have less energy than the alphas. Therefore it is important that the DD protons and D 3 He alphas have distinct scattering angles to help distinguish the two signals on the CR- 39. To account for the additional particles, a larger reduction ration would also be necessary to ensure the proton tracks and the alpha tracks do not overlap. Finally, the D 3 He protons must be accounted for. Since the CR-39 efficiently picks up tracks with energies between 0.5MeV and 8MeV, as long as the energy of these protons are high enough, they should not present a problem. 28

29 Chapter 4 Results Once the CR-39 was received, it was etched for 2 hours in NaOH at a temperature of The CR-39 was then placed under a computer-driven scanning microscope that counted the tracks. The software itself does not completely discern all noise of the CR-39 and required additional processing. Fig 4-1 shows the processed image. Each pixel in the pictures corresponds to a frame under the microscope ( 300pmx400jm) like the one in Fig 4-2. The brighter the pixel in Fig 4-1the more holes there are in the pixel. From both images we can discern that there is a good concentration localized in a single region with minimum noise and good separation between holes. Therefore we can trust the number of tracks found by the computer program. To determine the yield, the tracks were parsed into bins as in Fig 4-3. The data follows a Gaussian profile in horizontal space. From the fit the number of tracks under the Gaussian was determined to be N = 2142 tracks. An estimate for the number of D 3 He protons produced during the fusion process was calculated with the following equation: YD3He 47rR 2 N (4.1) Aph Where R is the distance from the source to the pinhole and Aph is the pinhole area. It was found that YD3He = 2.26e10 following equation: e10. The error was found with the

30 Figure 4-1: Image of proton tracks on the CR-39. The scan is done at 40x magnification and by specialized software that counts how may holes there are in each frame. Each frame corresponds to a pixel in the above images. 2 (DY 2 Dy OY \Y = AN 2 +- A2h 4.2 \ N OR DAph p AN 2 ANBKGND + AN 2 tat (4.3) The first term under the square-root corresponds to the uncertainty in our value of N; the second to the uncertainty in the distance from the source to the pinhole; and the third to the uncertainty in the pinhole area. Here ANBKGND = 100 (the uncertainty due to choosing different filtering options in the computer program), ANtat is the statistical error, AR = 0.75cm is the error in the distance from source to the pinhole substrate (due to the relatively large thickness of the pinhole substrate), 30

31 Figure 4-2: The above image shows a single frame of the microscope with 40x magnification. The proton tracks are very well spaced and no overlap is observed. and AA is the error from Table 1. An estimate for the 14.7MeV protons was also calculated with Wedge Range Finder proton spectrometry (WRF). This method estimated the yield to be 2.19e10. The WRF prediction is less than half a standard deviation away from the calculated yield using this experiment, supporting the validity of the estimate. From Fig 4-3 we find that o = 0.873mm. This length describes the approximate radius of the image on the CR-39. We had previously chosen the material in order to get a scattering angle 0 of approximately 70. By using Rtan(O) = s, where s is the expected radius on the CR-39, we find a value that we can compare to a-. The value of s = 0.957mm 0.092mm which falls within a standard deviation of the - value found. Where the error is found with the following equation: As = ARtan(O) (4.4) This not only further confirms the results found but is also an initial point to verify the relations between scattering angle, material thickness, and atomic number. 31

32 _TN1_ma5258_2h 40x_s2.cpsa (ix=472, iy=64-85) Gaussian fit for X (cn) = -0.3 to 02997: mean value = siga = FWHM = Tracks under Gaussian = X (an) (bin width ) Figure 4-3: Each bin corresponds to a number of pixels on Fig 4-1. The graph was made to exclude most of the area on the CR-39 that contains a lot of noise. By applying a Gaussian fit to the above, we get an estimate for the number of proton tracks on the CR-39 32

33 Chapter 5 Conclusion The experiment showed that 14.7MeV protons can easily be observed in high-yield experiments with the use of a scattering pinhole. By checking our yields with the WRF results we find that this method is very accurate. This means that the scattering pinhole setup can be used to double check WRF yields, perform experiments where WRF would not be able to give accurate yields, and possibly to develop more sophisticated forms of spectrometry. This also calls for the development of models that can be used to easily choose parameters (material, thickness,etc) for scattering pinholes. To further build on this technique, an alpha detector can be built an implemented. By building better models that not only relate the scattering angle to material thickness and atomic number but also to the energy lost by the particle, the best design choices can be made. 33

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