Construction of Hirsch-Meeks Fusor for the Creation And

Home , Plasma parameters

A Star on Campus: Construction of Hirsch-Meeks Fusor for the

creation and conﬁnement of Plasma

Brian Kelleher William Flynn

May 5, 2010 A thesis submitted in partial fulﬁllment of the requirements for the

degree of

Bachelor of Science

Physics

at the

AMERICAN UNIVERSITY

2010

DEPARTMENT CHAIR:______

ADVISOR:______Acknowledgments

This project has been a long and surprising road which has tested our personal strength and that of the people around us. While we have been in the lab for many hours thinking, building, and experimenting, others have been selﬂessly giving their own time to help us to accomplish our goals. We would like to make it clear that this project would not be as successful, or not successful at all, if it was not for Jonathan Newport’s generosity, be it with his expertise of machining, vacuum systems, or electronics. Over half the parts in the fusor could be attributed to Jonathan in some way; his friendship and expertise was invaluable, and he is a true asset to this department.

We would like to also issue a special thank you to Bill Parsons, who’s passion for careful data taking drilled us into the mindset of ‘measure twice, cut once.’ Bill also provided extensive monetary guidance and support which allowed us to make the most out of our money and when we ran out he provided the materials needed to take the experiment to the next level.

Another thank you needs to be given to Professor UJ Soﬁa who supplied us with the space and support required to complete this experiment.

The previous year, our mutual friend, Adam Goler, played a key role in our physics futures. Adam pressured us to work harder, try harder, and to persevere in order to make the most out of our education. For this, we are forever in his debt.

Brian would like to thank Antonia for her continued support, be it academic or emotional, during the past four years at American University. Although it has been a arduous journey, Brian hopes that there will be many more a jaunt in the future.

Bill would like to thank Carrie for her love, encouragement and tremendous understanding, and his family for their unwavering support through the last twenty-one years.

The project could not have even been started if it was not for a generous grant that was supplied by the American University Honors Department. For this we would like to extend our gratitude to the honors staﬀ and grant committee. Finally, we would like to thank each other. Each of us ﬁt a niche the other could not. Contents

1 Introduction 9

1.1 What is a Fusor? ...... 9

1.2 A Short History ...... 10

1.3 Potential Applications ...... 12

2 Physical Concepts 13

2.1 Plasma ...... 13

2.1.1 Ionization of a Gas ...... 13

2.1.2 Inﬂuence of Electric and Magnetic Fields ...... 14

2.1.3 Nuclear Fusion ...... 15

2.2 Quantifying a Plasma ...... 17

3 Construction of the Fusor 19

3.1 Possible Designs ...... 19

3.2 The Gol3tron ...... 19

3.2.1 The Vacuum Chamber ...... 20

3.2.2 Spherical Grids ...... 21

3.2.3 High Voltage Supply ...... 23

3.2.4 Vacuum Pump ...... 24

5 4 Measurement 27 4.1 Introduction to Plasma Diagnostics ...... 27 4.2 Langmuir Probe Theory ...... 28 4.3 Triple Langmuir Probe ...... 29 4.4 Langmuir Probe Construction ...... 31 4.4.1 Probe Construction ...... 32 4.4.2 Aluminum Housing Construction ...... 33 4.4.3 Triple Probe Assembly ...... 34 4.5 Direct Display of Plasma Parameters ...... 35 4.6 Data Acquisition with LabVIEW ...... 37 4.6.1 Features ...... 37 4.6.2 Use of the Virtual Instrument ...... 38

5 Operation 41 5.1 Operating Parameters ...... 41 5.2 Modes of Operation ...... 42 5.2.1 Jet Mode ...... 43 5.2.2 Star Mode ...... 44 5.3 Bremsstrahlung ...... 45 5.4 Heat Production ...... 48

6 Experimentation 49 6.1 Measurements of Sparse Plasma ...... 49 6.1.1 Calibration and Conﬁrmation of Valid Data ...... 49 6.1.2 Indirect Observation of Electron Beam Lensing ...... 50 6.2 Quantifying the Electron Beam ...... 50 6.2.1 Electron Temperature ...... 51 6.2.2 Bi–Modal Maxwellian Distribution ...... 52 6.3 Measuring the Core ...... 55

7 Conclusion 59 7.1 Results ...... 59 7.2 Final Thoughts ...... 59

Bibliography 59

List of Figures 63

List of Tables 65

Chapter 1

Introduction

1.1 What is a Fusor?

A fusor can be described as a spherical, plasma based, particle accelerator with potential to create a nuclear fusion reaction. The device centers around two concentric, spherical grids which are placed inside a vacuum chamber. The air is evacuated from the chamber and a slight amount of hydrogen, or other gas, is then introduced into the chamber between the outer (22) and inner (20) grid. The inner spherical grid (20) is given a high negative voltage, the outer grid (22) is given a slight positive voltage or is grounded, and the vacuum chamber itself (21) is grounded. The gas will ionize due to thermal electrons that will eject oﬀ the inner grid (22) towards the wall (21). The newly freed nuclei feel an extremely strong attraction to the negatively charged inner grid (20) and accelerate towards the negative potential (20). At the center (34) the nuclei will oscillate back and forth where they will either collide and fuse or capture an electron. Regardless of interactions, nuclei will collect inside the inner grid and when a large enough number of nuclei gather, they will repel one another out of the center. At this point the nuclei are then driven towards the outer grid (22). This cycle continues indeﬁnitely. By controlling the voltage, the strength of the collisions can be controlled, and hence the amount of nuclear fusion. If the voltage is too low, fusion will

9 Figure 1.1: The fusor cross section from Hirsch-Meek’s patent[6]. not occur. Similarly, pressure controls the reaction; a low pressure decreases the resistance of the gas which allows electrons to ﬂow through the gas, but if low, electrical resistance skyrockets, causing the plasma to extinguish. Control of these parameters is essential to the operation of a fusor.

1.2 A Short History

In the early 1930’s, Philo T. Farnsworth was experimenting with vacuum tubes and electron beams. One of the outcomes of his research was the television, but he also discovered another

10 effect that pioneered the fusor. If electrons traveling in a cathode ray tube were exposed to a high frequency magnetic field, they become trapped in the center of the tube. Once these electrons were released from the center, they would accelerate towards and collide with electrode, causing it to erode. Farnsworth called this the multipactor effect. The multipactor effect worked with electrons, but Farnsworth realized it also had the potential to work with ions. This revelation led Farnsworth to construct the first fusor, which used the multipactor effect to focus and concentrate gas ions in the center of a vacuum chamber.

Figure 1.2: Farnsworth’s design of the multipactor fusor from his original patent[5].

Dr. Farnsworth founded a lab to experiment with the device. He eventually recruited Dr. Robert Hirsch. Hirsch made a dramatic proposal. He suggested that Farnsworth replace the

11 ion guns with two concentric spherical electrodes. The design, now known as the Hirsch– Meeks fusor is widely used for experimentation and is a conﬁrmed fusion device.

1.3 Potential Applications

The most promising application of a fusor is neutron production. Depending on fuel, a fusor can produce neutrons with energies anywhere from 2 MeV to 14 MeV. Unlike a tokamak, or other fusion devices, the fusor is small, compact, and simple. This means it can be easily transported to places requiring a neutron source. Cargo ports, which need to check all imports for fissile material can use fusors in a call and response system. A fusor could pulse neutrons, and wait for response neutrons from fissile material, which would be the mark of fission reactions. The fusor can also be used to make a collimated beam of high energy photons which are guided through a view port. High energy photons can be used to irradiate objects, destroying bacteria and other harmful pests. As of now, a fusor does not seem to scalable to an energy producing power plant [13]. In order to do this ions would have to collide much more often then they do1. Due to the poor predictions, no efforts have been made to scale the Hirsch design. Others, such as Dr. Bussard, creator of the Polywelltm have attempt to revamp the fusor by using a magnetic trap. Still, efforts have been unsuccessful.

1Ions in a fusor tend to oscillate around the grid thousands of times before hitting another ion or recombining to form a neutral atom. One of these two options happens around once a second [14]

12 Chapter 2

Physical Concepts

2.1 Plasma

Plasma is a unique existence of matter that behaves diﬀerently from solids, liquids, and gases. Physically it is known as a superheated gas atoms–a atoms so hot that its thermal energy overcomes the Coulomb force that holds the electrons around the nuclei. Mathematically it can be described as a cloud of billiard–ballesque particles, a ﬂuid, or as an electromagnetic entity.

The majority of the observable universe is composed of plasma [2]. Although it mani- fests itself terrestrially through phenomena such as lightning, it is readily observable as the main state of matter of each star in the universe. By studying plasma, stars can be better understood and fusion potentially replicated.

2.1.1 Ionization of a Gas

In order to create a plasma, a gas must ﬁrst be ionized. Ionization begins with two oppositely charged electrodes. Due to a statistical event, such as interacting with a cosmic ray, an atom between these two electrodes could ionize. The ionization of hydrogen in Equation 2.1:

13 H + γ → H+ + e− (2.1)

Ionization causes the atom to split into two separate entities: the ion and the electron. The ion immediately feels a strong attraction to the negatively charged electrode, while the electron feels a pull towards the positively charged electrode. As the ion and electron accelerate towards their respective electrodes they collide with other neutral atoms. If they have enough kinetic energy, they can ionize these atoms.

H+ + e− + 2H → 2H+ + 2e− (2.2)

This process is called an electron cascade, as each collision has the potential to release many electrons, especially in high Z atoms.

As the electron cascade continues, a current is formed. When the electrons from the cascade touch the anode, and the ions touch the cathode, a circuit is completed. Once a circuit is completed, electrons can ﬂow as long as a voltage is applied without the need for a statistical event.

The electron cascade process can be ampliﬁed further by reducing the pressure in a chamber, which expands the mean free path of cascading electrons, allowing for a whole gas volume to be ionized. These conditions allow for the creation of plasma and are key in development an operational fusor.

2.1.2 Inﬂuence of Electric and Magnetic Fields

Once an gas has become suﬃciently ionized the individual particles begin to feel electrical and magnetic forces. The electrical forces in a fusor are due to the electrodes in the conﬁg- uration. The charged particles also exert forces on other charged particles in a plasma. The forces allow for development of waves and another interesting phenomena without particles

14 physically whacking each other. These long range interactions1 allow plasmas to function collectively even at low densities[2]. As the charged particles move they create a magnetic field. Plasma can be extremely hot, which means the particles can be moving very quickly. A fast charged particle creates a large magnetic field which responds readily to a resident magnetic field. Magnetic interactions between other particles can arise and cause fluxuations also[2]. By placing electrodes properly, particles in a plasma can be accelerated to high velocities and confined in numerous configurations. Many devices take advantage of this precise control over the plasma and attempt to confine enough particles in a small volume to create nuclear fusion. There are many different devices which do this, but there exist only two ways to achieve fusion. The first, and most promising method, is magnetic confinement fusion. The most auspicious device that works off this effect is called a tokamak, which uses a polodial magnetic field to squeeze plasma ions close enough to fuse. The second method is called inertial confinement, which uses a particle’s own momentum towards self confinement. The fusor describe in this article is an electrostatic inertial confinement fusion apparatus[6].

2.1.3 Nuclear Fusion

When two particles are brought close enough to each other their nuclei have the potential to overcome the repulsive Coulomb force and enter the realm of the nuclear force. This is not an easy task, as the nuclear force acts only on a scale of one to ten Fermi2. This distance is minuscule compared to the long range repulsion or attraction of the Coulomb force. Particles that get close enough to overcome the Coulomb repulsion will be attracted to each other through the nuclear force. This is the basic description of any fusion reaction. Each nuclear reaction has a probability of occurring known as a cross section. Cross sections are experimentally determined values of usually highly complex, statistical events, which change with system energy. It is given in units of area. A larger cross section area

1r 10−10m 2A Fermi is a unit of measurement named after Enrico Fermi. One to ten Fermi is equivalent to 1 × 10−15m – 10 × 10−15m

15 translates to a larger probability of interaction. In fusion, three reactions are unique, due to their high cross section at relatively low interaction energies. These reactions are given in Equations 2.4–2.6.

2 3 4 0 1D +1 T →2 He + n (2.3)

2 2 3 + 1D +1 D →1 He + p (2.4)

2 2 3 0 1D +1 D →2 He + n (2.5)

2 3 4 + 1D +2 He →2 He + p (2.6)

Whose cross sections are given as a function of energy in Figure 2.1:

Figure 2.1: Nuclear fusion cross sections of the most important fusion reactions [1].

16 From this graph it is apparent that the deuterium–tritium reaction is the most proﬁtable in terms of energy. Its cross section peaks at the low energy of 100 KeV which corresponds to a temperature of one billion degrees Kelvin3. Tritium is a radioactive gas which raises safety concerns, decreasing its appeal for use in amateur experiments. The next accessible reaction in the low energy region is the deuterium–deuterium reaction. Deuterium is non–radioactive and available for amateur use. While most professional facilities use deuterium–tritium, amateurs always use deuterium–deuterium to produce neutrons. Other reactions, such as ones that involve helium–3, are always excluded. Helium–3 is extremely expensive; it is only plentiful in areas that are exposed to solar wind, such as the moon.

2.2 Quantifying a Plasma

In order for a fully ionized gas to be considered a plasma, three conditions must be met [2]:

1. λD << L

2. ND >>> 1

3. ωτ > 1

The first condition that states that the Debye length, λD, must be much less than the length of the chamber in which the plasma is contained. In order to do this, the plasma must be sufficiently dense. This can be seen in the equation defining Debye length:

k T !1/2 λ = 0 b e (2.7) D ne2

The density, n must scale with electron temperature Te in order for the Debye length to stay less than the length of chamber.

The second condition requires that the number of particles, ND, in a sphere of radius λD be greater than one. If there are not enough particles in this volume, the plasma would not

3Plasma physicists use electron volts interchangeably with Kelvin. 1eV = 11605K.

17 exhibit statistically collective behavior. The number of particles in a Debye sphere is stated as:

4 N = nπλ3 (2.8) D 3 D

Finally, in order for a plasma to be governed by electromagnetic forces and not hydrody- namic forces, the plasma frequency, ω multiplied by the mean time between collisions should be greater than one. If all three of these criteria are met, than an ionized gas is truly a plasma.

18 Chapter 3

Construction of the Fusor

3.1 Possible Designs

Since Hirsch and Meeks patented their design, many amateur scientists have constructed their own device. Each one of these users has their own unique design, although trends are noticeable. Many users fabricate a spherical vacuum chamber, which acts as the outer grid. Using a spherical chamber eliminates the need for an outer grid and the associated infrastructure. It also increases the user’s accuracy to place the inner grid in the center of the outer grid. However, a fusor is not required to be spherical; some users have made cylindrical designs as well.

3.2 The Gol3tron

The Gol3tron, named after Adam Goler1, is a Hirsch–Meeks fusor built inside of a four way cross. It is a standard spherical grid fusor which uses a nitrogen-oxygen gas mixture for plasma.

The design is standard in that it contains a high voltage feed through, a view port, and a vacuum outlet. It deviates from the normal amateur fusor as it contains ‘experimentation

1Washington State University, Physics, http://www.physics.wsu.edu/personnel/people/grads/Goler_Adam.jpg

19 Figure 3.1: The Gol3tron’s ﬁnal prototype design. port’. This experimentation port has space to host any instrument or experimental device of which the user could think. Previously, it held two tungsten ﬁlaments but currently, it holds a triple Langmuir probe.

3.2.1 The Vacuum Chamber

The Gol3tron vacuum chamber centers around a four–way, six inch conflat cross. Each end of the cross is utilized for a specific task. The top port in Figure 3.1 contains a 2.75” conflat high voltage feed through which is rated for ±30000V . The high voltage feed through is attached to the chamber through a six inch to 2.75 inch zero–length conflat reducing flange.

20 Moving clockwise in Figure 3.1, the next port is the vacuum port. It contains another six inch to 2.75 inch zero–length conflat reducing flange which has a conflat to KF16 adapter attached to it. The adapter is attached to a three way KF16 tee, which hosts the pressure gauge. The butt end of the tee is attached to a pressure valve which is attached to the vacuum pump through two KF16 bellows. Opposite of the high voltage feed through is a six inch view port2. The final port on the vacuum chamber is a experimentation port which houses an additional six inch to 2.75 inch zero–length conflat reducing flange. Attached to the reducing flange is a four port BNC electrical feed through.

The chamber has a few non-stock modifications to it. Two of the conflat reducing flanges have holes tapped in them in order to support various components inside the chamber. The reducing flange that houses the high voltage feed through has two holes which hold screw in supports which hold the outer grid in place. The reducing flange which supports the BNC electrical feed through has two holes tapped in it which support the aluminum housing around the Langmuir probe.

3.2.2 Spherical Grids

The spherical grids are critical to the operation of the device. The inner grid is composed of three one inch diameter, 0.47 inch 316 stainless steel spring wire loops. The rings are welded together at right angles forming a spherical grid with geodesics at the equator and at the 0◦ and 90◦ longitudes. This design was chosen for several reasons. First, the design is simple to manufacture using a spot welder. Secondly, as symmetry is essential for proper operation, and the design’s simple geometry grants maximal leniency regarding maintaining symmetry. Finally, grids with less wire encounter fewer electrons and thus heat less during operation.

Heating is a prime concern when constructing the inner grid as it is constantly bombarded with very energetic ions. With a melting point near 1700K, the stainless steel spring wire was the best material available at the time construction, and has tolerated two months of

2Kodial glass

21 bombardment without eroding. An in-plane support wire is welded at the midpoint of the equator of the inner grid at the 45◦ longitude. By way of this support wire, the inner grid is seated at the end of the high voltage feed through using a beryllium coupler, secured with a set screw.

Figure 3.2: The complete grid assembly with inserted inner grid and supported outer grid.

The outer grid was not immediately implemented due to the complexity related to its manufacture. Unlike the inner grid, the outer grid is composed of thinner 0.025 inch Nichrome wire and is comprised of nine 3.9 inch diameter rings. The basic three-geodesic shape of the inner grid is implemented, but at each of the six right angle junctions between to geodesics, two perpendicular geodesics have been welded, bisecting the right angles. This complex geometry is diﬃcult to manufacture as there are many welds to be made. Additionally, the spring wire was not conducive to welding such large diameter rings. The outer grid, however, is not subject to the immense heat and ion bombardment of the inner grid, so thicker wire with a high melting point is not needed. Thus, the grid was constructed using the thinner, and easier to machine Nichrome wire.

22 To support the outer grid inside the chamber, two grounded, bored support rods were tapped into the zero-length reducing ﬂange which houses the high voltage feed through. Two support wires were welded to two of the six poles of the outer grid and were secured within the support rods with set screws. This holds the outer grid in place in the center of the chamber. To allow for placement of the inner grid, a hole was cut around a third pole and the secured with a welded ring. This allows the inner grid and high voltage feed through to slide through the hole and be placed in the center of the outer grid. Limited by the length of the high voltage feed through and placement of the support wire on the inner grid, there is some trouble achieving symmetry. Ideally, the inner grid should be centered within the outer grid and the equator, 0◦ and 90◦ longitudes of both grids should be aligned. However, due to the sum of the lengths of the high voltage feed through, the grid support wire and beryllium coupler not being long enough, the inner grid is not centered within the outer grid. Also, the additional mass at the end of the high voltage feed through, and its lack of support within the chamber, causes the inner grid to sag below the middle plane of the chamber. Lastly, the fact that the inner grid support wire is not welded at one of the six junction welds results in that the 0◦ and 90◦ longitudes of both grids being misaligned.

3.2.3 High Voltage Supply

The Bertan high voltage power supply is highly versatile 300W supply3 that can be interfaced with an external controller via a 25-pin D-subminiature. It allows for two 5V -scaled input voltages to control the high voltage and current outputs as well as two 10V -scaled output voltages used to monitor true high voltage and current outputs. The subminiature also contains digital inputs and outputs; two digital inputs are used to enable high voltage output and set the polarity of the output, and three digital outputs monitor polarity, operating mode4, and whether high voltage output is enabled. The supply is operated with a computer

3Bertan 835-30N. 4The two operating modes are constant–current mode and constant–voltage mode.

23 via a LabVIEW virtual instrument. The high voltage output is connected directly to the vacuum chamber’s high voltage feed through with high voltage cable.

It is noteworthy to add that at low voltages5, the high voltage output is diﬃcult to control. This may be because although the high voltage is enabled, output is not generated unless there is an input signal received by the supply and this input signal likely has a minimum threshold voltage which must be met. Given that the input signal is on a 0V − 5V scale, the relationship between input and output voltages is

Vinput = Voutput/6000. (3.1)

Output voltages in the 0V to 2000V range only correspond to an input range of 0V to 0.33V , which may be the cause of the control diﬃculty at low voltages. Additionally, at these low voltages, the supply quickly oscillates between constant current and constant voltage operating modes which indicates the supply is having diﬃcult assessing whether to generate

6 an output voltage. Current is scaled in a similar way, Iinput = Ioutput/2 , but scales correctly at all currents.

3.2.4 Vacuum Pump

The vacuum pump used is a two stage, oil sealed rotary vane pump7 connected to the vacuum chamber via a to-air vacuum valve on a standard KF 16 tee. There a pressure gauge8 sits as well to monitor pressure. The pump is operated manually, but the pressure gauge interfaces with a computer by the use of the LabVIEW virtual instrument.

The pump has two operating modes, essentially ‘on’ and ‘oﬀ’. Pressure is controlled simply by adjusting the vacuum valve while the pump is powered on. An oil-mist ﬁlter is used because pump exhaust often contains aerosolized oil when operating at pressures above

5Voltages in question range from 0V to 1500V . 6Current measured in mA 7Leybold Trivac D4B 8Lesker 275i Series Gauge with Integrated Controller and Display

24 10−6 Torr. The beneﬁts of this ﬁlter are apparent; the oil remains inside the pump and the workspace remains uncontaminated. Additionally, because the required pressure for this work is only 10−3 Torr, there is no need for a secondary pump.

25 26 Chapter 4

Measurement

4.1 Introduction to Plasma Diagnostics

Measurement of a plasma parameters is no simple task. Similar to quantum mechanics, any direct measurement of the plasma itself disturbs to the operating conditions significantly. This fact has forced experimentalists to find ways of measuring plasma parameters indirectly. Optical diagnostics have been performed, but accurate results are difficult to achieve, and the data incomplete[8].

Another problem that interferes with measuring plasma parameters is the enormous temperature present in a plasma. The heat created by an energetic plasma can easily destroy any delicate equipment which is introduced into it. For this reason, internal probes must be signiﬁcantly robust, cheap, and simple. Devices that meet these criteria have been produced, but their measurement accuracies are debated. Simply put, a plasma’s parameters can be debated and vary based on the technique used to obtain them [8] [4]. Despite this, estimates within ten percent can be made with relative ease that allow the experimentalist to have a fairly precise idea of the plasma’s state. One device that allows such measurements is a Langmuir probe.

27 4.2 Langmuir Probe Theory

Francis F. Chen best describes the Langmuir probe as:

“Of all the ways to measure a plasma, the Langmuir probe is probably the simplest, since it consists of sticking a wire into the plasma and measuring the current to it at various applied voltages. However, it is an intrusive, not remote, technique; and the wire must be carefully designed so as not to interfere with the plasma nor be destroyed by it. Worse than that, the interpretation of the current-voltage (I–V) curves is diﬃcult and has spawned a large literature of theoretical papers.” [3]

A Langmuir probe is a conducting device which is placed in the plasma where it will be measured. The probe is biased to a certain voltage and the resultant current that ﬂows through the probe is recorded. The biased voltage is then varied until the current becomes independent of changes in the voltage. A typical curve is shown in Figure 4.1.

Figure 4.1: A typical Langmuir curve. The blacks line depicts the actual data while the red line (20Ii) and blue line (0.5Ie) are ampliﬁed lines which allow the viewer to see the ion saturation current and the electron saturation current easily[10].

28 There are two important parts of this curve. The ﬁrst is the ion saturation current, denoted Ii and the second is the electron saturation current, Ie. The ion saturation current is much smaller than the electron saturation current due to the mass diﬀerences between particles. Thus all data from a single Langmuir probe is determined from the electron saturation current.[10] The reason that saturation currents take place is because an ion sheath forms around the probe tip which inhibits electrons from contacting with the surface of the probe. By measuring the electron saturation current and knowing the bias voltage at which it was obtained, the temperature of the electrons, and subsequentially, the electron density can be determined. However, despite being accurate, this system requires a full sweep through a wide range of voltages which can take a considerable amount of time. For time dependent plasma, a single probe will not be able to provide sound data.

4.3 Triple Langmuir Probe

The triple Langmuir probe, unlike its predecessor, is able to make instantaneous measurements of plasma with resolution as fast the data can be recorded1 . There are no required voltage or frequency sweeps that to be done, nor are there graphs from which data must be interpolated[4]. The triple probe bypasses all of this overhead by giving a time accurate measurement of the plasma parameters. With the triple probe, temperatures and densities can be plotted in real time along with voltages, pressures, and currents. Rapidly changing plasmas and fast phenomenon can be recorded eﬀortlessly with the triple probe. The triple Langmuir probe is very similar to single Langmuir probe. It requires a three probe tips, instead of one, located less than a millimeter apart from each other. The probe tips must be mostly insulated from the plasma, exposed only for a few millimeters, and each probe tip must have a electrical terminal that lies outside the chamber. Most importantly,

1All of the instruction on the theory, construction, and operation of the triple Langmuir probe is illustrated in S. Chen and T. Sekiguchi’s paper,“Instantaneous Direct-Display System of Plasma Parameters by Means of Triple Probe.” A thorough explanation lies in this text.

29 the probe must be able to resist high temperatures, it must not out gas heavily, and it must be able to be replaced in case of heat damage. In order to perform a measurement with a probe two voltage supplies must be used, called

Vd2 and Vd3. Two ammeters must be wired in series with probe two and three, and all three probes must be wired in parallel as per the circuit diagram shown in Figure 4.2.

Figure 4.2: a.) The proper circuit diagram for a triple probe. b.) The relative voltages of the three probes. [4].

Once all these variables are determined by instrumentation they can be substituted in to the following equation:

−φVd2 I1 + I2 1 − e = −φV (4.1) I2 + I3 1 − e d3

th where In is the current coming from the n probe and Vd2 and Vd3 are the two voltage supplies. φ is deﬁned as:

e φ = (4.2) kbTe where the constants kb and e are Boltzmann’s constant and the fundamental charge constant

30 respectively. With these two equations, the user can measure currents and voltages and then solve for the electron temperature.

4.4 Langmuir Probe Construction

Figure 4.3: The initial design of the Langmuir triple probe.

For materials in a potentially fusing plasma, resilience to temperature is the greatest concern. If a material cannot withstand extremely high temperatures and it may melt and damage the instrument and potentially the vacuum chamber. Superseding material concerns, a

31 probe must be functionally sound as well. The main concerns of design are overall function, shielding all electrical components from the plasma, creating a secure structure, allowing easy assembly and adjustment, and creating electrical contact to the outside world. The final prototype probe design addressed these issue and is depicted in Figure 4.3. This schematic consists of three parts. The first part, the base, consists two vacuum flanges that are screwed together. From this, a machined piece of aluminum housing is attached which contains a slot for the final part: the probe.

4.4.1 Probe Construction

When constructing the Langmuir probe tips, research was conducted to decide which metal is best suited for the application. The metal must have a high melting point and must be conductive. Table 4.1 shows the options availible.

Table 4.1: Highest Elemental Melting Points and Corresponding Electrical Conductivities [9] Rank Element Melting Point (◦F ) Electrical Conductivity (S/m) 1 Carbon 6422 1.0 × 105 2 Tungsten 6192 2.0 × 107 3 Rhenium 5767 5.6 × 106 4 Osmium 5491 1.2 × 107 5 Tantalum 5463 7.7 × 106 6 Molybdenum 4753 2.0 × 107 7 Niobium 4491 6.7 × 106 8 Iridium 4471 2.1 × 107 9 Ruthenium 4233 1.4 × 107 10 Hafnium 4051 3.3 × 106

Although it possess the highest melting point, carbon is quite brittle nature and is lack- luster conductor, so tungsten was chosen for use as the probe tips. Tungsten is also brittle, so a straight probe would have to be constructed in order to use tungsten. Also, tungsten can be found in many forms such as wire, plates, and rods; ﬁnding tungsten that would work for the construction of this instrument would be much easier than ﬁnding carbon. For

47 this probe, 7 inch long, 1000 inch thick pure tungsten welding rods from McMaster–Carr are used.

32 The probe tips need to be completely insulated from the plasma, except for a few millimeters at one end. Therefore, a electrical insulator that could also withstand high heat loads is required. It also needs to be able to give structural support to the tungsten rods. Lastly, it needed to have three holes in it for three probe tips. The perfect solution for this is alumina tubing [12]. Alumina has an extremely high melting point of 3761◦F , is very rigid, and is an excellent insulator. More importantly, it is widely manufactured in short segments with bored holes. These bored holes had to match the tungsten rods diameter to

187 a few thousandths of an inch to create a secure ﬁt. A 5 inch long, 1000 inch thick, 4 bore 50 tube with 1000 inch thick bore diameter was chosen from McMaster–Carr.

4.4.2 Aluminum Housing Construction

Once the actual probe was designed, the probe support structure had to be built around it. The main concerns were shielding all electrical components from the plasma, creating a secure structure, allowing easy assembly and adjustment, and creating electrical contact to the outside world. The solution to all of this is a machined part made of aluminum. This machined part has several characteristics. First, there is a hole in the center of the housing used to support the probe. The probe is then secured with a set screw. Below this hole is a large bored out hollow that houses the wires that connect the probe to the BNC port. These wires are attached to the probe tip tungsten rods with high vacuum Hysol epoxy. Not only does the housing support all these parts, it also acts as a Faraday cage for these components. The whole assembly is fastened to the zero–length reducing ﬂange via two tap holes. A tiny hole exists that equalizes the pressure on the outside of the housing with the inside of the housing.

Precautions need to be taken when assembling the probe. If the probe tip to BNC wires are too long they will bend as the housing is attached to the con ﬂat reducing ﬂange, potentially grounding the connections by touching the wall of the housing. This will destroy the triple probe circuit and probe measurements will be meaningless. An indicator of this

33 Figure 4.4: Langmuir probe and housing together before and after assembly on conﬂat.

scenario is if Vd2 does not change with Vd3.

4.4.3 Triple Probe Assembly

Occasionally the probe is replaced with a new probe of different length, or an undamaged probe. In order to smoothly assemble and disassemble the triple probe, a certain order of operations must be followed. To assemble the device, the housing must first be centered and attached to the conflat reducing flange with two screws. After this is done, the probe should be attached to the BNC connecting flange. While holding the reducing flange with the attached aluminum housing pointing downward the probe should be dangled by the BNC connecting flange and guided through the hole in the housing. The probe should be pulled to

34 the desired length and then secured by tightening the set screw. This order can be reversed for disassembly

If the probe is new, connecting wires should first be clipped appropriately so when the BNC connecting flange is seated on the reducing flange the wires to not buckle and press against the walls of the bored hole. Care should also be taken that the wires are not cut too short that they make attaching the probe to the BNC connecting flange overly difficult. Additionally, the probe tips should be tested for electrical connectivity with a digital multimeter. The tests should be taken to ensure that the wires are not touching the aluminum housing.

4.5 Direct Display of Plasma Parameters

Figure 4.5: The new circuit which allows the direct display of the electron temperature and density.

35 The simplest direct display configuration of the triple Langmuir probe requires several modifications to the original circuit diagram. The fixed voltage supply Vd2 needs to be removed, allowing probe two to float at the plasma potential. The voltage between probe two and probe one needs be measured using a high input impedance device. Additionally, the measurement of probe currents is not needed in the direct display circuit. This new circuit is depicted in Chen [4] and in Figure 4.5.

Error results if the device measuring the potential difference Vd2 does not have high input impedance. This is because a high input impedance device can measure the plasma without altering it, which is the main problem of a Langmuir probe. To test this, four different digital multimeters were used at the same pressure, voltage, and current. Each gave a different measurement:

Table 4.2: Direct Display Errors with Low Input Impedance Multimeters Multimeter Measured Voltage (V) Input Impedance (Ohms) NI USB-6009 .3 47, 000 Protek D-910F 1.2 10, 000, 000 Fluke 87-V 1.4 10, 000, 000 Agilent 34401A 1.7 10, 000, 000 Variable

These results question the validity of any voltage measured, but the Agilent 34401A is designed with high input impedance in mind. The measurement taken from this device is assumed to be as accurate as possible. More tests need to be done concerning the eﬀect of impedance on the measurement. The most valid measurements were taken with the available time, money, and expertise.

Once the fixed voltage supply Vd2 is removed from the circuit, and I2 → 0 is assumed. This means that Itotal = I3 = I1 which effectively gets rid of I2 and simplifies the measurement equation from 4.1 to Equation 4.3:

1 1 − e−φVd2 = (4.3) 2 1 − e−φVd3

Now, the only measurement that needs to be taken is Vd2.

36 4.6 Data Acquisition with LabVIEW

The ability to control most aspects of the device from a central point is very important, from the perspective of safety and ease of operation. As most of the devices used to manipulate the plasma are not USB Plug-and-Play, the need for a standalone product with which to script each device into a central software application is immense. The software package LabVIEW and a USB DAQ2 is used to create an virtual instrument that grants users control over the high voltage power supply, high impedance digital multimeter, video feed, and various subcomponents of these devices.

4.6.1 Features

The instrument, dubbed the “Fusor Master Control Board”, was originally written to allow users only to monitor device voltage, current, pressure and X-ray counts, but quickly grew to accommodate much more. The Control Board currently possesses the ability to:

• Enable and disable high voltage output.

• Manipulate high voltage output, current output.

• Monitor high voltage output, current output, pressure output, high voltage polarity and operating mode.

• Monitor statistics (mean, standard deviation, etc.) of high voltage output, current output, pressure output.

• View the interior of the fusor via an eight mega pixel web cam.

• Communication with a high impedance DMM, used to read triple Langmuir probe voltages and calculate electron temperature.

• Export collected data to a spreadsheet.

2National Instruments USB-6009 Multifunction DAQ

37 4.6.2 Use of the Virtual Instrument

The virtual instrument must first be initially calibrated before first use, primarily for proper communication with the high impedance digital multimeter. The multimeter is connected to the computer via a virtual serial connection and the specifics of that connection. Baud rate, parity, stop bits, etc. must be specified before executing the instrument. Once the interface has started, the user is first prompted for location and file name which the instrument will use when exporting the collected data. Once a filename is selected, video input from the web cam and data logging of time, pressure, voltage and current begins immediately but the high voltage is not enabled nor is the multimeter collecting data from the Langmuir probe. The high voltage output can be enable by moving the ‘HV Enable’ switch to the ‘On’ position. The high voltage output remains at zero until both an output current and a voltage are selected. The high voltage can be disabled by either returning the ‘HV Enable’ switch to its ‘Off’ position or by pressing any of the ‘Stop’ buttons located around the virtual instrument. Interfacing with the Langmuir probe is also made simple by the use of three buttons which communicate with the high impedance multimeter using its native machine language. These buttons allow three separate functions: prepare the multimeter for measurement, take direct measurements of the probe voltage, and display errors. The process of preparing the multimeter for data taking involves first switching the device to remote operation mode, then configuring the device for the desired measurement, which in this case is voltage. The command dictates the correct type of voltage measurement and specifies the range within which to expect future measurements and the resolution with which to take those measurements. Once prepared for measurement, the multimeter is put in a ‘waiting-for-trigger’ state in which it will continually read a single measurement and send it to the device’s output buffer for extraction at each trigger. The measurement button simply sends a trigger to the multimeter and receives a single voltage which it displays on screen. To extract electron temperature using the measured and bias voltages, Equation 4.3 is

38 used. Solving for electron temperature requires non-algebraic methods, and thus Equation 4.3 must be solved numerically. The virtual instrument uses a Newton-Raphson root finder to approximate the zero of the function. It scans from 10−6 to 102 and determined φ to an accuracy of 10−8, with which we can extract the electron temperature. In order to simplify data taking and provide abundant data, a current sweep mechanism has been implemented which sweeps through a desired subinterval of the maximum current range of the high voltage power supply. As the power supply is current limited at operating voltages, the current sweep limits the voltage output, effectively sweeping through both at a constant pressure. Noise has been problematic during data-taking. Both the USB DAQ and the multimeter can only take a limited amount of measurements every second. Unfortunately, there has been difficulty in synchronizing these two sampling rates. An artifact of this problem is that data files contain multiple values of pressure, voltage, current, etc. for the same value of electron temperature because the sampling rate for electron temperature is much slower than that of the rest of the parameters. To remedy this problem, a python script was created to scan through each data file and remove identical adjacent values. This easily prepares data for analysis, especially methods that consider frequency of measurements. Currently, this data-filtering technique is solely used to create histograms of electron velocity.

39 40 Chapter 5

Operation

5.1 Operating Parameters

During the operation of the fusor there are three parameters that can be controlled instanta- neously. The most dominant of these three parameters is the pressure. The pressure directly increases or decreases the resistance of the plasma because the high voltage power supply outputs constant current and voltage. It is controlled by manually powering on the vacuum pump and a manually adjusting the pressure valve. Interestingly, at pressures of a few mTorr the resistance of the gas becomes very low1, which allows current to ﬂow at relatively low voltages. As the pressure is decreased even more, the resistance rises exponentially. If constant current is to continue at these high resistances, the voltage must increase too. Voltage and current are the last parameters that can be controlled. The exponential increase of resistance can be clearly seen in Figure 5.1.

Interestingly, all of the operating parameters are interlinked through Paschen’s Law, which is governed by Equation 5.1.

apd IR = V = (5.1) breakdown log(pd) + b

1For most of the operating range of the fusor, the plasma resistance is about 200, 000Ω

41 Figure 5.1: Electrical resistance of the fusor.

In this equation a and b are parameters unique to a certain gas, p is the pressure of the gas, and d is the distance between two electrodes. Here, I and R are the familiar current and resistance associated with Ohm’s Law. The curve of this equation is depicted in Figure 5.2. It can be seen in this curve that the resistance, or breakdown voltage, has a minimum value which occurs as the pressure decreases. At a certain point, however, the resistance increases again. It does this exponentially, more rapidly than it initially decreased. During the fusor’s runs, achievable pressure regimes only allowed observation of later end of the Paschen curve.

5.2 Modes of Operation

As the the pressure decreases in the fusor, the shape, color, and spread of the plasma changes. Two modes were observed: jet mode and star mode. The most important of all these two modes is the star mode, which is an indicator of fusion conditions.

42 Figure 5.2: A Paschen curve for a gas with a = b = d = 1.

5.2.1 Jet Mode

As the pressure decreases from 150 mTorr, the poissor, or center ion concentration, ejects a plume out of an opening in the inner grid. The direction that the poissor picks is predictable as long as the geometry is not changed. As pressure decreases to around 80 mTorr the plume gradually enlarges, until it juts out of the inner grid. At this point jet mode begins. The plume stretches and fades into a blue haze which shoots out of the inner grid at a spread angle of around 45 degrees. As the pressure decreases even more the spread blue haze is rapidly concentrated to a bright blue beam, the epitome of jet mode. At 30 mTorr, it beings to fade.

Jet mode is the ejection of electrons from the inner grid to the outer grid. As positive ions and neutral atoms readily surround the inner grid in an attempt to shield the plasma from

43 Figure 5.3: The evolution of jet mode. The jet begins to form at 80 mTorr, grows in concentration untill 50 mTorr, and then fades at 30 mTorr. the electric ﬁeld, the electrons have an increasingly hard time of trying to ﬁnd an escape point. Unsurprisingly, the electrons take the path of least resistance, which at this pressure is through one opening in the inner grid which forms the plume and the blue haze. As the pressure decreases further, the inner grid’s voltage can increase, which then focuses the blue haze, much as a cathode ray tube would.

5.2.2 Star Mode

At around 15 mTorr the tightly bound blue jet of electrons disappear. Star mode is a sign of a well built fusor. Many amateurs consider star mode to be a huge accomplishment. In order to produce a star mode a fusor needs to have a clean vacuum system with a strong pump, a voltage supply capable of extreme voltages, and most importantly, well aligned, symmetric inner and outer grids. As in jet mode, the beams in star mode are largely composed of electrons taking the easiest way out of the inner grid but the exact reason that this process occurs is unknown. It is proposed that when the mean free path of the electrons becomes larger than the diameter of the chamber, the electrons do not care which hole out of the inner grid has the shortest path to the ground–any path to the ground would be collisionless. This would then allow the electrons to take any path from the inner grid to the grounded outer grid. As they do this, they are lensed by the grid, creating the star mode. It was determined in the Gol3tron that the star mode electron beams only form in pairs of

44 Figure 5.4: A star mode made at 7 mTorr at -25000 V. Multiple microchannels can be seen, including one hitting the glass. two. A beam radiates out of two opposite openings in the grids. If an opening is blocked by an object, such as a Langmuir probe, both electron jets will not form. This is an interesting and unexplainable characteristic of star mode that needs more attention.

5.3 Bremsstrahlung

During the modes of operation in the fusor, electrons hit the walls of the chamber with very high velocities. This causes them to rapidly decelerate, which releases high energy photons. This process is called Bremsstrahlung, which means breaking radiation. As the voltage is increased, the x–ray risk increases.

From this graph, it is apparent that for safety is a concern at certain voltages and that

45 Figure 5.5: Plot of x-rays produced in the fusor with only the inner grid present. shielding would need to be implemented. X-rays can be absorbed by all elemental materials. The eﬀectiveness of absorption varies with diﬀerent elements. In general, higher Z nuclei make better shields. Lead bricks2 were salvaged from previous experiments and are used to construct an enclosure that surrounds the view port of the device. It was then imperative to determine the number of x–rays that would penetrate this level of shielding. Data for X-Ray shielding is ubiquitous. In order to determine shielding for the fusor, NIST values were used[7]. NIST gives the equation for shielding as:

−(µ/ρ)x IOut = IIne (5.2) 2Dimensions of the lead bricks: 8 inches×4 inches × 2 inches.

46 Figure 5.6: Bill Parsons investigates the lead enclosure while the fusor is creating x-rays.

In this equation µ/ρ is a experimentally determined quantity that varies with energy of the

3 2 x-ray and the material, x is the mass thickness of the stopping material in g/cm , and IOut and IIn is the intensity out and in, in counts or counts per time. Setting up the equation with values of 10 KeV from NIST’s lead table, the amount of penetrating x–rays created by -10000 volt accelerated electrons can be determined. The µ/ρ value for this scenario is 1.36 × 102. The intensity in will be the experimentally measured 160 counts/minute. The lead bricks thickness is approximately 10 cm at a density of 11.34 g/cm3

160e−(1.36×102)113.4 = 2.19 × 10−6696 (Counts Per Minute) (5.3)

This is extremely small amount of x–rays. 160 counts per minute is a low amount of counts, though. At the fusor’s highest output voltage, -30000 V, electrons have energies of 30 KeV which have been recorded at 350000 counts per minute. The corresponding µ/ρ for

3x = ρ ∗ t where ρ is the density of the stopping material and t is the thickness.

47 these energies is 3.032 × 101. The thickness remains the same. This is the highest energy of x-rays coming through the view port, which will be the most diﬃcult to shield. If these x–rays cannot pass through the shielding, no x–rays will pass through.

350000e−(3.032×101)113.4 = 2.06 × 10−1488 (Counts Per Minute) (5.4)

At the highest energies users are amply shielded.

5.4 Heat Production

Creating the conditions for thermonuclear fusion requires high temperatures. During star mode operations where the operating voltage climbs higher than −11000V the vacuum chamber rapidly heats up. This means that fast electrons are hitting the chamber. Temperatures on the outside of the chamber measured with a Watlow 96 thermocouple have exceed 100◦ C. A positive side eﬀect of the extreme temperatures produced in the fusor, materials put into the device do not have to go in oil and dust free; the fusor is able to burn up the oil and dust into its composition particles which stops out gassing. The fusor is essentially a vacuum chamber that bakes itself.

48 Chapter 6

Experimentation

6.1 Measurements of Sparse Plasma

The ﬁrst probe used to measure the electron temperature was the shortest probe, which was about two inches long and was placed an inch outside of the outer grid. Its purpose was to diagnose the plasma parameters outside of fusing regions where the temperatures would be less intense and the voltages smaller. By working in this region, the likely hood of destroying an instrument decreases. As measurement conﬁdence increased, newer probes could be introduced that probed into more chaotic regions.

6.1.1 Calibration and Conﬁrmation of Valid Data

As soon as the Langmuir probe was inserted into the plasma, conﬁrmation of proper results was the primary goal. Several runs were taken at diﬀerent Vd3 voltages. Each run’s electron temperature was plotted against the voltage Vd2 and compared to Chen’s results, which were applicable for all gases[4].

The most exciting run was that accomplished at Vd3 = 10. These results were almost identical to Chen’s curves which indicates that the probe was properly measuring electron temperatures.

49 Figure 6.1: Comparison of Vd2 vs. Temperature curves. Both are at Vd3.

6.1.2 Indirect Observation of Electron Beam Lensing

In plots of temperature vs. operating voltage with the short Langmuir probe, lensing can be seen as bumps in the temperature vs. operating voltage. The bumps show rapid decreases in electron temperature at −2000V . This is due to electrons being rapidly focused into microchannels at this voltage. Electrons stop hitting the probe which decreases the probe’s measured temperature. This is the transition into jet mode. However, at voltages of around −5000V the bumps appear again and this too involves lensing. As jet mode starts to disappear, the electrons begin exiting from all openings in the inner grid, which allows the probe to catch more electrons.

6.2 Quantifying the Electron Beam

The fusor attracts much attention because of its two distinct modes: star mode and jet mode. Both of these modes of operation are based oﬀ of microchannels emanating from the center of the fusor. Measuring these beams and probing their composition and temperature is important to understanding how a fusor operates. The geometry of the Langmuir probe allows it to be positioned directly in front of a jet mode electron beam which becomes a star

50 Figure 6.2: Plot of operating voltage versus electron temperature. The bumps are due to electrons being lensed. mode microchannel at lower pressures and higher voltages.

6.2.1 Electron Temperature

Data taken when the Langmuir probe was placed in the electron beam revealed an apparent trend — the temperature in the elctron beam ﬂuxuated very rapidly. This meant that electrons are not just accelerating away from the inner grid. The data suggests that electrons in the fusor’s jet display a distribution of temperatures, which means they are traveling at diﬀerent velocities. Further investigation of electron temperatures in the fusor yielded the results seen in Figure 6.3. It can be seen that the sharpest particle gradient in Figure 6.3

51 lies at the lowest temperature, but there is also a less dense concentration of particles at the upper limit.

Figure 6.3: The electron temperature versus time. V = −992V , I = 2.33mA, P = 89mTorr

6.2.2 Bi–Modal Maxwellian Distribution

To gain insight into electron dynamics inside the plasma, histograms were created plotting the velocity of the electrons in hopes of obtaining a Maxwellian distribution. The measured electron temperatures were converted into a velocity assuming a Maxwellian distribution:

s 3k T v = b (6.1) m

52 In Equation 6.1, m is mass of the electron and kb is Boltzmann’s constant. The formula yields an approximate measurement of velocity from the temperatures gathered. The results were striking:

Figure 6.4: The electron temperature versus time. V = −992V , I = 2.33mA, P = 89mTorr

The temperatures of the electrons are spread into a bi–modal distribution. It was observed that in all runs the temperature could be shifted left or right, but the ﬁrst peak was always large and sharp while the second peak was shorter and wider. The measurements remained the same, regardless of pressure and current, but were heavily dependent on the plasma mode and operating voltage.

To take these measurements the plasma was placed in a conﬁguration that allowed a

53 blue electron beam to propagate on or nearby the probe tip. If the plasma is creating ions near the probe, in other words is not in jet mode, the temperatures will be reduced and the Maxwellian should be different. Next, the plasma had to remain stable in respect to voltage and plasma for the duration of the measurement which could take anywhere from five to thirty minutes. If the voltage or pressure changed it would cause the electron temperature distribution to migrate, giving an inaccurate reading. The data sets in which the electron temperature differed the least are shown on top of each other:

Figure 6.5: The overlap of two Maxwellians from diﬀerent runs. The black run was run at a much higher pressure. Both runs have close average operating voltage.

These two trials remained stable throughout the entire trial, allowing accurate and repro- ducible data.

54 The reason for these bi–modal Maxwellian is currently unknown. It is thought that the two species of ions, oxygen and nitrogen, are overlapping their separate Maxwellians. Concurrently, it is presumed that two species of electrons are being produced inside the fusor: electrons expelled from ionized fast neutral particles and electrons emitted from the inner grid. These two ideas have not yet been probed.

6.3 Measuring the Core

Figure 6.6: The long Langmuir probe in the center of the fusor, investigating the poissor.

Probing the conditions in the core has turned out to be a diﬃcult task. The probe can easily be placed inside the inner grid and measurements can be taken, but the system is unpredictable and violently swings between temperatures with minor shifts in operating voltages. Moreover, the probe measures intense positive voltages on Vd2 which were not seen

55 outside the grounded grid. The intense voltages break down Equation 4.3, causing it to transition across the y-axis:

Figure 6.7: A graph portraying the equation’s transition from a solvable region to an unsolvable region.

In order to do this, the voltages must violate the inequality:

V V ≥ d3 (6.2) d2 2

When this occurs, the x-intercept moves into the negative portion of the real line. It is presumed that this happens because the large concentration of positive ions on the center congregate around the probe tips artificially. Even though there is a positive voltage that should push them away, the accelerating voltage is much too large for the probe’s power supply to counter. The positive ions then make an artificial positive voltage which causes the poor measurements. Unfortunately, this cannot be fixed without using a Vd3 that is similar to the operating voltage. The equipment to perform this is not available at the time. Another adverse effect of probing the center of the fusor is arcing. If the voltage is allowed to exceed −5000V , the current from the inner grid moves down the alumina rod on the tungsten wires and out the BNC port to ground, potentially damaging sensitive electronics. Arcing through the probe was observed at pressures as high as 30 mTorr which corresponds to a voltage of −5000V . A purple corona inside the alumina tube accompanied

56 the phenomena. The arcing insured that fusing conditions could not be probed as the voltage to create fusion is six times as high as the arching voltage. This potentially could be avoided by setting up a high voltage circuit, but the equipment needed here is also not available. Lastly, the probe’s location in the center destroyed the symmetry of the electrodes. This caused the poissor to appear in diﬀerent locations depending on Vd3. Other times it would ﬂicker between positions. Electron beam jets from jet mode were seen emanating from the probe tips as well. Due to the alteration of the symmetry, the Langmuir probe failed to measure the temperature at the center of the fusor.

57 58 Chapter 7

Conclusion

7.1 Results

As of now, electron temperatures have been measured in three locations: outside the outer grid has provided sound data, between the grids has also provided interesting data; and data from the inner grid has been inconclusive. The most interesting and unique of all these results was the determination of the bi–modal Maxwellian distribution function of the plasma between the two grids. This result has not be observed before, as Langmuir probes have not been extensively used to characterize fusors.

7.2 Final Thoughts

Plasma physics a beautiful and complicated ﬁeld. Unlike some physics, the images of a plasma and the accompanying phenomena are stunning and easy for laymen to appreciate. Unfortunately, plasma physics is also diﬃcult. Measurements are esoteric; large temperatures and rapid oscillations do not allow the scientist to have a gut intuition of what is occurring. Moreover, plasma is created in a shell with which the user cannot directly interact. It takes time to become familiar with a plasma, but this time is often the most rewarding.

59 60 Bibliography

[1] Bosch, H. -S, and G. M. Hale. “Improved Formulas for Fusion Cross-sections and Thermal Reactivities.” Nuclear Fusion 32 (1992): 611. Print.

[2] Chen, Francis F. Introduction to Plasma Physics and Controlled Fusion. New York: Springer, 2006. Print.

[3] Chen, Francis F. “Mini-Course on Plasma Diagnostics.” Lecture. IEEE-ICOPS Meeting. Korea, Jeju. 5 June 2003. Web. 18 Apr. 2010.

[4] Chen, Sin-Li, and T. Sekiguchi. “Instantaneous Direct-Display System of Plasma Pa- rameters by Means of Triple Probe.” Journal of Applied Physics 36.8 (1965): 2363-375. Print.

[5] Farnsworth, Philo T. Method and Apparatus for Producing Nuclear-Fusion Reactions. Reuben Epstein, assignee. Patent 3386883. June 1968. Print.

[6] Hirsch, Robert. Apparatus for Generating Fusion Reactions. Reuben Epstein, assignee. Patent 3530497. Sept. 1970. Print.

[7] Hubbell, J. H., and S. M. Seltzer. “Tables of X-Ray Mass Attenuation Coeﬃcients and Mass Energy-Absorption Coeﬃcients.” Physical Reference Data. NIST, July 2004. Web. 28 Apr. 2010. .

[8] Hutchinson, I. H. Principles of Plasma Diagnostics. Cambridge [Cambridgeshire: Cam- bridge UP, 1987. Print.

61 [9] Lide, D. R. (Ed.). CRC Handbook of Chemistry and Physics. 87th ed. CRC Press, 2006.

[10] Merlino, Robert L. “Understanding Langmuir Probe Current-Voltage Characteristics.” American Journal of Physics 75.12 (2007): 1078-085. Print.

[11] Moore, John H., Christopher C. Davis, Michael A. Coplan, and Sandra C. Greer. Build- ing Scientiﬁc Apparatus. Cambridge, UK: Cambridge UP, 2009. Print.

[12] Pace, David C. “Construction of a Triple Probe for Use on the LArge Plasma Device.” David Pace - Downloads. UCLA, 2 Aug. 2005. Web. 18 Apr. 2010. .

[13] Rider, Todd H. “A General Critique of Inertial-electrostatic Conﬁnement Fusion Sys- tems.” Thesis. Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1994. Massachusetts Institute of Technology. Web. 29 Apr. 2010. .

[14] Rosenberg, M., and Nicholas A. Krall. “The Eﬀect of Collisions in Maintaining Non- Maxwellian Plasma Distribution in a Spherically Convergent Ion Focus.” Physics of Fluids B. 4.7 (1992): 1788-794. Print.

62 List of Figures

1.1 The fusor cross section from Hirsch-Meek’s patent[6]...... 10

1.2 Farnsworth’s design of the multipactor fusor from his original patent[5]. . . . 11

2.1 Nuclear fusion cross sections of the most important fusion reactions [1]. . . . 16

3.1 The Gol3tron’s ﬁnal prototype design...... 20

3.2 The complete grid assembly with inserted inner grid and supported outer grid. 22

4.1 A typical Langmuir curve. The blacks line depicts the actual data while the

red line (20Ii) and blue line (0.5Ie) are ampliﬁed lines which allow the viewer to see the ion saturation current and the electron saturation current easily[10]. 28

4.2 a.) The proper circuit diagram for a triple probe. b.) The relative voltages of the three probes. [4]...... 30

4.3 The initial design of the Langmuir triple probe...... 31

4.4 Langmuir probe and housing together before and after assembly on conﬂat. . 34

4.5 The new circuit which allows the direct display of the electron temperature and density...... 35

5.1 Electrical resistance of the fusor...... 42

5.2 A Paschen curve for a gas with a = b = d = 1...... 43

5.3 The evolution of jet mode. The jet begins to form at 80 mTorr, grows in concentration untill 50 mTorr, and then fades at 30 mTorr...... 44

63 5.4 A star mode made at 7 mTorr at -25000 V. Multiple microchannels can be seen, including one hitting the glass...... 45 5.5 Plot of x-rays produced in the fusor with only the inner grid present. . . . . 46 5.6 Bill Parsons investigates the lead enclosure while the fusor is creating x-rays. 47

6.1 Comparison of Vd2 vs. Temperature curves. Both are at Vd3...... 50 6.2 Plot of operating voltage versus electron temperature. The bumps are due to electrons being lensed...... 51 6.3 The electron temperature versus time. V = −992V , I = 2.33mA, P = 89mTorr ...... 52 6.4 The electron temperature versus time. V = −992V , I = 2.33mA, P = 89mTorr ...... 53 6.5 The overlap of two Maxwellians from diﬀerent runs. The black run was run at a much higher pressure. Both runs have close average operating voltage. 54 6.6 The long Langmuir probe in the center of the fusor, investigating the poissor. 55 6.7 A graph portraying the equation’s transition from a solvable region to an unsolvable region...... 56

64 List of Tables

4.1 Highest Elemental Melting Points and Corresponding Electrical Conductivi- ties [9] ...... 32 4.2 Direct Display Errors with Low Input Impedance Multimeters ...... 36