Feasibility of a Plasma Contact for Faraday

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FEASIBILITY OF A PLASMA CONTACT FOR FARADAY

GENERATORS

THESIS

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the

Graduate School of The Ohio State University

Dheeraj Chalasani, BE (Hons)

Graduate Program in Mechanical Engineering

The Ohio State University

2013

Master‟s Examination Committee:

Dr. Vish Subramaniam, Advisor

Dr. Anthony Luscher, Co-advisor

Dheeraj Chalasani

2013

ABSTRACT

A Faraday disc generator is a direct current power source that works on the principle of electromagnetic induction. Michael Faraday discovered this generator effect in 1831. Since then a lot of improvements were made upon the original design but the

Faraday disc generator has not enjoyed wide spread success. One of the chief reasons for this is the use of contact brushes. The wear of the contact brushes significantly affects the current carrying capacity of the disc. The current distribution in a Faraday disc as a result of energy extraction through a brush contact results in Eddy currents in the Faraday disc which significantly reduces the energy efficiency of the disc. As an alternative, the use of ionized gas or plasma as an electrical contact is considered. The use of plasma as an electrical contact in Faraday disc generators is a new and a novel idea as such an idea has not been suggested by anyone until now.

The current work examines the feasibility of using plasma as an electrical contact instead of the conventional brush contacts for energy extraction from a Faraday disc generator from the perspective of plasma attachment and current-voltage characteristics.

An experimental apparatus has been designed to simulate the conditions of a Faraday disc generator envisioned as receiving power from a wind or a hydraulic turbine. The setup consists of co-axial electrodes with an air gap of 1mm with the inner electrode being the anode that can be rotated about its axis as required. Experiments were performed at 9.1 ii

torr, 9.55 torr and 10.6 torr to determine the current-voltage characteristics for the cases of rotating anode and stationary anode using a DC power supply.

It was observed that the current-voltage characteristics in both the cases of rotating anode and non-rotating anode are qualitatively similar. The various operating regimes of DC plasma were identified qualitatively from the plotted current –voltage characteristics and by visual inspection. As far as plasma attachment is concerned, it seemed to be diffuse and looked to follow the characteristics of a glow regime with by gradually covering the annular gap as the current was increased and stayed diffuse after covering the entire air gap. From the experimental results and observations it was determined that using plasma as an electrical contact is feasible but there are problems that have to be addressed. Based upon the observations and results of the experimental work, two possible self-sustaining configurations for energy extraction were proposed.

Finally, a plasma de-coupler design was provided as a solution to the problem of high current densities in the energy extraction area of the plasma.

iii

Dedicated to my beloved parents and grandparents

ACKNOWLEDGMENTS

I would like to take this opportunity to express my sincere gratitude to my thesis advisor, Dr. Vish Subramaniam, for his guidance, assistance and support throughout the course of this work. He has always been a source of inspiration and encouragement for me. I would also like to thank Dr. Anthony Luscher, my co-advisor, who has provided me the support and guidance to push through the final stages of the project. I would like to extend my sincerest thanks to Mr. Joe West for providing his valuable insights and guidance all along the way.

In addition, I would like to thank John and Jason of the Student Electronics Lab for helping me with manufacturing of components. Special thanks go to the unidentified stakeholders from the organizations that shared their data and recollections with us.

Finally, I wish to thank my family for their motivation and immense support both financially and spiritually during my stay at Ohio State.

VITA

2011……………………………………………...BE (Hons), Mechanical Engineering,

M.Sc (Hons), Mathematics

Birla Institute of Technology, Pilani

2011 - Present………………………………..….Graduate Student,

The Ohio State University,

Columbus, OH, USA

FIELD OF STUDY

Major Field: Mechanical Engineering

Primary Area: Energy, Fluid and Thermal Systems

TABLE OF CONTENTS

ABSTRACT ...... ii

ACKNOWLEDGMENTS ...... v

VITA ...... vi

TABLE OF CONTENTS ...... vii

LIST OF FIGURES ...... ix

LIST OF TABLES ...... xi

Chapter 1 : INTRODUCTION...... 1

Chapter 2 : BACKGROUND...... 10

2.1 Gas discharges and electrical breakdown ...... 10

2.1.1 Townsend mechanism ...... 10

2.1.2 . Paschen Curve ...... 15

2.2 Plasma ...... 18

2.2.1 DC Plasma: Current - Voltage Characteristic ...... 20

2.2.2 Glow discharge ...... 22

2.2.3 Arc discharges ...... 26

Chapter 3 : EXPERIMENTAL APPARATUS AND PROCEDURE ...... 28 vii

3.1 Experimental Apparatus ...... 29

3.1.1 Experimental chamber and Air handling system …………………………29

3.1.2 Electrode setup and magnetic coupler ...... 32

3.1.3 Electrical power supply, connections and data acquisition apparatus ...... 36

3.2 Experimental Procedure ...... 37

Chapter 4 : EXPERIMENTAL RESULTS & DISCUSSION………………….…… 42

Chapter 5: CONCLUSIONS & RECOMMENDATIONS FOR FURTHER

WORK………………………………………………………………………………..55

REFERENCES…………………………………………………………………….…64

viii

LIST OF FIGURES

Figure 1.1: Faraday disc generator, courtesy by [5]………………………………..…….2

Figure 2.1: Paschen curves for Air, H2 and N2, courtesy by [17]………………………..16

Figure 2.2: V-I characteristic of DC plasma in Neon gas at 1 torr and planar electrode spacing of 50 cm, courtesy by [22]…………………………………………………..…..19

Figure 3.1: Bell Jar and the Stainless Steel Base……………………………..………….30

Figure 3.2: Stainless Steel Base……………………………………………...…………..30

Figure 3.3: Process Flow Chart of Gas Handling System……………………….………31

Figure 3.4: Analog Manometer…………………………………………………………..32

Figure 3.5: Electrode Assembly……………………………………………………….…33

Figure 3.6: Isometric View of Electrode Assembly……………………….……………..33

Figure 3.7: Magnetically Coupled Discs………………………………………….……..35

Figure 3.8: Completely Assembled Experimental Apparatus…………………...……….37

Figure 3.9: Circuit Diagram of the System………………………………………………38

Figure 4.1: Current-Voltage characteristics of rotating anode and stationary anode at 9.1 torr………………………………………………………………………………………..46

Figure 4.2: Current-Voltage characteristics of rotating anode and non-rotating anode at

9.55 torr……………………………………………………………………..……………46

Figure 4.3: Current Voltage Characteristics of rotating anode and stationary anode at 10.6 torr…………………………………………………………………………/.……………47

Figure 4.4: Plasma attachment from left and right ends at P…………………….………48

Figure 4.5: Plasma attachment from left and right ends at Q…………………...……….48

Figure 4.6: Plasma attachment from left and right ends at R…………….………………49

Figure 4.7: Plasma attachment from left and right ends at S…………….………………49

Figure 4.8: Effect of angular velocity on CVC………………………………...……...…52

Figure 5.1: Plasma De-coupler Design – First View…………………………………….61

Figure 5.2: Plasma De-coupler Design - Second View………………………….………61

LIST OF TABLES

Table 2.1 Values of parameters A and B for different gases, courtesy by [17]…...……..15

Table 2.2 Typical discharge parameter ranges of Thermal and Non-thermal arc discharges courtesy by [25]…………………………………………………………………...……..27

Table 3.1: Sample data set 10 torr & 127.7 rpm………………………………..………..40

Table 4.1 Experimental Data Set for First Run for 9.1 torr - Stationary Anode

Case…………………………………………………………………………………...….44

Table 4.2. Experimental Data Set for Repeated Run for 9.1 torr - Stationary Anode

Case………………………………………………………………………………………44

CHAPTER 1: INTRODUCTION

The Faraday disc, also called a homopolar generator, is a DC electrical generator which works on the principle of electromagnetic induction. It is a low voltage – high current device. The generator effect was first observed by Michael Faraday during the course of his experiments on electromagnetic induction in 1831 [1]. The experiments employed carbon contact brushes as electrical contacts. Since then, the homopolar generator has been studied and a lot of improvements [2] have been made upon Faraday‟s original design but the homopolar generator has not enjoyed widespread success. One of the main problems is the use of brush contact which is subject to wear. The focus of this thesis is on examining the use of ionized gas or plasma as electrical contact as an alternative to conventional brushes. The idea is novel and if determined to be practical can have a huge impact on the energy extraction from the Faraday disc generator. A literature review on this idea of plasma brushes has not yielded any publications or a reference to such an idea. The following paragraphs describe the Faraday disc generator from a historical perspective, explain the physics governing the operation of the generator and discuss the problems associated with the energy extraction from the generator using carbon contact brushes that can be potentially overcome with the novel idea of replacing the contact brush with plasma.

Of all the numerous experimental setups constructed by Faraday during his investigations into electromagnetic induction, one setup is of particular interest for the subject matter at hand. A schematic of Faraday‟s experimental setup is shown in Figure 1.1.

Figure 1.1: Faraday disc generator, courtesy by [5]

The setup consisted of a cylindrical steel magnet, a copper disc and a galvanometer. The magnet and copper disc were axially aligned by connecting the axle of the copper disc to the magnet. But they could also be independently rotated about their respective axes. The galvanometer was connected to the rim and the axle of the copper disc through brush contacts at A and P as shown in Figure 1.1. Michael Faraday performed three experiments using this apparatus:

Experiment 1: The disc was held stationary and the magnet was rotated

Experiment 2: The magnet was held stationary and the disc was rotated

Experiment 3: Both the magnet and disc were rotated at the same angular velocity and in tandem

In the first experiment, where the disc was held stationary and the magnet was rotating, no current was observed while in both the other experiments a current was observed in the galvanometer.

In so far as explaining the physics governing this phenomenon and the observed results, what is now known as Faraday‟s law of electromagnetic induction didn‟t seem to be the answer at that time. From the lines of flux standpoint, an induced electromotive force is a result of the rate of cutting the lines of flux. Therefore, this view would predict a current in the galvanometer in Experiments 1 and 2 as the lines of flux are cut in both the cases of only the magnet rotating and only the disc rotating. As a direct consequence of the same theory, no current should be registered in the galvanometer if the lines of flux are not cut when the disc and the magnet rotate together i.e. Experiment 3. But these predictions are in contradiction to the experimental observations in Experiments 1 and 3.

In order to resolve this paradox, Faraday proposed that the magnetic lines of flux remained stationary even as the magnet rotated [3]. Logically, this assumption explains the results of all the three experiments. But some physicists, most notably Weber, did not accept this explanation and firmly believed that the lines of flux rotated along with the magnet. In 1831, Weber confirmed Faraday‟s experiments and put forth a competing theory that the induced current was a result of relative motion between the disc and 3

external circuit (galvanometer) but not between the disc and the magnet. Weber, among other physicists, believed that the lines of force interacted both with the disc and the external circuit. This explains the results of all the three experiments but Weber incorrectly assumed that the phenomenon was a result of single pole of magnet and hence called it Unipolar Induction. As a result, the physicists all over the world were divided in their opinions. Some physicists believed that the lines of flux remained stationary; a second group believed that the lines of flux rotated with the magnet; others believed that the lines of flux were only a representation of field and had no physical meaning. There was no way of deciding upon this issue as it was really difficult to design an experiment to unambiguously state which group was right.

Much later, only after the discovery of electron, postulation of Maxwell‟s equations, elucidation of the Lorentz force and principles of relativity that a consensus emerged among the physicists about the physics governing the phenomena of homopolar induction. One such simple model describing the phenomena was presented for the case of electromagnetic induction across the axle and rim of a rotating steel encased magnet

[4]. In a later paper [5], a similar simple model is presented to explain the electromagnetic induction across the axle and rim of a rotating copper disc. As long as the magnetic field B is independent of time, the magnetic field is constant. And in the particular case of cylindrical magnets, due to the radial symmetry of the field, the magnetic field B is constant irrespective of whether the magnet is rotating or not. The physics of electromagnetic induction in the homopolar generator is then explained using the Lorentz force. From the frame of reference of the magnetic field, as the copper disc rotates, the conduction electrons also appear to rotate with the same angular velocity as 4

that of the disc. From the Lorentz force, it can be deduced that the perpendicular magnetic field will cause the conduction electrons to experience a force in the plane of the disc and perpendicular to both the velocity and magnetic field vectors. At any instant of time, this Lorentz force is either directed radially outwards or inwards. This direction is dependent on the direction of disc rotation and magnetic field direction. As a result, the conduction electrons are either directed towards the center of the disc or towards the rim of the disc. This distribution of surface charge results in setting up an electromotive force across the center and the rim of the disc. This is an explanation based on a simple model and other explanations [6], [7], [8] from different points of view can be found in the literature.

Although there was a lack of consensus on the physics governing the operation of a Faraday disc until the early part of 20th century, physicists agreed that the phenomenon exists and attempts were made to make commercialize the device as a working generator.

A lot of patents were filed for homopolar generators. Some of the early patents were awarded to [9], [10] and [11]. Some of the later patents were awarded to [12] and [13].

Much later, homopolar generators were used as giant power sources for experimental purposes at Australian National University [14]. It was called the Canberra Homopolar

Generator and was capable of sourcing 1.5 million amps at about 800 V for 0.1 s. Similar devices [15], [16] were constructed by Parker Kinetic Designs at University of Texas at

Austin for powering rail guns and as electrical welding sources.

The Faraday disc generators mentioned in the previous paragraph employed contact brushes. The various factors that affect the performance of a carbon contact brushes can be classified into mechanical, electrical and environmental ones 5

(http://www.mersen.com/uploads/tx_mersen/5-carbon-brush-technical-guide- mersen.pdf). The mechanical factors include surface tribology of contacting surface – ideally the contact surface should neither be too smooth nor too rough, variable friction co-efficient of the brush, vibrations of the device that can damage the brush and carbon brush pressure on slip ring to enable good contact between the brush and the slip ring.

The electrical problems include that of the contact potential drop and non-uniform distribution of current in the brush. The environmental problems include deposition of undesirable layers of metal oxides or dust and presence of corrosive gases that damage the contact surface and eventually the brush.

The cumulative effect of the above mentioned contact brush problems results in the generation of eddy currents in the Faraday disc generator as energy is extracted. Eddy currents or Foucault currents are induced electric currents within a conductor by a changing magnetic field. The presence of eddy currents is detrimental in two ways.

Firstly, the eddy currents result in Joule heating of the disc. Secondly, the presence of eddy currents increase the torque required to maintain the rpm of the disc at the same value. This is a direct consequence of conservation of energy as the energy dissipated in the form of Joule heating has to come from the external mechanical torque. There are two possible ways for formation of eddy currents in the Faraday disc generator. One of them is the result of misalignment of the axes of the disc and the magnet. If the axes are not aligned properly, the rotation of disc would cause the conducting disc to experience a repetitive time varying magnetic field that induces eddy currents. The other possible way is through the extraction of current using contact brushes. This is a direct consequence of

Lenz‟s law. As the current, which is the result of magnetic induction, is drawn from the 6

generator, a magnetic field is generated by the drawn current which tends to oppose the magnetic field which induced the current in the first place. This secondary magnetic field tends to distort the homogeneity of the current inducing magnetic field which in turn sets up eddy currents in the disc. As was mentioned earlier, the homopolar generator is a low voltage-high current device. And if the generator were designed to operate at a few volts, the use of contact brushes would mean a contact potential drop that could be significant as compared to the voltage differential across the center and rim of the disc. Also, there is the problem of erosion of contact brushes due to frictional heat generated by the rotation of disc at high angular velocities. A sample calculation to get a sense of the magnitude of angular velocities is provided below.

Let E be the electromotive force induced across the Faraday disc, φ be the magnetic flux associated with the disc, ω be the angular velocity of the disc, R be the radius of the Faraday disc and B be the magnetic field of the cylindrical disc permanent magnet.

Then,

Therefore,

From the above equation, to have an electro-motive force of 10 volts induced across a 3” (Diameter) Faraday disc that is experiencing a 0.4 Tesla magnetic field, the angular velocity of the Faraday disc has to be 34445 radians per second which corresponds to 329087 revolutions per minute.

The contact with surface rotating at high angular velocities causes the erosion of the brush material that significantly affects the current carrying capacity of the brushes.

As a result, the brushes have to be replaced periodically and performance of the device as a generator suffers. All of the above discussed issues tend to make energy extraction from a Faraday disk generator highly inefficient.

It is quite clear from the above discussion that the electrical contact (contact brushes) to the external circuit is the major source of concern for efficient extraction of electrical energy from the generator. A solution to this problem could be to use plasma as an electrical contact. It is a new and a novel that can entirely get rid of the eddy currents problem and all the other associated issues with the use of contact brushes. Since the

main goal of the current work is to determine the feasibility of using a plasma as an electrical contact instead of the conventional contact brushes, Chapter 2 provides a background on electrical breakdown of gases and plasmas.

This thesis is organized as follows. The following chapter provides a background on plasmas. Chapter 3 describes the experimental apparatus and the employed procedures in detail. The experimental results, along with studies of repeatability and error analysis are presented and discussed in Chapter 4. Chapter 5 provides the conclusions of this work and recommendations for future work.

CHAPTER 2: BACKGROUND

2.1 Gas discharges and electrical breakdown

Gases are typically excellent insulators with very low current conduction. But when large fields are applied across the gas, the gas molecules are ionized and the medium becomes electrically conductive i.e. electrical breakdown occurs. The nature of the discharge and its properties are determined by many factors. A few of these factors are the nature of gas, its pressure, the distance across which the field is applied and the physical and electrical properties of electrodes employed. Depending on these factors, the breakdown mechanisms can also be different such as Townsend mechanism, Spark mechanism, Avalanches, Streamers and Leaders. But all of these usually start with a phenomenon called electron avalanche which is discussed in the next section.

2.1.1 Townsend mechanism

Electrical breakdown is a multistage threshold process that only happens at some critical value of electric field. The breakdown mechanism discussed below is called the

Townsend Mechanism which is valid for p.d ≤ 4000 torr.cm, p is the gas pressure in torr and d is the electrode gap distance in centimeters. Only this mechanism is of interest for

the topic at hand. Although gases are good insulators, they have a current conduction of the order of 10-10 A/cm2. This can be explained by ionization effect of cosmic radiation and presence of radioactive materials in normal atmosphere. But when large fields are applied across the gas, the charged particles generated by the cosmic radiation can gain very high energies before the collisions. These collisional impacts could cause ionization of neutral molecules. This electron impact ionization process is usually the initial step of any breakdown process which results in multiplication of primary electrons. This is called the avalanche effect or cascade ionization.

Consider the case of a simple parallel plate capacitor with electrode gap, d, and a

DC voltage, V, applied across the plate. It is reasonable to assume the formation of some primary electrons near the cathode surface. Let this small initial current be io. Now, each of these primary electrons drifts towards the anode. As these electrons drift, under the effect of the field, they successively ionize neutral gas species. The newly generated electron avalanche acts as a source of primary electrons. This continuous evolution in time and space results in massive multiplication of electrons. The reason for the threshold nature of the electrical breakdown can be deduced from the fact that the primary electrons should have enough energy to ionize the gas molecules as they drift towards the anode.

Let n0 be the initial number of electrons leaving the cathode surface. After a distance, let n be the new number of electrons. As these n electrons move through a distance dx, they produce dn electrons.

Therefore,

dn= α.n.dx (2.1) where, α is called the First Townsend coefficient or Townsend ionization coefficient

Solving (2.1) with the initial condition that at x=0, n=n0 gives

α.x n=n0.e (2.2)

Writing (2.2) in terms of current and at a distance, d, gives

α.d I=I0.e (2.3)

It should also be noted that all the generated electrons are assumed to contribute to successive ionizations without any electron-ion recombination and attachment to electronegative atoms. Electron-ion recombination is neglected due to the very low degree of ionization in this phase and electron attachment is only significant in electronegative gases.

From (2.3), it can be concluded that each primary electron generates eα.d-1 electrons and positive ions. The produced positive ions, under the influence of external field, move towards the cathode. These ions impinge on the cathode surface as they accelerate towards the cathode and result in secondary emission of electrons from the cathode surface. Here, γ, secondary electron emission coefficient or the second Townsend coefficient is used to account for the probability of secondary electron emission from the cathode surface. Let n1 be the number of electrons emitted due to impact of positive ions.

Then, 12

α.d n= (n0+n1). E (2.4)

Since n represents the total number of electrons reaching the anode, number of electrons from gas molecules is given by,

n-(n0+n1) (2.5)

Accounting for the secondary electron emission coefficient,

n1=γ. [n-(n0+n1)] (2.6)

From (2.4) & (2.6)

(2.7)

Writing (2.7) in terms of current,

(2.8)

From (2.8), the critical condition for Townsend breakdown can be determined.

For the self-sustenance of a discharge at a particular voltage, the discharge should be able to increase the supply of electrons by itself. Analytically, this would mean that the current, I, in (2.8) should approach infinity. Therefore, setting the denominator to 0 gives

(2.9)

Or, = ln[(1/ )+1] (2.10)

(2.9) provides the minimum critical conditions for electrical breakdown of gas.

From (2.9),

Or, * exp(α.d)≈1 (2.11)

The qualitative implication of the above equation is that for self-sustenance of the discharge, i.e. a discharge able to sustain itself without a further increase in the externally applied field for supply of electrons, each impinging positive ion on the cathode surface should produce a secondary electron.

2.1.2 Paschen Curve

Townsend has proposed that the first Townsend coefficient, α, can be related to the field E in a semi-empirical way as follows:

(2.12)

A and B are numerical parameters for calculation of α. The tabulated values are as follows:

Gas A[1/cm/torr] B[V/cm/torr] Air 14.6 365 N2 12.39 342 CO2 20 466 H2 5 130 H2O 12.9 289 He 2.8 34

Table 2.1 Values of parameters A and B for different gases, courtesy by [17]

From (2.10) and (2.12),

(2.13)

The above relation described by equation (2.13) that relates breakdown voltage,

V, to the parameter (p.d) is called the Paschen curve.

Figure 2.1: Paschen curves for Air, H2 and N2, , courtesy by [17]

As can be seen from Figure 2.1, the Paschen curve predicts a minimum breakdown voltage, Vmin, for a particular value of p*d for different gases. Let the corresponding (p.d) value be (p.d)min. It is interesting to note that on either side of

(p.d)min, the breakdown voltage, V, is greater than Vmin.

This trend can be explained qualitatively by examining the curve either at a fixed pressure, p, or for a fixed electrode gap, d. Assuming p to be constant, for (p.d) > (p.d) min, even though the primary electrons from the cathode suffer more collisions at (p.d) than at (p.d)min, the energy gained after successive collisions is comparatively less which reduces the probability of successive ionizations. As a result, a much higher voltage is required for breakdown. On the other hand, for (p.d) < (p.d) min, there are not enough collisions for successive ionization of gas molecules at smaller gap distances. As a result, a much higher voltage is necessary to increase the number of primary electrons from the

cathode. A similar qualitative argument can be made by keeping the electrode gap, d, constant to explain the trend observed in the Paschen curve.

2.2 Plasma

A plasma is often referred to as fourth state of matter [18]. It is a mixture of electrons, ions and neutrals moving in random directions and, on an average, electrically neutral. The presence of these free charge carriers makes the plasma electrically conducting. Electric discharges in gases are generators of plasma. Plasmas can be both manmade and natural. Plasmas can be found everywhere in the universe in the form of solar corona, solar wind and ionosphere [19]. Even the phenomenon of lightning is a plasma process [20]. Plasmas are widely used in industrial applications. In semiconductor industry, it is widely used to sputter deposit materials and create sub micrometer features

[21]. In environmental control, emissions are treated with plasma to reduce the pollutants being released into the atmosphere. Plasmas also find application in welding industry. A lot of research has also gone into energy conversion using plasma to enable fusion reactions.

As was mentioned earlier, electric discharges in gases are responsible for generation of plasma. The generated plasma can be classified in many ways. A few of them are discussed below.

1. Pressure Classification: Plasmas

can be classified based on the pressures at which they are operated as high

pressure plasmas (atmospheric plasmas) and low pressure plasmas (p<10 torr).

Low pressure plasmas are characterized by lower energy densities and

relatively cold cathodes while high pressure plasmas are usually hot and have

high power densities.

2. Electrode classification: This

classification is based on the presence or absence of electrodes for plasma

generation and operation. For example, inductively coupled RF and

microwave discharges do not require the presence of electrodes.

3. Sustenance classification: When

an external secondary source of electrons in the form of electron beams, lasers

and UV radiation is used to sustain plasma, it is called a non-self-sustained

discharge.

4. Thermal and non-thermal

discharges: This classification is primarily based on the working temperatures

of the plasma. In thermal plasmas, ions and electrons are in thermal

equilibrium and results in a very hot plasma. In non-thermal plasma, the ions

and electrons are not in thermodynamic equilibrium. As a result, the plasma

operates with its heavy particles (neutral species and positive ions) near room

temperature. This is also called cold cathode operation.

Even though the above classifications have overlaps, it is quite clear that a lot of different plasmas are possible. But the DC plasma is of particular interest to this work.

So, a general current-voltage characteristic description of DC plasma is provided in the following sub-section. 19

2.2.1 DC Plasma: Current - Voltage Characteristic

The current-voltage characteristic of a DC plasma is very useful in identifying the various phases and the corresponding transition points of the plasma as the supply voltage is increased. Such a curve is produced by connecting a high voltage DC supply across the electrodes through a ballast resistance to limit the amount of current and to hold it steady. A typical current-voltage characteristic for DC plasma is depicted in

Figure 2.2. The voltage, V, plotted on y-axis is the voltage across the electrodes. The current, I, plotted on x-axis is current in the circuit. Let Vs be the supply voltage.

Figure 2.2: V-I characteristic of DC plasma in Neon gas at 1 torr and planar electrode

spacing of 50 cm, courtesy by [22]

The curve B-D in Figure 2.2 represents the dark Townsend region. This region corresponds to the Townsend mechanism of breakdown discussed earlier in section 2.1.1.

As the supply voltage is increased or the external resistance is decreased, a transition is observed at point D associated with a decrease in voltage across the electrodes. This point is associated with a significant reconstruction of electric field near the cathode. Along the curve D-F, the plasma is transitioning to glow discharge from the dark Townsend region.

This intermediate phase discharge is called a sub-glow discharge. The curve from F-G is associated with almost a constant voltage across the electrodes with an increase in the current. This region is called the normal glow discharge. During the normal glow discharge phase, the cathode current density remains constant. The increase in current in this phase is associated with an increase in the electrode surface area coverage by the plasma while the cathode current density is constant. After the entire available cathode surface area is covered by the plasma, a further increase in current is associated with increase in cathode current density. This new phase of the plasma is called the abnormal glow discharge. This transition can be associated with point H in Figure 2.2. The curve

H-I is called the abnormal glow discharge region. This phase is associated with an increasing V-I characteristic. The cathode current density increases until a certain critical value is reached. At this point, I, a transition from the abnormal glow phase to an arc phase is observed. The curve I-J-K represents the arc phase of the plasma. After the point, any small increase in supply voltage, Vs, would result in a rapid fall of electrode voltage,

V, and a rapid rise of current, I. This transition can usually be seen at around a few amperes of current and associated with electrode voltages in the range of 50-75 V. These figures are only typical but that actual voltages corresponding to the points identified on 21

the V-I curve can vary from discharge to discharge. Ultimately, these points are determined by the cathode current density and material properties of electrodes.

The glow regime is of particular interest to the current work. The following sub- section provides relevant background about this regime.

2.2.2 Glow discharge

As the name suggests, this particular regime is characterized by emission of light.

This is the result of the electron-gas molecule collisions in the plasma. The special significance of this particular regime is that there is no heating of the cathode (cold cathode operation). The general structure of glow discharge can be broadly divided into a cathode layer, a positive column and an anode layer. The cathode and anode layers can be further divided into various regions. The cathode layer holds special significance for the glow discharge. The necessary processes that sustain the discharge happen in this layer.

Understanding the physics governing the processes in the cathode layer helps in understanding the behavior of glow discharge.

A very clear and qualitative model of cathode layer was provided by [23]. Let d be the distance from the cathode surface until which the cathode layer extends. This model assumes that electric field, E, is zero at d. This is a reasonable assumption as a very high local electric field is setup at the cathode surface to supply the necessary primary electrons and also the relative low mobility of ions makes the ion current insignificant.

Assuming a linear variation of electric field along the cathode layer,

E(x) = Ec(1-x/d), 0

Let Vc be the cathode potential drop. Then,

Vc=Ec*d (2.15)

Also, from gas breakdown physics (Townsend mechanism), a relation between α,

γ and E(x) has been developed as follows,

d 0∫ α. [E(x)].dx= (γ+1)/γ (2.16)

From (2.14), (2.15) & (2.16)

Vc & Ec (2.17)

The values of parameters A and B can be found from Table 2.1.

It is worth mentioning that (2.17) is very similar to the equation for the Paschen curve, (2.13).

The only difference is that the „d‟ in the equation for the Paschen curve is the electrode gap distance while the „d‟ in (2.17) represents the cathode layer thickness.

From (2.17), the minimum cathode potential drop, (Vc)min, and the associated cathode layer thickness, (pd)min, can be determined just as in the case of the equation for the Paschen curve. Using the above equation, an expression for cathode current density, j, can be developed and jmin, corresponding to (Vc)min, can be determined. The significance of (Vc)min, (pd)min and jmin is understood by employing Steenbeck‟s minimum power principle that can be put as “at ﬁxed current, the heat power, and thus the voltage drop between the electrodes, is minimal in a gas discharge” [24]. It has to be noted that it is a commonly accepted statement that is useful in explaining various observed discharge phenomenon like the normal glow discharges and, striations and channels in thermal arcs.

But, this principle cannot be derived from fundamental physical laws. Therefore, it cannot be used for a strictly theoretical analysis except for illustrative purposes. The employment of the Steenbeck principle shows that the current density, electrode voltage drop and cathode layer thickness in the normal glow discharge are equal to the minimum values of current density, electrode voltage drop and cathode layer thickness determined from 2.17.

As was discussed earlier, in normal glow discharge phase of plasma, the current density always remains constant. This current density is called the normal current density, jn. Interestingly, it was also observed that the associated cathode potential drop (normal cathode fall, Vn) and the similarity parameter for cathode layer thickness (normal cathode layer thickness), (pd)n), also remained constant. The particular implication of the minimum power principle for cathode layer is that the power released in the cathode layer is always minimized. Using Steenbeck Minimum Principle, it can be shown that:

jn = jmin 24

Vn = Vmin

(pd)n = (pd)min

The expression for power released in cathode layer is as follows:

d Pc(j) = A. 0∫ j. E. dx

Or, Pc(j) = A. j. Vc(j)

Or, Pc(j) = I.Vc(j),

A = surface area of cathode covered by plasma

I = Cathode current

Minimization of power would mean to minimize Vc(j) .But, In a normal glow discharge,

J = jn, Vc = Vn, (pd) = (pd)n

From (2.17) and the explanation following it, [Vc(j)]min= (Vc)min. And (Vc)min is associated with (pd)min and jmin.

Therefore,

jn = jmin

Vn = Vmin

(pd)n = (pd)min

It can be observed from (2.17) that Vmin is only a function of pd. Therefore, Vn is also only a function of pd. The implication of the above results is that the current density, the cathode potential drop and the cathode layer thickness remain constant at any value of supply voltage and current driven through the system as long as the plasma is in the normal glow region and pd is kept constant.

After the glow regime, plasma enters the arc regime. The following sub-section provides a very brief introduction to arc discharges.

2.2.3 Arc discharges

As the current density increases during the abnormal part of the glow regime, the cathode starts to heat up. At a certain current density, the cathode starts emitting electrons that are produced by processes that are quite different to those responsible for electron emission in the glow discharge. At this point, the discharge is called an arc discharge.

Arc discharges are different from glow discharges as the processes responsible for the supply of electrons are different. The primary electron emission mechanisms in an arc discharge are thermionic and field emission [25].

Thermionic emission is the phenomenon of electron emission due to elevated temperatures. At elevated temperatures, the kinetic energy of the electrons increases. At high enough temperatures, if the electrons‟ kinetic energies are more than the work function of the metal, electron emission starts. But some electrons might remain close to the cathode and prevent further electron emission. This brings up the concept of saturation current density. These electrons are generally driven away by cathode electric field and saturation current density is obtained [25].

If the field is further increased beyond the saturation current density, it tends to decrease the work function of the metal. As a result, the current increases. The decrease of this work function in presence of external electric field is called Schottky effect.

Schottky effect is also observed in field electron emission mechanism. In this mechanism,

high external electric fields, apart from decreasing the work function, extract electrons through quantum mechanical tunneling [25].

Another emission mechanism is the thermionic field emission. As the name suggests, both field and thermionic emissions are at work here. This can happen when a high external field is applied on a high temperature cathode. There are other emission mechanisms such as secondary electron emission and surface impact ionization. But the contribution of these processes is not significant [25].

Based upon these emission mechanisms and other factors such as metal evaporation and operating pressure, arcs can be classified as follows:

1. Hot cathode spot arcs: Due to the high current densities involved in arcs, not

all metals can continuously withstand the high temperatures. Emissions in

such low-melting metals happen through cathode spots that appear and

disappear. This results in localized heating in the vicinity of cathode spot

while the rest of cathode is cold.

2. Thermionic cathode arcs: This is possible with metals that can withstand

high temperatures. The entire cathode is at very high temperatures. The entire

cathode participates in the thermionic emission.

3. Low pressure arcs: These arcs are essentially non-equilibrium arcs. These

operate under sub-torr pressures. These are similar to glow discharges but

have much higher current densities.

4. High pressure arcs: Atmospheric pressure arcs come under this category.

These are thermal arcs with very high power densities. Higher operating

pressures result in denser plasmas. 27

A broad classification of arc discharges would be thermal and non-thermal arc discharges. The following table gives the ranges of plasma parameters for this classification.

Plasma Parameter Thermal arc discharge Non-thermal arc Gas Pressure 0.1-100 atm 10-3-100 torr discharge Arc current 30 - 30 kA 1-30 A Cathode current 104-107 A/cm2 102-104 A/cm2 Voltage 10-100 V 10-100 V density Gas temperature 1-10 eV 300-6000 K Electron temperature 1-10 eV 0.2-2 eV

Table 2.2 Typical discharge parameter ranges of Thermal and Non-thermal arc discharges

courtesy by [25]

The discussion on arc discharges is limited to this point as any further discussion is beyond the scope of this work. The following chapter describes the experimental apparatus used to examine the behavior of plasma on a rotating anode and the associated experimental procedure.

CHAPTER 3: EXPERIMENTAL APPARATUS AND PROCEDURE

The experimental apparatus is designed to simulate the conditions of a

Faraday disc generator envisioned as receiving power from a wind or hydraulic turbine.

In order to do so, the choice of the electrode system has to be coaxial. As the present work is an effort in the direction of energy extraction from a Faraday disc with plasma as an electrical contact replacing a conventional brush contact and since the disc has a circular profile, one of the electrodes must also have a circular profile. Also, as discussed in Chapter 1, any non-uniform distribution of current in the Faraday disc as the energy is extracted from the Faraday disc results in production of eddy currents in the disc. The implication is that the electrode system has to be co-axial. The choice of the co-axial electrode system and the aim to simulate the condition of a Faraday disc determines the polarity of the electrodes in the system. The inner electrode is made the anode while the outer electrode is grounded, i.e. the cathode. Such a configuration of electrode polarity corresponds to a case of energy extraction from the Faraday disc whose rim is at a higher potential than the center of the disc. The parallel to the higher potential rim is the anode in the present experimental apparatus. Also, the design of the experimental apparatus facilitates the rotation of the anode which is the case with the Faraday disc. The following sections 3.1 and 3.2 describe the experimental apparatus and the procedure employed for experimentation.

3.1 Experimental Apparatus

The experimental apparatus can be broadly classified into the following subsystems: Experimental chamber and air handling system, electrode setup and magnetic coupler and lastly, electrical power supply and data acquisition apparatus.

Each of these is described in detail next.

3.1.1 Experimental chamber and Air handling system

The experimental chamber consists of a rubber gasketed bell jar placed on a stainless steel base. The bell jar serves as the vacuum chamber within which the electrodes and magnetic coupler are placed. Figure 3.1 shows the image of the 2.5 inch thick Pyrex glass bell jar and the stainless steel base. The bell jar sits on a stainless steel base that has eight 1inch inlet ports with a collar diameter of 1.3 inch. All the ports are sealed off with O-rings on collared stainless steel cylinders. All the eight cylinders have threaded holes through them for mechanical fastening of the cylinders to the stainless steel base with bolts. Of the 8 cylinders, four of them have through holes and the others have blind holes. The cylinders with through holes can be externally accessed for creation of vacuum within the chamber and to control pressure and type of gas for experimentation.

Figure 3.1: Bell Jar and the Stainless Steel Base

Figure 3.2: Stainless Steel Base

A Precision Vacuum Pump-Model D150 is used for creation of vacuum in the experimental chamber. Figure 3.3 shows the process flowchart of the gas handling

system along with the experimental chamber. The vacuum pump pumps out air through the inlet nipple controlled by metering valve B and are exhausted into the ambient.

Figure 3.3: Process Flow Chart of Gas Handling System

Vacuum chamber pressure is measured using a dual case Wallace & Tieman analog manometer. The first dial indicator casing E is calibrated for measuring pressures less than 800 torr while the second dial indicator casing F is employed for precision measurement of pressures less than 20 torr. A shut off valve is used to control the operation of second case. The shut off valve C is manufactured by Whitey while the metering valve G is manufactured by Nupro Company. Cajon fittings are used for all pipe connections in the system. The vacuum pump A is connected to the experimental chamber D through the shut off valve V. The tubing used is ½ “ Swagelok flexible polyethylene tubes. The experimental chamber D has an inlet port controlled by the metering valve G to introduce air into the vacuum chamber as desired. In order to get a

much better control over the flow-rate of air into the vacuum chamber D the needle valve

H is connected in series with the metering valve G. The vacuum chamber D is connected to the 2 casings of analog manometer E-F through an ¼ “ Swagelok flexible polyethylene tubing. A shutoff valve is connected in series with the second casing of the analog manometer F in order to protect the dial indicator mechanism which is designed for operation at pressures lower than 20 torr. Figure 3.4 shows the image of the analog manometer.

Figure 3.4: Analog Manometer

3.1.2 Electrode setup and magnetic coupler

As can be seen in Figure 3.1, the electrode setup is on a ½“ acrylic base as the stainless steel base is hollow at the center (refer to Figure 3.2). Figure 3.5 shows an

image of the electrode assembly and Figure 3.6 shows the isometric view of the assembly with the parts labeled.

Figure 3.5: Electrode Assembly

Figure 3.6: Isometric View of Electrode Assembly

In Figure 3.6, the anode is a 0.125 inch 403 stainless steel shaft. The shaft was purchased from McMaster Carr. The shaft is supported by aluminum support columns.

These were salvaged from a Sterling engine model in the Student Electronics Shop. To facilitate the rotation of the shaft, ABEC, V stainless steel ball bearings were procured from McMaster Carr. The cathode is a 1080 Steel rectangular block. A through hole of

0.209” diameter and 0.845” length was drilled through the rectangular block. An Oriel lens holder is used to support the rectangular block. The lens holder has three threaded holes on the rim through which 8-32 screws can be screwed in. One of the threaded holes is used to support the rectangular block by screwing in an 8-32 screw into the corresponding hole drilled into the rectangular block. The depth of the hole was kept to a minimum in order to ensure that the hole does not interfere with the plasma generated between the electrodes. Also, in order to contain the plasma to within the annular gap of the electrodes, Kapton insulating tape is used as seen in the image presented in Figure

3.5.

The last aspect of the design is the rotation of the anode as desired. This is realized by magnetic coupling of the 316 stainless steel circular disc with the 316 stainless steel rectangular disc. The rectangular disc is mounted on the shaft of a motor outside the vacuum chamber. Figure 3.7 shows an image of the magnetically coupled discs.

Figure 3.7: Magnetically Coupled Discs

The reason for the use of magnetic coupling to rotate the anode is to keep the experimental conditions as similar as possible to the idea of energy extraction from

Faraday disc using plasma as an electrical contact. Because if the idea were to be successful, it is reasonable to assume that the plasma would be operated in vacuum and the device (for e.g. wind turbine) that provides the torque for the rotation of Faraday disc cannot also be inside the vacuum boundary. Both the discs in Figure 3.7 have 4 cylindrical N-52 rare earth disc magnets with their poles arranged such that there is an attraction between any pair (the pair doesn‟t include magnets on the same disc) of magnets. The motor driving the rectangular disc is powered by a HQ Power power supply. The face of the rectangular disc not facing the magnet by used to determine the angular velocity of rotation of the disc. The angular velocity is measured by an optical tachometer.

3.1.3 Electrical power supply, connections and data acquisition apparatus

Since the Faraday disc is a low voltage-high current device, the power supply used for experimentation is a Glassman High Voltage DC power source (see Figure 3.7).

The power source is capable of sourcing 10 kilovolts at 60 milliamps. The electrical leads of the power source are used as insulated vacuum feed-throughs to provide electrical contact to the electrodes (refer to Figure 3.7). Two of the stainless steel cylinders that sealed the ports of the stainless steel base of the vacuum chamber are replaced with similar cylinders but manufactured with nylon stock. A through hole, the diameter of which corresponds to the diameter of the insulated vacuum feed-through, was drilled through the nylon cylinders and the electrical leads of the power supply were inserted through the holes. Epoxy glue was used to seal the ends of the drilled hole after the insertion of the electrical leads. And degassing from the epoxy glue would not be a problem at the pressures that can be obtained with the experimental apparatus in the current work. The electrical connections to the electrodes are provided as shown in the image in Figure 3.5. For the anode, the electrical lead is attached to one of the bases of the support columns while the electrical contact for cathode was provided through the fastener screw attached to the cathode. Figure 3.8 shows the completely assembled system.

Figure 3.8: Completely Assembled Experimental Apparatus

The electrical parameter that is recorded during experimentation is voltage. For this purpose, a high voltage probe connected to a HP 3479A multi-meter is employed.

The output of the high voltage probe gives the reading that is 1/1000 of the actual voltage value. The grounding rod shown in Figure 3.8 is connected to the high voltage DC power supply as the power supply is grounded.

3.2 Experimental Procedure

After completion of the electrical connections and placement of the bell jar, the vacuum pump is switched on. Initially the shut off valve C (refer to Figure 3.3) is closed. Once the pump is switched on, the intake nipple of the roughing pump is opened and then the shutoff valve C is opened. Now, the nylon cylinders with insulating feed-

throughs are put into their places so that O-rings on their collars fit into the undercut grooves in the vacuum chamber. These are held in their places for a brief moment. At this point, the air inside the chamber starts to get pumped out and the generated pressure differential holds the nylon cylinders in their places. Once the pressure starts dropping below 20 torr, the shutoff valve on the second casing F (refer to Figure 3.3) of the manometer is opened so that an accurate pressure reading can be obtained. As the pressure drops below 10 torr, the intake metering valve G (refer to Figure 3.3) of the chamber is slightly opened. Now, the needle valve H connected to the intake valve is used to regulate the airflow into the chamber and therefore the pressure inside the vacuum chamber. In order to make sure that the pressure doesn‟t keep changing during the course of data collection and pressure equilibrium has reached, a 15-20 minute gap is maintained between the last adjustment of the needle valve and switching on the DC power supply.

Figure 3.9: Circuit Diagram of the System

After pressure stabilization, the DC power supply is switched on. All the experiments are run in voltage control mode. This is realized by setting the current

controlling knob on the power supply to a very high value while keeping the voltage at zero. If the experiments are run in current control mode, one should have to track both the supply voltage and the anode voltage simultaneously which would be very impractical.

The circuit diagram of the system is shown in Figure 3.9. To begin the experiment, the voltage knob is slowly turned and the high voltage probe is used to measure the voltage at the anode (V2). As the voltage is increased slowly, at some point, the voltage, V2, starts to decrease. This is the breakdown voltage. At this point, both the readings V1 and V2 are taken. Now, the voltage knob is turned again to increase the supply voltage, V1. The corresponding voltage V2 is noted down. Each successive reading is taken at around 250

V difference from the V1 of previous reading. This process is continued until a certain time (usually 3 readings) after the annular gap between the electrodes is completely covered by plasma. This concludes the current experimental run. Next, V1 is slowly brought down to zero and the supply turned off. Any metallic parts of the chamber as well as electrical contacts are grounded using the grounding rod shown in Figure 3.9.

After this, the DC power supply is turned on again and the same process is employed again to get a second set of readings for checking repeatability.

After the high voltage DC power supply is turned off at the completion of repeatability run, the power source connected to the motor for driving the external magnetic coupling disc is turned on. It has to be noted that the voltage should be turned up slowly so that the second internal disc (and therefore the shaft) has some time to couple strongly with the external disc. An optical tachometer is used to determine the rpm of the external disc and the voltage is adjusted to get the required angular velocity.

Now, the high voltage DC power source is turned on and the previously mentioned 40

procedure is employed to obtain the necessary data. As was done previously, a second repeatability run is also performed. A similar procedure is employed at different pressures. A sample data set at 10 torr and rotating anode at 127.7 rpm has been presented in Table 3.1.

V1 (Volts) V2 (Volts) 437.94±0.02 386.5±0.5 468.3±0.02 376.2±0.3 628.3±0.05 355.7±0.2 866.38±0.04 355.92±0.1 1015.95±0.01 356.16±0.09 1254.03±0.04 356.33±0.04 1514.75±0,05 356.56±0.04 1752.08±0.05 356.99±0.01 1979.57±0.03 356.31±0.02 2202.09±0.03 357.19±0.01 2450.5±0.05 357.5±0.03 2723.2±0.05 358.36±0.02 3116.7±0.1 360.99±0.02 3418.8±0.1 364.15±0.03 3610.7±0.1 366.39±0.05

Table 3.1: Sample data set 10 torr & 127.7 rpm

After the completion of experiments, care should be taken while shutting down the whole apparatus. Firstly, the shutoff valve on the second casing of the manometer is closed. Then, the shutoff valve is closed. And then, the inlet nipple of the roughing pump is closed. Finally, the roughing pump is turned off. If the pump were turned off without properly closing the open-shut valve and the inlet nipple, the vacuum pump oil would rush through these open valves into the vacuum chamber and then the manometer.

The following chapter presents and discusses the results of the data obtained using the procedures described in the above section.

CHAPTER 4: EXPERIMENTAL RESULTS & DISCUSSION

Results from three different sets of experiments are presented here. The choice of pressures was determined by two factors. Firstly, unique current-voltage characteristics

-6 cannot be obtained at p.d values close to (p.d)min [26]. For air, (p.d)min is 7.5*10 meter. atmosphere which corresponds to 5.7 torr for 1 millimeter air gap. Since the air gap of the experimental setup used is 1 millimeter, the base pressures for the experiments are chosen to be higher than 5.7 torr. The second factor was the current limitation of the experimental apparatus. Considering these two factors, the pressures corresponding to the three sets of experiments were chosen to be 9.1 torr, 9.55 torr and 10.6 torr. Each of these sets comprises two subsets of experiments. One subset corresponds to the case of both the electrodes being non-rotating (stationary). The other subset corresponds to the case of a rotating anode and a stationary cathode. All the experiments have been repeated and a second data set is obtained for each of the experiments performed. The experimental results for the rotating versus stationary anode and effect of angular velocity are presented and discussed.

Before performing the experiments for the case of rotating versus static anode, a cursory investigation was done to see if the polarity of the rotating electrode had an effect on plasma attachment. It is observed that when the rotating electrode is the cathode the

plasma also appeared to rotate with the rotating cathode. On the other hand, when the rotating electrode is the anode the plasma attachment appeared to be stationary and not rotating with the electrode. This may be understood by considering the cathode spot.

Since the primary mechanisms sustaining the glow discharge plasma happen in the cathode layer, which is in the immediate vicinity of cathode spot, the point (or area) of attachment of plasma on the cathode may be taken to be fixed. This assumption is valid particularly in the case of glow discharge, as immediately after electrical breakdown of the gas the voltage across the electrodes drops. This renders the possibility of formation of a second cathode spot unlikely since the voltage across the electrodes is now well below the breakdown voltage. If the plasma is sustained by the single cathode spot formed after breakdown, the plasma would be expected to rotate with the electrode since the cathode spot is attached to the electrode as it rotates. The stationary attachment of the plasma in the case of a rotating anode and stationary cathode follows from the same argument.

As was mentioned at the beginning of this chapter, the experiments are performed at pressures of 9.1 torr, 9.55 torr and 10.6 torr and repeated to obtain a second set of data.

Table 4.1 and Table 4.2 present the data sets obtained at 9.1 torr with a stationary anode for the first experimental run and the repeated run respectively.

Supply voltage V1(volts) Anode voltage V2(volts) 427.83±0.03 392.15±0.08 455.68±0.01 378.91±0.02 546.85±0.01 367.95±0.01 643.14±0.03 355.36±0.02 872.13±0.03 355.99±0.01 1068.74±0.03 356.6±0.01 1218.12±0.01 356.92±0.01 1428.60±0.02 357.16±0.01 1782.25±0.04 356.7±0.01 1965.68±0.01 357.52±0.02 2432.03±0.08 358.35±0.01 2866.6±0.1 359.15±0.01

Table 4.1 Experimental Data Set for First Run for 9.1 torr - Stationary Anode Case

Supply voltage V1(volts) Anode voltage V2(volts) 436.94±0.05 387.4±0.03 496.2±0.03 373.63±0.01 559.57±0.01 368.14±0.01 663.47±0.01 355.83±0.01 872.06±0.01 456.28±0.01 1070.88±0.02 356.85±0.01 1216.06±0.02 356,77±0.01 1443.4±0.02 357.51±0.02 1791.92±0.03 357.01±0.02 1966.02±0.02 357.65±0.01 2430.47±0.01 358.57±0.01 2869.66±0.01 259.59±0.02

Table 4.2. Experimental Data Set for Repeated Run for 9.1 torr - Stationary Anode Case

As can be seen from the sample data presented in Table 4.1, each data point corresponds to 3 different points and the same is true for any data point in Table 4.2. As an example, consider the data corresponding to the first row in Table 2 which is 45

(436.94±0.05, 387.4±0.03). This data is considered to correspond to (436.89, 387.37),

(436.94, 387.4) and (436.99, 387.43). Following the same procedure for every point in

Table 4.2 produces three complete sets of data. The same is true for the data in Table 4.1.

So, at 9.1 torr, when comparing the cases of a rotating anode versus stationary anode, the six data sets obtained from Tables 4.1 and 4.2 are used to generate the current-voltage characteristic for the stationary anode case by placing error bars about the mean of the 6 data points. Similar method is employed to plot the current-voltage characteristic of the rotating anode case.

Figures 4.1 – 4.3 compare the cases of rotating and stationary anodes at 9.1 torr,

9.55 torr, and 10.6 torr respectively. An effort has been made to maintain the angular speeds of rotation in all three cases. The corresponding angular speeds are 127.6, 127.9 and 127.1 revolutions per minute respectively.

Figure 4.1: Current-Voltage characteristics of rotating anode and stationary anode at 9.1

torr

Figure 4.2: Current-Voltage characteristics of rotating anode and non-rotating

anode at 9.55 torr

Figure 4.3: Current Voltage Characteristics of rotating anode and stationary anode at 10.6

torr

It can be seen from Figures 4.1 – 4.3 that the current-voltage-characteristic (CVC) in each of the rotating cathode cases are quite similar to the typical curve shown in Figure

2.2. The CVCs in each of the experiment corresponds to the curve D-F-G-H in Figure

2.2. A complete CVC for the experiments cannot be produced due to limitations in the experimental apparatus. The portion of CVC before point D cannot be obtained since the ballast resistance of 100 KΩ is too small to limit the current after breakdown. A significant portion of the non-uniform glow region (H-I in Figure 2.2) cannot be obtained as the current required to generate this portion of curve is much higher than the 60 mA current limit of the power source.

Figures 4.4 – 4.7 show the plasma attachment between the two electrodes at point

P (Initial breakdown), Q (A general point in sub glow region), R (A general point in

uniform glow region) and S (A general point in the non-uniform glow region) marked in

Figure 4.3. The images on the left and right sides of each of the Figures 4.4, 4.5, 4.6 correspond to the photos taken from the left end and right end of the electrodes respectively. It has to be noted that P, Q, R & S are general points that can be identified on all the plotted CVCs and are not specific to only the CVC in Figure 4.2. Figure 4.2 has only been chosen for marking the points P, Q, R and S for the sole purpose of illustration of plasma attachment at these points in various regimes.

Figure 4.4: Plasma attachment from left and right ends at P

Figure 4.5: Plasma attachment from left and right ends at Q

Figure 4.6: Plasma attachment from left and right ends at R

Figure 4.7: Plasma attachment from left and right ends at S

The point P is associated with electrical breakdown of the air gap between the electrodes and the attachment of plasma can be seen as a faint bluish glow between the electrodes. The breakdown occurred at the right end of the electrode system. At this point, in all the experiments, the plasma is observed to cover only a small part of the circumference of the cathode as seen in Figure 4.4. As the supply voltage, V1 (refer to

Figure 3.9), is increased the plasma makes a transition into the uniform glow regime.

Point Q is associated with this transition region from breakdown into normal glow regime. As can be seen from Figure 4.5, the circumferential plasma attachment has increased at the right end and a very faint extension of the plasma can be seen from the right end. Point R is encountered in the normal glow regime. From Figure 4.6, it can be

seen that there is complete circumferential plasma attachment at the right end and the plasma has significantly extended along the axis of the cylindrical cathode towards the left end. In this regime, the electrode surface area coverage of the plasma is observed to increase as the current was increased. Also, the electrode voltage is observed to remain almost constant during this phase of the plasma. This behavior is consistent with that of a normal glow discharge. Since the current density (normal current density) remains constant in the normal glow regime of the plasma, it follows that any increase in current would have to be associated with an increase in the cathode surface area coverage of plasma. Also, as was discussed in section 2.2.2, the normal glow regime is also associated with a normal cathode fall which remains constant in the normal glow regime.

The observed flat portion (constant electrode voltage) of the CVCs in Figures 4.1, 4.2 and

4.3 is a direct consequence of the cathode fall remaining constant and the anode fall being insignificant as compared to the cathode fall. As the external current is further increased, at some point, it was observed that the entire cathode surface and the air gap were completely covered by the plasma. As the current is further increased beyond this point, the intensity of the bluish glow was observed to increase and started to become very bright. Point S can be associated with this regime of plasma. From Figure 4.7, it is very clear that the plasma has completely covered the air gap between the electrodes and is much brighter in this figure as compared to Figures 4.4, 4.5 & 4.6. This region is associated with a steep increase in the CVCs represented in Figures 4.1, 4.2 and 4.3. This is the abnormal glow regime of the plasma and was observed after the normal glow regime of the plasma. From the CVCs, in this regime, it can be observed that the electrode voltage and the current start to increase rapidly. This can be explained from the 51

physical observation that the plasma has covered all the available cathode surface area.

From this point on, any increase in current has to be associated with an increase in the current density of the plasma. In order to support these high current densities, the voltage drop across the cathode layer has to increase in order to provide the necessary supply of electrons. Consequently, the voltage drop across the electrodes has to increase. This is precisely what is observed in the segments of CVCs corresponding to the non-uniform glow regime. The observed increasing trend in the brightness and the intensity of the plasma in this regime can be explained by considering the increasing current densities as the external current is increased. Since the plasma volume is fixed in this region, the increase in the current densities would mean a corresponding increase in the number density of electrons within the plasma. The increased electron concentration results in an increased number of energetically excited species in the plasma. The radiative de- excitation of these species results in emission of some part of energy in the form of visible radiation. As a result, the brightness and the intensity of the plasma are observed to increase in this region.

Figures 4-6 also show that there is no significant departure of the CVC of the rotating anode from that of a stationary anode. To further confirm this trend, the CVCs at

9.9 torr for 174.9 rpm, 120.8 rpm and 77.3 rpm are compared in Figure 4.8.

Figure 4.8: Effect of angular velocity on CVC

An interesting observation from these experiments is that the spatial coverage of the air gap between the electrodes of the plasma changes as the current is increased. As can be seen in Figure 4.4, immediately after the breakdown of air gap, the plasma only covers a small part of the annular gap region (radial direction) and the extent of cathode surface area coverage is also small in the longitudinal direction (along the axis of the cylindrical anode). It was experimentally observed that at the pressures corresponding to the CVCs shown in Figures 4.1, 4.2, 4.3 the plasma first tends to extend along the longitudinal direction for a short distance. This can also be inferred by comparing the right end pictures shown in Figures 4.4, 4.5 & 4.6. In Figure 4.5, a small portion of plasma can be seen from the left end too while in Figure 4.4 it cannot be seen from the left end. In the same figure, it can also be seen from the right end picture that the plasma hasn‟t completely covered the air gap in transverse direction. In Figure 4.6, the plasma

can be seen from both ends but now it has completely covered the air gap in transverse direction. This effect was much pronounced when the same experiment was performed at

15 torr. The plasma has extended a greater distance in the longitudinal direction before it completely covered the air gap in radial direction. Neither the particular point at which this happened could be determined nor could the regime in which this happened be determined. It cannot be categorically stated if the observed spatial coverage pattern by the plasma is random or pressure dependent from the experiments conducted in this work.

The relevance of this observed behavior is that it can have an impact on the way the current is being drawn from the homopolar generator even when the plasma is operating in the glow regime as in an ideal energy extraction process it would be desirable to have a plasma that covers the annular region first and then extends along the longitudinal direction. The reason behind this is that extension in the longitudinal direction before covering the air gap in the radial direction would mean asymmetrical extraction of current from the rim of the Faraday disc.

Another point of interest is the proper alignment of the axes of the anode and cathode. It was observed that during the breakdown of air gap with a rotating anode, the plasma extinguished at times immediately after breakdown when the supply voltage was very close to the breakdown voltage. This can probably be accounted for the misalignment of axes of the electrodes. Axes misalignment would mean that electrode gap distance from the point of attachment on cathode to the anode surface changes with the rotation of anode. The problem of the plasma getting extinguished after initial breakdown does not pose such a big threat for the operation of plasma as this can be taken care by increasing the supply voltage beyond the minimum necessary breakdown 54

voltage. But this observed phenomenon with misalignment of axes actually poses a much bigger question of uniformity of current distribution with in the plasma that comes with misalignment of electrodes‟ axes. It can be inferred from this observation that a misalignment of axes tends to distort the spatial current distribution with in the plasma.

The spatial current distribution pattern is a manifestation of the degree of ionization of chamber gas at various points within the plasma volume and the subsequent inference being that there is a non-uniform spatial electrical resistance distribution in the plasma.

The potential ramification of electrode misalignment for the operation of homopolar generator using plasma as an electrical contact is that even if the mode of plasma operation is a diffused glow discharge, there would be a non-uniform extraction of current from the circumference of the conducting disc of the Faraday generator. The severity of this problem is dependent on the degree of misalignment of axes of the electrodes.

The following chapter provides a brief summary and conclusions of this work.

Also, recommendations for further work are provided at the end of the chapter.

CHAPTER 5: CONCLUSIONS & RECOMMENDATIONS FOR FURTHER WORK

The feasibility of using plasma as an electrical contact instead of carbon or mercury contact brushes in a Faraday disc generator has been explored in this work. An experimental apparatus has been designed to simulate the conditions of a Faraday disc generator. The behavior of the plasma with reference to attachment and current-voltage characteristics is studied. In this chapter, conclusions are drawn from this work and recommendations for future work are described.

Experimental results have been presented for a system with coaxial electrodes with an air gap of 1 mm powered by a DC power supply. The outer electrode was the cathode while the inner electrode was the anode. The apparatus has been designed to have the anode rotating about its axis whenever desired. Firstly, the attachment of the plasma and the current-voltage characteristics of the case of a stationary anode has been examined at different pressures. Under the same conditions, the attachment of the plasma and current-voltage characteristics is examined for the case of the rotating anode. The experiments have been repeated to check for the repeatability of the obtained results.

Qualitatively, in all the experiments, the current-voltage characteristic for the case of a stationary anode is in good agreement with theory. The current-voltage characteristic for the case of the rotating anode is found to be in good agreement with theory. The various operating regimes of DC plasma were identified qualitatively from 56

the plotted current –voltage characteristics and by visual inspection. The plotted current- voltage characteristics of a rotating and a stationary anode cases are found to be qualitatively very similar. It cannot be categorically said that the rotation of the anode does not significantly affect the current-voltage characteristic of the plasma. As far as the attachment of the plasma is concerned, in the case of the rotating anode, it does follow the established expected variation. After the electrical breakdown of air gap and the transition into the normal glow regime, the cathode surface area coverage by the plasma increases as the external current in increased, while maintaining the electrode voltage constant. The cathode surface area coverage is only limited by the external current. Given enough amount of external current, the plasma completely covers the annular region between the electrodes at some value of the current. The discharge is apparently diffuse and remains diffuse even after the external current is increased beyond the point at which the annular gap is first found to be completely covered by the plasma. The final conclusion is that it is feasible to use plasma as an electrical contact instead of carbon brushes in the Faraday disc generator. But it is associated with problems, discussed in

Chapter 4, that have to be overcome.

In the remainder of this chapter, two possible ways for extraction of electrical energy from a Faraday disc and critically analyze them. It has to be noted the proposed models are speculated based on the results and the conclusions of the current work. Ultimately, the proposed models have to be experimentally verified. The motivation behind these suggested designs is to give a good direction for future work on energy extraction from a Faraday disc using a plasma as an electrical contact.

Configuration 1:

The first proposed model discusses a possible mode of operation in the glow regime of plasma. The system consists of the Faraday disc generator setup with a high voltage DC source to initiate the breakdown of the gap between the rim of the disc and the co-axial cathode. The early studies into electrical breakdown of different gases have led to determination of their minimum breakdown voltages. Helium has the lowest minimum break-down voltage of 155 volts at pd=4 torr.cm [23]. Also, from the CVCs in

Figures 4.1 - 4.3, it can be inferred that after the initial breakdown, the electrode voltage drops down substantially in the normal glow regime of the plasma. Based upon the above mentioned statements, a general working scheme for configuration 1 is discussed in the following paragraph.

Let the working gas in the system designed for energy extraction from Faraday disc generator be Helium at 1 torr and the electrodes be separated by a distance of 4 cm.

A high voltage DC power source is used to breakdown the helium gap at 155 volts. After the breakdown, for the sake of argument, let the electrode voltage at the transition point of the normal and abnormal glow regimes be 80 volts. At this point, the plasma is self- sustaining. If the electromotive force induced by the magnet across the conducting disc is

80 volts, the DC power supply can be shut off as the plasma can be sustained by the electromotive force setup across the disc. It has to be noted that, with the DC power supply switched on, the CVCs of the system with and without the induced electromotive force would be different. This is a direct consequence of current being extracted from the

Faraday disc when the induced electromotive force is present. In this case, the normal to abnormal transition point is obtained much faster as compared to that of the system 58

without the induced electromotive force across the Faraday disc. So, if the DC power supply is switched off at this transition point, the plasma will operate in the normal glow regime but the entire surface area of the cathode would not be covered by the plasma as exactly half the current is lost by switching off the DC power supply. So, the DC power source has to be switched off in the abnormal glow regime when the current is at-least twice the amount of current at the transition point to make sure the plasma mode of operation of the Faraday disc generator without the DC power supply is the normal glow regime and the plasma has completely covered the helium gap.

The advantage of such a system is that it does not require a continuous operation of the primary DC power source. The primary source has to be active only until the design point discussed in the previous paragraph is obtained. Also, it is a cold cathode operation which does not necessitate any thermal management and can be run perpetually. The major disadvantage of the proposed model is the necessity to have a high value of electromotive force induced across the Faraday disc. This might be very impractical when one considers the angular velocity of the Faraday disc required to achieve such a high induced electromotive force across the disc. An estimate can be obtained from the sample calculation provided in Chapter 1. There are two possible ways to get around the requirement of high angular velocity. From the sample calculation in

Chapter 1, it can be seen that the angular velocity is inversely proportional to the magnetic flux of the disc. And the magnetic flux is directly proportion to the magnetic field and the square of the radius of the disc. So, the required angular velocity can be manipulated by manipulating the magnetic flux of the disc.

Of course, there is still the problem of anode current density that was discussed in Chapter 4. A solution to this problem has been proposed in the next suggested design. But the proposed solution to the anode current densities can very well be implemented to Model- 1 as well.

Configuration 2

It is quite obvious that one cannot hope to extract more energy from the

Faraday disc generator than that is being put in to the system by a DC power source to maintain the glow discharge. The only exception is the case of the induced electromotive force across the Faraday disc being more than the voltage across the electrodes needed to sustain the glow discharge. So, the only other alternative is to have a self-sustaining discharge without the aid of an external power supply. One such method was discussed in model-1. The proposed model-2 is very similar in its operation to model-1. A primary DC power source is used to facilitate the breakdown of electrode gap and obtain the necessary optimum conditions. Once these conditions are obtained, the primary power source can be turned off. As the electrode gap breaks down, a small current can be observed in the Faraday disc generator circuit as well. If the Faraday disc generator circuit has a circuit element or a circuit, in series with the electrode gap, that steps up the

DC voltage to the electrode voltage of normal glow discharge operation, the primary power source can be turned off. The power source has to be turned off at such a point that the plasma sustained by the Faraday disc generator circuit operates at the transition point of the normal and the abnormal glow regimes. The design of the DC voltage step up circuit required for the operation of model-2 has to be investigated. 60

As for the problem of high anode current densities resulting from a small energy extraction surface area on the rim of the Faraday disc, a probable solution would be decouple the plasma so as to prevent a direct interaction with the rim of the Faraday disc.

The solution is based upon the qualitative difference between the electrode current density and the plasma current densities at the surface of the electrodes. Although, the electrodes are relatively cold in glow discharges, the same cannot be said about the surfaces of the electrodes participating in the plasma processes. The electrode surfaces are locally at high temperatures, due to their participation in plasma processes such as electron emission and surface bombardment by ions and energetic neutrals, while the bulk of the electrodes‟ material is cold. On the other hand, the electrode current density only results in Joule heating which is dependent on the internal resistance of the conductor and current density. As a result, by removing the plasma attachment from the energy extraction surface on the rim of the Faraday disc, the localized heating of the energy extraction surface is not a problem anymore. The only concern would be the Joule heating of the energy extraction surface which is similar to that found on the surface of the disc facing the magnet as current is drawn from the Faraday disc generator. Figures

5.1 and 5.2 show a design that could be used to decouple the plasma from the energy extraction surface of the rim of a Faraday disc.

Figure 5.1: Plasma De-coupler Design – First View

Figure 5.2: Plasma De-coupler Design - Second View

Figures 5.1 and 5.2 show the Faraday disc that has the concentric rim extension in physical contact with the complete area of the Faraday disc. The Faraday

disc is connected to the axle that is connected to the hollow shaft through a ceramic disc.

The disc connector connects the rim extension to the hollow shaft. The coaxial conducting shell is concentric with the hollow shaft.

As the Faraday disc rotates about its axis, except for the co-axial conducting shell all the other parts rotate along with the disc. The rotation of the disc in the presence of an external magnetic field sets up an electromotive force across the surface of the disc facing the magnet. As the Rim extension is in physical contact with all the points on the rim of the disc, the Disc connector and the Shaft are at the same potential as the energy extraction surface of the rim of the Faraday disc. As a result, the shaft can be used as an anode with co-axial conducting shell acting as the cathode. The co-axial electrode system can be used to generate the plasma that acts as the electrical contact for energy extraction from the setup. The purpose of the ceramic disc is to electrically isolate the shaft from the Faraday disc.

Apart from decoupling the plasma from the rim of the Faraday disc, there are other advantages to this design. Firstly, the glow discharge does not need to completely cover the electrode gap in the longitudinal direction as long as there is complete plasma coverage in the radial direction. The complete plasma coverage in the radial direction ensures a symmetrical current distribution in the disc connector as they are radially symmetric. Secondly, the design offers flexibility with the mode of plasma operation. As long as thermal management does not become an issue, the plasma can be operated in the upper abnormal glow regime as well. In order to ensure that the current distribution in the anode is uniform, the anode should have very high thermal conductivity in order to have a uniform temperature distribution across the anode as temperature increases the 63

resistance of the conducting path in metals. So, copper could be a good choice of material for the anode. Also, a hollow shaft is suggested instead of a solid shaft as air cooling and cooling pipes can be used to ensure a uniform temperature distribution on the anode.

The major concern with such a design is the uniformity of current distribution when the plasma coverage of the electrode gap is incomplete in the radial direction. Apart from this, the proposed design looks promising as it resolves the problem of localized heating in the energy extraction area on the rim of the Faraday disc.

The current work looked into the attachment and characteristics of the rotating anode DC plasma and identified potential problems to use plasma as an electrical contact for energy extraction from the Faraday disc and certain qualitative models have been proposed to overcome the problems and extract energy. A thorough investigation into the necessary electrical circuitry for simultaneous operation of the Faraday disc generator and the primary power source is required. It is essential to build a Faraday disk generator and experiment with plasma as the electrical contact as this was never done before. The lack of any literature on this subject makes it all the more important to experiment as there could be other problems with using plasma as an electrical contact that the current work did not foresee. Apart from looking into designs and experimenting with energy extraction from the Faraday disc generator using the plasma initiated by a DC power supply, the behavior of the rotating anode plasmas initiated by microwave and radio frequency wave power sources should also be investigated to determine the feasible operating regimes of plasma for efficient energy extraction from Faraday disc generators.

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