Eindhoven University of Technology BACHELOR Using Solid State Nuclear Track Detectors in a FUSOR to detect charged particles Duffhues, J.C.J.

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Eindhoven University of Technology

BACHELOR

Using Solid State Nuclear Track Detectors in a FUSOR to detect charged particles

Duffhues, J.C.J.

Award date:

2017

Link to publication

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TU/E

Using Solid State Nuclear Track Detectors in a

FUSOR

To detect Charged Particles

Job Duffhues 4/20/2017

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Abstract

This paper studies the potential of TasTrak SSNTD’s for use in measuring radiation and fusion products inside a FUSOR. For measurements of the fusion rate inside the FUSOR a Studsvik neutron detector is used to determine the amount of neutrons created during D-D fusion. However since some fusion reactions are aneutronic, a different measurement method is used to detect charged particles. Here we investigate if a passive plastic detector is suitable for this task. The detectors are first calibrated using an Am-241 alpha source and an Am- 241/Be-9 neutron source. The tracks formed by the alpha particles and neutrons are

categorized by diameter and grayscale until they can be discriminated from one another. The alpha particles fall within the diameter range of 10 to 35 micrometers and the grayscale range of 0 to 150. The neutrons fall within the diameter range of 0 to 10 micrometers and the grayscale range of 0 to 100, and therefor these tracks can be distinguished from one another.

To verify if the detectors measure the same fusion rate as the neutron detector, the FUSOR is loaded with deuterium to create DD-fusion. In this case both neutron as charged particles are created. The output from the Studsvik neutron detector and the SSNTD’s are compared to determine the feasibility of the SSNTD’s. The calculated fusion rate from the SSNTD’s deviates too much between magnifications and detectors to precisely and unambiguously calculate the fusion rate. The energy dependency of the alpha particles can be observed in the calibration results with different energy, and follows a power fit curve according to theory.

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1 Introduction

In this experiment a Solid State Nuclear Track Detector (SSNTD) will be used. This particle detection method is widely used in medical applications as dose badges. The difference in the tracks the particles create tells us which type of radiation it is exposed to and what energy this radiation had. The Andrzej Soltan Institute for Nuclear Studies in Poland [1] [2], as well as several other institutes in Poland [3] and around the world [4], experiments with the SSNTDs to determine if this method is compatible with the nuclear fusion reactors currently built. In the field of inertial confinement fusion CR-39 offers a charged particle detection technique which is immune to electromagnetic pulses as it is a passive, plastic detector [5].

At the Technical University of Eindhoven a Studsvik neutron detector is present to detect the amount of neutrons, this amount will give information on the fusion rate inside the reactor.

However there is not a standard measurement for the amount of reactions when the fusor is loaded with Boron and protons. In this paper a SSNTD will be used to determine the amount of Helium particles in the Deuterium loaded fusor. The Deuterium-Deuterium fusion reaction produces equal amounts of protons, Tritium, neutrons and Helium-3. Measurements for neutrons are standardized to the point that several neutron detectors are on the market [6]. To measure and detect the different particles in the fusion reaction a solid state nuclear track detector will be used. The SSNTD will be TASTRAK detector from Track Analytic Systems Limited [7].Measurement methods for Helium-3 are not so standardized. For this purpose the SSNTD’s from TASL are used to detect the charged particles from the DD-fusion. The output from the Studsvik will give a solid baseline to compare the results from the track detectors. Since the density of the gas in the FUSOR is low spectroscopy is not used as a measurement method. The nuclear track detector is exposed to the fusion products and these particles create tiny holes in the detector. These holes are broadened by etching away the detector using an alkaline solution of sodium hydroxide to be seen with an optical

microscope. The diameter and gray scale of the tracks give information regarding the type and energy of the particle [8] [3]. Several experiments have been done to determine the curves of energy versus the track diameter of alpha particles. These curves will be used to determine the species of the particles, since the energies of the fusion products are known. By counting the amount of tracks and determining their energy the amount of Helium particles can be determined, and there for the fusion rate.

The D+D fusion reaction is suitable for such an experiment, because the amount of neutrons can be measured precisely using a neutron detector. This amount is equal to the amount of Helium-3 particles, which gives a clear baseline for the measurements. When the experiment is successful the same method for measuring the Helium particles may be implemented by the Boron-Proton fusion reaction which produces Helium-4. This gives more data about the amount of fusion reactions when configured with Boron and protons.

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2 Theoretical background

Solid State Nuclear Track Detectors are normally used in medical or nuclear facilities as dose badges. In this application the amount of radiation and type of radiation is important and after an amount of radiation has interacted with the badge it can be processed and determined how much and what type of radiation someone has been exposed to.

The nuclear track detectors are in fact just specialized pieces of polymer. These detectors are exposed to some sort of radiation and the inbound particles create microscopic tracks in the detector. To better visualize these tiny tracks an etchant is used to, not dissolve but actually break up the polymer and enlarge the tracks. These tracks give information regarding the particle that created it.

During the Deuterium-Deuterium reaction we well be experimenting with, the reactions are as follows:

𝐷 + 𝐷 = 0.82 𝑀𝑒𝑉 𝐻𝑒₂³ + 2.45𝑀𝑒𝑉 𝑛₀¹ 𝐷 + 𝐷 = 3.02 𝑀𝑒𝑉 𝑝₁¹ + 1.01𝑀𝑒𝑉 𝑇₁³

With an even chance of getting one of the two reactions stated. So 25 percent of the reaction products will be ₂³𝐻𝑒 which we need to measure using our SSNTD.

The Fusion reaction of Boron-proton

5𝐵

11 + 𝑝₁¹ = 3 𝐻𝑒₂⁴ + 8.7𝑀𝑒𝑉

, which does not produce neutrons and therefor the neutron measurements to determine fusion rate cannot be used, the SSNTD however can detect charged particles and can be used for this purpose.

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2.1 Track parameters

2.1.1 Track diameter and etch ratios

During the etching process the tracks of the

radiation are enlarged and become conical in shape.

The speed at which the polymer is disintegrated by the etchant is the track etch rate 𝑉_𝑡 the speed at which the etchant removes polymer from the top layer is the bulk etch rate 𝑉_𝑏. In order to determine the bulk etch rate an experiment can be done to determine the width loss of an unexposed detector after a specified amount of etching time. The track etch rate can be determined by measuring the track diameter.

For this purpose we assume cylindrical coordinates and we assume a collection of circles with which are described by:

Equation 2.1 𝑥²+ 𝑦²= 𝑟² 𝑎𝑛𝑑 𝑧 = 𝜆

Nikezić and Kostić [9] derived a two dimensional equation in 1997 to describe the etch pit wall in the form:

Equation 2.2

𝑦(𝑧) = ∫ 𝑑𝜉

√𝑉²(𝜉) − 1

𝐿

𝑧

Nikezić [10] adapted the two dimensional equation to envelop three dimensions. The equation where the assumption is made that the track etch rate is constant has the form:

Equation 2.3 𝐷 = 2𝑉_𝑏𝑇√𝑉_𝑡− 𝑉_𝑏

𝑉_𝑡+ 𝑉_𝑏

In which the 𝐷 is the diameter increase factor of the tracks and 𝑇 is the square root of the etching time. This is only the track widening factor, the initial track diameter is influenced by the particle type and energy. And the equation where the track etch rate is not constant, which takes the form:

Equation 2.4 𝐷 = |𝑦₁| + |𝑦₂| 𝑦_1,2= ± 1

𝑆𝑖𝑛 (𝜃) ∫ 𝑑𝜉

√𝑉²(𝜉) − 1

𝐿

𝑦_1,2 𝐶𝑜𝑠(𝜃)+𝑧₀

Figure 2.1: visual representation of an etched track. The plane π1 is the original plane of the detector; the plane π2 is the plane after the etching is done. The black lines are the walls of the track.

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Where the y values are the y-coordinates of the opening of the track. If the values differ from one another the track opening is non-symmetrical and the incident angle of the particle was not perpendicular.

The track etch rate can vary along the trajectory [11] [12] [13] [14] as long as the particle does not end up in the detector but goes through it. This can be calculated using formulas from Azooz et al. [15].

By calculating the bulk etch rate and the track etch rate the etch rate ratio can be evaluated using

Equation 2.5 𝑉 =𝑉_𝑡

𝑉_𝑏

This total etch rate ratio has a correlation with the restricted energy loss. This is the energy loss of a particle as it passes through the detector. However in this experiment we will focus on the End of Range tracks. By maximizing the total etch rate ratio will be achieved by a 6.25N NaOH solution, this results in improved track contrast and detection.

Though the track diameter is heavily dependent on the energy and type of the particle, it can be ambiguous. As different particles create different tracks and diameters, the overlap may occur that one diameter can be created by various particles with varying energies. Only measuring the track diameter is not enough to determine the energy of the particles.

2.1.2 Mean gray value

In Immé et al. [8] a new parameter for determining particle energy is introduced the gray mean level. This method depends on the reduction of light intensity due to refraction of the microscope light. Several differences in gray scale are created as the tracks refract the light differently than the rest of the detector. A gray threshold is set and tracks darker can be isolated. These darker tracks have a lower mean gray level and the level ranges from 0

(completely dark) to 255 (complete light transmission). As the particle energy becomes larger the mean gray level drops. However as with the track diameter solely using the mean gray level gives rise to ambiguous results, varying particles with different energies may have the same mean gray level. Combining the mean gray level with the track diameter in a point plot, where diameter is on the y-axis and grayscale on the x-axis, gives a more precise result in determining the energy and type of the incident particle.

Ultimately the conversion from track diameter and mean gray level to particle energy is done by first calibrating the detector. From a large amount of different tracks created by known particles with a determined energy a spectrum can be made. When a detector is exposed to a particle which is to be determined one can compare the results to the spectrum and read out the particle energy and type.

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2.2 Acceptance and sensitivity

2.2.1 Alpha Particles and protons

The sensitivity of the TASTRAK detectors for alpha particles and protons is approximately 100% [16] since the particles are relatively large and cannot penetrate the detector of 1400μm depth [5] and the particles will impinge perpendicular on the detector therefor no particle will impinge at or over the critical angle. The proton response is more extensively studied the paper of Sinenian et al. [5]. When experimenting with the Fusor, energies around 1MeV for the alpha particles are common. This means that compared to most alpha particles this is in

the low energy spectrum. Malinowska et al. [3] used the combined method of track diameter and mean gray value to plot these versus the energy of the particles. This can be seen in Figure 2.2. However in the low energy spectrum (0.07MeV-1MeV) both the track diameters and mean gray values are very difficult to distinguish between protons, deuterons and alpha particles of the same energy.

2.2.2 Neutrons

The detection efficiency of TASTRAK for neutrons is experimentally determined and is 1,1 ± 0,2 ∗ 10⁻⁴ [17]. While Lounis et al. [18] shows a response of 3.01 ± 0.34 ∗ 10⁻⁴. Another study [19] shows a sensitivity of 668 ± 12 𝑡𝑟𝑎𝑐𝑘𝑠 𝑐𝑚⁻²𝑚𝑆𝑣⁻¹, however this is for a PADC plastic produced by Intercast Europe S.p.A. in 2000. A more recent study [20]

shows a sensitivity of 203 ± 22 𝑡𝑟𝑎𝑐𝑘𝑠 𝑐𝑚⁻²𝑚𝑆𝑣⁻¹ for the TASTRAK PADC in 2007.

This rate is much lower because neutrons have the tendency to penetrate the detector without any interaction or collision between the particle and the crystalline structure. Since the

detection rate of neutrons is much lower than that of alpha particles, most tracks will be alpha particle or proton tracks.

In addition to the tracks from incident particles, background tracks will also be present due to radon particles [21]. These background tracks will have a smaller diameter than the alpha and proton tracks on the detectors.

Figure 2.2: left: the energy of the particles in MeV vs. the track diameters in microns. Right: the energy of the particles vs. the mean gray value. Both are from Malinowska [3]

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2.3 Calibration Curves from literature

2.3.1 Calibration curves for alpha particles

Since every batch of detectors is slightly different, the most ideal circumstances would be to fully calibrate the detector before experimenting. It is however prudent to take a look at the calibration curves of other studies. In figure Figure 2.3 and Figure 2.4 the calibration curves of Immè et al. [8] is shown. With these values combined the different species of particles can be distinguished from one another.

Figure 2.3: Calibration curve of Immè et al. the track diameter vs. the Energy of alpha-particles.

The black line is calculated by TRACK_VISION. [8]

Figure 2.4: Calibration curve of Immè et al. the mean gray value vs. the energy of alpha-particles.

[8]

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When the data of the tracks of the different particles are separated, the calibration curve of Lounis et al. [22] can be applied to determine the energy of the various particles. The curves can be seen in Figure 2.5. The experimental data can be compared to the existing calibration curves to determine the energy of the particles that formed the tracks. But since the energy of the alpha particles by a D+D fusion reaction is known the expected track diameter can be determined and compared with the mean gray value to calculate the amount of alpha particles created by the fusion reaction. In the calibration section of the Results literary calibration is compared to the experimental calibration.

Figure 2.5: the mean track diameter is the evolution of the track diameter as a function of the etching time. This mean track diameter is plotted for several energies for (a) protons and (b) alpha-particles. Curves are taken from Lounis et al. [22].

2.3.2 Calibration curve of Am-241 alpha-source

For the calibration of the detectors an Am-241 will be used to determine the range of diameter and grayscale in which the alpha particles will fall. An americium source radiates alpha particles with an energy of 5.48MeV to determine the diameter and grayscale ranges of the alpha particles from the fusion the Am-241 particle energy must be lowered to 0.82MeV, to determine the distance between the detector and the alpha source Figure 2.6 is used.

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Figure 2.6: energy loss of radiated alpha particle energy from an Am-241 source in air. The distance on the horizontal axis is in centimeters and the vertical axis is the energy in Mega electron volts. Image from [23]

2.4 Calculation of total counts

The count on the detector is determined by the TRIACII code (see section 3.4). The

dimensions of the magnified image are dependent on the magnification; the count of tracks is a measure for the total amount of particles created by the fusion reaction. The used equation for the total produced particle count is

Equation 2.6 𝐴_{𝐹𝑈𝑆𝑂𝑅}

𝐴𝑑𝑒𝑡𝑒𝑐𝑡𝑜𝑟𝑖𝑚𝑎𝑔𝑒∗ 𝑁_{𝑐𝑜𝑢𝑛𝑡𝑠}

In which the 𝐴𝑑𝑒𝑡𝑒𝑐𝑡𝑜𝑟𝑖𝑚𝑎𝑔𝑒 is the area of the image of the detector and 𝐴_{𝐹𝑈𝑆𝑂𝑅} the area of the FUSOR both in 𝑚² and the 𝑁_{𝑐𝑜𝑢𝑛𝑡𝑠} the amount of track counts on the image of the detector.

For this purpose the images with lower magnification and therefor more tracks provide the best results. In Table 1 the actual dimensions of the images are shown to determine the area of the image.

Table 1: Dimensions of the images of the detectors at different magnifications. The dimensions are calculated by using the scale of the image and extrapolating the actual image size.

Magnification Actual Image size [𝜇𝑚]

25 5330 × 4470

50 2650 × 2220

100 1330 × 1110

200 660 × 550

500 270 × 220

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3 Experimental setup

3.1 Calibration of the detectors using alpha sources

For this experiment the TASTRAK detectors are calibrated by exposing it to an active alpha source for the duration of 3 minutes. This source emits alpha particles which in turn collide with the detector leaving holes. This calibration is done with an Americium-241 alpha source.

Since Am-241 radiates alpha particles with approximately 5,5MeV the detectors are held at distances ranging from 0 cm to 3 cm with intervals of 0.25cm. The second calibration is done by holding the detectors at distances ranging from 0 to 1,5 cm with intervals of 0,5cm. The calibration parameters are given in Table 2. These holes are then widened by etching the detector using a sodium hydroxide solution of 6.25M for 6 hours at 78°C.

After the etching and gathering of the images of the detectors the MatLab program TRIACII will count the amount of tracks as well as their diameter and gray level. This will give an indication of what the diameter and gray level of the tracks of alpha particles of the known energy will leave. When the calibration of the detectors is done, a rough estimate can be established about the expectancy of the Helium-3 atoms’ track diameter and gray level. This will be used to determine the diameter and gray level range to characterize the alpha particles created by the fusion reactions.

Table 2: Detector parameters for the experimental calibration.

Detector number

Particle source Particle type

Distance [mm]

Approximate energy of particle [MeV]*

Irradiation time [s]

4 Am-241 Alpha 28 2.4 60

6 Am-241 Alpha 28 2.4 60

7 Am-241 Alpha 28 2.4 60

8 Am-241 Alpha 32 1.6 70

12 Am-241 Alpha 5 5 180

13 Am-241 Alpha 10 4.5 180

14 Am-241 Alpha 15 4 180

15 Am-241 Alpha 20 3.4 180

16 Am-241 combined

with Be-9

Neutron 5 2 – 10 ** 180

17 Am-241 combined

with Be-9

Neutron 5 2 – 10 ** 180

18 Uranium ore*** Alpha 1 4.2 180

19 Uranium ore*** Alpha 1 4.2 180

*taken from Figure 2.6

**taken from [24]

*** Uranium ore containing 99.284mass% U-238, 0.711mass% U-235 and 0.0053mass% U- 234. Taken from [25].

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3.2 Exposing the detectors to deuterium-fusion products

The FUSOR at the Eindhoven Technical University is operated on deuterium to create Deuterium-Deuterium fusion. The measurement of the product Helium-3 is paramount for this experiment, because the helium atoms cannot penetrate the shell of the FUSOR, the detectors must be mounted at the inside of a flange. This is done by opening up the FUSOR and using double sided tape to attach the detector to the inside of the flange. The FUSOR is operated with an open grid to accelerate the atoms and create fusion with the fast moving Deuterium-ions and the background Deuterium. While the fusion reaction is running the detector will be exposed to all the fusion reaction products that come into contact with it. For statistical arguments the amount of particles that collide with the detector must be as large as possible, however due to the optical properties of the microscope and the resolution of the taken image the tracks cannot exceed 10⁵ per square cm [26]. The specific experimental settings are given in Table 3, since shots vary in duration only the total neutron count will give an indication of the amount of fusion reactions.

Because the inside of the FUSOR is operating at a pressure of ±1,5 Pa the detectors will stick to the inside of the flange due to the adhesive tape. For these purposes the protective layer of plastic at the backside of the detector is not removed. This results in much easier removal of the detectors and less risk of damaging them during removal. The Neutron count is measured using a Studsvik 2202D Neutron detector, this measurement gives a solid baseline to

calculate the amount of fusion reactions occurring. This will give an indication to the amount of tracks that must be formed on the detector. The standard measurements are done inside the FUSOR to expose the detectors to all the fusion products. In addition a neutron measurement is done by attaching the detectors to the outside of the FUSOR essentially measuring only the neutrons. Beside the neutron measurement a proton measurement is executed by covering the detector inside the FUSOR with a 16.2 𝑚𝑔/𝑐𝑚² aluminum film effectively stopping the alpha particles and dissipating some of the energy of the protons, this will result in smaller proton tracks. For the calculation of the actual neutron production see section 7.2.

Table 3: The exposure details of the detectors.

Detector number Amount of shots

Shot numbers

Total neutron count by Studsvik

Actual neutron production [∗ 10⁶]

Specifications

1 18 75 tm 92 14082 4.40 Inside FUSOR

2,3,5 (same batch) 2 185, 186 8013 2.50 Inside FUSOR

9,10,11 (same batch)

23 329 tm 352 9930 3.10 Inside FUSOR

20 9 363 tm 371 1613 0.50 Inside FUSOR

21 3 372 tm 374 7471 2.33 Inside FUSOR

22 1 375 10560 3.30 Inside FUSOR

23, 24, 25, 26, 30 (same batch)

5 372 tm 376 18481 5.78 Directly on the outside

of the FUSOR 27,28,29 (same

batch)

10 372 tm 381 35967 11.24 Directly on the outside of the FUSOR

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31 4 376 tm 379 12356 3.86 Inside FUSOR

32 2 380, 381 5580 1.74 Inside FUSOR shielded

by 16.2 𝑚𝑔/𝑐𝑚² aluminum thin film n.b. Detector 21 was lost due to falling in the FUSOR chamber

When handling the TASTRAK detectors the recommended way is to minimize handling at all times to avoid stress and background exposure to the plastic.

3.3 Development of the detectors

The etching solution of sodium hydroxide is highly caustic and can in small amounts dissolve the skin. Because of this caustic behavior and the high concentration needed to etch the detectors the etching is done in a controlled environment by using a fume hood. The solution is made with an alkaline drain cleaner (Sodium hydroxide) in solid form. The grains of the sodium hydroxide are added to water to create a 6.25M solution. The detector is put in the solution for 6 hours, then taken out, rinsed and put under an optical microscope. Since the tracks will be in the range of 25 microns the magnification is varied between 5 and 200 times.

When the image is sharp a photograph will be taken using the microscope at the set

magnification and saved. The optical microscope and the TRIACII code will detect tracks up to a density of 10⁵ tracks per 𝑐𝑚².The etching of the detector is done by 70 degrees Celsius for 6 hours, these are the recommended etch conditions for the TASTRAK detector [7] [27].

After the etching the detectors must be handled with plastic gloves at all times, this prevents the grease of the skin to fill up the etched tracks and making them less visible.

3.4 Image processing of the detector images

The images of the detectors are loaded into MatLab using the TRIACII code [28]. An image of the backlight of the microscope is also necessary for the program to determine the correct gray values of the tracks. In order for TRIACII to load the images a text file is made which contains the names of the image files. When TRIACII is started using MatLab Figure 3.1 comes up to insert the input parameters. The images must be in the same workspace as the TRIACII MatLab files and a text file containing the image names must be inserted in the upper input slot. The group name string length is the amount of characters of the image file names which will be counted among the same group. The number of clusters refers to the K- means algorithm [29] and is usually taken to be 3. The morphological values determine the threshold of smallest objects and the threshold of largest objects; this effectively sets the range of the tracks measured. The two other options create a bar plot in MatLab these plots contain the output parameters either per image or per group. Mode I calculates the number of tracks, track diameter and track brightness or gray level. Mode II calculates the Axis length, both major and minor, the track brightness and the orientation of the track. Mode I is

primarily used because the incident angle of the fusion production particles will be perpendicular, so major and minor axis and the orientation will not be of interest.

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Figure 3.1: The TRIACII start figure. The input parameters are image file names in a text file, the Group name string length, number of Clusters and two morphological values. There is also an option to create bar plots for the output parameters per image and per group.

The histograms calculated by the code will give an indication which diameters and which gray levels are most common. However the combined values are not directly given, so the gray level is not combined with the diameter. Thus an extra step is needed to combine the two parameters. The data extracted from the image by TRIACII will be stored in an Excel-file.

The code as seen in appendix A will take this Excel file and read the data of the tracks in order to compute a scatter-plot of the data, see Figure 4.1 for an example. The scatter plot gives us more information about which tracks fall in the range of the helium track diameter and gray values seen in the detector calibration section. For a quantitative analysis of the detector a lower magnification will be used to capture the most amount of tracks on the image of the detector. This image is used to determine the amount of tracks on the detector. An image taken with higher magnification gives a more qualitative analysis of the individual tracks and with these more detailed tracks, the type can be distinguished.

The parameters ‘Number of Clusters’ and ‘Statistical size check’ are at all times kept constant at 3, the parameter ‘Morphological value’ is varied for different magnification of the images.

These values range from 50 to 800. To determine the morphological value the Calibration I option is used to determine which value results in consideration of the most genuine tracks.

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4 Results & Discussion

4.1 Quantitative analysis and Track count

4.1.1 Calibration

Alpha particle radiation was used for calibration of the detectors. The source of the radiation was an Am-241 source with an activity of 185 kBq for the first half of the detectors and a piece of uranium ore consisting of 99,3% U-238, 0,7% U-235 and trace amounts of the other isotopes of uranium for the second half of the detectors. The Am-241 alpha particles irradiating on the detectors had

approximately 5MeV, 4,5MeV, 4MeV and 3.4MeV for the distances of respectively 0,5cm, 1cm, 1,5cm, and 2cm distance from the source. The results of the alpha calibration are given in Figure 4.1. The alphas of 4MeV are given in this graph however the actual measured alpha particles produced by the FUSOR will have an energy of 1MeV. The calibration is done with higher energy because the distance of the active Am-241 source and the edge of the container was not precisely known and therefor the calibration done by a distance of 3,5cm from the source yielded no incident particles on the detector.

Figure 4.1: Alpha calibration with alpha particles from an Am-241 source with an approximate energy of 4MeV. The data points are filtered to give a more precise picture of the diameters and grayscale values of the particles. There appears to be a set range of diameters and grayscales for this particular type of particle with the energy of 4MeV.

According to Immè el al. [8] the alpha track diameter of a particle with energy ±4MeV is approximately 14𝜇𝑚. The grayscale of a particle with energy ±4MeV is approximately 55.

According to the calibration data observed in Figure 4.1 the diameter falls within the range of 10 to 25𝜇𝑚 and the grayscale ranges from 20 to 140. The grayscale of the tracks was influenced by the

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different lighting conditions and optical properties of the microscope. Although the settings were the same in terms of backlight intensity, the microscope and software tries to create the best fit of an image in terms of contrast and color scheme. Another reason may be the difference in specific CR-39 Detector, since Immè et al. did not specify the manufacturer of the detector, this experiment may have been conducted with a different detector which may lead to different outcomes.

The data points of the alpha calibration are filtered due to faults in the TRIACII code and the background of the detector, counting more tracks than present on the detector. This noise can be filtered out by only plotting the tracks with a diameter of 10 or higher.

When the calibration with the Am-241/Be-9 neutron source is added to the alpha calibration figure, an overall view of the alpha particle diameter/grayscale range and neutron particle

diameter/grayscale range can be distinguished in the plot, see Figure 4.2. These ranges will be used to distinguish the alpha particles and neutrons in the data sets from the FUSOR detectors. Although the alpha particles in the calibration had an approximate energy of 4MeV, the alpha particles created by DD fusion will have an energy of 0.82MeV.

Figure 4.2: The Alpha calibration with the neutron calibration plotted in one graph. The alpha particle tracks have larger diameters than the neutron tracks, which can be used to distinguish the two from one another. The ranges of the diameters and grayscales of both the alpha particles and the neutrons will be used to determine the type of track in the FUSOR experiments.

The total amount of tracks that have been cut from the alpha particle calibration will be a measure of noise and impurities for the FUSOR experiments. The percentage of tracks with a diameter lower than 10 will be considered noise and impurities on the detector. In the calibration of the alpha particle detectors 24 % of the tracks were considered noise.

Due to the amount of noise on the detector and the acceptance, the neutron particles will be cut from the analysis. The count of the charged particles will be divided by 3 since the fusion reaction creates Helium-3, protons and Tritium.

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17 4.1.2 Fusor Experiments

In Figure 4.3 the results of detector 1 can be seen, when comparing detector 1 with the other

detectors, the diameter of detector 1 is smaller. This is due to a lower temperature during the etching process essentially slowing down the process, and etch less of the detector away. This will result in smaller tracks. For this reason the noise cannot be separated from the actual tracks and this detector is not further analyzed.

Figure 4.3: Diameter vs Grayscale of detector 1. The detector was placed inside the FUSOR In Figure 4.4 the results of detectors 9, 10, and 11 are shown. The track diameters range from 0 to 30, which indicates several different particles created the tracks. The amount of noise on the detector is 13% of the total counts. The tracks with a diameter lower than 10 have been filtered out.

Figure 4.4: Diameter vs Grayscale of the detectors 9, 10, and 11. The detectors were placed in the same batch on the inside of the FUSOR. The grayscale of all the tracks is within 40 and 150.

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Some interesting results can be seen in Figure 4.5, this detector was placed inside the FUSOR but for some reason had little tracks. One possible explanation, although unlikely, is that the grid was

blocking the detector; this would result in only detecting the neutrons on the detector.

Figure 4.5: Diameter vs Grayscale of the detector 20, placed inside the FUSOR.

In Figure 4.6 the tracks of detector 22 are shown. The results are similar to Figure 4.4 with the exception of some tracks having a higher grayscale.

Figure 4.6: Diameter vs Grayscale of the detector 22, placed inside the FUSOR.

The results seen in Figure 4.7 are very interesting since the detectors 23 up to and including 30 were placed on the outside of the FUSOR. This would result in only neutrons irradiating the detectors.

However the track parameters of these detectors do not coincide with the calibration results of the neutron calibration. The tracks seem to be alpha or proton tracks judging on the diameter and grayscale of the tracks.

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Figure 4.7: Diameter vs Grayscale of the detectors 23 up to and including 30, the neutron measurement placed on the outside of the FUSOR.

The results seen in Figure 4.7 are very interesting since the detectors 23 up to and including 30 were placed on the outside of the FUSOR. This would result in only neutrons irradiating the detectors.

However the track parameters of these detectors do not coincide with the calibration results of the neutron calibration. The tracks seem to be alpha or proton tracks judging on the diameter of the tracks.

Figure 4.8: Diameter vs Grayscale of the tracks from detector 31 placed inside the FUSOR.

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The results of detector 31 do not reflect the amount of particles that have been produced by the fusion reaction. This may indicate that the particles may have been prevented to hit the detector.

Figure 4.9: Diameter vs Grayscale of the tracks from detector 32, placed inside the FUSOR shielded by 16.2 𝑚𝑔/𝑐𝑚² aluminum film.

From these figures, Figure 4.3 up to and including Figure 4.9, the total count of particles incident on the detectors can be calculated. On the basis of the calibration the tracks with a diameter lower than 10 will be considered neutron tracks, impurities and noise. Tracks with a diameter greater than 10 will be considered alpha, proton and tritium tracks.

In Figure 4.9 the tracks of detector 32 are shown. Detector 32 was placed inside the FUSOR shielded by a 16.2 𝑚𝑔/𝑐𝑚² aluminum thin film. This aluminum film effectively blocks both the alpha

particles and the protons, allowing only the neutrons to pass. There are however several tracks on the detector with smaller diameters and therefore smaller energies. These tracks are likely background tracks.

Because the different images have different parameters imposed by the software of the microscope the grayscale of the background varies in different images. This may result in varying grayscale values of the tracks. There exists also a large uncertainty in the diameter of the measured tracks. This originates in the way the TRIACII code works, this code essentially measures the radius of the tracks in pixels. This way the diameter of the tracks is discreet with steps of 2. Since different

morphological values may give different pixel values for the diameters the uncertainty is higher in the case of higher magnification as a result of scaling. However with low magnification more noise is counted due to the fact the tracks are smaller.

Table 4: the calculated fusion rates for the Studsvik and the SSNTD’s per detector. The SSNTD fusion rate is calculated by taking the different magnifications and using TRIACII and Equation 2.6. The Studsvik fusion rate is calculated with Equation 7.2 and Table 3: The exposure details of the detectors.Table 3. The morphological values which were used at the TRIACII code are included as are the different magnifications.

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21 Morphological

value

- 80 100 250 800

Magnification - 25 50 100 200

Detector Fusion rate (Studsvik)

*10^6

Fusion rate (SSNTD)

*10^6

Fusion rate (SSNTD)

*10^6

Fusion rate (SSNTD)

*10^6

Fusion rate (SSNTD)

*10^6

9 3.1 ± 0.5 1.0 ± 0.5 3.7 ± 1.7 1.8 ± 0.8 2.2 ± 1.0

10 3.1 ± 0.5 0.5 ± 0.3 1.4 ± 0.6 0.4 ± 0.2 0.9 ± 0.4

11 3.1 ± 0.5 3.2 ± 1.5 3.8 ± 1.8 4.9 ± 2.3 5.7 ± 2.7

20 0.5 ± 0.1 0.1 ± 0.1 0.5 ± 0.2 0.5 ± 0.3 0.5 ± 0.2

22 3.3 ± 0.5 0.0 ± 0.0 0.7 ± 0.4 0.3 ± 0.2 0.6 ± 0.3

31 3.9 ± 0.6 0.1 ± 0.0 1.2 ± 0.6 0.4 ± 0.2 0.4 ± 0.2

32 1.7 ± 0.3 0.2 ± 0.1 1.0 ± 0.5 1.9 ± 0.9 1.8 ± 0.9

The uncertainty in the calculations is due to the imperfections on the detector as well as background radiation. The TRAICII code also counts several of these imperfections when counting tracks.

Furthermore the density of the tracks may vary over the detector, in this case only some small parts of the detector were used to take an image of. This will affect the amount of tracks counted. Also the calculation of the area of the detector and the FUSOR will have an uncertainty which must be taken into account. When operating the TRIACII code a morphological value is inserted as one of the parameters to count the tracks since this value is determined by a trial and error process there is a decision uncertainty to were the line is between noise and tracks. All of these factors combine into the given uncertainty. Calculation of this value is given in the Appendix.

The fusion rate calculated for detectors 9, 10, and 11 give several different values suggesting that the fusion rate cannot be unambiguously determined using SSNTD’s. Also the different magnifications should give the same values for the fusion rate, but these values vary greatly also supporting the observation that the fusion rate cannot be precisely measured with SSNTD in the FUSOR.

As seen in the appendix the images from detector 10, 22 and 31 show little to no tracks. The track density of these detectors is very low compared to the other detectors. This may simply be from images of parts of the detector with lower track density or blockage of the incoming particles.

Another explanation may be the handling of the detectors, some grease may have been present on the detectors, which will block the tracks and lessen the visibility of the tracks.

The charged particle tracks on detectors 24, 25, 27, 28, 29 and 30 are interesting and suggest charged particles outside the FUSOR. This may be due to background radiation or neutron activation of the FUSOR materials.

The relative error in the fusion rate between the Studsvik results and the SSNTD results are given in Table 5.

Table 5: The relative error of the SSNTD results of the fusion rate compared to the Studsvik results for the fusion rate. All errors are given in percentage.

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22 Magnification >

Detector ∨ 25 50 100 200 Error per

Detector

9 67.7% 19.4% 41.9% 29.0% 39.5%

10 83.9% 54.8% 87.1% 71.0% 74.2%

11 −3.2% −22.6% −58.1% −83.9% 42.0%

20 80.0% 0.0% 0.0% 0.0% 20.0%

22 97.4% 78.8% 90.9% 81.8% 87.2%

31 100% 69.2% 89.7% 89.7% 87.2%

32 88.2% 41.2% −11.8% −5.9% 36.8%

Error per magnification 74.3% 40.9% 54.2% 51.6%

4.2 Qualitative analysis and Difference in energy

In order to better distinguish the different tracks a qualitative analysis is done where the actual tracks are examined. This will provide more insight in the difference between proton, alpha and neutron tracks on the detectors. The calibration is done with both alpha and neutron particles, protons were not measured as a calibration but could theoretically be filtered out when the expected track parameters of alpha particles and neutrons are known.

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The calibration is done with 4 different energies of alpha particles originating from the Am-241

source. In

Figure 4.10 two images are shown with alpha particle tracks from different detectors with different energies. In both images the tracks of alpha particles are highlighted and measured. In the left picture of Figure 4.10 the tracks are 27.05𝜇𝑚 and 28.37𝜇𝑚, in this case the alpha particles had an energy of 3.4MeV. In the right picture the tracks are 30.56 𝜇𝑚 and 37.35𝜇𝑚, in this case the particles had an energy of 5MeV. In both pictures are also smaller and lighter tracks, these tracks are created by alpha particles with lower energy than the normal incident energy, or may be background radiation tracks due to radon.

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Figure 4.10: Two images (zoom 50x) of tracks on a detector. The left-side image has tracks created by alpha particles with an approximate energy of 3.4 MeV (detector 15); the right-side image has tracks created by alpha particles with an approximate energy of 5 MeV (detector 12).

In Error! Reference source not found. the alpha particle calibration is shown, on the left-hand-side the particles had an energy of 3.4MeV and on the right hand side the particles had an energy of 5MeV. In terms of diameter the tracks cannot be distinguished visually, however the difference in grayscale can be seen with the naked eye. The tracks on the left hand side are generally lighter than the tracks on the right hand side.

The mean diameter is taken from the 4 different detectors of the calibration and set in a graph in Figure 4.11. In this case only 4 datapoints are plotted due to a fault in the earlier calibration done with lower energies. According to [8] the curve must look like a power fit with a point in the origin of the axle system. For a better presentation of the energy dependence of the diameter more data point in the lower energy spectrum are desired. However the diameter difference is present in the different energies, suggesting that with B-p fusion the energy of the Helium particles can be distinguished with the SSNTD.

0 1 2 3 4 5

-5 0 5 10 15 20 25 30

Mean Diameter [um]

Energy of alpha particle [MeV]

Figure 4.11: The mean diameter for the different energies of alpha particles a power fit with 𝑦 = 𝐴|𝑥 − 𝑥_𝑐|^𝑝 is used. With 𝑥_𝑐 = 0.01, 𝐴 = 12.65, 𝑝 = 0.42744.

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5 Conclusion

The SSNTD TasTrak of TASL are suitable for detection of alpha particles and larger particles.

However the distinction between the particles proves very difficult resulting in inconclusive results for the FUSOR experiments. For neutron measurement the noise on the detector is too large to accurately measure the neutron count. This is largely due to the reduced acceptance of neutrons on the polymer and due to the background radiation. Handling of the detector will also leave marks on the polymer and create additional imperfections. Since these imperfections and noise leave marks on the polymer mainly in the order of several micrometers, which is the order of magnitude of the neutron tracks, the neutron tracks are indistinguishable from the noise with the magnitude and etch settings used in this study.

The quantitative analysis performed by TRAICII of the calibration of the detectors show that alpha particles with an energy within the range of 3 to 5 MeV have a diameter in the range of 10 to 35 micrometers. The neutron tracks are significantly lower and have a diameter in the range of 0 to 10 micrometers. The neutron tracks and charged particle tracks are distinguishable from one another.

The amount of tracks calculated using the SSNTD’s has an uncertainty of 47% and in most cases the amount of tracks is lower than the fusion count calculated using the Studsvik. The most promising results are from the 50 times magnification. In this case there are enough tracks and they are

distinguishable from the noise and impurities on the detector. In this case the use of SSNTD’s in the FUSOR is possible but the uncertainty is still very large. The results show no conclusive fusion rate from the detectors since the fusion rate for the same amount of fusion does not coincide.

To detect the different energies of charged particles the SSNTD’s can be used, this however requires a more precise tool than the TRIACII code as this will add uncertainty because the code calculates the radius in pixels and has a discrete step of 2 pixels in the diameter.

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6 References

[1] A. Szydlowski, M. Sadowski, T. Czyzewski, M. Jaskola, A. Korman and I. Fijal, "Detection characteristics of PM-355 solid-state nuclear track detector for normal incident light ions within MeV energies," Nuclear Instruments and Methods in Physics Research B, vol. 171, pp. 379-386, 2000.

[2] A. Szydlowski, B. Sartowska, M. Jaskola, A. Korman, A. Malinowska and J. Choinski,

"Calibration of PM-355 nuclear track detector: For C-ions within the energy range of 70-90 MeV," Radiation measurements, vol. 44, pp. 789-801, 2009.

[3] A. Malinowska, M. Jaskóla, A. Korman, A. Szydlowski and M. Kuk, "Characterization of solid state nuclear track detectors of the polyallyl-diglycol-carbonate (CR-39/PM-355) type for light charged particle spectroscopy," Review of Scientific Instruments, vol. 85, 2014.

[4] D. Gautier, J. Kline, K. Flippo, S. Gaillard, S. Letzring and B. Hegelich, "A simple apparatus for quick qualitative analysis of CR39 nuclear track detectors," in 17th Topical Conference on High-Temperature Plasma Diagnostics, Albuquerque, 2008.

[5] N. Sinenian, M. Rosenberg, M. Manuel, S. McDuffee, D. Casey, A.B.Zylstra, H. Rinderknecht, M. G. Johnson, F. Séguin, J. Frenje, C. Li and R. Petrasso, "The response of CR-39 nuclear track detector to 1-9 MeV protons," Review of Scientific Instruments, vol. 82, no. 103303, 2011.

[6] Canberra Industries Inc., "http://www.canberra.com/," 2016. [Online]. Available:

http://www.canberra.com/products/hp_radioprotection/neutron-instruments.asp. [Accessed 17 1 2017].

[7] Track Analysis Systems Ltd., "www.tasl.co.uk," 2015. [Online]. Available:

http://www.tasl.co.uk/brochures/TASTRAK_specification_sheetAlphaParticles.pdf. [Accessed 14 december 2016].

[8] G. Immè, D. Morelli, M. Aranzulla, R. Catalano and G. Mangano, "Nuclear track detector characterization for alpha-particle spectroscopy," Radiation measurements, vol. 50, pp. 253-257, 2013.

[9] D. Nikezic and D. Kostic, "Simulation of the track growth and determining the track parameters," Radiation measurements, vol. 28, pp. 185-190, 1997.

[10 D. Nikezic, "Three dimensional analytical determination of the track parameters," Radiation

(29)

27 ] measuremets, vol. 32, no. 4, pp. 277-282, 2000.

[11 ]

B. Dörschel, R. Bretscheinder, D. Hermsdorf, K. Kadner and H. Kühne, "Measurement of the track etch rates along proton and alpha particle trajectories in CR-39 and calculation of the detectrion efficiency," Radiation measurement, vol. 31, pp. 103-108, 1999.

[12 ]

B. Dörschel, H. Hartmann, K. Kadner and P. Röβler, "Studies on the variation of the track etch rate along alpha particle trajectories in CR-39," Radiation measurements, vol. 25, no. 1-4, pp.

157-158, 1995.

[13 ]

B. Dörschel, D. Hermsdorf, K. Kadner and S. Starke, "Dependence of the etch rate ratio on the energy loss of light ions in CR-39," Radiation measurements, vol. 35, no. 4, pp. 287-292, 2002.

[14 ]

B. Dörschel, D. Hermsdorf, K. Kadner and S. Starke, "Variation of the track etch rate along the trajectories of light ions in CR-39," Radiation measurements, vol. 35, no. 3, pp. 177-182, 2002.

[15 ]

A. Azooz, S. Al-Nia'emi and M. Al-Jubbori, "Empirical parametrization of CR-39 longitudinal track depth," Radiation measurements, vol. 47, pp. 67-72, 2012.

[16 ]

M. Rosenberg, F. Séguin, C. Waugh, H. Rinderknecht, D. Orozco, J. Frenje, M. G. Johnson, H.

Sio, A. Zylstra, N. Sinenian, C. Li, R. Petrasso, V. Y. Glebov, C. Stoeckl, M. Hohenberger, T.

Sangster, S. LePape and A. Mackinnon, "Empirical assessment of the detection efficiency of CR-39 at high proton fluence and a compact, proton detector for high-fluence applications,"

Review of Scientific Instruments, vol. 85, p. 043302, 2017.

[17 ]

J. Frenje, C. Li, F. Séguin, D. Hicks, S. Kurebayaschi, R. Petrasso, S. Roberts, V. Y. Glebov, D.

Meyerhofer, T. Sangster, J. Soures, C.Stoeckl, C. Chiritescu, G. Schmid and R. Lerche,

"Abslolute measurements of neutron yields from DD an DT implosions at the OMEGA laser facility using CR-39 track detectors," Review of Scientific Instruments, vol. 73, no. 2597, 2002.

[18 ]

Z. Lounis, S. Djeffal, M. Allab, M. Izerrouken and K. Morsli, "Characteristics of the CRS fast neutron personal dosemeter," Radiation measurement, vol. 28, no. 1-6, pp. 467-472, 1997.

[19 ]

E. Fantuzzi, B. Morelli, G. Falangi, L. Patrizii and V. Togo, "CR-39 acceptance test and

optimisation for fast neutron dosimetry applications," Radiation Protection Dosimetry, vol. 101, no. 1-4, pp. 573-578, 2002.

[20 ]

F. Mariotti, G. Falangi and E. Fantuzzi, "Comparison among two fast neutron CR-39 (R) materials: preliminary experimental studies," Radiation Measurements, vol. 44, no. 9-10, pp.

996-998, 2009.

[21 ]

R. Mishra, C. Orlando, L. Tommasino, S. Tonnarini and R. Trevisi, "A better understanding of the background of CR-39 detectors," Radiation measurements, vol. 40, pp. 325-328, 2005.

[22 Z. Lounis, S. Djeffa, K. Morsli and M. Allab, "Track etch parameters in CR-39 detectors for

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28

] proton and alpha particles of different energies," Nuclear Instruments and Methods in Physics Research B, vol. 179, pp. 543-550, 2001.

[23 ]

K. Yu, C. Yip, D. Nikezic, J. Ho and V. Koo, "Comparison among alpha-particle energy losses in air obtained from data of SRIM, ICRU and experiments," Applied Radiation and Isotopes, vol. 59, pp. 363-366, 2003.

[24 ]

QSA Global Inc, "QSA Global | Americium 241/Beryllium - QSA Global," QSA Global, 1 Januari 2015. [Online]. Available: http://www.qsa-global.com/americium-241beryllium/.

[Accessed 2 April 2017].

[25 ]

WISE Uranium Project, "Uranium Radiation Properties," 2 may 2016. [Online]. Available:

http://www.wise-uranium.org/rup.html. [Accessed 6 march 2017].

[26 ]

M. Yamamoto, N. Yasuda, M. Kurano, T. Kanai, A. Furukawa, N. Ishigure and K. Ogura,

"Atomic force microscopic analyses of heavy ion tracks in CR-39," Nuclear Instruments and Methods in Physics Research B, vol. 152, pp. 349-365, 1999.

[27 ]

R. Félix-Bautista, C. Hernández-Hernández, B. Zendejas-Leal, R. Fragoso, J. Golzarri, C.

Vázquez-Lópex and G. Espinosa, "Evolution of etched nuclear track profiles of alpha particles in CR-39 by atomic force microscopy," Radiation measurements, vol. 50, pp. 197-200, 2013.

[28 ]

D. Patiris, K. Blekas and K. Ioannides, "TRIAC II. A MatLab code for track measurements from SSNT detectors," Computer Physics Communications, vol. 177, pp. 329-338, 2077.

[29 ]

R. Duda, P. Hart and D. Stork, Pattern Classification, New York: Wiley-Interscience, 2001.

[30 ]

AB Atomenergi, "Neutron Counter Studsvik 2202D," 11 april 1973. [Online]. Available:

https://sftp.hs-

furtwangen.de/~neutron/download/lehre/radiation/Neutron%20Counter%20Studsvik%202202%

20D.pdf. [Accessed 28 march 2017].

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7 Appendix

7.1 Appendix A: Matlab code to compute scatter-plots from excel-data

prompt = {'Enter Imagefile name: ','Enter track count: ','Enter amount of tracks','Enter Helium Cut-off diameter','Enter Helium Cut-off grayscale'};

dlg_title = 'Input Parameters';

num_lines = 1;

defaultans = {'Sheet4','B7000','150','10','255'};

answer = inputdlg(prompt,dlg_title,num_lines,defaultans);

sheet = answer{1};

str2 = answer{2};

str1 = 'A5';

Data = xlsread('CircularTracks_PerImage.xls',sheet,[str1 ':' str2]);

Grayscale = Data(:,1);

Diameter = Data(:,2);

Cutoff = str2double(answer{4});

Diameter(Diameter < Cutoff)=0;

Cutoff2 = str2double(answer{5});

Grayscale(Grayscale > Cutoff2)=0;

% scatter plot

scatter(Grayscale,Diameter,10,[0 0 0],'filled')

title('Scatterplot of the diameters vs grayscale of the tracks') xlabel('Grayscale Value')

ylabel('Diameter of the tracks in microns') axis([0 300 0 40])

7.2 Calculation of the total neutron yield and uncertainty

To calculate the actual neutron production of the fusion reaction inside the FUSOR a

Studsvik 2202D neutron detector is used to measure the neutrons. This detectors output is the amount of pulses given when a neutron is detected. To calculate the total production the distance of the Studsvik to the center of the FUSOR is taken to be 60 cm. The Studsvik itself has a diameter of 21.5 cm. Since the neutrons of the fusion reaction will propagate in every direction the area of a sphere with radius = 60 cm is taken. The area of the Studsvik will tell us what percentage of the neutrons will be detected by the detector.

Equation 7.1

𝑎 = 𝜂 ∗𝐴_{𝑆𝑡𝑢𝑑𝑠𝑣𝑖𝑘} 𝐴_{𝑠𝑝ℎ𝑒𝑟𝑒}

Here the η is the efficiency of the Studsvik to detect neutrons with an approximate energy of 2,45 MeV, this is 0,4 according to [30], the user manual of the Studsvik 2202D detector. This

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fraction calculated by Equation 7.1 will be used to calculate the actual neutron production using the following formula.

Equation 7.2

𝑛𝑒𝑢𝑡𝑟𝑜𝑛 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 =𝐶𝑝𝑠 𝑎

The uncertainty of the area of the Studsvik and sphere is determined by the uncertainty of the radii. The diameter of the Studsvik has an uncertainty of ±0.5𝑐𝑚 and the diameter of the sphere ±5𝑐𝑚. The efficiency of the Studsvik is taken from the user manual fig. 2. This results in an uncertainty of ±0.05. The counts per second output is taken to have an uncertainty of 200 counts per 10000. The total uncertainty of the neutron production measured by the Studsvik is ^𝑆_𝑛^𝑛= 0.154. Which translates to 15.4%

7.3 Uncertainty of the fusion rate (SSNTD)

The uncertainty of the areas is dependent on the radius or dimensions. For the FUSOR the radius is the distance from the location of the reaction to the detector. This uncertainty is taken to be ±5𝑐𝑚. The dimensions of the detector have an uncertainty of 20𝜇𝑚 due to pixel values and extrapolating the dimensions from the scale of the image. The amount of counts has a considerate uncertainty due to noise, background radiation, and uncertainty in the TRIACII code and inconsistencies in the lighting of the images this uncertainty is taken to be 35%. This includes some decision uncertainty due to the morphological values taken for the different magnification. This combines to ^𝑆_𝑛^𝑛= 0.472, which translates to 47.2%

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7.4 Images of detectors

Figure 7.1: Image of Detector 9 with 50 times magnification.

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Figure 7.9 Image of Detector 27 with 50 times magnification.

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Eindhoven University of Technology BACHELOR Using Solid State Nuclear Track Detectors in a FUSOR to detect charged particles Duffhues, J.C.J.

Using Solid State Nuclear Track Detectors in a

FUSOR

To detect Charged Particles

Abstract

Table of contents

1 Introduction

2 Theoretical background

2.1 Track parameters

2.2 Acceptance and sensitivity

2.3 Calibration Curves from literature

2.4 Calculation of total counts

3 Experimental setup

3.1 Calibration of the detectors using alpha sources

3.2 Exposing the detectors to deuterium-fusion products

3.3 Development of the detectors

3.4 Image processing of the detector images

4 Results & Discussion

4.1 Quantitative analysis and Track count

4.2 Qualitative analysis and Difference in energy

5 Conclusion

6 References

7 Appendix

7.1 Appendix A: Matlab code to compute scatter-plots from excel-data

7.2 Calculation of the total neutron yield and uncertainty

7.3 Uncertainty of the fusion rate (SSNTD)

7.4 Images of detectors