Performance analysis of a monopole antenna with fluorescent tubes at 4.9 g hz...
IAS Report Final
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TOPIC 1:
OBSERVING THE HYSTERESIS CURVE IN A PLASMA SYSTEM UNDER
THE INFLUENCE OF VARYING MAGNETIC FIELD
TOPIC 2:
OBSERVING DIFFERENT INTENSITY CHARACTERISTICS OF ARGON
PLASMA UNDER VARYING MAGNETIC FIELD ACROSS LANGMUIR
PROBES
Anirudh Deshpande
Under the guidance
Of
Prof. A.N.S. Iyengar and Prof. M.S. Janaki
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1. ACKNOWLEDGEMENT
I would like to thank Professor A.N.S. Iyengar for giving me this opportunity to
work under his guidance wherein I happened to learn a lot. I would also like to
thank the Indian Academy of Sciences for considering my academia for the
position of an intern under its esteemed banner. A special thanks to Mr Sabuj
Ghosh and Mr Pankaj Kumar Shaw for guiding me through the respective
experiments and helping me out in times of need.
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2. ABSTRACT
This report presents the study of a plasma sheath and its nature in the vicinity of
varying magnetic field. The gas used in the said experiment happens to be Hydrogen
(H) which is fed to a gas chamber through a pipe connected to a cylindrical reservoir
of Hydrogen gas via a pump. This entire system is placed inside a toroidal system and
the magnetic field is varied following a certain pattern, while an oscilloscope is used
to track the varying voltage. The raw data so obtained is then analysed using
MATLAB. A brief video clip of the plasma sheath is also shot and is then used for
further analysis.
This report also presents a comparative study on the investigation of the effects of
bar magnet, in both its presence and absence, on the Floating DC potentials of 4
Langmuir probes and varying intensities of the plasma so polarized in the presence of
the magnet. The radial distance of the magnet from the hollow cathode is varied
from 1cm to 3cm. The gas used in this system is Argon (Ar) gas and it is used at
different pressures. A brief video clip of the plasma system is shot and then analysed
using softwares TRACKER and MATLAB.
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3. INTRODUCTION
Plasma is the 4th state of matter which is a collection of ions, electrons and neutral
ato s hi h e hi it olle ti e effe ts o ediu -like eha iou •. In plasma,
increasingly high electric fields arise over a very short distance near the material
boundaries that keep the electrons within the plasma and push the ions out, just
enough so as to make the net loss of charge zero. The plasma stays neutral and
relatively electric field free. This collective effect is called Debye Shielding. The
electrostatic potential structure is called the plasma sheath.
3.1 Plasma Sheath:-
In practicality, all plasmas are contained inside solid vacuum vessels. As can be
expected by the study of normal fluids, we observe a slightly different behaviour in
the plasma near the surface of the solid vessel. What actually happens is, when the
ions and electrons hit the surface, they recombine and are lost to the plasma. Now,
given that the electrons in plasma generally move much faster than the ions, the
initial electron flux into the wall greatly exceeds the ion flux. This flux imbalance
causes the wall to charge up negatively, and so generates a potential barrier which
repels the electrons, and thereby reduces the electron flux. Debye shielding confines
this barrier to a thin layer of plasma, whose thickness is a few Debye lengths, coating
the inside surface of the wall. This layer is known as the Plasma Sheath. The height
of the potential barrier continues to grow as long as there is a net flux of negative
charge into the wall. This process presumably comes to an end, and a steady-state is
attained, when the potential barrier becomes sufficiently large to make electron flux
equal to the ion flux.
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3.2 Langmuir Probe:-
A Langmuir probe is a device which is used for a different form of electric probe
diagnostics which are employed in the modern day. These probes measure the local
plasma parameters by using stationary or slow time varying electric fields to emit or
to collect charged particles from the plasma. This type of Langmuir probe is usually
well suited for low density cold plasmas, as low pressure electric discharges,
ionospheric and space plasmas.
3.3 Tokomak:-
A tokomak is a device that uses a powerful magnetic field to confine plasma in the
shape of a torus. Achieving stable plasma equilibrium requires magnetic field lines
that move around the torus in a helical shape. Such a helical field can be generated
by adding a toroidal field i.e. field travelling around the torus in circles.
In a tokomak, the toroidal field is produced by electromagnets that surround the
torus. These magnetic fields are used for confinement since no solid material can
withstand the extremity of high temperatures the plasma can reach.
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4. EXPERIMENTAL SETUPS
4.1 Hysteresis Experiment
The experimental setup consists of a gas chamber, a pump, a toroidal system,
which in this case happens to be a tokomak, an oscilloscope and a central
control system in order to vary the magnetic field.
The gas chamber is filled with Hydrogen gas with the help of a pipe connecting
a cylindrical tank reservoir to it via a pump which is used to regulate the
pressure of the gas inside the chamber. The gas chamber consists of an
electrode which plays an important role in the formation of plasma in the first
place. The mentioned pump is further connected to a machine which is used
to keep a track of, and vary the pressure using a set of knobs. The central
control system consists of a panel with a set of different knobs, buttons and a
display screen each for vertical magnetic field and toroidal magnetic field. The
knobs are used to vary the respective currents, which in turn change the
corresponding magnetic fields. The screen displays the voltage, current and
other such significant quantities. An oscilloscope is set up by connecting it to
the system with the help of two connecting wires. It is used to record the
variation of voltage with time as and when we change the two magnetic
fields.
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4.2 INTENSITY CHARACTERISTICS EXPERIMENT
The schematic diagram of the hollow Cathode DC glow discharge plasma
device shown below shows that it consists of a cylindrical cathode of length
and diameter 17 cm and 10 cm respectively, and a central anode rod of
diameter 0.5mm and length 5mm. These are kept inside a vacuum chamber
and pumped down to pressures (0.08, 0.13 and 0.2 mbar) using an oil-rotary
pump. The chamber is then filled with 99.9 % pure Argon (Ar) gas. The
forward discharge voltage is provided from High Voltage DC supply 0-1000V/
0-1A, Aplab H1010 series. The pressures applied are measured digitally with
the aid of Pirani gauges. There are 4 Langmuir probes, attached to the DC
plasma glow device and they have been used in measuring the floating dc
potentials using voltmeter. The first probe is set 1cm apart from the anode
and the rest 3 probes are set 1cm apart successively in radial positions. There
is also a provision of applying a uniform axial magnetic field using bar
magnet(s), whose position can be varied according to scale.
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5. EXPERIMENTAL PROCEDURE
5.1 Hysteresis curve in a plasma system under varying magnetic field
The supply of Hydrogen gas from the cylindrical tank to the gas chamber is
switched on with the help of a valve which allows passage of the gas from the
tank into the pipe and eventually to the chamber. A track of the pressure
exerted by this gas in the chamber is kept with the help of a pressure gauge,
and is allowed to stabilize for some time. A professional Mikrotron MC1362
camera which has the capability to capture upto 9000 frames per second is set
up in order to capture the movement of the plasma sheath as we vary the
magnetic field in the toroidal system. An oscilloscope is also set up in order to
record the voltage variations in the system with time. These values are
recorded as CSV (Comma Separated Values) files with the help of a pen drive
attached directly to the oscilloscope, and then are further analysed using
MATLAB.
Figure 1(a): Tokomak used as a toroidal system Figure 1(b): The central control panel
Once the pressure stabilizes, the experiment is started off by increasing the
vertical field current by an amount of 0.4 Amperes. The data from the
oscilloscope is recorded, and a brief video of 3-4 seconds is shot using the
a e a at high f a e ate e a li g us to stud the sheath’s o e e t i
more detail. Now, keeping the Vertical Field current constant, the Toroidal
field current is increased in intervals of 0.4 Amperes till a maximum of 8A.
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Data is recorded corresponding to each of the respective magnitudes of the
fields. Once it reaches 8 Amperes, the TF current is then brought back to zero,
again in intervals of 0.4A, and data is recorded at each step simultaneously.
This is further continued for different values of VF current between 0 to 3.5 in
intervals of 0.5A.
Figure 2: Plasma Sheath inside the gas chamber Figure 3: Oscilloscope
The data recorded in the form of CSV files is then transferred onto a desktop
with MATLAB pre-installed in it. These files are imported into MATLAB, and
with the help of various functions, we find out various analytical quantitites
for each of the files separately. These quantities include: (1)Skewness
(2)Kurtosis (3)Hurst Exponent
Skewness:- Skewness is a measure of symmetry, or more precisely, lack of
symmetry. A distribution, or data set, is symmetric if it looks the same to the
left and right of the center point. Mathematically, for a set of data, skewness
is defined as
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Kurtosis:- Ku tosis is a easu e of the tailed ess of the p o a ilit
distribution of a real-valued random variable. In a similar way to the concept
of skewness, kurtosis describes the shape of a probability distribution and,
just as for skewness, there are different ways of quantifying it for a theoretical
distribution and corresponding ways of estimating it from a sample from a
population.
Hurst Exponent:- Hurst exponent relates to the autocorrelations of the times
series, and the rate at which these decrease as the lag between the pairs of
values increases. It is also referred to as the "index of dependence" or "index
of long-range dependence". It quantifies the relative tendency of a time series
either to regress strongly to the mean or to cluster in a direction. A value
of H in the range 0.5–1 indicates a time series with long-term positive
autocorrelation, meaning both that a high value in the series will probably be
followed by another high value and that the values a long time into the future
will also tend to be high. A value in the range 0 – 0.5 indicates a time series
with long-term switching between high and low values in adjacent pairs,
meaning that a single high value will probably be followed by a low value and
that the value after that will tend to be high, with this tendency to switch
between high and low values lasting a long time into the future.
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5.2 Observing the intensity characteristics of a plasma system under
the influence of varying magnetic field on Langmuir probes
The entire experimental setup of Glow Discharge plasma is kept inside a
vacuum chamber. This chamber is isolated with the help of a rotary pump in
order to bring about the experimental conditions. After this, Argon gas is
supplied to the chamber with the help of a pipe and a set of valves connected
to a cylindrical reservoir which control the pressure at which the gas is
discharged. This pressure is usually kept around 2 millibars. The gas in the
chamber is then discharged with the help of a volmeter using which voltage
can be varied between 0 and 1000 volts.
Figure 3: Glow discharge plasma setup
The camera used earlier is set up in order to record the real life feed of plasma
whose intensity seems constant to the naked eye, but when shot at a high
framerate happens to prove otherwise. Then using the pressure of the gas
inside the chamber and the voltage applied as the varying parameters, the
experiment is started off.
A bar magnet is placed at varying distances so as to record short videos of 3-4
seconds at a framerate of 250 fps which are then further analysed using a
software by the name TRACKER. The different cases we happen to consider
while performing the experiment are: (1)Without bar magnet. (2) Magnet is at
a distance of 1cm from the cathode. (3) Magnet is at a distance of 2cms from
the cathode. (4) Magnet is at a distance of 3cms from the cathode
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The plasma when in the presence of the bar magnet shows a bright spot near
the wall where the magnet is placed. This bright glow shows that the
ionization in that particular area is much higher as compared to the other
regions. It is the intensity and position of this spot which varies with the
position of the bar magnet, and its variation with time is tracked using
TRACKER.
Figure 4: Pressure gauge and voltmeter
Figure 5: Bar magnet used to vary magnetic field
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6. RESULTS AND DISCUSSIONS
6.1 OBSERVING HYSTERESIS CURVE IN THE PLASMA SYSTEM
The following quantities were calculated with the help of the recorded data, and
were plotted for different Vertical Field currents.
(1) Mean Skewness
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The above two graphs very distinctly show that the path traced while
achieving the maximum TF current is higher than the one traced while coming
back to 0.
Hence, a hysteresis curve is observed over here.
(2) Hurst Exponent
VF – 1.14A
VF – 2.11A
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The above graphs of Hurst Exponent v/s time and Mean Kurtosis v/s time
respectively show distinct Hysteresis curves since the path traced back to 0 is
below the path traced while achieving maximum TF current.
Therefore, we can see that all the three analytical quantities show a hysteresis
curve, thus fulfilling the aim of our experiment.
6.2 OBSERVING INTENSITY VARIATIONS IN A PLASMA SYSTEM UNDER
VARYING MAGNETIC FIELD
Following are snaps of the plasma system as and when the bar magnet is moved and
the plasma is polarized. The pressure was kept constant at 130 mbar and the voltage
at 350 volts during this time.
(1) When magnet is 1cm away
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(4) In the absence of magnet
As can be clearly seen from these four images that as the bar magnet is pulled away
from the cathode, the local ionization i.e. the visible glow becomes less obvious and
eventually fades away when the magnet is taken away from its vicinity.
The intensity patterns of the local ionization are shown below in the form of graphs
between intensity and time.
Magnet is 1cm away
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Without magnet
As should be expected, the amplitudes of each of the graphs prove that the intensity
of the local ionization decreases as we take the magnet further away from the
cathode. Also, these graphs happen to show the chaotic nature of the intensity
variation.
Chaos Theory: - Chaos theory is the field of study in mathematics that studies the
behaviour of dynamical systems that are highly sensitive to initial conditions. Small
differences in initial conditions yield widely diverging outcomes for such dynamical
systems, rendering long-term prediction impossible in general. This happens even
though these systems are deterministic, meaning that their future behaviour is fully
determined by their initial conditions, with no random elements involved.
In order to enunciate more on the variation in intensity of the high ionization region,
we found the Fast Fourier Transforms i.e. FFTs of each of these intensity v/s time
graphs.
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As we can observe in each of the above graphs, a peak emerges at two frequencies
i.e. 50 Hz and 100 Hz. Also, it can be easily observed that the peaks at 100 Hz are
significantly higher as compared the peaks at 50 HZ in all four graphs which proves
that harmonics are in play, which in turn goes on to prove that the system has some
non-linear motion involved.
Also, as is apparent from the FFT graphs, the power of the glow i.e. the local
ionization decreases as the magnet is moved farther away from the cathode.
Considering all the above statements, we can conclude that the spectrums we
o se e f o the a o e g aphs a e Li e F e ue ies , a d he e the glo i the
plasma has to be observed at an even higher framerate in order to observe the
actual Fourier spectrum of the local ionization in the plasma system.
