Download FEASIBILITY OF A PLASMA CONTACT FOR FARADAY

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
By
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
Copyright by
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
iv
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.
/
v
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
vi
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
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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
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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
x
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
xi
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.
1
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:
2
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-guidemersen.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.
7
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
8
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.
9
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
10
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 i o. 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.
11
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
n=n0.eα.x
(2.2)
Writing (2.2) in terms of current and at a distance, d, gives
I=I0.eα.d
(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
n= (n0+n1). Eα.d
(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)
13
Or,
= ln[(1/ )+1]
(2.10)
14
(2.9) provides the minimum critical conditions for electrical breakdown of gas.
From (2.9),
* exp(α.d)≈1
Or,
(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:
15
Gas
Air
N2
CO2
H2
H2O
He
A[1/cm/torr]
14.6
12.39
20
5
12.9
2.8
B[V/cm/torr]
365
342
466
130
289
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.
16
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
17
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).
18
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]
20
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 subsection 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.
22
Assuming a linear variation of electric field along the cathode layer,
E(x) = Ec(1-x/d), 0<x<d
(2.14)
where, Ec is the electric field at the cathode surface and is assumed to be constant
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.
23
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:
Pc(j) = A. 0∫d 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.
25
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,
26
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.
density
Plasma Parameter
Thermal arc discharge
Non-thermal arc
Gas Pressure
0.1-100 atm
Arc current
30 - 30 kA
Cathode current
104-107 A/cm2
102-104 A/cm2
Voltage
10-100 V
10-100 V
Gas temperature
1-10 eV
300-6000 K
Electron temperature
1-10 eV
0.2-2 eV
10-3-100 torr
discharge
1-30 A
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.
28
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
29
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.
30
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
31
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
32
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
33
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
34
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.
35
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.
36
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.
37
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 feed38
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
39
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)
437.94±0.02
468.3±0.02
628.3±0.05
866.38±0.04
1015.95±0.01
1254.03±0.04
1514.75±0,05
1752.08±0.05
1979.57±0.03
2202.09±0.03
2450.5±0.05
2723.2±0.05
3116.7±0.1
3418.8±0.1
3610.7±0.1
V2 (Volts)
386.5±0.5
376.2±0.3
355.7±0.2
355.92±0.1
356.16±0.09
356.33±0.04
356.56±0.04
356.99±0.01
356.31±0.02
357.19±0.01
357.5±0.03
358.36±0.02
360.99±0.02
364.15±0.03
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.
41
The following chapter presents and discusses the results of the data
obtained using the procedures described in the above section.
42
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
cannot be obtained at p.d values close to (p.d)min [26]. For air, (p.d)min is 7.5*10-6 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
43
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.
44
Supply voltage V1(volts)
427.83±0.03
455.68±0.01
546.85±0.01
643.14±0.03
872.13±0.03
1068.74±0.03
1218.12±0.01
1428.60±0.02
1782.25±0.04
1965.68±0.01
2432.03±0.08
2866.6±0.1
Anode voltage V2(volts)
392.15±0.08
378.91±0.02
367.95±0.01
355.36±0.02
355.99±0.01
356.6±0.01
356.92±0.01
357.16±0.01
356.7±0.01
357.52±0.02
358.35±0.01
359.15±0.01
Table 4.1 Experimental Data Set for First Run for 9.1 torr - Stationary Anode Case
Supply voltage V1(volts)
436.94±0.05
496.2±0.03
559.57±0.01
663.47±0.01
872.06±0.01
1070.88±0.02
1216.06±0.02
1443.4±0.02
1791.92±0.03
1966.02±0.02
2430.47±0.01
2869.66±0.01
Anode voltage V2(volts)
387.4±0.03
373.63±0.01
368.14±0.01
355.83±0.01
456.28±0.01
356.85±0.01
356,77±0.01
357.51±0.02
357.01±0.02
357.65±0.01
358.57±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.
46
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
47
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
48
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
49
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
50
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 deexcitation 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.
52
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
53
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.
55
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 currentvoltage 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.
57
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 selfsustaining. 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.
59
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.
61
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
62
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.
64
REFERENCES
1
Fawwaz T. Ulaby, Eric Michielssen, Umberto Ravaioli, “Fundamentals of Applied
Electromagnetics”, New jeresy, NJ: Prentice Hill, 2010
2
G. Forbes, Dynamo Electric Machine, U.S. Patent 338169, March 16,1886
3
Faraday M, “Experimental Researches in Electricity”, New york, NY: Dover, 1965
4
Montgomery H, “Unipolar induction: a neglected topic in the teaching of
electromagnetism”, European Journal of Physics, 1999, 20: pp. 271-280
5
Montgomery H, “Current flow patterns in a Faraday disc”, European Journal of
Physics,2003, 25: pp.171-183
6
Lorrain P, ”Electrostatic charges in v x B fields: the Faraday disk and the rotating
sphere”, European Journal of Physics, 1999, 11: pp. 94-98.
7
Guala-Valverde J, Mazzoni P, Achilles R, “The homopolar motor: A true relativistic
engine” American Journal of Physics, 2002, 70:pp. 21-29
8
Bringuier E, “Electrostatic charges in v × B fields and the phenomenon of
induction”, European Journal of Physics, 2003, 24: pp. 21-29
9
A.F. Delafield, “Dynamo Electric Machine”, U.S. Patent 278,516, May 29, 1883
10
S.Z. De Ferranti, Unipolar Dynamo Electric Machine, U.S. Patent 341,097, May 4,
1886
65
11
Nikola Tesla, “Dynamo Electric Machine”, U.S. Patent 0,406,968, July 16, 1882
12
J.E. Noeggerath, “Unipolar Dynamo-Electric Machine “, U.S. Patent 895888,
August 11, 1908
13
R. Eickemeyer, “Dynamo-Electric Generator”, U.S. Patent 369400, September 6,
1886
14
E. K. Inall & J. L. Hughes, “Homopolar Generator as the Energy Store for a Large
Laser”, Nature, 1968, 220: pp. 1121-1121
15
W.L. Noble, J.M. Weldom, J.H. Gully, “Final Manufacture and Assembly of 60
Megajoule Pulsed Homopolar Power Supply”, IEEE Transactions On Magnetics,
1986, 22: pp.1623-1627
16
Pappas J.A., Weldon J.M., Wright J.C., Price J.H., Gully J.H., Brunson G.,
“Preliminary Design of a 1 Gigajoule Homopolar Generator”, IEEE Transactions on
Magnetics, 1993, 29: pp. 980-985
17
J.D. Cobine, “Gaseous Conductors- Theory and Engineering Applications”, New
york- NY: Dover, 1958
18
W. Crookes, “On Radiant Matter”, The Popular Science Monthly,1880, 16:pp. 157157
19
S -I Akasofu, S Yoshida, "The structure of the solar plasma flow generated by solar
flares" Planetary and Space Science, 1967, 1: pp. 39-47
66
20
H.W. Kasemir, “A Contribution To The Electrostatic Theory Of A Lightning
Discharge”, Journal of Geophysical Research, 1960, 65: pp. 1873–1878
21
Gottscho, Richard A., “Microscopic Uniformity In Plasma Etching”, Journal of
Vacuum Science & Technology B: Microelectronics and Nanometer Structures,
1992, 10: pp. 2133-2148
22
C.F. Gallo, “Coronas and Gas Discharges in Electrophotography: A Review”, IEEE
Transactions on Industry Applications, 1975, 11: pp. 739-748
23
A.von Engel, M.Steenbeck,” Electrische Gasentladungen: Ihre Physik und Technik”,
Germany: Springer, 1934
24
Thomas Christen, “Comment on “What is the Mathematical Meaning of Steenbeck's
Principle of Minimum Power in Gas Discharge Physics?”, J. Phys. D: Appl. Phys.,
2010, 43: pp.298001-2
25
A.Fridman, L.A. Kennedy, “Plasma Physics and Engineering”, New york, NY:
Taylor & Francis, 2004
26
Danijela, D. S Ijacic and Ute Ebert, “Transition from Townsend to Glow Discharge:
Subcritical, Mixed,or Supercritical Characteristics”, Physical Review, 2002
27
J.Kuffel, E. Kuffel, W. S. Zaengl, “High Voltage Engineering Fundamentals”,
Woburn, MA: Newnes, 2000
67