aCORN Alignment Michael Stephen Howard
Hamilton College Fall 2012
In Partial Fulfillment of the Requirements for the Degree Bachelors of Arts Physics
Table of Contents Acknowledgments……………………………………………………………………………….2 Abstract…………………………………………………………………………………………..3 Introduction………………………………………………………………………………………4 Background………………………………………………………………………………………5 The Standard Model…………………………………………………………………….5 a…………………………………………………………………………………………...6 Previous Experiments…………………………………………………………………..6 aCORN Theory…………………………………………………………………………………..8 A Simplified Approach to aCORN…………………………………………………..…8 Widening Acceptances………………………………………………………………..12 aCORN Apparatus……………………………………………………………………..15 Current Alignment System……………………………………………………………17 Supplemental Alignment Test………………………………………………………………...19 Electron Gun……………………………………………………………………………22 Detector…………………………………………………………………………………24 Implementation…………………………………………………………………………26 Experimental Results………………………………………………………………………….30 Discussion………………………………………………………………………………………32 Potential aCORN Supplemental Alignment Design………………………………………..36 Conclusion……………………………………………………………………………………...39 Appendix A: Works Cited………….………………………………………………………….40 Appendix B: CAD…………………………………………………………………………...….41
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Acknowledgements I would like to thank my two thesis advisors Dr. Brian Collett and Dr. Gordon Jones for their support and guidance throughout this project. I would also like to thank Nick Sylvester, my lab partner and friend.
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Abstract The aCORN experiment is an attempt to measure the beta-neutrino angular correlation coefficient, commonly referred to as ‘a’, to 1% fractional uncertainty. One of many requirements for an accurate measurement of a is that two components of the aCORN apparatus, the magnetic field and the proton collimator, must be correctly oriented with respect to one another. While there is a system being used to align aCORN currently, we wish to devise a supplementary test of aCORN’s alignment to convince the scientific community that we accurately measured a. This new alignment system consists of an electron gun and a detector. An electron gun extracted from a Sylvannia JANCHS3BP1 cathode ray tube produced an electron beam in a vacuum. We detected a current of 15 nA off of a metal plate detector. We have shown that this electron source is a viable choice as the basic components of aCORN’s supplemental alignment test system.
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Introduction aCORN is a neutron decay experiment currently running at the National Institute of Science and Technology (NIST) outside of Washington D.C. The experiment is a collaborative effort between Hamilton College, Indiana University, Tulane University, DePauw University, Harvard University, NIST, the University of Sussex, and is funded by the National Science Foundation (NSF) The experiment has been collecting data intermittently since 2009 in an attempt to measure the beta-neutrino asymmetry correlation coefficient, a, to 1% fractional uncertainty. The experiment is currently offline so that various systems may be upgraded with the hopes that fractional uncertainty will eventually be lowered to 1%. Another system that is being augmented while aCORN is offline is the way in which we test aCORN’s alignment; specifically the alignment of the proton collimator to the magnetic field. We believe the current alignment system sufficiently aligns aCORN but it has many small problems. It requires much of the apparatus to be disassembled during the alignment process. Troublingly, there is evidence that these components move when they are being put back in place after the alignment test. These movements fall barely within our allowable margins of error. In order to convince the scientific community at large that our measured value for a is correct we must prove that aCORN is properly aligned. Therefore, in 2004, Dr. Brian Collett and others at Hamilton College set out to design a non-intrusive alignment system. If the two tests agree, we have verified that the current alignment test is sufficient and that previously recorded data is still relevant. The goal of this paper is to document the continuing design of a supplemental alignment test system. First we will discuss what the neutron decay asymmetry correlation coefficient is. This ties directly into the next section detailing the theory behind the aCORN experiment. We will begin with a simplified version of aCORN to familiarize the reader with the underlying theories before explaining aCORN as a whole. We then explore the reasons why alignment is so important if aCORN is to succeed. Next, we detail the current two-stage alignment system and some of the problems associated with it. This motivates the supplemental alignment system’s design and implementation on a smaller scale at Hamilton College. Our findings are in the ‘Experimental Results’ section below. Naturally, we then analyze these results and discuss their meaning. We conclude the paper by suggesting the steps that should be taken next to improve the detectors and by proposing a potential design to insert the alignment system in aCORN at NIST.
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Background The Standard Model The Standard Model describes a world constructed of 12 fundamental particles and their antiparticle counterparts that interact through three distinct forces, the strong, the weak, and the electromagnetic force. There are two types of particles, fermions and bosons. Particles with half-integer spins are fermions and particles with zero or integer spins are boson [Kittel 152]. Some bosons are force carriers, particles that exchange forces between particles. Two of these bosons, ‘W’ and ‘Z’, are the weak interactions’ force carriers. Some of what the Standard Model describes are measurable quantities. Neutron decay, a pure example of the weak interaction, proves to be a relatively simple measurable quantity. Located at NIST, the National Institute of Science and Technology, aCORN, A Correlation in Neutron Decay, attempts to test the Standard Model’s interpretation of the weak force. A neutron is composed of an up quark and two down quarks. When a free neutron decays, one of the down quarks decays into an up quark by way of a ‘W’ boson emission. What was formerly the neutron is now a proton composed of two up quarks and a down quark. The ‘W’ boson is extremely short lived and quickly decays into an antineutrino and an electron. Ultimately, the products of neutron decay are a proton, an electron, an antineutrino, and the endpoint energy of mn-mp-me=1.29333 GeV-me !1.293 GeV [Beringer et al]. To detail the decay products, we turn to the Jackson Tremont and Wyld equation. The Jackson Tremont and Wyld equation, (1), describes all possible beta decay probabilities for spin ! to spin ! decays [Jackson]. Thus it describes the free neutron decay explained above. (1) Here is the electron’s energy, is the neutron’s decay lifetime, is the antineutrino’s energy, is the electron’s momentum, is the antineutrino’s momentum, and is the neutron spin’s polarization. The coefficients a, b, A, B, and D correspond to different angular correlation coefficients. The Standard Model alone does not dictate what these coefficients are. However, these coefficients are measurable quantities. All of these coefficients are related to the neutron weak-coupling ratio, . Specifically, ,
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,
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We can measure these coefficients experimentally and then use the above relationships to independently predict four "’s. We then compare these "’s as a test of the self-consistency of the
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Standard Model. If the Standard Model is self-consistent here, all four "’s should agree. The least precisely measured of the above coefficients is a. aCORN is an attempt to better characterize this least understood free neutron decay coefficient. On a larger scale, aCORN’s value of a may then be used as a test of the self-consistency of the standard model. a aCORN is, essentially, a test of the self-consistency of the Standard Model by exploring the boundaries of one such coefficent, a. Let us examine what a physically corresponds to. Consider a visual representation of a’s relationship to decay angles.
Figure 1: A plot depicting an isotropic distribution of angles, the blue circle, where a=0 and a non-isotropic distribution of angles, the green circle, where a!0
Here the relative magnitude of the distance from the origin to a point on the circle at a certain angle, theta, illustrates the likelihood of that angle occurring between the electron and antineutrino during free neutron decay. The blue circle is a plot of an isotropic angle distribution. In an isotropic distribution, all angles theta are just as likely as any other angle. This isotropic distribution of angles corresponds to a=0. The green circle depicts a#0. In this figure, the green circle illustrates that the decay angle "2 between the antineutrino and electron is more likely than the angle "1. Previous Experiments aCORN is an attempt to measure a the neutron decay asymmetry correlation coefficient. But aCORN is not the first experiment that attempted to measure a. Previous experiments have measured a to within 5% fractional uncertainty. The first attempt to measure a was conducted in 1967 by Grigor’ev, Grishin, Vladimirskii, Nikolaevskii, and Zharkov. The team employed a spectroscopic method and '"
analyzed the shape of the energy spectrum of recoil protons from an unpolarized neutron beam [Noid 22]. They then extracted a from this spectrum. Subsequent experiments since then have all relied on a similar technique of analyzing the shape of the recoil protons’ energy spectrum to find a. Most notably, a 1978 effort by Stratowa et al used this spectroscopic method to find the current value of a = -0.1017¹0.0051 [Stratowa 18]. The spectroscopic method has its limitations though. Due to such problems such as residual gas scattering, a is limited by systematic error. As such, the current value of a has 5% fractional uncertainty. This value for a is consistent with the Standard Model. aCORN attempts to lessen this fractional uncertainty to 1% using counting statistics, not spectroscopy.
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aCORN Theory aCORN aims to lower the fractional uncertainty of a from 5% to 1% using a counting method rather than a spectroscopy method. Perhaps one of the easiest way to measure a would involve a spherical detector surrounding a free neutron. This detector would be able to detect both antineutrinos and electrons. The neutron would decay and the detector would record the position of the resulting impact of the electron and antineutrino. From this position information, one could infer the angle between the momentum vectors of the electron and the antineutrino. Many neutrons would be placed in the center of the spherical detector and the process would repeat. After many of these instances, a would be calculated.
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Figure 2: A neutron placed inside an ideal spherical electron and antineutrino detector. The neutron decays and the antineutrino (green) and electron (blue) strike the detector at some angle
Unfortunately, it is extremely difficult to detect an antineutrino. Yerozolimsky detailed the theory behind aCORN at a seminar at NIST in 1996 [Yerozolimsky]. The method does not require antineutrinos to be detected; instead it relies upon measuring the angle between the neutron decay’s electron and proton and then using conservation of momentum to deduce the antineutrino-electron angle. So, by accurately measuring the coincidence rate of any two different angles of decay between the antineutrino and electron, one can find a counting rate asymmetry that is directly proportional to a. Note from Figure 2 that by comparing the precisely measured rates at two different angles, one can determine how far from an isotropic distribution a is, i.e. how far the blue circle is away from the green in Figure 1, i.e. how likely a decay is to occur at a given angle. Thus by measuring the likelihood of decay to occur at any two distinct angles, we can find a. Precisely measuring any two angles would suffice but it proves optimal to measure the angles 0o and 180o. Yerozolimsky and Mostovoy’s proposal suggests that time intervals, known as time of flight, should be used to differentiate between the two angles of decay. Observe the following simplified version of aCORN which best illustrates the method being implemented. A Simplified Approach to aCORN Unfortunately, we cannot detect antineutrinos so we must consider a way to deduce the antineutrino’s momentum vector from quantities that we can measure. Since we can detect the
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other two decay products, protons and electrons, we will use these two particles to find the antineutrino’s momentum vector using conservation of momentum. A cold neutron has very little kinetic energy. Cold neutrons from NIST’s reactor have a thermal energy of 20 to 400 meV [Williams]. So, for this explanation, we can treat the neutron as if it were at rest when it decays. Thus the neutron doesn’t give additional kinetic energy to its decay products, the proton, neutron, and antineutrino. During decay, since the proton is so relatively massive compared to the other decay products, it is emitted with a relatively low velocity. As such, the electron and antineutrino receive most of the decay energy. Recall that the decay energy is 1293KeV, the mass difference that is released as energy during neutron decay [Beringer et al]. If we can measure the electron’s kinetic energy, we know that the antineutrino’s energy is, to recoil order. Equation 3 allows us to determine the magnitude of the particles’ momentum from its energy. (3) This momentum, p, is a particles total momentum. The components of this total momentum vector may be divided up into two separate coordinates, axial momentum and transverse momentum. If a particles’ momentum is directed entirely on axis, it has no transverse momentum and vice versa. This allows us to describe the antineutrino’s momentum with the following circle in momentum space. As shown in figure 3, the magnitude of the radius of each of the vectors denotes a particles’ total momentum.
Figure 3: An exaggerated version of the momentum space diagram depicting small angle, Group 1 events, and large angle, Group 2 events. We restrict the proton’s momentum vector to be on axis. The transverse component of the antineutrino’s momentum is opposite in direction but equal in magnitude to the electron’s. Note that the proton momentum vectors (red) are not drawn to scale but are included to indicate the direction of the proton in Group 1 and Group 2 events
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In order to detect protons and electrons there exists a beta detector and a proton detector, which face each other and are shown on the y-axis of Figure 4 below. The beta detector measures electron energy and the proton detector simply records proton that coincide with a beta detection. Let a proton detection that coincides with a beta detection be an event. A cold neutron beam moving on the x-axis intersects the detector axis, the y-axis, as illustrated in Figure 4 below. Cold neutrons move slowly. Additionally, cold neutrons decay with a half-life of 880.1±.1s [Beringer et al.] so some decay while at the origin of Figure 4, in-between the two detectors. Protons and electrons resulting from unpolarized neutron decay are emitted in a spherical distribution of angles. The only electrons and protons that are recorded as events are those that travel directly towards their respective detectors. Let 0o be the angle associated with protons that travel directly towards the proton detector on the y-axis and let 0o events be known as Group 1 events. Recall that two angles are required in order to deduce a so we must measure decays at another angle. The electrostatic mirror, pictured in Figure 4, turns protons traveling on axis towards the beta detector around 180o and back towards the proton detector as depicted in Figure 5. Let these 180o events be known as Group 2 events.
Figure 4: The simplified apparatus consisting of a proton detector, an electron detector, and an electrostatic mirror
We differentiate between Group 1 and Group 2 events by proton time of flight (TOF). Proton TOF is the time it takes a proton to travel from the point of decay, the origin in Figure 3, to the proton detector. Since a Group 1 proton’s momentum vector points towards the proton detector initially, they are accelerated in the direction of their initial motion towards the proton detector. Hence their TOF is relatively short. Conversely, a Group 2 proton’s momentum vector points towards the beta detector initially. The electrostatic mirror slows Group 2 proton’s to a stop and then reverses their motion towards the proton detector. Thus Group 2 protons have a relatively long TOF. Note that proton TOF at 0o and 180o are the most distinct of any two angles. Using
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proton TOF, Group 1 events can be differentiated from Group 2 events. The resulting measurement produces counting asymmetry and, thereby, a.
Figure 5: Group 1 events reach the detector before Group 2 events because Group 2 events have a longer path length
Before running aCORN, experimenters ran a Monte Carlo pictured in Figure 6 below. We call the resulting simulation the wishbone because of its shape. Since Group 1 events take less time to reach the detector they are located on the bottom half of the wishbone and Group 2 events are located on the top half of the wishbone. Note that as electron energy increases, the difference between Group 1 and Group 2 TOF lessens until the two become indistinguishable. This is a direct consequence of conservation of momentum. Recall that the total energy of the decay is 1293KeV. Thus the sum of the energy of the decay products must equal 1293KeV. So, the more energy that the electron acquires, the less energy the proton has. As the proton’s energy decreases, Group 2 events are turned back towards the proton detector in less time. Therefore TOF between Group 1 and Group 2 events becomes increasingly similar. To differentiate between the two groups, we use data below the indicated cut off energy. Realistically, it would take an inordinate amount of time to record events that happened to occur precisely at 0o and 180o. Since aCORN relies upon detected events, it is beneficial to increase the rate of detection. One of the optimal ways to increase the event detection rate is to widen the range of acceptance. To do so, we introduce a collimator and a magnetic field. If a is to be measured accurately, it is crucial that the collimator be well aligned with respect to the magnetic field.
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Figure 6: A Monte Carlo of the experiment [Wietfeldt et al]
Widening Acceptances Since Group 1 and Group 2 protons were previously traveling on the experimental axis, they had no transverse momentum. To increase the number of accepted protons, we accept protons with small amounts of transverse momentum about 0o and 180o. To accept particles with small amounts of transverse momentum we must increase the detectable solid angle. The solid angle can be visualized as the three dimensional projection of an angle from the center of a sphere to a circular area on the surface of a sphere some distance, r, away. Here, the distance is from the point of decay, the neutron beam, to the proton detector and the area of interest is the surface area of our detector. So to increase the solid angle that we can detect we use a proton and electron detector with some small surface area rather than point detectors. Since protons with small amounts of transverse momentum are accepted, we must amend our momentum space diagram in Figure 4. But before we discuss widening acceptances, we note that since our detectors only detect on axis protons, the momentum vectors of the electron and antineutrino in the momentum space diagram are necessarily equal in magnitude. Note that by conservation of momentum, the momentum vectors sum to zero for any given decay. Now to widen the accepted angle; the momentum of the electron is unchanged, but if we accept a proton with some positive transverse momentum the antineutrino must have some negative transverse momentum by the conservation of momentum. So, in 3 dimensions, what were formerly points in momentum space in Figure 4 are now small areas on the surface of a sphere in momentum space represented by the circles in the figure below.
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Figure 7: The amended momentum space diagram. Now, a small range of proton transverse momenta are accepted, this broadens the antineutrino’s momenta to the two circles indicated at the tail of each large and small angle antineutrino momentum vectors. Again, the proton momentum vectors (red) are not drawn to scale but are included to indicate the direction of the proton in Group 1 and Group 2 events
To further widen our acceptances without using more detectors, we need a way to direct protons with some transverse momentum to the proton detector. To accomplish this, we introduce a magnetic field. When a charged particle is in a magnetic field it travels in a helical path. The radius of the helical path is known as the cyclotron radius and is given by
(2) where m is the mass of the particle, v is its transverse velocity, q is its charge, and B is the strength of the field. In aCORN, the detectors define an axis in space; this is represented by the y-axis in Figure 8 below. The magnetic field is oriented so that charged particles travel towards the detectors on this axis. Those with some transverse momentum travel towards the detector in a helical path while particles traveling directly along the field lines move in straight lines towards the detectors.
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Figure 8: Simplified aCORN with the electrostatic mirror and magnetic field added
While accepting protons with a range of transverse momenta increases the number of events and improves the counting statistics, it consequently decreases the difference between Group 1 and Group 2 TOF. If protons with too much transverse momentum are accepted, events begin to fill in the wishbone, the gap separating Group 1 and Group 2 events. In the extreme case, events that should be attributed to Group 1 may be attributed to Group 2 or vice versa. This would result in an inaccurate counting asymmetry and thus an inaccurate measurement of a. It is clear that there needs to be a way to limit the transverse momentum of accepted protons.
Figure 9: An illustration of the proton collimator’s purpose; the proton collimator is represented by the dotted black vertical lines. The two red vectors depict two possible proton trajectories. The accepted trajectory travels in a helical path until it strikes the detector. The radius of the accepted proton is less than the radius of the collimator. The rejected trajectory has a helical radius larger than that of the collimator and strikes the collimators wall.
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Recall that protons with non-zero momentum travel in a cyclotron radius in a magnetic field. We note from equation 2 above that the larger the transverse momentum, the larger the radius of cyclotron motion. It follows that in order to limit the accepted transverse momentum, we must limit the radius of cyclotron motion. This is done using a proton collimator. The radius of the proton collimator limits the accepted cyclotron radius, given by (2), and therefore limits the accepted transverse velocity. The collimator is depicted as a series of vertical dotted lines in Figure 9 above. It now proves useful to explore the aCORN apparatus in some detail before discussing the main scope of this thesis, alignment. aCORN Apparatus This section deals with only the portions of the apparatus that play a role in the system’s alignment. The actual aCORN apparatus is a more complicated version of the simple case presented earlier. The apparatus is designed in such a way that decay particles are in always in a vacuum. Hence, the entire path the decay product particles take, the cylindrical region between the beta and proton detector is housed in a vacuum tube. The vacuum allows electrons and protons to travel along the paths given by their initial momentum. Without a vacuum the electrons and protons’ initial path would be disturbed by interacting with gas in the tube. This would yield false information at the detector about the particles’ initial momentum.
Figure 10: A cross-section of aCORN’s vacuum tube. The neutron beam enters through the bottom most hole on the tube’s wall
Recall that in order to detect particles with some transverse momentum, there needs to be a magnetic field. To create the desired field, magnetic field coils surround the vacuum tube. The stack of flat coils produces a 400 Gauss magnetic field. Typically, a solenoid is used to generate uniform magnetic fields. However, a solenoid cannot be used here because aCORN requires a circular opening into the vacuum tube, pictured in Figure 10, which allows the neutron beam to enter the apparatus. This opening requires that the solenoid be segmented. Computer simulations revealed that a stack of flat coils produce a sufficiently uniform magnetic field. Thus aCORN uses flat coils. !&"
Figure 11: aCORN’s vacuum tube surrounded by magnetic coils. Credit: aCORN Collaboration Drawing
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3 Figure 12: A cross-section of the ‘Insert’ housing the proton collimator [1]. The electrostatic mirror [2] is located below the collimator. The ferrule [3] supports the weight of the entire insert and grounds the entire insert to the bottom of the vacuum tube. For clarity, the electron collimator has been omitted
The proton collimator, the apparatus that limits aCORN’s transverse momentum acceptance, is located between the cold neutron beam and the proton detector. It only accepts protons whose radius of cyclotron motion is less than the radius of the proton collimator. The
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collimator is one piece of the insert; a long cylindrical amalgamation of apparatus that is lowered in through the top of the vacuum tube. Along with the proton collimator, the insert houses the electrostatic mirror, and an electron collimator. On the top of the insert is a spider that allows the insert to be rocked back in forth in the vacuum tube for the purpose of aligning the vertical axis of the proton collimator to the magnetic field. When limiting the range of transverse momentum it is crucial that the same range is accepted for both Group 1 and Group 2 events. Consider the case when more Group 2 events are accepted than Group 1 events. This falsely implies that Group 2 events are relatively more likely to occur than they actually are. One of the ways in which Group 1 and Group 2 events can have different ranges of transverse momentum acceptance is if the proton collimator’s axis is not precisely aligned along the magnetic field lines. In order for Group 1 and Group 2 events to have an equal likelihood of reaching the detector, the magnetic field must be well aligned to the collimator and the field must be uniform. By well aligned, we mean that in order for our aCORN to achieve a value for a with 1% fractional uncertainty, the magnetic field must be aligned to the vertical axis of the proton collimator within one-tenth of a milliradian. The proton collimator is 1.39 m long so one-tenth of a milliradian here corresponds to 0.139 mm or six one thousandths of an inch. This is a fairly stringent demand so we must take care to precisely and accurately align the magnetic field to the proton collimator’s axis. Further, if the two are not correctly aligned, there would be no way to know that the measured a was inaccurate. In other words, the resulting data would not suggest that anything was wrong. If we do not carefully test the alignment of the proton collimator and magnetic field, we are likely to measure an inaccurate a. Thus it is crucial that the two are well aligned. Current Alignment System aCORN has been collecting data at NIST since 2010. Alignment has always been understood to be an essential component of aCORN’s success. There is an alignment system that is already in place and we believe this alignment system to be sufficient but it is far from ideal. In order to convince the scientific community at large that aCORN’s measured value for a is correct, an additional system to measure aCORN’s alignment will be devised that is completely independent of the current alignment method. We will refer to this new system as the supplementary alignment system. Since the supplementary alignment system will be independent of the current one, an agreement between the two alignment systems suggests that we precisely know aCORN’s alignment independent of undetectable systematic flaws associated with each method. That is, the supplemental alignment system is complementary to he current alignment system because it has different systematic errors. The current alignment system is a two-step process. First, the magnetic field is aligned with respect to the ends of the vacuum tube. Second, the proton collimator is aligned with respect !("
to the ends of the vacuum tube. In order for the proton collimator to be aligned with the magnetic field, we assume that nothing has changed between the two steps of the alignment test. This assumption proves to be a dangerous one to make since so many pieces of the experimental apparatus are moved during alignment. Let us examine the current alignment systems’ two steps in more detail to see why we desire a supplemental alignment test. In 2006, David Shapiro designed the magnetic field mapper at Hamilton College. The mapper’s purpose is to detect both the alignment and non-uniformities in aCORN’s 400 Gauss magnetic field. The mapper is an insert that travels vertically in the vacuum tube. Either end of its track is placed in ball bearings; one in the middle of the top vacuum tube plate and the other in the middle of the bottom vacuum tube plate. These ball bearings ideally allow for the mapper’s vertical motion to be aligned with respect to the experimental axis. This is not, however, an ideal world, so the mapper must test this assumption. Most likely, the mapper will be misaligned to both the experimental axis, i.e. the ball bearings will not be placed in the exact middle of the top and bottom of the tube, and the magnetic field, i.e. the magnetic field lines will be non-parallel to the experimental axis [Shapiro]. To account for this troubling possibility, the mapper rotates inside of the tube and takes readings at both 0o and 180o. For small angles, these two possibilities can be separated into two independent equations [Shapiro 30]. To correct for non-uniformities in the magnetic field correction coils are added outside of the vacuum tube and the mapper is run again until it detects no transverse field above the order of 10-4 gauss. The magnetic field is now uniform and aligned to the rotational axis. The next step in this two-step alignment process is to align the proton collimator to the experimental axis of the vacuum tube, thus indirectly aligning the magnetic field to the proton collimator. A series of optics align the proton collimator to the top and bottom of the vacuum tube. Since we are only able to adjust the proton collimator’s position by adjusting the insert as a whole, the proton collimator must be well aligned with the entire insert. So first, the insert is optically aligned offline. The insert is then placed inside of the apparatus. A light source whose beam travels perpendicular to the vacuum tube’s axis is placed near the base of the apparatus. The entire beta detector is removed from the base of the vacuum tube so that a mirror can be put in its place to direct the light up into the experimental chamber. Next, the entire proton detector is removed from the top of the vacuum tube. Optics can now be placed at the top and bottom of the vacuum tube. The set of optics is then adjusted until the light shines from the center of the bottom of the vacuum tube to the center of the top of the tube.
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Figure 13: Step 1 of Current Alignment: Optical Alignment. The black bars represent the proton collimator. Light shines off a mirror and up into the vacuum tube. Sets of optics, crosshairs, are used to align the collimator to the top and bottom of the tube. Vacuum tube section credit: aCORN Collaboration Drawing
To align the proton collimator to the vacuum tube, another set of optics is placed on either end of the collimator, one in the center of the top of the collimator and another in the center of the bottom of the collimator. The insert is then adjusted until the proton collimator is well aligned with the vacuum tube. Now we trust the proton collimator to be aligned. In order to remove the set of optics, the insert must be pulled out of the vacuum tube and then placed back inside. This is clearly, less than ideal since the insert has to be removed and replaced after it has been aligned. There is evidence that the insert moves when it is put back. This movement was barely within the acceptable margin of error. Such movements, if outside of the margin of error, could yield a false a. Once the set of optics is removed from the insert, the beta detector is put back in place. Many key experimental components were physically disturbed during this process. While we believe this alignment system to be sufficient, a supplemental alignment test ensures that our measurement of a is, indeed, accurate. This supplemental alignment test should be undisruptive and should ideally measure the magnetic field’s position directly with respect to that of the collimator’s position rather than relying upon some exterior datum. The following sections detail the design of a supplemental aCORN alignment system.
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Figure 14: Step 2 of Current Alignment: Magnetic Align. The mapper, black box, measures the magnetic field as it moves up and down in the vacuum tube and about the axis of its vertical movement.
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Supplemental Alignment Test We design this supplemental alignment test with the intent that it be nonintrusive. The fewer components of apparatus moved, the more confident we are that portions of the apparatus did not shift during the alignment test. We also want this new alignment system to test aCORN’s alignment in a different way than the current alignment test, that is, we want to have our new alignment system rely upon a different set of parameters. By differentiating how the two tests determine alignment, if the two systems agree we can be confident that aCORN is aligned. With all this in mind we chose to use an electron gun and a detector as the main components of the supplementary alignment system. Before exploring the components of the alignment system in depth, it is useful to first step back and understand how the entire alignment system works as a whole. To understand the shape of the magnetic field lines, we use a particle whose path mimics the field lines. Recall equation (2) which describes the cyclotron radius of a charged particle in a magnetic field. We wish to use a particle whose path in a magnetic field very closely mimics the field lines, so to minimize r we choose a particle with a small mass that is easy to generate and detect. Electrons prove to be a good choice. aCORN’s field at NIST is 400 gauss while the test field at Hamilton College is 100 gauss. Table A illustrates the cyclotron radius of an electron in aCORN’s magnetic field with a kinetic energy of 400 eV.
Table A: The cyclotron radius for 400eV electrons in a 400 gauss magnetic field at two different angles away from parallel to the field lines
Note from the table that even in the extreme case when the 400eV electron’s initial kinetic energy vector points 15o from parallel with the magnetic field lines, the cyclotron radius is a mere 0.9mm. Thus the path of an electron in aCORN’s magnetic field directly yields information about the shape of the magnetic field lines. Recall that we need the experimental axis of the proton collimator to be well aligned to the magnetic field. If the two are well aligned, the magnetic field lines are parallel to the walls of the collimator. Therefore, we wish for a field line that starts in the middle of the top of the proton collimator to pass through the middle of the bottom of the proton collimator. Since electrons mimic the field lines, this is analogous to an electron traveling through the middle of the top of the proton collimator and then traveling through the middle of the bottom of the proton collimator. So, for our alignment system, we hope to shoot a beam of electrons through the exact middle of the top of the proton collimator and then detect the position of the electrons once they reach the bottom of the electron collimator. Clearly, in order to accomplish this, we need to generate a beam of electrons. To create this beam we employ an electron gun and the principles of thermionic emission. #!"
Electron Gun An electron gun consists of a hot filament, a Wehnelt cylinder, cylindrical electrodes, and an accelerating plate. The hot filament is the source of the electrons. It is a wire that gets so hot that the thermal energy of the electrons overcomes the work function of the metal; the electrons effectively boil off of the filament. The electrons that were emitted from the filament are distributed in a wide distribution of angles about the filament. To create the desired beam we must focus these electrons. To achieve this, the gun has a Wehnhelt cylinders and an array of cylindrical electrodes. The Wehnelt cylinder is the innermost cylinder surrounding the filament. After the Wehnhelt cylinder are three cylindrical electrodes. The four elements of the electron gun focus beams of electrons akin to convex lenses that focus beams of light; the same basic principles apply. There is a small hole located in the bottom of each cylinder through which electrons travel. A voltage is applied across the cylinder. The charged edges of the cylinder repel the electrons and cause the fringes of the beam to bend inwards as pictured in Figure 15 below. Increasing the potential difference on a cylinder bends the fringes of a beam more sharply causing the focal point to move closer to the gun. This is akin to using a fatter lens to bring the focal distance of a beam of light closer to the lens.
Figure 15: The charged edges of the Wehnelt Cylinder forces the electron beam to bend inwards, away from the charged walls
Many of these cylinders are placed in succession as pictured in Figure 16. The first three cylinders’ function is to direct as many electrons as possible to the third cylinder. The fourth and final cylinder is the focusing cylinder. It is attached to a variable resistor. By increasing the resistance from the power supply to the third cylinder we subsequently decrease the voltage across the fourth cylinder. Consider the following models that depict the
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Figure 16: The electron gun CRT schematic. The variable resistor attached to the last cylindrical electrode allows us to change the focal length of the electron beam.
Model A: Nick Sylvester produced these two FEMM models of the electron gun. Unlike the circuit pictured in Figure 16, the voltage here goes from -400V at the cylinder around the filament, to ground at the accelerating plate. The same basic ideas, however, still apply. The difference between the two models is the voltage on the fourth cylinder, the focusing cylinder. In the model on the left the focusing cylinder is at -250V in the model on the right the focusing cylinder as at -400V. Note that the field lines are more intense, i.e. the electron beam is bent more, in the model on the right. This is because there is a larger potential difference between the final cylinder and the accelerating plate.
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directions of the field lines in an electron gun. As seen in Model A, the less voltage on the focusing cylinder, the less severely the electron beam bends away from the walls of the cylinder, the further the focal point moves from the gun. So the variable resistor and fourth cylinder allow us to effectively vary the radius of the electron dot on our detector. After the beam has emerged from the cylinders, it passes by the accelerating plate, the final component of the electron gun. A voltage is applied across this plate. This pulls the electrons and provides them with additional kinetic energy. This ensures that the electrons will possess a detectable amount of energy. Now that we have produced a beam of electrons, we need a detector to determine the beam’s position. Detector To detect the beam of electrons we consider two viable possibilities: a metal plate or a phosphor and camera. Let us first consider the simpler of the two, the metal plate detector. When electrons strike the metal detector, we can detect a current from the plate to ground using an ammeter. A current from the plate to ground informs us that the electron beam is striking our detector. Clearly, if our detector just consists of one large plate, measuring a current tells us little about the position of the beam on the detector, i.e. the beam could be hitting the detector anywhere on it’s surface.
Figure 17: Depicted above are two scenarios in which the electron beam (the red dot) strikes the large plate detector (the gray circle). The current read from each plate is exactly the same but on the left the dot is far from the center of the circle. The large plate detector provides no discernable way to tell between the two scenarios detailed above
Since we wish to detect the beam when it is in the exact middle of the bottom of the proton collimator, this is insufficient. Alternatively, if we make our plate too small we will have no information about the position of the beam until it hits our detector. So if our beam is missing our small detector in the bottom of the proton collimator we do not know by how large a margin we are missing our detector. To remedy these two conflicting issues we use multiple plates.
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Figure 18: In the two scenarios detailed above, the current read from the small plate is zero but the dot is much closer to the center in the right hand scenario. This plate provides no data until the dot is already close the center of the small plate
Consider a four-way segmented plate detector pictured in Figure 19 below. By reading current off of each segment of the plate we can determine which segmented plate the beam strikes. When the beam is in the middle of the detector, the current read off of each plate should be equal.
Figure 19: Two scenarios with a four-way segmented plate are depicted above. On the left, the beam strikes the detector off center and more current would be read off of the bottom left plate. On the right, the beam strikes the detector in the center and an equal amount of current would be read off of each plate
While this segmented plate detector does provide us with adequate information, it would be preferable to actually see where the beam is with pixel-like resolution. We can achieve this more informative detection system by using a phosphor. A phosphor is a surface, that when struck with electrons, emits visible light. So, the electron beam appears as an illuminated circle on the phosphor. Note that with a phosphor, since the information we are analyzing is visual, we can have extremely precise information about where the electron beam strikes the detector. We would place a reference point like a crosshair in the middle of the bottom of the proton collimator, and if the magnetic field were well aligned to the collimator, the dot would be directly on the crosshair. However, aCORN is housed in an opaque vacuum tube so we cannot peer in at the phosphor without some assistance. In order to see inside the vacuum tube we pair the phosphor with a video camera. We may then analyze the
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electron beam’s position even when it is housed deep within the apparatus. If the phosphor, for some reason, proves too difficult to implement, we can always use a segmented plate detector. In order for this alignment system to be viable we need to determine the position of the electron dot to one-tenth of a milliradian or 0.14 mm. Thus, in order to detect variations on this level, we need the resolution of our detector to be finer than 0.14 mm. With a phosphor, assuming we can make the edges of our dot sharp rather than blurry, the resolution is limited by the precision with which we can determine the center of the dot after processing the video signal. With a segmented plate detector, the resolution is not as simple to determine. One factor that may limit the resolution of this detector is if the beam spot is not symmetric. This would mean that even if the beam were striking the exact middle of the segmented plate detector, the current read off of the plates would not be equal and we would incorrectly infer that the beam was not striking the middle of the detector. Additionally, we are limited by the noise of our detector. At both Hamilton and NIST, if the electron beam isn’t striking the detector at its center additional correction coils may be wrapped around the solenoid to create fluctuations in the magnetic field that will change the electron beam’s path. Thus, in order to fix any nonuniformities in the magnetic field, we need to confirm that we can add some discrete number of coils to rock the electron dot to the center of the detector. Coils will be added until the electron dot strikes the middle of the detector. The optimal focal point of the electron beam changes once it is placed inside a magnetic field, like its eventual location in aCORN. Previously, in the CRT, the beam had to be focused on the phosphor located roughly 10 cm away from the gun. In aCORN, the phosphor is located at the other end of the proton collimator. But recall that once inside a magnetic field, electrons have a small cyclotron radius and travel essentially parallel to the field lines. This means that in order to minimize the radius of the electron dot, the electron beam should be thin and directed parallel to the field lines . We dictate that the beam should be directed parallel to the field lines to ensure that the transverse momentum of the electrons is minimized. If the electrons had a range of transverse momentum upon entering the field, the beam would disperse as each electron traveled in a path with its own cyclotron radius determined by its transverse momentum. Implementation Before we install this supplemental alignment system in aCORN, we need to ensure that it works. We will extract the electron gun and detector from a cathode ray tube (CRT). A CRT is an electron gun and phosphor encased in a vacuum tube. With the CRT, we achieved an electron dot radius of 0.5mm. We hope to reproduce these results after the electron gun has been extracted from the CRT and placed in our own vacuum tube.
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Before extracting the electron gun from the CRT, we determined the basic construction of the electron gun circuit by looking through the glass walls of the CRT. The circuit was depicted in Figure 16 above and is reproduced here for convenience. From a pre-existing introductory physics laboratory power supply built for these CRT’s, we determined which voltages to place on which pins to produce the desired electron ‘dot’ on the phosphor. As explained above, by varying the voltages of Wehnelt cylinders we can adjust where the electron beam focuses. We connected the CRT to variable power supplies and adjusted the voltages until the electron dot was small, well defined, and bright. These voltages are recorded in Figure 16. Recall that while these voltages prove optimal for focusing the beam on the phosphor in the CRT, we will need to adjust these voltages once the gun is placed in the vacuum.
Recall Figure 16: The electron gun CRT schematic
The apparatus at Hamilton, pictured in Figure 20 below is much simpler and smaller than that at NIST. Here, a 1.53 m long vacuum tube lies horizontally in a solenoid that produces a uniform magnetic field.
Figure 20: The vacuum tube at Hamilton College surrounded by the solenoid. Connections run from the power supplies on the rack to the electron gun and detector through feedthroughs on either end of the tube
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The electron gun, pictured in Figure 21 below, was extracted from a purchased Sylvannia JANCHS3BP1 cathode ray tube (CRT).
Figure 21: The electron gun resting in its mica spider. Here, a single metal plate detector has been attached to the end of the mica support
The gun is mounted to a spider as depicted in Figure 21. The spider is constructed from mica so it is electrically insulated from the walls of the vacuum tube. A similar spider supports the detector apparatus that lies opposite the electron gun in the vacuum tube as seen in the cross section, Figure 22. We will attempt to see a dot with a phosphor detector first.
Figure 22: A horizontal cross section of the vacuum tube
The phosphor, a piece of glass taken from the shattered end of the CRT with phosphor on it, is taped to one piece of mica. An OV5016A Low Resolution Black and White EIA video camera points towards the phosphor as pictured in Figure 23 below. An LED is inserted into the mica next to the camera. The LED can be turned on and off independent of the camera. After the vacuum tube is sealed and under vacuum, we turn the LED on before looking for a dot to confirm that the camera is on and pointed at the phosphor.
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Figure 23: The camera and phosphor detector supported by a mica spider
To increase the likelihood of seeing a dot we place the electron gun close to the phosphor. If we observe a dot we will then add a crosshair and determine the resolution of the detector. If we do not observe a dot, we may use a plate detector instead of a phosphor. A plate could be inserted a few centimeters away from the end of the gun to ensure contact with the beam. A cross section of the plate addition is presented in Figure 24.
Figure 24: An extended brass rod connects the electron guns two mica supports. A third piece of mica at the end of the extended rod supports a metal plate detector
After we are pleased with the resolution and precision of the new alignment system, we hope to design an apparatus to non-intrusively and extremely precisely insert the supplemental alignment system to the ends of the proton collimator in aCORN’s vacuum tube.
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Experimental Results Once the gun and detector were placed inside of the vacuum tube, we achieved a vacuum pressure of 0.5 x 10-5 torr an acceptable vacuum in which to operate our electron gun. The LED placed next to the camera shone enough light to confirm that the camera was on and pointed at the detector. The LED was then turned off, as a darker chamber would make a dot of any brightness easier to observe. Many attempts were made to position the camera so that the entire phosphor was in view. At it’s best only the bottom # of the phosphor was in view. At first the polarity of the electron gun was incorrect and the gun did not operate. We corrected this problem and the gun worked properly before the following results occured. From all observable evidence, the components of the electron gun acted just as they did when housed in the CRT. The current to the filament was set at .7 amps to achieve a voltage of 6.8 volts across the filament. The voltages of the power supplies are noted in Figure 16 above. After the filament was given time to heat up, the camera revealed that the filament was glowing inside the vacuum tube. But, even with the detector placed extremely close to the end of the gun, we were unable to observe a dot on the phosphor. Possible reasons for this are discussed in the section below. Since the phosphor had failed to reveal an electron dot, a plate detector was used instead. The plate was attached to mica on the end of the extended brass rod as pictured in Figures 21 and 24. When the appropriate voltages were applied to the electron gun, we observed a current of 15 nA on the plate. Note that this current was sufficiently above the noise of the current in the wire, around 0.3 nA. Further, when the variable resistor was tuned, the current read off of the plate changed. When the resistance of the variable resistor was turned all the up, the voltage across the focusing cylinder was hovering around -250V and the current read off of the plate reached a maximum of 15 nA. Conversely, when the variable resistor was turned all the way down, i.e. when there was little resistance, the current read off of the plate was drowned in noise. The following table illustrates currents read off of different components of the electron gun. Two trials were conducted with the electron gun in the CRT and one trial was conducted with the electron gun our vacuum tube. When the electron gun was in the CRT, current was recorded once the gun had produced a desirable dot on the phosphor. Sometimes, however, this dot disappeared when the ammeter was added to the circuit. When the electron gun was inside the vacuum tube, current was recorded at different focusing voltages. It should be noted that much time was spent preparing CAD drawings of aCORN. This was done with the hopes that, had a dot been observed, CAD would be used to design the apparatus that would hold and insert the supplemental alignment system. The drawings are attached in the CAD appendix. In the ‘Potential aCORN Supplemental Alignment Design’ section below, these drawings will be used to plan a potential supplemental alignment apparatus.
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Table B: Current read off of different components of the electron gun. It should be noted that Trial 2’s results were recorded after the current was given minutes to stabilize
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Discussion For a long period of time we struggled to correctly operate the electron gun in our vacuum tube since we made a crucial mistake that we only rectified at the every end of the semester. In the CRT, the cylinder closest to the filament is at ground while the accelerating plate and the walls of the CRT are at 400V as pictured in Figure 16 above. The electrons traveled from low potential to high and accelerated toward the phosphor as desired. But, once we put the electron gun in our detector, we failed to realize that the same voltages would no longer work since the walls around the electron gun, the vacuum tube, was now at ground instead of 400V. This would cause electrons that had just exited the electron gun to turn back around to the high potential accelerating plate, preventing dots from reaching our detector.
Figure 25: The electron gun rewired so that it operates properly in the vacuum tube. The accelerating plate is now at ground so electrons travel out of the gun and toward the detector
To fix this problem, we would need to start the cylinder nearest the filament at a a high negative voltage and have the accelerating plate and the walls of the vacuum tube at ground. Note that electrons would still travel from the first cylinder towards the electron plate because of the potential difference. But now, once electrons exited the gun, they enter an effectively electrical potential field free region and continue to travel toward the detector. The circuit is pictured in Figure 25 above. The lack of an observable dot on the phosphor is disappointing. There are a few possibilities for why we were not observing a dot. The most probable are: either the beam is missing our phosphor or the beam is striking our detector but the phosphor is failing to emit an observable number of visible photon. Let us explore both of these possibilities in more detail. The beam may be missing our detector for a number of reasons. The phosphor is currently not connected to ground. So if the electron beam is initially hitting the phosphor, the phosphor may be bombarded with electrons, become negatively charged, and then repel the electron beam. Attaching the phosphor to ground through some large resistor could eliminate this $#"
charging and subsequent repelling of the electron beam. If the phosphor is indeed becoming charged, we should see some visible photons emitted from the phosphor when the beam first strikes it, i.e. when the phosphor is ‘charging up’. Unfortunately, we have not seen any discernable evidence that the beam is ‘charging up’ the phosphor. Another reason why the beam may be missing our phosphor is that the electron gun may not be pointed at the detector. So even if the electron gun is emitting a beam, the beam may be striking the mica support or the walls of the vacuum tube. This is likely since the glass fragment of phosphor is small, a triangle roughly 3cm wide and 2 cm tall. Additionally, The mica holding the electron gun is flexible and tends to bend and contort as it is moved down the vacuum tube. This would explain why the gun or detector might be pointed in an unwanted direction. To test this assumption, after the filament was hot and glowing, we waived magnets around the outside of the vacuum tube near detector’s location. This should have caused the electron beam to move across the phosphor, even briefly but we saw no evidence of a beam. Admittedly, this is an imprecise method that relies upon some amount of luck. We turned on the solenoid surrounding the vacuum tube and attempted to move magnets near the detector again to deflect the beam towards the detector. But we failed to see a dot. Since this method is imprecise, it is difficult to say whether or not the beam is missing the detector. It should also be noted that while the entire phosphor is not visible on the external monitor, the # that is in the camera’s view should be ample room for us to observe a dot. Therefore it is unlikely that there exists a dot on the phosphor that is simply out of view of the camera. Another possible reason for why we did not observe a dot on the phosphor is that there may have not been enough phosphor left on the piece of glass that we used as detector. After the CRT was broken, the fragments of glass with phosphor were left unattended and exposed. After a week, we observed that the phosphor dust had fallen off of some of the pieces of glass. So it is entirely possible that phosphor also fell off of the CRT glass shard used as a detector in our vacuum tube. If this were the case, an electron dot would be difficult to observe. To circumvent the inconclusively of our phosphor detector, we turned to a metal plate detector. The metal plate detector was a rough circle with a diameter of 4 cm. The tube’s radius is 8 cm so the detector is relatively large. We placed the detector 3 centimeters away from the end of the electron gun so that the segmented plate would be much more likely to intercept the electron beam. Fortunately, we have proof that the electron gun did in fact produce an electron beam since we measured a current on the plate detector well above the background noise. The current read off the plate detector increased monotonically as the voltage across the focusing cylinder was increased from -400 V to -250V. At -250V the current off of the detector reached a maximum of 15nA When the focusing cylinder was at -400V, the detector’s current was just
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noise. We should note that 15 nA is a surprisingly low amount of current for an electron gun operating at this accelerating potential. Analyzing the field lines of the electron gun may explain why current read off of the detector was noise when the focusing cylinder was set at -400V. Note that in the field line model, Model A, after electrons have passed by the third cylinder the field lines direct electrons back towards the third cylinder. When the focusing cylinder is at -400 V the electric field intensely directs electron back toward the third cylinder. So, when the focusing cylinder is set at -400V, a detectable number of electrons may never even leave the electron gun. Conversely, when the focusing cylinder is set at -250 V, the field lines about the exit of the third cylinder are less intense, i.e. the electric field bend’s the electron beam but is not intense enough to prevent the electron beam from exiting the electron gun. Table B is a disappointing and perhaps misleading result. We would hope that the electron gun would operate similarly in the CRT and the vacuum tube, Table B, however, suggests that this was not the case. Had the gun operated similarly in each apparatus, the recorded currents should have been similar. But we must be careful how much we trust the accuracy of Table B’s currents. Note that when the gun was in the CRT, recorded current varied wildly between two control trials, trial 1 and 2. This suggests that the currents in Table B are probably not accurate and that we may have used the ammeter incorrectly. Once current has been measure correctly, the immediate next step in this process would be to determine the radius of electron beam when it strikes the detector. Thin strips of metal could be placed on a nonconductive surface as pictured in Figure 26 below. By reading the current off of each strip of a known width, we could determine the size of the electron dot by measuring the number of detector strips with current flowing. So, for example, if we used strips 1mm thick separated by 1 mm gaps and if we read current off of two strips we could infer that the beam’s radius, r, was 2 mm < r < 4 mm. Once we determine the size of the dot a segmented plated detector could be constructed.
Figure 26: The metal strip detector. 1 mm wide detector strips (gray) are separated by 1mm wide gaps. The electron dot strikes two strips. We read current off of these two strips and infer that the dot is somewhere between 2mm and 4 mm in width. Strip size can be reduced to increase precision
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Alternatively, a phosphor screen could be purchased and the more desirable cameraphosphor detector system could be attempted once again. The detector should then be placed at the opposite end of the vacuum tube to illustrate that the alignment system is effective in a magnetic field when the electron gun and detector are placed roughly 1 m apart. This distance mimics the eventual distance of the two components inside of aCORN as is discussed in the next section. After the dot’s size has been determined, the dot’s shape should be found; we desire a symmetric dot after all. If the dot is not symmetric, attempts should be made to make the dot as symmetric as possible by varying the voltages supplied to various parts of the electron gun. But we suspect the dot is sufficiently symmetric. We should then confirm that we can vary the electron beam’s path by adding correction coils near the vacuum tube. Final steps should then be made to put this supplemental alignment system in place inside aCORN at NIST. In order to do this, we must design the apparatus that supports and places the electron gun and detector system.
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Potential aCORN Supplemental Alignment Design If, in the coming months, a dot is detected with acceptable resolution, the next step is to design a way to insert this alignment system into aCORN. Recall that we wish to insert this supplemental alignment system as non-intrusively as possible. Note from Figure 10, reproduced below, that there are only three ways inside of aCORN’s vacuum tube: the top of the vacuum tube, the bottom of the vacuum tube, and the two holes in the walls of the vacuum tube. A beta detector lies at the bottom of the vacuum tube. Additionally, there is little room, a mere twenty inches, between the bottom of the vacuum tube and the floor so it would be unnecessarily difficult to insert something rigid in the bottom of the tube that would reach the areas of interest, the top and bottom of the proton collimator. Hence the bottom of the vacuum tube is a poor entry point.
Recall Figure 10: A cross-section of aCORN’s vacuum tube. The neutron beam enters through the bottom most hole on the tube’s wall
The larger of the circular two holes on the wall of the vacuum tube, the bottom most, is already in use as the cold neutron beam access port. The smaller hole is located about 3 inches below the bottom of the proton collimator. The smaller of the two circular holes is an option but it would be difficult to accurately place the detector. Recall that the detector must be placed in the middle of the bottom of the center of the proton collimator. If the detector slid in through this hole, it would be extremely difficult to determine when the center of the detector reached the middle of the bottom of the proton collimator. Since the detector would be moving on an axis parallel to the bottom of the collimator, it would prove needlessly complicated to reference the position of the detector to the bottom of the collimator located above it.
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The best point of entry for the supplemental alignment system is the top of the vacuum tube. The ceiling of the building that houses aCORN is greater than the length of the tube away from the top of the vacuum tube. This means that a rigid structure could be lowered down the length of the tube. In addition, the only meaningful portion of the apparatus, that is, a piece of the apparatus that could alter our interpretation of a, that needs to be removed to gain access to the proton collimator is the proton detector. So once the proton detector is removed, the alignment system could be conveniently lowered into the apparatus without interference. The proton collimator must not be damaged so it is essential that the insert does not interfere with aCORN. Now that it is clear that the supplemental alignment system should be lowered through the top of the apparatus, we must determine if the electron gun or detector should be placed on top of the proton collimator and which should be placed on the bottom. There is only 4.5 inches of clearance below the proton collimator and roughly 20 inches of clearance above the collimator, so the larger of the two elements should lie on top of the proton collimator. The electron gun section of the apparatus will be taller than the detector, as is the case in our tests, so it should be placed on top of the collimator. Recall that the axis of the proton collimator must be aligned to the magnetic field within 0.14mm. Since we must place both the entry point and detect point of the beam, to ensure that the total error of the beamâ&#x20AC;&#x2122;s position is 0.14mm or less, the total error in placement of each of the two elements has to be reduced to one half of 0.14mm or 0.07mm. This means that the beam must enter the proton collimator within 0.07 mm of the middle of the top of the proton collimator. Since we trust our machine alignment but not the direction that the beam exits the electron gun, one potential solution would be to place a well-fit disk in the top of the proton collimator with a small hole in the middle through which the electron beam may travel. The gun could be placed above the proton collimator and facing the hole. Thus the beam would only travel to the electron beam detector if it passed through the desired point on top of the collimator. Similarly, the reference point that marks the center of the detector must be placed within 0.07 mm of the middle of the bottom of the proton collimator. Placing the detector is more difficult than placing the gun since the bottom of the proton collimator is deep within the vacuum tube. We cannot reach in and place the detector there manually. The entire detector must descend through the proton collimator to its bottom. This limits the entire detector section of the apparatus to be less than the diameter of the proton collimator, 8 cm, while it descends through the collimator. One potential solution would be to design an expandable spider. As the spider moved through the proton collimator by wire, its legs would be retracted. Its legs would expand once it reached the bottom of the collimator. The legs of the spider would fit snugly with the bottom of
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Figure 27: The electron gun (gray) mounted to the top of a disk (blue) with a hole cut in its center. The disk fits snuggly into the top of the proton collimator so the beam enters the proton collimator through the middle of the top
the proton collimator as pictured below. This way the detector could be guaranteed to be in position with respect to the walls of the collimator. Since the detector would lie in the middle spider, the center of the detector would be in placed in the middle of the bottom of the proton collimator as desired.
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2.
3. Figure 28: The detector (gray) rests in the middle of the support (blue) and is lowered into place in a three-step process. 1. The detector is lowered through the proton collimator 2. The apparatus exists the proton collimator and extends its legs 3. The apparatus is drawn back up. Notches on the legs ensure that the apparatus fits snugly in the bottom of the proton collimator
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Conclusion In order to help substantiate aCORN’s results, we set out to design a supplemental alignment system. This new alignment system would operate in addition to the current alignment system in use and if the two systems agreed, the scientific community would be even more likely to accept the veracity of our value for a. We hoped to use electrons, whose path in a magnetic field mimic the field lines, to determine whether or not the magnetic field and proton collimator were well aligned. Before implementing the new alignment system at NIST we attempted to demonstrate its success at Hamilton College. A smaller vacuum tube and solenoid were used to mimic aCORN’s apparatus at NIST. Unfortunately, while the electron filament was getting hot and ‘boiling off’ electrons, there was no evidence of an electron beam on our phosphor detector. We then turned to the less desirable of our two options for a detector, the plate detector. When the plate was placed about 3 cm from the end of the electron gun we detected a current of 15 nA off of the plate; sufficient proof that the electron gun was indeed producing a beam of electrons. Going forward, a segmented plate detector could be used in conjunction with the current electron gun. Steps should then be taken to refine the resolution of the alignment system until it achieved a resolution of 0.1 milliradians or 0.14 mm. If this supplemental alignment system proves to be viable, i.e. if it can achieve sufficient resolution, the system then needs to be non-obtrusively inserted in aCORN at NIST. CAD drawings can help aid this process to ensure that there is no interference between the alignment system and the aCORN apparatus. In conclusion, we found that the electron gun used at Hamilton College was able to produce a detectable electron beam but many more steps must be taken before the supplemental alignment system can be used in aCORN at NIST.
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Appendix A: Works Cited Beringer, J. et al. Review of Particle Physics (Particle Data Group), Phys. Rev. D 86, 010001 (2012). Jackson, J. D., S. B. Treiman, and H. W. Wyld, Jr. “Coulomb Corrections in Allowed Beta Transitions.” Nuclear Physics 4 p206-212. 1957. Print. Kittel, Charles and Herbert Kroemer. Thermal Physics. 2nd Edition. New York: W. H. Freeman and Company, 1980. Print. Noid, George. “The aCORN Experiment.” Indiana University Department of Physics. Phd, Dec. 2010. Print. Shapiro, David S. “Magnetic Field Mapper for the aCORN Experiment.” Hamilton College Physics Department. Senior Thesis, Fall 2006. Print. Stratowa, Chr, R. Dobrozemsky, and P. Weinzierl. “Ratio |gA/gV| derived from the proton spectrum in free-neutron decay.” Physical Review D Vol. 18 #11. 1 Dec. 1978. Print. Williams, NIST Nuclear Engineer Dr. Robert E. “The NIST Research Reactor and Cold Neutron Source.” Powerpoint presentation, 28, June 2007. <http://www.ncnr.nist.gov/summerschool/ss07/bob_williams.pdf>. Wietfeldt, F.E., et al. “aCORN: An experiment to measure the electron-antineutrino correlation in neutron decay”. Nuclear Instruments and Methods in Physics Research A 611. p207 210. 2009. Yerozolimsky, B. “New Approaches to Investigations of the Angular Correlations in Neutron Decay.” Restored copy of text distributed at the seminar at NIST, Washington D.C., 1996. <http://arxiv.org/pdf/nucl-ex/0401014.pdf>.
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Appendix B: CAD The following are screenshots of an isentropic view of the â&#x20AC;&#x2DC;insertâ&#x20AC;&#x2122; drawn in AutoCAD 2013. Unless otherwise noted, all diagrams of the proton collimator, vacuum tube, and insert were drawn in and then exported from AutoCAD 2013.
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