Download Dust Grain Charge Process in Negative Ion Plasma AThesis

Republic of Iraq
Ministry of Higher Education
And Scientific Research
University of Baghdad
College of Science
Dust Grain Charge Process
in Negative Ion Plasma
A Thesis
Submitted to the Department of physics
College of Science-University of Baghdad
In partial Fulfillment of the Requirements for
The Degree of Master of Science in Physics
By
Zainab Abdulla Mankhi
(B. Sc. 2006)
Supervised by
Dr. Thamir H. khalaf
January, 2012
Rab’i Al-awal, 1433
‫جوهىريت العراق‬
‫وزارة التعلين العالي والبحث العلوي‬
‫جاهعت بغداد‪ /‬كليت العلىم‬
‫عوليه شحي الحبيبت الغباريت‬
‫في بالزها ذاث االيىى السالب‬
‫رسالة هقدهة إلى قسن الفيزياء‬
‫كلية العلوم – جاهعة بغداد‬
‫وهي جزء هي هتطلبات ًيل درجة الواجستير‬
‫في الفيزياء‬
‫هي قبل‬
‫زينب عبداهلل منخي‬
‫(بكالىريىس ‪) 0226‬‬
‫بأشراف‬
‫د‪ .‬ثامر حميد خلف‬
‫ربيع االول ‪0311,‬‬
‫كاًوى الثاًي ‪2102‬‬
‫بِسْمِ اللّهِ الرَّحْمَنِ الرَّحِيمِ‬
‫ك الَ ِع ْل َم لَ َنا‬
‫َقالُو ْا ُسب َْحا َن َ‬
‫ك أَ َ‬
‫نت‬
‫إِالَّ َما َعلَّمْ َت َنا إِ َّن َ‬
‫ْال َعلِي ُم ْال َح ِكي ُم‬
‫{البقرة‪}32/‬‬
Supervisor’s Certification
We certify that this thesis was prepared by Zainab Abdullah Mankhi
under our supervisionat the Physics Department, College of Science- University
of Baghdad as partial requirement for the degree Master of Science in physics.
Signature:
Name: Dr. Thamir. H. khalaf
Title: Assist Professor
Address: Collage of Science
University of Baghdad
Date: /
/ 2012
In view of the available recommendation, I forward this thesis for debate
by the examination committee.
Signature:
Name: Dr. RaadM.S.Al-haddad
Title: Professor
Address: Chairman of Physics Department
College of Science University of Baghdad Date:
/
/2012
Examining Committee Certification
We certify that we have read this thesis and examined “Dust Grain Charge
Process in Negative Ion Plasma" and as an examining committee the student
Zainab Abdullah Mankhi in its contents and in what is related with it, and in
opining, it has adequate standard of the thesis of the degree of Master of
Science in Physics.
Signature:
Signature:
Name:Dr. Mahdi HadiJasim
Name: Dr. KadhimAbdulwahidAadim
Title: Assistant Professor
Title: Assistant Professor
Data:
Data:
/ /2012
(Chairman)
/ /2012
(Member)
Signature:
Signature:
Name: Dr. Khalid Abbas Yahya
Name:Dr. ThamirHamidkhalaf
Title: Assistant Professor
Title: Assistant Professor
Data: / /2012
Data:
(Member)
/ /2012
(Supervisor)
Approved by the Department of Physics / College of Science / University
of Baghdad.
Signature:
Name: Dr. Saleh Mahdi Ali
Title: Professor
Dean of the College of Science.
Data: / /2012
To my father’s soul,
To my mother, who embraced me with her love
and kindness.
To my brothers and sisters, who encourage me.
To my best friends, who helped me to see my
success.
Zainab
Acknowledgements
First of all, thanks to Allah are due for helping me to
complete this thesis.
Then, I would like to express my sincere appreciation and
deep gratitude to my supervisor Dr. Thamir Hamid Khalaf for
suggesting the topic of this thesis, guidance, suggestions and
continuous encouragement throughout the research.
My special thanks are exposed to the staff of the department
of Physics in Baghdad University for their assistant and support
during the years of my study and research.
Finally, my thanks are also given everyone who helped me in
one way or another, and who contributed in making this thesis
possible particularly.
I
Abstract
This work presents a computer studying to simulate charging process
of dust grain immersed in plasma (electrons-K+ potassium ions) with
negative ions (
sulfur hexafluoride ions) by basing on discrete model. In
this work, the discrete model is developed to take into account effect
negative ions on charging process of dust grain.
The model was translated to a numerical calculation by using
computer programs. The program of model has been written in FORTRAN
programming language to calculate the charging process for a dust particle
in a plasma with negative ion, the time distribution of a dust charge, number
charge equilibrium and charging time for parameter
(ratio of number
density of electron to number density of positive ion) =10-1, 10-2, 10-3, 10-4,
10-5, and different grains size. The phase speed for negative ion dustacoustic wave has been calculated at different value of
(ratio of number
density of negative ion to number density of positive ion).
The results of the work reveal that the charging of dust grains in
negative ion plasma can be controlled by varying the relative fraction of
negative ions in the plasma. As the negative ion density is increased in
plasma, more electrons become attached by negative ion and there is a
corresponding reduction in the negative current of electrons and allow the
more mobile positive ions to charge the dust. Therefore, the negativity of
charge number on dust grain decreases gradually to positive charge number.
II
The results also revealed that the effect of negative ions concentration
and negative ions temperature on phase speed negative ion dust-acoustic
wave.
III
List of Symbols
a
The grain radius
µm
D
d
The grain diameter
Intergrain distance
The electric field
the electric field in the strata
The electron charge
the acceleration due to gravity
The ion current
The electron current
The negative ion current
The positive ion current
The Boltzmann constant
The dust grain mass
The ion mass
The electron mass
The negative ion mass
The number density of electron
The number density of positive ion
The number density of negative ion
The number density of dust grain
The electrostatic pressure on the surface
charges
The probability per unit time for electron
The probability per unit time for ion
The probability per unit time for negative ion
The probability per unit time for positive ion
The electron temperature
The ion temperature
The dust thermal energy
The negative ion temperature
The positive ion temperature
µm
µm
Volt
Volt
C
m/sec2
A
A
A
A
J/Ko
kg
kg
kg
kg
m-3
m-3
m-3
m-3
C2/m4
e
mi
me
Te
Td
IV
Sec-1
Sec-1
Sec-1
Sec-1
eV
eV
eV
eV
eV
Wi
Wf
mfp
the phase speed of the dust-negative ion
acoustic wave
The negative ion thermal energy
The ionization potential energy
The work function of the dust grain material
The number of charges on the surface of dust
grain
The number of charges of negative ion
The collisional mean-free-path
the dust plasma frequency
the ion plasma frequency
m/sec
The Coulomb coupling parameter
The thermal speed of the species of plasma
particle z
The permittivity constant for space
The ratio of number density of dust grain to
number density of positive ion
The ratio of number density of electron to
number density of positive ion
The ratio of number density of negative ion
to number density of positive ion
Debye shielding distance
The Debye lengths associated to electrons
The Debye lengths associated to ions
The surface charge density
The scattering cross section
The dust-neutral collision frequency
The electron-neutral collision frequency
The ion-neutral collision frequency
The plasma frequency
the electron plasma frequency
m/sec
The dust grain floating (surface) potential
The secondary electron yield
The charging time
Volt
sec
V
J
J
J
µm
Hz
Hz
farad/m
µm
µm
µm
C/m-2
m2
Hz
Hz
Hz
Hz
Hz
Contents
Subject
Chapter One
Page
Introduction
1.1 Introduction
1
1.2 Dusty plasma in space
4
1.3 Basic dusty plasma characteristics
7
1.3.1 Macroscopic neutrality
7
1.3.2 Intergrain spacing
8
1.3.3 Debye length
9
1.3.4 Coulomb coupling parameter
10
1.3.5 Characteristic frequencies
10
1.4 Dust charging mechanisms
12
1.4.1 Collection of plasma particles
12
1.4.2 Secondary electron emission
13
1.4.3 Photo-detachment
15
1.4.4 Thermionic emission
1.4.5 Field emission
16
16
1.5 Production of Dusty Plasmas
17
1.5.1 Modified Q-machine
17
1.5.2 DC Discharges
19
1.5.3 RF Discharges
20
1.6 Literature review
22
1.7 Aim of the work
28
Chapter Two
Theoretical Background
2.1 Introduction
29
2.2 Orbital-motion limited theory
30
2.3. Particle charging
32
2.3.1 Continuous Charging Model
33
2.3.2 Discrete Charging Model
35
2.4 The Dust-Negative Ion Acoustic Wave
Chapter Three
36
Simulation and Results
3.1 Introduction
38
3.2 The Phenomenon modeling
39
3.3The Simulation
40
3.4 The program of model
42
3.5
3.3.1The Program Input Data
44
3.3.2 The Program Calculations
45
The Results
47
3.5.1
The charge dust grain fluctuations
47
3.5.2
The Time Distribution of a Dust Charge
52
3.5.3 The Equilibrium Charge Number
56
3.5.4 The dust surface potential
60
3.5.5 The Charging Time
62
3.5.6 RMS Level of Charge Fluctuation
65
3.5.7 The Dust-Negative Ion Acoustic Wave
67
3.6 Conclusions
70
3.7 Future works
71
Reference
72
CHAPTER ONE
INTRODUCTION
1.1 Introduction
About 80 years ago Tonks and Langmuir (1929) first coined the term
„plasma‟ to describe the inner region (remote from the boundaries) of a
glowing ionized gas produced by means of an electric discharge in a tube.
The term plasma represents a microscopically neutral gas containing many
interacting charged particles (electrons and ions) and neutrals. It is likely
that 99% of the matter in our universe (in which the dust is one of the
omnipresent ingredients) is in the form of a plasma. Thus, in most cases a
plasma coexists with the dust particulates. These particulates may be as large
as a micron. They are not neutral, but are charged either negatively or
positively depending on their surrounding plasma environments. An
admixture of such charged dust or macro-particles, electrons, ions and
neutrals forms a“dusty plasma” [1].
Dusty plasmas are low-temperature multispecies ionized gases
including electrons, ions, and negatively (or positively) charged dust grains
[2]. Dust grains are massive (billions times heavier than the protons) and
their sizes range from nanometers to millimeters. Dust grains may be
metallic, conducting, or made of ice particulates [1]. The size and shape of
dust grains will be different, unless they are man-made. Dust particles that
are dispersed into plasmas for experimental studies, tend to be glass or plastic
particles (melamine formaldehyde is a commonly used particle) and are
spherical with a very narrow distribution of diameters. For example, a
typically used particle may have a diameter of 3.50 ± 0.05 μm and a mass ~
3×10−11 kg. Such narrowly sized particles are termed monodisperse. Some
experiments used fine powders, such as aluminum silicate (kaolin) with a
broad size distribution ranging from the sub-micron to tens of microns, and
contain particles having laminar shapes with jagged edges [3]. However, they
1
CHAPTER ONE
INTRODUCTION
can be considered as point charges [1] figure (1.1.a). In such circumstances,
The dust particles can be charged due to the collection of electron and ion
currents from the background plasma, the grain charges negatively owing to
the larger electron mobility [4, 5], photoelectric emission in the presence of a
flux of sufficiently energetic ultraviolet (UV) photons, thermionic emission
when the grain is heated, or secondary electron emission in the presence of
higher energy (
50 eV) electrons, dust grains acquire a positive charge. [6]
In this work investigated the charging of dust in a plasma consisting of
positive ions, electrons and negative ions (this is referred to a negative ion
plasma).
The charged dust grains can effectively collect electrons and ions from
the background plasma. There has been a considerable interest in new wave
modes, electrostatic potential and energy loss of charged projectiles in dusty
plasmas recently and this is currently a rapidly growing area in dusty plasma
physics. Numerous unique types of electrostatic and electromagnetic waves
exist in dusty plasmas because of the dust charging process. For typical space
and laboratory plasmas, the condition a ≪
, d is fulfilled, where a,
, and
d are respectively the grain radius, Debye shielding distance and the average
intergrain distance. In the case where
< d, the dusty plasma can be
considered as a collection of isolated screened grains (which may be referred
to as dust-in-plasma) whereas in the case where d <
, the charged dust also
participates in the screening process and therefore in the collective behavior
of the ensemble (a true dusty plasma) [7].
Dusty plasmas are ubiquitous in the universe; examples are protoplanetary and solar nebulae, molecular clouds, supernova explosions,
interplanetary medium (figure (1.1.b)), circumsolar rings, and asteroids.
2
CHAPTER ONE
INTRODUCTION
Within the solar system there are the planetary rings, cometary tails and
comate [3, 8], and dust clouds on the moon. Closer to earth, are the
noctilucent clouds composed of small ice particles that form in the summer
polar mesosphere at an altitude of about 85 km where the temperature can
dip as low as 100 K0.
Dust also turns out to be common in laboratory plasmas, such as
tokamaks, plasmas used in the processing of semiconductors, and even in
electron storage rings. In plasmas used to manufacture semiconductor chips,
dust particles are actually formed in the discharge from the reactive gases
used to form the plasmas. These particles can then grow by agglomeration
and accretion and eventually fall onto the semiconductor chips contaminating
them, resulting in an overall significant reduction in yield [8]. Impuritycontaining plasmas are also relevant to many laboratory and technological
plasmas, such as low temperature rf and dc glow discharges, rf-plasma
etching and the wall region in fusion plasmas [5].
Because the positively charged dust occurs in the presence of strong
ultraviolet (UV) radiation or fast electrons, plasmas with positive charged
particles occur widely in space and also in the earth‟s mesosphere [9].
a
b
Figure (1.1) a: An SEM image of the 3±1 μm polydisperse dust used in this experiment
[10]. b: The appearance of interplanetary dust particles [1].
3
CHAPTER ONE
INTRODUCTION
The largest in the increase of the interest in dusty plasmas came
from a completely different field - the semiconductor industry. Dust appeared
to be a critical issue in the development of microelectronics. As the
semiconductor industry aims at miniaturization, the contamination of the
processing plasma with even very small particles became crucial. Initially, it
was considered that contamination originates from external sources, but soon
it was discovered that the plasma itself can create dust particles. Many efforts
have been dedicated to investigate and understand the particle growth,
charging and transport in plasmas [1].
In the meantime, positive aspects of the dusty plasma have been
discovered. For example, the specific feature of dusty plasma to decrease the
density of free electrons and, respectively, to increase their energy can be
used for dust-plasma-enhanced chemical vapor deposition. Another area
showing high interest in dusty plasmas is the solar cell industry. Initially, this
industry (just like the microelectronics) was interested in removal of the dust,
which grows in glow discharges in silane. Later, it has been shown that the
incorporation of nanometer-sized dust particles in the amorphous silicon film
can substantially increase the stability of the solar cell [11].
1.2 Dusty plasma in space
The attention is focused on dusty plasmas in space where they occur in
a wide variety of environments. Dust is present in such diverse objects as
interstellar clouds, solar system, cometary tails, planetary rings and
noctilucent clouds etc. See figure (1. 2). Since charged dust grains are
common in low earth orbit and in the interplanetary medium, the presence of
this charged material can cause both physical damage and electrical problems
for spacecraft. The charged dust particles in space plasmas may help to
4
CHAPTER ONE
INTRODUCTION
explain the formation of the planets, planetary rings, comet tails and nebulae.
Given the variety of arenas in which a dusty plasma may play a role, it is
important to understand the physical properties of this plasma system in
space. The space between the stars is filled with cosmic dust and elements
like hydrogen and helium which make up the “interstellar medium”[12].
Figure (1.2): Examples of dusty plasmas: (a) the Orion Nebula, (b) Halle Bop comet, (c)
Saturn‟s rings, (d)fire and the soot particulate matter suspended in it. (Figures courtesy of
NASA)[9]
The interstellar medium is mainly made of hydrogen atoms. The
density of hydrogen in interstellar space is on average about 1 atom per cubic
centimeter. In the extremes, as low as 0.1 atom per cubic centimeter has been
found in the space between the spiral arms and as high as 1000 atoms per
cubic centimeter are known to exist near the galactic core[7].
The interstellar medium also contains cosmic dust. These particles are
much bigger than hydrogen atoms. However, there are far fewer particles of
cosmic dust than there are hydrogen atoms in the same volume of space. It is
5
CHAPTER ONE
INTRODUCTION
estimated that cosmic dust is 1000 times less common than hydrogen atoms
in the interstellar medium. The dust grains in the interstellar or circumstellar
clouds are dielectric (ices, silicates, etc.) and metallic (graphite, magnetite,
amorphous carbons etc.) [7, 12]. Typical parameters of dust-laden plasmas in
interstellar clouds are ne = 10−3–10−4 cm−3
cm−3,
a
0.2 μm, nn
104 cm−3
, Te
12
,
nd
10−7
,and a/λD ≤ 0.3. The most important
part of our Earth‟s environment, where the presence of charged dust particles
are observed, is the polar summer mesopause located between 80 and 90 km
in altitude. The most significant phenomenon observed in the polar summer
mesopause is the formation of a special type of cloud known as „noctilucent
clouds‟ (NLCs). Figure (1. 3). The NLCs were reported for the first time in
1885 and were, from the beginning, recognized as being different from other
clouds [1].
Figure (1.3): Noctilucent clouds [Photographed by P. A. Dalin, Space Research Inst.,
Russia, 1999][2].
6
CHAPTER ONE
INTRODUCTION
1.3 Basic dusty plasma characteristics
To understand the basic dusty plasma principles properly, it seems
useful to re-examine some basic characteristics such as macroscopic
neutrality, intergrain spacing, Debye length, Coulomb coupling parameter
and characteristic frequencies, etc. In the following few sections:1.3.1 Macroscopic neutrality
When no external disturbance is present, like electron–ion plasma a
dusty plasma is also macroscopically neutral. This means that in an
equilibrium with no external forces present, the net resulting electric charge
in a dusty plasma is zero. Therefore, the equilibrium charge neutrality
condition in a dusty plasma reads [1]
where
is the concentration of plasma electrons, singly charged
positive ions (with charge e) and dust particles respectively, e is the
magnitude of electron charge and
is the amount of
charge present on the dust grain surface when the grains are positively
(negatively) charged with
being the number of charges residing on the
surface of dust grain. Note that the charge of the dust particle can vary
significantly depending on plasma parameters. In studying the basic physics
of dusty plasmas, the third term on the left in equation (1.1) carries very
interesting implications. The presence of the dust particles in the plasma
allows the formation of electric fields within the plasma, alters the local
plasma potential profile, modifies the transport of particles in the plasma,
modifies certain types of ion plasma waves, and introduces new dust plasma
wave modes [12].
7
CHAPTER ONE
INTRODUCTION
1.3.2 Intergrain spacing
A multi-component dusty plasma are composed of electrons, positively
charged ions, and extremely massive charged dust grains, in a neutral
background. The dust grain radius a is usually much smaller than the dusty
plasma Debye length
than
. When the intergrain spacing d is much smaller
, the charged dust particulates can be treated as massive point
particles similar to multiply charged negative (or positive) ions in a multispecies plasma. Note that for dusty plasmas
and the dust particles
can be considered as massive point particles where the effect of neighboring
particles can be significant. For dust-in-plasma
, and in this situation
the dust particles are completely isolated from their neighbors [7] .
d
a d
d
a
a
b
Figure (1.4): a: The Debye length is greater than the average distance between ions.
b: The Debye length is less than the average distance between the ions.
8
CHAPTER ONE
INTRODUCTION
1.3.3 Debye length
The Debye length is an important physical parameter in a plasma: it
provides the distance over which the influence of the electric field of an
individual charged particle is felt by other charged particles (such as ions)
inside the plasma. The charged particles actually rearrange themselves in
order to shield all electrostatic fields within a Debye distance. In dusty
plasmas, the Debye length can be defined as follows [12]:
√
Where
√
√
and
are the Debye lengths
associated to electrons and ions respectively, and ,
,
and
are the
electron and ion mean temperatures and densities.
Dust grains of radius a, separated by a given distance d, can only be
considered as individual isolated grains if the criterion
is met,
i.e. if the physical dimensions of the plasma are large enough for the
shielding to take place. If so, considering that the electron‟s mobility is
higher than that of the ions, shielding is primarily performed by electrons and
equation (1.2) becomes [7]:
√
9
CHAPTER ONE
INTRODUCTION
1.3.4 Coulomb coupling parameter
One other important special characteristic of a dusty plasma is its
Coulomb coupling parameter
which is defined as the ratio of the dust
potential energy to the dust thermal energy [1].
Charged dust grains can be either weakly or strong correlated
depending on the strength of the Coulomb coupling parameter [2]
⁄
Where
is the intergrain spacing, nd0 is the initial
dust density,
is the dust charge, Td is the dust thermal energy.
When
, the dust is strongly coupled and this condition is met in
several laboratory dusty plasmas, such as dust “plasma crystals”. A dusty
plasma is considered as a weakly coupled as long as
[2].
1.3.5 Characteristic frequencies
A dusty plasma is macroscopically neutral, Like the usual electron-ion
plasma. The disturbance of such a plasma from its equilibrium position can
result in collective particle motions and hence can lead to the built up of an
internal space charge field. This internal space charge field in turn will then
try to restore the original space charge neutrality but due to inertia, there will
be a collective oscillation of plasma particles around their equilibrium
positions. These collective oscillations are characterized by the frequency of
oscillation
known as the plasma frequency. In order to derive an
expression for the plasma frequency, the continuity equation, momentum
equation and poison‟s equation for the electrons, ions and dust particles shall
be taken into account. Linearization and simplification these equations results
10
CHAPTER ONE
INTRODUCTION
in the following expression for the plasma frequency associated with species
z[1]:
∑
∑
Where z = e for electrons, for ions and d for the dust .This can be
understood in the following fashion. For the purpose of understanding, over
attention is focused to the electron motion only. In this case, the internal
space charge field (which is build up when the plasma particles are displaced
from their equilibrium position) will try to attract electrons back to their
equilibrium positions but due to inertia, the electrons will overshoot and
move to the other extreme and will again be pulled back by the space charge
field of opposite polarity. In this way, the electrons will continuously
oscillate around their original positions with a frequency
called the
electron plasma frequency. A similar analogy can be true for ions and dust
particles and they will oscillate around their equilibrium positions with ion
plasma frequency
and dust plasma frequency
respectively. Since the
frequency of such oscillations depends on mass, charge and number density
of plasma particles, it is different for the electrons, ions and dust grains [7].
The electrons oscillate around ions with the electron plasma frequency
⁄
⁄
, ions oscillate around the charged dust grains with the ion
⁄
plasma frequency
⁄
and dust particles oscillate around
their equilibrium positions with the dust plasma frequency
⁄
⁄
.
In partially or low ionized plasma when there is a significant number
of neutral particles present inside the plasma, the collisions is encountered
11
CHAPTER ONE
INTRODUCTION
frequent between plasma particles (electrons, ions and dust grains) and
neutrals. These collisions can be characterized by collision frequencies.
There are three types of collision frequencies known as electron-neutral
collision frequency
collision frequency
frequency
, ion-neutral collision frequency
and dust-neutral
respectively. The general expression for collision
for scattering of plasma species z by the neutrals can be written
as [12]
Where
cross section and
the number density of neutral particles,
√
is the scattering
is the thermal speed of the species z.
1.4 Dust charging mechanisms
The dust charge is an important property of dust grains since it affects
the particle dynamics. The main point in dealing with the study of dusty
plasmas is the understanding of the charging of dust grains once they are
immersed/ introduced into the ordinary electron-ion plasmas. There are many
elementary processes like the collection of plasma particles, photoemission
and thermionic emission…etc. which can lead to the charging of grains.
These processes could be quite complex and mainly depend on the
environment around the dust grain itself. Assuming that the particles that are
formed in the plasma from monomers or externally added are initially
neutral, and then there exist different mechanisms for charging. They are:
1.4.1 Collection of plasma particles
When a particle of solid matter is immersed in a plasma, it acquires an
electric charge. The plasma particles (electrons and ions) start impinging on
12
CHAPTER ONE
INTRODUCTION
the surface of these newly introduced dust particles and some of them get
collected on the dust grain surface. As the electrons possess much higher
thermal velocities as compared to ions and therefore, the electrons will reach
the dust grain surface much earlier than the ions this will make the dust grain
charge and its surface potential negative [13]. On the other hand, the
collections of positively charged ions tend to make the dust grain charge and
its surface potential positive. These electron and ion currents are also affected
by the grain surface potential. When the grain surface potential is negative, it
starts repelling the electrons and attracting the ions. In other words, the
current carried by the electrons is reduced while the current carried by the
ions is increased and vice versa [12]. The charge on a grain of solid matter
immersed in a plasma is an unknown parameter, which depends on the size
of the particle and the plasma conditions. The charge is not a constant, but
can fluctuate randomly, or in response to fluctuations in plasma parameters
such as the electron density [14].
1.4.2 Secondary electron emission
The electrons and ions bombarding the dust particle can have an
additional effect if they are very energetic. They can lead to the secondary
electron emission by ionizing the dust particle material and ejecting electrons
from it, the dust grain acquires positive charge. The probability for secondary
electron emission depends on the energy of the bombarding particles as well
as on the secondary electron yield
(the average number of electrons emitted
per incident ion), which in turn depends on the work function W [11].the
electron and ion impact can be explained in detail as following
13
CHAPTER ONE
INTRODUCTION
 Electron impact
In case of electrons, secondary electron emission is a phenomenon that
occurs when electrons impact on a dust grain surface with sufficient energy
to „knock‟ additional electrons from the surface of that grain. This electron
outflow can be considered as positive current onto the particle. Generally,
one electron gives rise to several secondary electrons. When the electron
strikes the dust grain surface, several things can happen: An electron may be
scattered or reflected by the dust grain surface without penetration. It may be
stopped and stick at the grain surface. If the electron penetrates the dust grain
surface, it may excite other electrons which may then be emitted at the
surface. Some electrons may pass through the grain and leave with a little
loss of energy [7]. For plastic materials similar to the grains used in most of
the experiments, high electron and ion energies are necessary for producing
secondaries, and thus the contribution of the secondary electron emission to
the particle charging is small (negligible) [12].
 Ion impact
The electron secondary emission can also be produced by ion
bombardment. When the low energy ions are incident on a dust grain surface,
these ions may become neutralized by the electrons tunneling from within the
grain across the potential barrier [7, 12].
The energy released in this process may excite additional electrons
which can then be emitted from the dust grain surface. The number of excited
electrons depends on the available potential energy (after neutralization)
which is determined by the ionization potential energy Wi and the work
function Wf of the dust grain material. When a conduction electron is
captured by the incident ion, it makes available a maximum energy of
14
CHAPTER ONE
INTRODUCTION
Wi − Wf. At least Wf of this must be used to free another electron from the
material so that the condition for the secondary emission is Wi > 2Wf [1].
1.4.3 Photo-detachment
When photons with energies above the work function interact with the
dust, electrons can be removed through the effect of photo-detachment. Many
plasmas in space are exposed to intense ultraviolet radiation, for instance
plasmas around young stars, and also the dusty plasma in the ionosphere. In
fusion reactors there can also be significant UV fluxes. Plasma itself can also
emit UV radiation, even though the intensity is relatively weak, however,
commercially available UV sources are abundant, which could provide an
interesting tool to control dust charge in laboratory dusty plasmas [13].
Absorption of UV radiation releases photoelectrons; hence it causes a
positive charging current. Just like secondary electron emission, it can make
the particle positively charged. The electron emission depends on the
material properties of the particle (its photoemission efficiency). It also
depends on the particle‟s surface potential, because a positively charged
particle can recapture a fraction of its photoelectrons [14].
a
b
c
Figure (1.5): Charging of dust particles in a dusty plasma takes place mainly by (a)
collection of plasma particles,(b) photoemission and (c) secondary electron emission[12].
15
CHAPTER ONE
INTRODUCTION
1.4.4 Thermionic emission
One of the important charging processes which charge up the dust
grains positively is thermionic emission [1]. When a dust grain is heated to a
high temperature, for instance by recombination of the collected charged
plasma particles, the electrons and ions collected on the surface gain thermal
energy. When this energy becomes larger than the binding energy, the
collected particles can be emitted into the plasma. For the negatively charged
particles this is most likely for the electrons, due to the repelling potential
[13]. Electrons or ions may be thermionically emitted from the dust grain
surface. The thermionic emission may be induced by laser heating or by
thermal infrared (IR) heating or by hot filaments surrounding the dust grain
[1]. In this work, the electrons and ions is low thermal energy, which
collected on the surface gain. Therefore, thermionic emission is not included
here.
1.4.5 Field emission
Charged particles can be emitted from a surface when the local
electric field is high enough. Assume a spherical particle with radius a and a
surface charge density
then given by
charges is given by
is had. The electric field at the surface is
, and the electrostatic pressure on the surface
, which acts outwards, against the forces
binding the charges onto the surface.
For metal tip field emitters, such as used in field emission
microscopes, it can be as large as 1-10 V nm-1. Such strong fields then require
sharp points or edges, which locally enhance the macroscopic field [13].
However, in this thesis results of particles are only presented which are
assumed to be perfectly spherical, so that field emission plays no role. In
16
CHAPTER ONE
INTRODUCTION
many experiments, specially fabricated dust particles are used, which are
spherical, or have other pre-defined shapes, but are typically very smooth. Insitu grown particles can have a different shape, for instance fractal-like. In
that case, field emission might play an important role also, for the smaller
particles. It results in a reduction of the number of electrons carried by the
dust.
1.5 Production of Dusty Plasmas
To produce/confine dusty plasmas in laboratories, a number of
techniques have been developed in the last few years. Explanation of some
techniques/methods was done below:
1.5.1 Modified Q-machine
A simple device for producing dusty plasmas is a dusty plasma device
(DPD), which is a single-ended Q-machine modified to allow the dispersal of
dust grains over a portion of the cylindrical plasma column in which a
potassium plasma column of ~ 6 cm diameter and ~ 1 m long is produced by
surface ionization of potassium atoms from an atomic beam oven. The atoms
are ionized on a tantalum surface which is heated by electron bombardment
to a temperature of 2300 K0. For this The surface will be hot enough to emit
large amounts of thermionic electrons which, together with the K+ ions . The
plasma is radially confined by a longitudinal magnetic field of 0.3 T. The
electrons and ions have roughly the same temperature of 0.2 eV at a density
of 1010 cm−3 [15, 16]. The main diagnostic is a planar (2 mm diameter disk)
Langmuir probe with its surface normal parallel to the magnetic field. Dust
grains can be dispersed into a portion of the plasma column using a rotating
cylinder described in detail by Xu et al [15] the rotating cylinder surrounds a
17
CHAPTER ONE
INTRODUCTION
30 cm portion of the plasma column and is lined with aluminum wool into
which dust particles are embedded. As the cylinder rotates around the
plasma, dust grains fall through the plasma where they are charged by
collection of electrons and ions, A schematic illustration of a DPD is shown
in figure (1.6).
Figure (1.6): Schematic of the negative ion dusty plasma device [17].
The dust grains were hollow glass microspheres with a relatively broad
size distribution, with the majority if particles having a diameter of
approximately 35 µm.
A plasma containing negative ions was produced by leaking into the
vacuum chamber the highly electronegative gas sulfur hexafluoride SF6 at
partial pressures in the range of 10−6−10−3 Torr. The sulfur hexafluoride gas
is admitted into the vacuum chamber through a variable leak valve. The
attachment efficiency depends on the electron energy and is most pronounced
18
CHAPTER ONE
INTRODUCTION
for electrons with energies in the range of a few tenths of an eV, which
coincides quite well with the electrons in the Q machine plasma.
At higher electron energies, dissociation of the SF6 molecule becomes
increasingly likely, leading to the formation of additional negative ion
species such as
and F−. For this reason the Q machine is an ideal device
in which to form negative ion plasmas. In fact, it is possible to produce a
negative ion plasma in which the electron concentration relative to the
positive ions, ne/n+, is so small that the positive ion/negative ion plasma is
had essentially [17].
1.5.2 DC Discharges
Dusty plasmas are produced by suspending micron-sized dust particles
in a stratum of a dc neon glow discharge(Fortov et al 1997) .The discharge is
formed in a cylindrical glass tube with cold electrodes. A 3 cm inner
diameter and 60 cm long glass tube is positioned vertically. The electrodes
are separated by 40 cm. The discharge current is varied from 0.4 to 2.5 mA,
the pressure of neon is varied from 0.2 to 1 Torr. These conditions allow the
formation of the natural standing strata in between two electrodes as shown
in figure (1.7). A few grams of micron-sized particles are placed in a dust
dropper in the upper side of the glass tube. The falling grains are trapped and
suspended in the strata where the gravitational force
acceleration due to gravity and
(g is the
is the electric field in the strata) [1, 18].
19
CHAPTER ONE
INTRODUCTION
Figure (1.7): Schematic illustration of how dusty plasmas are produced in strata of a dc
neon glow discharge (after Fortov et al 1997)[1].
1.5.3 RF Discharges
Radio-frequency (RF) discharges between parallel electrodes are the
main tool of dusty plasma research because RF discharges easily tolerate
impurities and they are also used in plasma processing where dustcontamination occurs. RF discharges for dusty plasma research are typically
operated at 13.56 MHz at relatively low RF powers (usually <10 W) and gas
pressures in the range between 1 and 100 Pa. The general setup for dust
experiments in RF parallel plate discharges is shown in Fig. (1.8a).
A discharge is operated between the parallel electrodes, usually the
lower is RF powered and the upper is grounded. Often, the upper electrode
20
CHAPTER ONE
INTRODUCTION
has openings or is transparent to have optical access from top. The dust
grains are then dropped into the discharge using dust containers with tiny
holes. Typical dust for basic research consists of spherical plastic grains of
well-defined diameter in the micrometer range (see Figure 1.8b). For
micrometer particles, the dominant forces are the electric field force and
gravity.
A force balance is achieved in the plasma sheath above the lower
electrode where the electric field is strong enough to levitate the grains
against their weight. Since the electric field is increasing towards the
electrode the force balance is fulfilled at a unique vertical position and the
grains are confined in an effective vertical potential well (Figure 1.8c) [14].
Figure (1.8): a) Scheme of the experimental setup in a typical experiment on complex
plasmas. The particles are illuminated by vertical and horizontal laser sheets. The particle
motion is recorded from top and from the side with video cameras. b) Electron micrograph
of the melamine-formaldehyde (MF) particles typically used in the experiments. c)
Trapping of the particles in the sheath of an rf discharge [14].
21
CHAPTER ONE
INTRODUCTION
1.6 Literature review
The increased interest in dusty plasmas was due to two major discoveries in
very different areas: (1) the discovery by the Voyager 2 spacecraft in 1980 of
the radial spokes in Saturn‟s B ring, and (2) the discovery in the early 80‟s of
the dust contamination problem in semiconductor plasma processing devices.
1. Wenjun Xu et al [15] described a rotating-drum dust-dispersal device,
which thy have used, in conjunction with an existing Q machine, to
produce extended, steady state, magnetized plasma columns. The dusty
plasma device (DPD) is to be used for the investigation of waves in
dusty plasmas and of other plasma/dust aspects in 1992.
2. Chunshi Cui et al [19] studied theoretically fluctuation of charge on a
dust grain in a plasma in 1994.
3. A .Braken et al [20] investigated experimentally charging of micronsized dust grains in a plasma. Dust grains were dispersed into a fully
ionized, steady-state, magnetized plasma column consisting of
electrons and K+ ions, both at a temperature of≈0.2 eV in 1994.
4. S. J. Choi, and m. j. Kushner [21] reported on Pseudoparticle-in-Cell
(PIC)Simulation of Dust Charging and Shielding in low pressure Glow
Discharges in1994.
5. Y. N. Nejoh [5] investigated the effects of the dust charge fluctuation
and ion temperature on large amplitude ion-acoustic waves in a plasma
with a finite population of negatively charged dust particles by
numerical calculation in 1997.
6. E. Thomas and M. Watson [22] used The Fisk Plasma Source (FPS) is
a plasma device operating at Fisk University Dusty plasmas in the FPS
device are produced by suspending 40 µm diameter silica (SiO2)
particles in an argon dc glow discharge plasma. They measured the
22
CHAPTER ONE
INTRODUCTION
charging of silica particles and showed that the dust particles become
negatively charged with up 105 electrons in 2000.
7. Samarian et al [9] observed experimentally the trapping of dust
particles in a dc abnormal glow discharge dominated by electron
attachment. A dust cloud of several tens of positively charged particles
was found to form in the anode sheath region. An analysis of the
experimental conditions revealed that these particles were positively
charged due to emission process, in contrast to most other experiments
on the levitation of dust particles in gas-discharge plasmas where
negatively charged particles are found. They take into account the
processes of photoelectron and secondary electron emission from the
particle surface in 2001.
8. S. I. Popel et al [23] considered the nonstationary problem of the
evolution of perturbation and its transformation into nonlinear wave
structure in dusty plasmas .They based on a set of fluid equations,
Poisson‟s equation, and developed a charging equation for dust For
this purpose two one-dimensional models in 2001.
9. Konstantin Ostrikov et al [24] studied accounting for the background
density variation associated with electron capture and release by the
dust grains. They showed that if the dust charge and density are
sufficiently high, the effect of the background electron density
variation on dust-charge relaxation is important. The equilibrium dust
charge and its rate of variation are obtained for dusty plasmas subject
to strong UV irradiation. The latter releases photoelectrons from the
dust surface and can significantly affect the equilibrium dust charge,
its variation rate, as well as the overall charge neutrality in the plasma
in 2001.
23
CHAPTER ONE
INTRODUCTION
10.In 2003, Mamun and Shukla[25] examined the role of negative ions on
the charging of dust grains in plasma. They considered two models for
negative ion distributions, the first is streaming negative ions, and the
second is Boltzmannian negative ions.
11.M. K. Islama and Y. Nakashima[26] improved estimation in dust grain
charging current in the retarding field is presented in the case of
streaming dusty plasmas, where the particles streaming velocity is
much larger than their thermal velocity in 2003.
12.Barbara Atamaniuk and Krzysztof Zuchowski[27] considered the
influence of dust charge fluctuations on damping of the dust-ionacoustic waves. They considered Fluid approximation of longitudinal
electrostatic waves in unmagnetized plasmas, and they showed that for
a weak acoustic wave the attenuation depends on a phenomenological
charging coefficient in 2003.
13.In 2005, A.G. Zagorodny[28] developed the kinetic theory of
electromagnetic fluctuations in dusty plasmas on the basis of the
microscopic description of the grain charging dynamics. The main
difference of such a theory from that formulated with the use of a
phenomenological assumption is that the effective charging crosssections are replaced by the k-dependent quantities describing the
electron and ion absorption by grains with regard for the influence of a
plasma inhomogeneity on the fluxes of absorbing particles.
14.Muhammad Shafiq[7] reported analytical results for the electrostatic
response to a test charge moving through dusty plasma in his licentiate
thesis. Two particular cases for a slowly moving test charge, namely,
grain size distribution and grain charging dynamics are considered.
Analytical results for the delayed shielding of a test charge due to
24
CHAPTER ONE
INTRODUCTION
dynamical grain charging in dusty plasma are also reported. In the first
case, he considered a dusty plasma in thermal equilibrium and with a
distribution of grain sizes. In the second case, he presents an analytical
model for the shielding of a slowly moving test charge in a dusty
plasma with dynamical grain charging for the both cases with and
without the collision effects in2005.
15.Muhammad Shafiq reported analytical and numerical results for the
electrostatic response to a test charge moving through dusty plasma in
his doctoral thesis in 2006[12].
16.Su-Hyun Kim and Robert L. Merlino[16] investigated experimentally
charging of dust grains in a plasma with negative ions. When the
relatively mobile electrons are attached to heavy negative ions, their
tendency to charge the grains negatively is reduced. The grain charge
can be reduced in magnitude nearly to zero (“decharging” or charge
neutralization) in 2006.
17.Su-Hyun Kim and Robert L. Merlino[17] investigated experimentally
the effect of negative ions on the charging of dust particles in a
plasma. A plasma containing a very low percentage of electrons is
formed in a single-ended Q machine when SF6 is admitted into the
vacuum system. The relatively cold Q machine electrons (Te≈0.2 eV)
readily attach to SF6 molecules to form
negative ions.
Calculations of the dust charge indicate that for electrons, negative
ions, and positive ions of comparable temperatures, the charge of the
dust can be positive if the positive ion mass is smaller than the
negative ion mass and if the ratio of the electron to positive ion
density, is sufficiently small in 2006.
25
CHAPTER ONE
INTRODUCTION
18. Robert L. Merlino[18] studied a dusty plasma is an ionized gas
containing dust particles, with sizes ranging from tens of nanometers
to hundreds of microns. The interaction of the dust particles with the
plasma and ambient environment results in a charging of the dust
grains ,and reported applications of dusty plasmas in space, industry
and the laboratory in 2006.
19.S.A. Maiorov et al [29] numerically investigated various kinetic
characteristics of micron-sized dust grains in plasmas of gas discharge.
They considered two-temperature stationary and moving plasma. For
the simulation, they employed particle-in cell (PIC) method when a
heavy macroparticle is placed in the center of the simulation Box and
Newton equations are solved for the system involving also plasma
particles. They simulated the process of charging of grain absorbing all
electrons and ions colliding with its surface characteristics of the
transitional and stationary regimes in 2007.
20.In 2007, K. Matyash et al [30] newly developed 3-dimensional
Particle-Particle Particle-Mesh (P3M) code is applied to study the
charging process of micrometer size dust grains confined in a
capacitive RF discharge. In their plasma model, plasma particles
(electrons and ions) are treated kinetically (Particle-in-Cell with Monte
Carlo Collisions (PIC-MCC)), which allows to self-consistently
resolve the electrostatic sheath in front of a wall.
21.I. Goertz et al [31] studied experimentally ion acoustic waves in
plasmas containing dust or negative ions in 2007.
22.V.R.Ikkurthi et al [32] computed dust charge and potential on static
spherical dust grains located in argon rf discharge using a threedimensional particle-particle-particle mesh code in 2008.
26
CHAPTER ONE
INTRODUCTION
23.Erica K. Snipes[10] investigated experimentally thermal effects in the
dispersion relations for a vertically propagating dust acoustic wave in a
dc glow discharge dusty plasma. It was found that, the dust has a
temperature that is well above the room temperature in 2009.
24.F. X. Bronold et al [33] proposed a surface model for the charge of a
dust particle in a quiescent plasma which combines the microscopic
physics at the grain boundary (sticking into and desorption from
external surface states) with the macrophysics of the discharge (plasma
collection fluxes). Within this model the charge and partial screening
of the particle can be calculated without relying on the condition that
the total electron collection flux balances on the grain surface the total
ion collection flux in 2009.
25.S. Ali [34] investigated theoretically and numerically the modification
in the Debye–Huckel and wake potentials due to the effects of dust
relaxation rate, dust absorption frequency, dust grain radius, and
negative ion temperature, and employed fluid equations to obtain the
dielectric constant of the dust-negative-ion acoustic wave involving
the negative ions and dust charge fluctuation effects in 2009.
26.S. S. Duha [35] investigated theoretically dust negative ion acoustic
shock waves in a dusty multi-ion plasma with positive dust charging
current by employing the reductive perturbation method in 2009.
27.S. Ratynskaia et al [36]carried out laboratory experiment where
submicron dust was produced in a gas phase and diagnosed by surface
analysis of samples and by measurements of its influence on the
plasma density fluctuation spectra. Quantitative comparison of the
latter with the theory yields information on dust density, size, and
27
CHAPTER ONE
INTRODUCTION
distribution in agreement with the results of the surface analysis in
2010.
28.S. S. Duha et al [37] investigated theoretically nonlinear dust-ionacoustic waves in a multi-ion plasma with trapped electrons in 2011.
1. 7 Aim of the work
This work aims to study charging process of dust grain immersed in
negative ions plasma by computing simulation and reveals the effect of
negative ions concentration on the magnitude of the dust charge is reduced
and a transition to positively charged dust and phase speed dust-negative ion
acoustic wave in dust plasma with negative ion .
It also reveals the fluctuation of the charge on the surface of grain and
other related calculations.
28
CHAPTER TWO
THEORETICAL BACKGROUND
2.1 Introduction
When dust grains are immersed in a gaseous plasma, the plasma
particles (electrons and ions) are collected by the dust grains which act as
probes. The dust grains are therefore, charged by the collection of the plasma
particles falling onto their surfaces. Since ions are much heavier than
electrons, initially the ion current (Ii) is much smaller than the electron
current (Ie), and the dust grain becomes negatively charged. This increases
| | and decreases | | until| |
| | .
When energetic plasma particles (electrons or ions) are incident onto a
dust grain surface, they are either backscattered/reflected by the dust grain or
they pass through the dust grain material. During their passage, they may lose
their energy partially or fully. A portion of the lost energy can go into
exciting other electrons that in turn may escape from the material. The
emitted electrons are known as secondary electrons. The release of these
secondary electrons from the dust grain tends to make the grain surface
positive.
The interaction of photons incident onto the dust grain surface causes
photoemission of electrons from the dust grain surface. The dust grains,
which emit photoelectrons, may become positively charged. The emitted
electrons collide with other dust grains and are captured by some of these
grains which may become negatively charged [1, 25].
The charging of dust grains in a plasma consisting of positive ions,
negative ions and electrons. In typical laboratory plasmas containing
electrons and positive ions, dust grains acquire a negative charge. In negative
ion plasmas, charging due to the negative ions, in addition to positive ions
and electrons, must be taken into account.
29
CHAPTER TWO
THEORETICAL BACKGROUND
A number of theoretical and experimental investigations have carried
out for understanding the charging of dust grains in a plasma under different
conditions [25].
2.2 Orbital-motion limited theory
Most theories for predicting the charge of a dust grain in a plasma
were originally developed to model electrostatic probes in plasmas. A dust
grain is just a solid object immersed in plasma. One can view the dust
particle as essentially a small probe, except that the dust grain has no wires
connected to it. The starting point of these theories is a prediction of the
electron and ion currents to the probe. The currents are termed “orbitlimited” when the condition a ≪ D ≪ mfp applies, where a is the particle
radius, D is Debye length, and ¸mfp is a collisional mean-free-path between
neutral gas atoms and either electrons or ions. In that case, the currents are
calculated by assuming that the electrons and ions are collected if their
collisionless orbits intersect the probe’s surface [14, 38].
In this work the charging of dust is investigated in plasma consisting
of positive ions, electrons and negative ions (this plasma is called a negative
ion plasma).
a. The dust grain charge:Consider an isolated spherical dust grain of radius a introduced into a
plasma consisting of electrons of density ne, singly charged positive ions of
density n+, and singly charged negative ions of density n−. Define
30
CHAPTER TWO
THEORETICAL BACKGROUND
…………………….. (2.1)
As the fraction of negative ions relative to positive ions. Using the
charge neutrality condition [16]
………………… (2.2)
We have that
………………………… (2.3)
Analytic models including the OML model typically assume that the
particle is spherical, and its surface is an equipotential. In this case, even if
the particle is not made of a conductive material, it can be modeled as a
capacitor [14]. The charge
is then related to the particle’s surface
potential as, with respect to a plasma potential of zero, by
……………………………… (2.4)
Where a is the radius of the dust particle, and s is the dust grain
surface potential relative to the plasma potential. [17].
b. Currents to the dust grain:For the collection of Maxwellian electrons and ions, characterized by
temperatures Te and Ti, the orbit-limited the electron and positive ion
currents to the isolated spherical dust grain of radius (a) are given by [16]:
{
…….. (2.5)
31
CHAPTER TWO
THEORETICAL BACKGROUND
{
……. (2.6)
The negative ion current participates in the charging of a dust grain in a
plasma is [25]:
{
……. (2.7)
The intial currents Ie0 , I-o and I+0 represent the current that is collected
for s = 0, and are given by[16]
(
)
The temperatures of the positive ions, electrons and negative ions are
T+, Te and T-, respectively. nj is the number density of plasma species j(the
positive ions, electrons and negative ions) [16]. The grain surface potential is
then obtained by requiring this condition [17]:-
2.3 Particle charging
A grain of solid matter acquires an electric charge, if it is immersed in
plasma. This charge is in many cases, the reason that the particle is
interesting. It is therefore of great interest to know how large the charge is.
Ordinary plasmas consisting of only electrons and ions are
complicated enough, but at least a physicist can trust that the charge of the
constituents is known. For a dusty plasma, one cannot trust even that. In
32
CHAPTER TWO
THEORETICAL BACKGROUND
general, the charge on a particle of solid matter immersed in a plasma is an
unknown parameter, which depends on the size of the particle and the plasma
conditions. The charge is not a constant, but can fluctuate randomly, or in
response to fluctuations in plasma parameters such as the electron density.
To estimate the charge of a grain, there are several theoretical models
and some experimental methods as well. In general, none of them yields a
result with perfect precision. Here the theoretical models of charging will be
considered, which in general are useful for estimating the charge with an
accuracy of about a factor of two. These models will also be useful for
gaining a conceptual understanding of how the charge varies with plasma
parameters, and how it can vary in time [14]. There are some models, often
implemented numerically to calculate the charge and potential of grain in a
plasma, as described below.
2.3.1 Continuous Charging Model
A dust grain with zero charge that is immersed in plasma will
gradually charge up, by collecting electron and ions currents, according
to[19]
∑
The currents are continuous quantities, and the dust particle’s charge
Qd is allowed to vary smoothly, rather than in integer multiples of the
electronic charge. To find the equilibrium, one can set
in Eq. (2.10).
This yields the steady-state potential fl and steady-state charge 〈
〈
〈
〉
〉⁄
33
〉.
CHAPTER TWO
THEORETICAL BACKGROUND
Where the coefficients
and
are functions of Ti/Te and mi/me, and
the ion flow velocity, and they must be determined numerically. Useful
values for these coefficients are listed in table 2.1 for cases with no ion flow.
The charging time  indicates how rapidly a particle’s charge can
vary, when plasma conditions vary. One way of defining a charging time is
the ratio of the equilibrium charge and one of the currents, electron or ion,
collected during equilibrium conditions. Another definition assumes that
hypothetically the particle has no charge and is suddenly immersed in a
plasma with conditions that remain steady, so that the grain’s charge
gradually varies from zero toward its equilibrium value; in this case the
charging time has been defined as the time required for a grain’s charge to
reach a fraction (
) of its equilibrium value. The charging time varies
inversely with plasma density and grain size, according to [14]
√
Where for a non-drifting plasma K is a function of Ti/Te and mi/me.
The fact that  is inversely proportional to both a and ni means that the fastest
charging occurs for large particles and high plasma densities [14]. Values of
the constant K are summarized in table 2.1.
Table (2 .1): Coefficients for fl , Q and  appearing in Equations (2.11), (2.12) and
(2.13). These values were found by a numerical solution of the continuous charging
model, assuming non-drifting Maxwellians and no electron emission [19].
Ti/Te
0.05
1
0.05
1
34
CHAPTER TWO
THEORETICAL BACKGROUND
2.1.2 Discrete Charging Model
Continuous charging model neglects the fact that the electron and ion
currents collected by the grain actually consist of individual electrons and
ions. Therefore a charging model developed that includes the effect of
discrete charges. The charge on the grain is an integer multiple of the
electron charge, Qd = Ne, where N changes by -1 when an electron is
collected and by zi when an ion is absorbed. Electrons and ions arrive at the
particle’s surface at random times, like shot noise. The charge on a particle
will fluctuate in discrete steps (and at random times) about the steady-state
value〈
〉 [14, 21].
There are two key aspects of the collection of discrete of plasma
particles (the term “plasma particle” is to refer to either electron or ions).
 First is that the time interval between the absorption of plasma
particles varies randomly.
 Second is that the sequence in which electrons and ions arrive at the
grain surface is random.
But neither of these is purely random; they obey probabilities that depend on
the grain potential s.
Let us define pe(s) and pi(s) as the probability per unit time for
absorbing an electron or ion, respectively. As the grain potential becomes
more positive, more ions will be repelled and more electrons will be attracted
to the grain, so pi should decrease with s and pe should increase.
pj(s) (j refers to the ions, electrons) is calculated from the OML
currents Ij(s),
35
CHAPTER TWO
THEORETICAL BACKGROUND
This equation is the key to developing the discrete charging model.
Basically, it converts the OML currents into probabilities per unit time of
collecting particles. This relates the discrete charging model with its
probabilities to the continuous charging model with its currents.
The total probability per unit time of collecting plasma particle is [19]
∑
The currents Ij depend on the grain surface potentials, so ptot also
depends on s and hence on charge Qd.
This assumption retains an important part, but not all, of the physics
arising from the discreteness of the charge carriers. The discrete nature of an
electron or ion is recognized when it is absorbed from the plasma by the
grain, but not when it remains in the Debye sheath surrounding the grain.
This is equivalent to treating the plasma with a continuum model that is
characterized by the currents, Ij [19].
2.4 The Dust-Negative Ion Acoustic Wave
A dusty multi-ion plasma system consisting of electrons, light positive
ions, negative ions, and extremely massive (few micron size) charge
fluctuating stationary dust have been considered. The electrostatic waves
associated with negative ion dynamics and dust grain charge fluctuation. The
equilibrium state of the dusty multi-ion plasma system under consideration is
defined as [35]:
⁄
Where
is the dust grain charge at equilibrium. When electron and
ion currents at equilibrium, it is noted here that in order to have a nonzero
36
CHAPTER TWO
THEORETICAL BACKGROUND
, | |⁄
negative ion current, i.e.,
⁄
it must be had which reduces to
,where[37]
√
In which
|
|
√
,
⁄
,
⁄
,
and
. The linear dispersion relation for the ion acoustic waves
associated with negative ions, which are significantly modified by the
presence of the charge fluctuating stationary dust is [37]
Where
mn
is
the
,
negative
,
| |
, T- is the negative ion thermal energy,
ion
mass,
,
,
,
,
[35]. If no dust (ηd=0) and cold negative
, and
ion (T-=0) limits, the phase speed of this wave is equal to[37]
√
⁄
This means that the DNIA (Dust-Negative Ion Acoustic) waves are
associated with dynamics of negative ions, where the inertia comes from the
mass of the negative ions and restoring force is provided by the thermal
pressures of electrons and light ions [37].
37
CHAPTER THREE
3.1
SIMULATION AND RESULTS
Introduction
In recent years computer simulations are playing an important role in
theoretical investigations in various branches of human activities. Similarly is
the situation in the research of dusty plasma that is interesting not only for
astronomers (interstellar clouds, comet tails etc.) but also in for finding the
place the complicated technological processes like powder modification,
plasma etching of semiconductor devices and plasma diagnostic. The
understanding of processes like charging and dynamics of dusty particles is
necessary for the effective development of technological devices.
In this work, the discrete charging module have been employed in
order to simulate the dust charge on spherical dust grains in plasma
consisting of positive ions (K+ potassium ions), electrons and negative ions
(
sulfur hexafluoride ions), for this plasma is called a negative ion
plasma.
The computation of dust charges dates back to earliest probe theories,
Probe theories calculate the current to an electrostatic probe as a function of
probe potential and probe shape. The floating potential is derived as the point
where ion and electron currents balance. First probe theories based on orbit
motion limited (OML). Later, Probe theory has been applied to dust
charging.
38
CHAPTER THREE
SIMULATION AND RESULTS
3.2 The Phenomenon modeling
This model of charging is considered to be the development for
discrete model that includes the effect of negative ion on the charging
process of dust grain in a plasma negative ion instead of plasma electron-ion.
The model will be useful for gaining a conceptual understanding of how the
charge varies with plasma negative ion parameters, and how it can vary in
time, which in general is useful for estimating the charge of dust grain.
The model has described the charging process of an isolated dust grain
immersed in a negative ion plasma and assumed a spherical grain with radius
a which initially uncharged under the condition
the particle radius,
is Debye length, and ¸
, where a is
is a collisional mean-free-
path between neutral gas atoms and either electrons or ions In this case. The
charging process is characterized by:
1. It is based on the assumption that the plasma particles arrive to grain
surface at random time intervals
, which is not fixed
2. The probabilities of arriving electrons or ions (negative or positive) in
equations (2.14) depend on the surface potential of the dust grain.
3. The total probability per unit time of collecting plasma particle is
calculated from equation (2.15)
4. The time interval
depends on the potential of the grain
and the
random number R1 that we generated.
5. The model assumes that plasma particles (electron, positive ion, or
negative ion) arrive in a random sequence in consistent with the
probabilities.
39
CHAPTER THREE
SIMULATION AND RESULTS
6. To recognize the plasma particle type electron or ion (negative or
positive), it must compare the probability
with another random
number R2.
7. The charge
of the dust grain would be changed after each electron or
ion (negative or positive) collection, and it is increased or decreased by
one charge.
3.3
The Simulation
Our simulation converts the physical discrete charging model to
program which simulates the charging process of a dust grain immersed in
plasma with negative ion.
At first the dust grain would be uncharged so the experiment starts
with a zero charge
at a time step equal zero
where j refers to
plasma particle electron, negative ion or positive ion, then the two steps will
be repeated for plasma particles which will fall on the grain.
A. First Step: Choose a Random Time Interval
This step is based on the physical discrete charging model, which
assumes that the plasma particles arrive at random time intervals, there will
be one time step per particle that is collected and it corresponds to:
………………………………….. (3-1)
The currents
must be calculated from equations (2-5, 2-6,
and 2-7) that are predicted by the OML theory to find the probabilities.
40
CHAPTER THREE
SIMULATION AND RESULTS
The random time step
collecting a plasma particle
depends on the probability per unit time of
,
,
and the total probability
is given in equation (2-15).
The probability of collecting a plasma particle is [19]:
……………………….. (3-2)
To calculate the random time interval one must generate a random
number R1 where
and equate it to the previous equation of
probability to yield [19]:
……………………….. (3-3)
B. Second Step: Choose Electron, Negative ion or Positive ion
The plasma particle arrives in a random sequence. Generate a random
number R2 to determine whether the next collected particle is an electron or
an ion (negative or positive), where
.
Probability that the next particle is electron, negative ion or positive
ion will be
i.
If
and compared with R2 as follows:
then, the charge will be
process is electron collection. However, at state
that means the
that means
process isn’t electron collection. The probability of other particle must be
examined.
ii.
If
then, the charge will be
the process is negative ion collection.
41
that means
CHAPTER THREE
iii.
If
SIMULATION AND RESULTS
then, the charge will be
that means
the process is positive ion collection.
3.4
The program of model
The model was translated to a numerical calculation by using
computer programs. The program has been written with FORTRAN
programming language to simulate computer experiment of the charging
process for a dust grain in negative ion plasma. the discrete charging model is
employed in this simulation to calculate statistical fluctuations such as the
time distribution of a dust charge, number charge equilibrium and charging
time for different value of
(ratio of number density of electron to number
density of positive ion) and different grains size, and also the phase velocity
negative ion dust acoustic wave has been calculated for different value of
(ratio of number density of negative ion to number density of positive
ion). The flow chart of program is illustrated in figure (3.1)
42
CHAPTER THREE
SIMULATION AND RESULTS
Start
tj=0,Qj=0
Calculate j,
Random no.R1,
Calculate p,
Calculate ∆tj,
Calculate Ie, I-, I+
Random no.R2
Kind of
particle
Electron
Negative ion
No
Done for
enough time
Positive ion
Yes
Calculate fluctuations Q(t)
Calculate fluctuations statistics
Calculate the phase speed DNIA wave
Stop
Figure (3.1): Flow chart of the program
43
CHAPTER THREE
SIMULATION AND RESULTS
3.4.1 The Program Input Data
The results of program are computed from the electron, positive ion
and negative ion currents from the orbital motion limited theory from
equations (2.5), (2.6) and (2.7) in chapter two, and electric potential of dust
particle from equation (2.4). For all these calculations the input data are:
1. Positive ions (K+ potassium ions) mass m+= 39 amu, negative ions
(
sulfur hexafluoride ions) mass m-= 146 amu.
2. The electron temperature (Te), negative ion temperature (T-), and positive
ion temperature (T+) equal to 0.2 eV.
3. The number density of the plasma n=1016 m-3.
4. The number density of the grain nd=103 m-3.
5. The ratio of number density of negative ion to number density of positive
ion (ηn) can be changed from 0 to 10-1.
6. A spherical dust grain is assumed with diameter d that can be changed
from 0.1-10 µm.
7. The charging process starts with an isolated and uncharged grain so
initially the charge number N=0 on the grain surface.
8. The time required to calculate the charge from zero to the suitable time
that we choose, called the experiment time.
9. Some of a well-known physical constants are:
=9.109*10-31 Kg.
a.
The electron mass is
b.
The electron charge=1.602*10-19C.
c.
The permittivity constant for space
d.
Boltzmann constant KB=1.38*10-23 J/Ko.
44
=8.854*10-12 farad/m.
CHAPTER THREE
SIMULATION AND RESULTS
3.4.2 The Program Calculations
The results of program are a sequence of the calculations process
which is done according to the following steps (subroutines):
a. The Charge Fluctuations on Dust Grain
The first output data of program give a picture about the charge
fluctuation on dust grain when it is immersed in plasma with negative
ion. The data represented that charge on the grain is an integer multiple
of the electron charge at random times
b. The fluctuations statistics
1. The Histogram
It indicates the fraction of dust particle having a certain charge at
limited time, by using the output data of the first subroutine, it can
determine the charge distributions from the time series by making a
histogram of the time spent at each charge level, and the peak is called
level balance.
2. The Equilibrium Charge Number
The charge Q on a dust grain is related to its surface (or floating)
potential
. (relative to the plasma potential) by
, where a
is the radius of the (spherical) grain. The surface potential of a dust
particle in a negative ion plasma is determined by balancing the
currents due to positive ions, negative ions, and electrons. The charge
number (N=Q/e) on a dust particle at balance level is called the charge
number equilibrium. It can be determined by using the output data of
the histogram subroutine.
45
CHAPTER THREE
SIMULATION AND RESULTS
3. The charging time
The particle has no charge and is suddenly immersed in a plasma
with conditions that remain steady, so that the particle’s charge
gradually varies from zero toward its equilibrium value; in this case the
charging time has been defined as the time required for a particle’s
charge to reach to equilibrium value. The charging time can be
determined by using the output data of the first and the Equilibrium
charge number subroutines.
4. RMS Fluctuation Level
The root mean square level calculates the amplitude of the
fluctuations. By using the time series N(t) from first subroutine, we can
get Q(t) then find ∆Q and normalized it by the equilibrium charge
〈 〉,to find the root mean square level
〈 〉 .RMS reveals simple
power law relation[19].
〈 〉
|〈 〉|
⁄
………. (3-4)
c. The Phase velocity Dust-Negative Ion Acoustic Wave
We can calculate the phase velocity dust-negative ion acoustic
wave is given in equation (2-18) by using the output data of the charge
number equilibrium subroutine and studying the different parameters
effect on the phase speed.
46
CHAPTER THREE
3.5
SIMULATION AND RESULTS
The Results
The results of the simulation to study the charging of dust grain
immersed in plasma with negative ion and dust-ion acoustic wave, the results
presented as the same sequence of the subroutines with grouping them
according to the effect of parameters such as number density of negative ion
and grain size.
3.5.1 The charge dust grain fluctuations
For the comparison purpose, our simulation employed to show the
charging process in an electron grain in this plasma (e-
ion plasma. The presence of the dust
ion) leads to charging the dust negatively because
the mobility of electrons larger than the mobility of ions .The charge on the
grain will reach the equilibrium state in which the charge Q will fluctuate
around the equilibrium charge<Q>. Figure(3.1) showes the chraging process
for a dust grain by collecting electrons, and positive ions from plasma with
out negative ion, notes that the range of the charge fluctutions between -35
and -20.
Calculations show the chraging process for a dust grain with dimeter =
0.1µm immersed in K+ plasma if a significant fraction of the electrons are
attached to negative ions; the magnitude of the charge on the dust particles is
reduced. If the ratio ηe= ne/n+ of the electron density to positive ion density is
sufficiently small and the positive ions are lighter than the negative ions, then
the dust charge can be positive. The ions and electrons have equal
temperatures T+ = Te =T-= 0.2 eV.
47
CHAPTER THREE
SIMULATION AND RESULTS
Negative ion plasma is formed by attachment of electrons on the
highly electronegative sulfur hexafluoride SF6 molecule by the reaction
When the SF6 density is added into K+ plasma, some electrons become
attached to form
ions and there is a corresponding reduction in the
negative current due to the fact that the
ions are considerably less
mobile than the electrons, as Figure (3.2) shows that the range of the charge
fluctutions is between -25 and -5 and the range drifts towards the positive
comparison with Figure (3.1).
When the SF6 density is increased in K+ plasma, more electrons
become attached to form
ions and there is a corresponding reduction in
the negative current of electrons. Therefore, the negativity of charge number
on dust grain decreases gradually to positive charge number. Figures (3.3),
(3.4), (3.5), and (3.6) show that the range of the charge fluctuations is about
(-8 –4), (-6 – 6), (-2 – 8), and (-2–10) respectivly.
48
CHAPTER THREE
SIMULATION AND RESULTS
0
D=0.1µm
Charge Number(N=Q/e)
-5
ηe =1
-10
-15
-20
-25
-30
-35
-40
0.0E+0
1.0E-3
2.0E-3
3.0E-3
Time(Sec)
4.0E-3
5.0E-3
6.0E-3
Figure (3. 1): Charge number on surface grain as a function of time when D=0.1µm, ηe
=1 (no negative ion)
0
D=0.1µm
ηe=10-1
Charge Number(N=Q/e)
-5
-10
-15
-20
-25
-30
0.0E+0
1.0E-3
2.0E-3
3.0E-3
Time(Sec)
4.0E-3
5.0E-3
6.0E-3
Figure (3.2): Charge number on surface grain as a function of time when D=0.1µm,
ηe=10-1
49
CHAPTER THREE
SIMULATION AND RESULTS
10
D=0.1µm
8
ηe=10-2
Charge Number(Sec)
6
4
2
0
-2
-4
-6
-8
-10
0.0E+0
1.0E-3
2.0E-3
3.0E-3
Time(Sec)
4.0E-3
5.0E-3
6.0E-3
Figure (3.3): Charge number on surface grain as a function of time when D=0.1µm,
ηe=10-2
8
D=0.1µm
ηe=10-3
6
Charge Number(N=Q/e)
4
2
0
-2
-4
-6
-8
0.0E+0
1.0E-3
2.0E-3
3.0E-3
Time(Sec)
4.0E-3
5.0E-3
6.0E-3
Figure (3.4): Charge number on surface grain as a function of time when D=0.1µm,
ηe=10-3
50
CHAPTER THREE
SIMULATION AND RESULTS
14
D=0.1µm
12
ηe=10-4
Charge Number(N=Q/e)
10
8
6
4
2
0
-2
-4
0.0E+0
1.0E-3
2.0E-3
3.0E-3
Time(Sec)
4.0E-3
5.0E-3
6.0E-3
Figure (3.5): Charge number on surface grain as a function of time when D=0.1µm,
ηe=10-4
12
D=0.1µm
ηe=10-5
10
Charge Number(N=Q/e)
8
6
4
2
0
-2
-4
0.0E+0
1.0E-3
2.0E-3
3.0E-3
Time(Sec)
4.0E-3
5.0E-3
6.0E-3
Figure (3.6): Charge number on surface grain as a function of time when D=0.1µm,
ηe=10-5
51
CHAPTER THREE
SIMULATION AND RESULTS
3.5.2 The Time Distribution of The grain Charge
After the collection of charges by dust grain, these charges will
approach the equilibrium value <Q> and the probabilities for collecting
electrons, negative ions, and positive ions are less unequal so the charge will
always fluctuate around the equilibrium value. The charge distributions are
determined from the time series by making histogram of time spent at each
charge level to calculate charge equilibrium value, the equilibrium charge
number takes larger time from the computer experiment time. Figures (3.7),
(3.8), (3.9), (3.10), (3.11), and (3.12) show distribution functions for each
case in section 3.5.1.
In figure (3.7) the chraging process for a dust grain by collecting
electrons and positive ions (K+) from plasma. Ions are much heavier than
electrons. Therefore, the dust grain becomes negatively charged. The
equilibrium charge number is -29 because this level takes longer time
compared with the other levels.
When the SF6 density is added into K+ plasma, some electrons become
attached to form
ions and ηe=10-1, the negativity of charge number on
dust grain decreases and The equilibrium charge number becomes -12. See
figure (3.8).
If the SF6 density is increased in K+ plasma so as to ηe=10-2, the
equilibrium charge number becomes -1 as in the figure (3.9).
52
CHAPTER THREE
SIMULATION AND RESULTS
8.0E-4
D=0.1µm
7.0E-4
ηe=1
Charge Distribution(Sec)
6.0E-4
5.0E-4
4.0E-4
3.0E-4
2.0E-4
1.0E-4
0.0E+0
-20 -21 -22 -23 -24 -25 -26 -27 -28 -29 -30 -31 -32 -33 -34 -35 -36
Charge Number
Figure (3.7): Charge distribution function for grain of D=0.1µm, ηe=1 (no negative ion).
The equilibrium charge number is=-29
1.4E-3
D=0.1µm
ηe=10-1
Charge DIistribution
1.2E-3
1.0E-3
8.0E-4
6.0E-4
4.0E-4
2.0E-4
0.0E+0
-6 -7 -8 -6 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24
Charge Number
Figure (3.8): Charge distribution function for grain of D=0.1µm, ηe=10-1.The equilibrium
charge number is=-12.
53
CHAPTER THREE
SIMULATION AND RESULTS
2.5E-3
D=0.1µm
ηe=10-2
Charge Distribution(Sec)
2.0E-3
1.5E-3
1.0E-3
5.0E-4
0.0E+0
0
-1
-2
1
2
-3
-4
-5
-6
-7
3
4
5
-8
-9
6
7
Charge Number
Figure (3.9): Charge distribution function for grain of D=0.1µm, ηe =10-2.The
equilibrium charge number is=-1.
In this state, the ratio of number density of electrons to number density
of positive ions equals 10-3, the charge number on dust grain becomes
positive and equals one that is to say the positive current dominates on
charging process of dust grain because the positive ions are lighter than the
negative ions and number density of electrons is sufficiently small. See figure
(3.10).
The positively of charge on dust grain is increased .Whenever, the
ratio of number density of electron to number density of positive ion is
decreased as figure (3.11) shows the charge number equilibrium becomes
three when the ratio of number density of electron to number density of
positive ion (ηe) equals 10-4. But figure (3.12) shows the charge number
equilibrium remains constant when the ratio of number density of electron to
number density of positive ion (ηe) equals 10-5 because the main effect of
electron is neglected.
54
CHAPTER THREE
SIMULATION AND RESULTS
4.5E-3
D=0.1µm
4.0E-3
ηe=10-3
Charge Distribution(Sec)
3.5E-3
3.0E-3
2.5E-3
2.0E-3
1.5E-3
1.0E-3
5.0E-4
0.0E+0
0
1
2
-1
-2
-3
-4
3
4
5
-5
-6
6
Charge Number
Figure (3.10): Charge distribution function for grain of D=0.1µm, ηe =10-3.The
equilibrium charge number is=1
2.5E-3
D=0.1µm
ηe=10-4
Charge DIistribution(Sec)
2.0E-3
1.5E-3
1.0E-3
5.0E-4
0.0E+0
0
-1
1
2
3
4
5
6
-2
-3
7
8
9
10
11
Charge Number
Figure (3.11): Charge distribution function for grain of D=0.1µm, ηe =10-4.The
equilibrium charge number is=3
55
CHAPTER THREE
SIMULATION AND RESULTS
2.5E-3
D=0.1µm
ηe=10-5
Charge Distribution(N=Q/e)
2.0E-3
1.5E-3
1.0E-3
5.0E-4
0.0E+0
0
-1
1
2
3
4
5
6
-2
-3
7
8
9
10
Charge Number
Figure (3.12): Charge distribution function for grain of D=0.1µm, ηe =10-5.The
equilibrium charge number is=3.
3.5.3 The Equilibrium Charge Number
The charges on grain approach the equilibrium value 〈 〉, after the
collection of charges by dust grain, The charge on a grain will fluctuate in
discrete steps (and at random times) about the steady-state value〈 〉 ,but the
continues model neglects the fact that the electron and ion currents collected
by the grain that actually consists of individual electrons and ions.
a. Effect of Parameter ηe on the equilibrium charge number
A plot of the equilibrium charge number on dust (
for the parameter
) as a function
for the case in which the positive ion is potassium
and the negative ion is
as shown in figure (3.13) for dust grain
diameter equals 0.1µm. Notice that the charge on the dust is reduced as the
parameter ηe increased, and the dust surface charge can be positive.
56
CHAPTER THREE
SIMULATION AND RESULTS
4
Charge Number Equilibrium
2
0
1.0E-5
-2
1.0E-4
1.0E-3
1.0E-2
1.0E-1
1.0E+0
-4
-6
-8
-10
-12
-14
ηe=ne/n+
Figure (3.13): the equilibrium charge Number grain as a function the parameter ηe when
D=0.1µm.
When the relation between equilibrium charge number and parameter
is plotted for different dust grain diameters, this relation takes same
behavior (as in figures (3.14) and (3.15)) but the charge number equilibrium
increases when grain size increases.
57
CHAPTER THREE
SIMULATION AND RESULTS
40
Charge Number Equilibrium
20
0
1.0E-5
-20
1.0E-4
1.0E-3
1.0E-2
1.0E-1
1.0E+0
-40
-60
-80
-100
-120
-140
-160
ηe=ne/n+
Figure (3.14): the equilibrium charge number grain as a function of the parameter ηe
when D=1µm.
400
Charge Number Equilibrium
200
0
1.0E-5
-200
1.0E-4
1.0E-3
1.0E-2
1.0E-1
1.0E+0
-400
-600
-800
-1000
-1200
-1400
-1600
ηe=ne/n+
Figure (3.15): the equilibrium charge number grain as a function of the parameter ηe
when D=10µm.
58
CHAPTER THREE
SIMULATION AND RESULTS
b. The Effect of Grain Size on the equilibrium charge number
The grain size is an important parameter that effects on the charge
collected by dust grain. Figure (3.16) shows the equilibrium charge number
as a function of grain size for different value of parameter ηe and
=
=
=0.2eV.
The surface charge has been determined by the computer simulation
for various diameter of spherical grains that lead to increase dust surface area
exposed to plasma, so the collection of electrons, negative ions, and positive
ions currents become large and equilibrium charge number on the dust grain
are also large. These results are in agreement with the equation (2.4) in
chapter two, the relation between the grain charge and radius is linear.
This figure notes that the change of equilibrium charge number is
slowly as a function grain size when ηe =10-3,10-4, and 10-5 because the
positive and the negative currents dominate on charging process of dust grain
and both the negative and positive ions is heavier than electron while the
electron and positive ions currents dominate on charging process of dust
grain when ηe =10-1, and 10-2 .Therefore, the change of equilibrium charge
number is rapidly as a function grain size.
59
CHAPTER THREE
SIMULATION AND RESULTS
ηe=1.00E-1
ηe=1.00E-2
ηe=1.00E-3
ηe=1.00E-4
ηe=1.00E-5
400
200
Charge Number Equilibrium
0
-200
0
2
4
6
8
10
12
-400
-600
-800
-1000
-1200
-1400
-1600
diameter (µm)
Figure (3.16): The charge number equilibrium as a function of grain diameter when ηe
-1
=10 ,
10-2,10-3,10-4,and 10-5 respectively.
3.5.4 The dust surface potential
When the dust is charged by the collection of the plasma particles
flowing onto it surface, it acquires surface potential, this potential depends on
the charge that acquired by grain surface according to equation (2.4).
The dust surface potential (
parameter
) is plotted as a function for the
for the case in which the positive ion is potassium
the negative ion is
and
for different size of grins as in Fig. (3.17). Notice
that the positive ion is the lighter species. Thus, in the presence of a heavy
(compared to the positive ion) negative ion, the charge on the dust is reduced,
and the dust surface potential can be positive. Where the positive ion,
negative ion, and electron are at the same temperatures and equal to 0.2 eV.
60
CHAPTER THREE
SIMULATION AND RESULTS
These results are in agreement with the experimental results of Robert
Merlino et al (2006) [17].
D=0.1µm
D=1µm
D=10µm
0.1
potential on Dust Grian (V)
0.05
0
1.0E-5
-0.05
1.0E-4
1.0E-3
1.0E-2
1.0E-1
1.0E+0
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
-0.4
-0.45
-0.5
Figure (3.17): The dust surface potential
of electrons in the plasma. T+ = Te = T-.
ηe=n-/n+
as a function for the fractional concentration
Figure (3.18): Difference between the probe floating potential and plasma space potential,
. for various SF6 pressures (the experimental results of Robert Merlino et al
(2006))[17].
61
CHAPTER THREE
SIMULATION AND RESULTS
3.5.5 The Charging Time
a. The effect of Parameter ηe on the charging time
From the results of computer simulation, the effect of negative ions
can be studied when added to plasma on charging time of grain. Figure (3.19)
shows the charging time of grain as a function of parameter ηe.
Notice that the charging time decreases when the number density of
electrons reduces from ηe= 10-1 to 10-2 because the negativity of equilibrium
charge on dust grain decreases gradually. Therefore, the time is needed to
reach the equilibrium charge number decreases to equilibrium charge
become-1. Hence, the charging time is trivial when the parameter ηe equals
10-2.
When the parameter ηe equals 10-3 , the positive ions current
dominates on charging process of dust grain .Therefor, the equilibrium
charge becomes positive but has a little value and equals one. Hence, the
charging time is trivial.
Whenever the positivity of equilibrium charge on dust grain increases
gradually, the charging time also increases when the value ηe changes
from10-3 to 10-4. But, when ηe changes from 10-4 to 10-5, the charging time
becomes constant because the equilibrium charge number is constant. From
this figure, it can be concluded the charging time is proportional with the
absolute value of equilibrium charge number.
62
CHAPTER THREE
SIMULATION AND RESULTS
6.E-5
Charging Time (Sec)
5.E-5
4.E-5
3.E-5
2.E-5
1.E-5
0.E+0
1.0E-5
1.0E-4
1.0E-3
ηe= ne /n+
1.0E-2
1.0E-1
Figure (3.19): The charging time as a function of the parameter ηe when D=0.1µm.
Figure (3.20) shows the charging time of lager grain (D=1µm) as a
function parameter ηe. It can be seen from this figure that the charging time
decreases for all the values of parameter ηe.
2.E-5
2.E-5
Charging Time (Sec)
1.E-5
1.E-5
1.E-5
8.E-6
6.E-6
4.E-6
2.E-6
0.E+0
1.0E-5
1.0E-4
1.0E-3
ηe =ne /n+
1.0E-2
Figure (3.20): The charging time as a function of the parameter ηn when D=1µm.
63
1.0E-1
CHAPTER THREE
SIMULATION AND RESULTS
Whenever the grain size increases, the charging time decreases for all
value of parameter ηe and also the difference in the charging time becomes
very simple.as in figure (3.21).
1.6E-6
Charging Time (Sec)
1.4E-6
1.2E-6
1.0E-6
8.0E-7
6.0E-7
4.0E-7
2.0E-7
0.0E+0
1.0E-5
1.0E-4
1.0E-3
ηe=ne/n+
1.0E-2
1.0E-1
Figure (3.21): The charging time as a function of the parameter ηe when D=10µm.
b. The Grain Size Effect on the charging time
The charging time is the time required for a grain’s charge to reach its
equilibrium value that is inversely proportional with dust grain size as in
equation (2.13). Figure (3.22) reveals that the charging time as a function of
grain diameter for different value of parameter ηe and Te=T-=T+=0.2eV.Notce
in this figure, the relation between the charging time and dust grain size is
inversely proportional when ηe = 10-1, 10-4, and 10-5 because the dust surface
area exposed to plasma increases, so that the collection of electrons and ions
currents become large. But the value of ηe = 10-2 and behavior of diameter
=0.1 µm is irregular behavior because the grain reaches equilibrium state at
the first electron collects on the grain. Therefore, the charging time is trivial,
64
CHAPTER THREE
SIMULATION AND RESULTS
also the value of ηe = 10-3 and diameter =0.1 µm is irregular behavior, when
the first positive ion collects on the grain, the grain reaches equilibrium state
and charge equilibrium of this grain equals 1.
5.0E-5
1.00E-01
1.00E-02
4.5E-5
1.00E-03
1.00E-04
4.0E-5
1.00E-05
Charging Time (Sec)
3.5E-5
3.0E-5
2.5E-5
2.0E-5
1.5E-5
1.0E-5
5.0E-6
0.0E+0
0.1
1
diameter (µm)
10
Figure (3.22): The charging time as a function of grain diameter at ηe = 10-1, 10-2, 10-3,
10-4, and 10-5.
3.5.6 RMS Level of Charge Fluctuation
RMS of charge fluctuations is inversely proportional to the square
root of equilibrium charge number. Small dust grain collects few charges and
the fluctuation around the equilibrium charge value are slow with high
amplitude,but increasing particle size leads to collect more electrons and ions
on its surface and the charge number equilibrium increases, so the fluctuation
amplitude will be decreased.
65
CHAPTER THREE
SIMULATION AND RESULTS
Figure (3.23) represents the RMS fluctuations as a function of
equilibrium charge number for different value of parameter ηe and Te=T=T+=0.2eV. This figure shows no affect turning charge on dust grain between
positive and negative charges because the RMS fluctuations depends on
absolute value of equilibrium charge number.
0.5
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
0.45
0.4
0.35
0.3
RMS
0.25
0.2
0.15
0.1
0.05
0
1
10
100
equilibrium Charge Number (N)
1000
10000
Figure (3.23): RMS level of fluctuation as a function the equilibrium charge number on
dust grain when ηn = 10-1, 10-2, 10-3, 10-4, and 10-5.
66
CHAPTER THREE
SIMULATION AND RESULTS
3.5.7 The Dust-Negative Ion Acoustic Wave
According to equation (2.18), it represents that the relation between
the phase velocity dust-negative ion acoustic wave and the negative ion
temperature is linear; this velocity is calculated by using the equilibrium
charge from computer simulation. The phase speed of these wave increases
as the negative ion temperature increases because dynamics of negative ions
increase. Figure (3.24) shows the phase velocity dust-negative ion acoustic
wave as a function of the negative ion temperature for ηe =10-1, D=10µm and
Te =T+=0.2eV.
450
440
430
vo(m/Sec)
420
410
400
390
380
370
360
350
0.1
0.12
0.14
0.16
0.18
0.2
0.22
Negtive Ion Temperature (eV)
Figure (3.24): The phase velocity dust-negative ion acoustic wave as a function of the
negative ion temperature (eV) for D=10µm.
It implies that for no dust ηd=0 cold negative ion T-=0 limits, the phase
velocity of this wave is equal to
√
⁄
. This means that the Dust-
Negative Ion Acoustic (DNIA) waves are associated with dynamics of
negative ions, where the inertia comes from the mass of the negative ions and
restoring force is provided by the thermal pressures of electrons and light
67
CHAPTER THREE
SIMULATION AND RESULTS
ions. It is also clear that for fixed light ion number density, i.e., n+=constant,
the phase speed of these wave increases (decreases) as the negative ion
(electron) number density increases. Figure (3.25) shows the phase speed
dust-negative ion acoustic wave as a function ηn (ratio of the number density
of negative ion to number density of positive ion). These results are
agreement with the experiment results of I. Goertz et al (2007) [31].
350
vo(m/Sec)
300
250
200
150
100
50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ηn=n-/n+
Figure (3.25): The phase velocity dust-negative ion acoustic wave as a function of the
parameter ηn with T- =0 and no dust
Figure (3.26): Full circles: phase velocity ofthe ion acoustic wave as function of the SF6
admixture (ne =5×1015 m−3,Te = 2 eV).
68
CHAPTER THREE
SIMULATION AND RESULTS
The connection between the phase velocity dust-negative ion acoustic
waves and the parameter ηn (ratio of the number density of negative ion to
number density of positive ion) for Te=T+=0.2, Tn=0.125Te is provided by the
calculation of the phase velocity waves
at state presence and absence dust,
as a function of ηn, shown in Fig.( 3.27). For absence dust, the phase speed
increases as the parameter ηn increases.
For presence dust, the dust particles remain at rest and influence the
wave propagation only by their effect on the overall charge balance. The
presence of large dust particles leads to a reduction of plasma density;
therefore, it leads generally to slow the phase velocity dust-negative ion
acoustic waves as the parameter ηn increases.
390
without Dust
340
vo(m/Sec)
290
With Dust
240
190
140
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ηn=n-/n+
Figure (3.27): The phase velocity dust-negative ion acoustic waves as a function of the
parameter ηn with dust and no dust.
69
CHAPTER THREE
3.6
SIMULATION AND RESULTS
Conclusions
1. The charging of dust grains in negative ion plasma can be controlled by
varying the relative fraction of negative ions in the plasma. As the
negative ion density increases, the magnitude of the negative dust
charge is reduced and a transition to positively charged dust.
2. The charge distribution function has peak at the equilibrium charge
value.
3. The increasing in the surface area of dust grain leads to increase the
charges that fall on the grain surface.
4. The increasing of dust grain size leads to decrease the charging time so
larger dust particle charges so fast and collects more positive ions and
electrons than smaller one.
5. RMS of charge fluctuations is inversely proportional to the dust grain
size.
6. The phase velocity dust-negative ion acoustic waves increase as the
negative ion temperature increases.
7. The phase velocity DNIA waves increase as the number density of
negative ion increases.
8. The phase velocity DNIA waves for absence dust are larger than the
phase velocity DNIA waves for presence dust in the same
circumstances.
70
CHAPTER THREE
3.7
SIMULATION AND RESULTS
Future works
According to the results obtained from this study, it can be suggested:
1. Developing the simulation of charging process of grain in the
plasma with negative ion to deal with the effect of secondary
electron emission.
2. Studying the effect of fluctuation of grain charge on the phase
velocity dust-negative ion acoustic wave.
71
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‫اخلالصة‬
‫هذا انبحث يقدو حماكات حاسوبيه ندراسة عًهيهه حهحٍ ايبيبهات انرباريهة اررًهورال م ب سيها(انكهونٌ‪-‬ايهوٌ انبوجاسهيوو حتحهو‬
‫ايوَات سانبه (ايوَات سداسي فهوريد انكربيهث‬
‫باالعحًها عههم يو يهم ريايهي ي هًم يو يهم انحهحٍ ارصل هم بتهد جههويز‬
‫نيححو جأثري االيوٌ ان انب م عًهيه ححٍ ايبيبات انربارية‪.‬‬
‫نهذا ارو يم مت حتويهه اىل ح ابات عد يه باسحخداو انربايج اياسهوبية نانربَهايج اياسهوبي ار هحخدو م ههذا انتًهم مت كحابحهه بهرهة‬
‫انلههورجزاٌ نبيههاٌ عًهيههه انحههحٍ ن سيههٍ جوسيههس انحههحصات نح ههاز حههحصه ايبيبيههة نسيههٍ انحههحٍ نقههيى لحهلههة يههٍ ‪ َ( ηe‬ههبه كفافههه‬
‫االنكونَههههات اىل كحافههههه االيوَههههات ارو بههههة = ‪ 10-5,10-4,10-3,10-2,10-1,‬كهه هذنا ح ههههاز سههههزعه ههههور ارو ههههات‬
‫(‪. negative ion-dust acoustic‬‬
‫نَحائج انبحث انيحث ايكاَيه انححكى م عًهيه ححٍ ايبيبة يٍ خ ل جرري َ به اإلنكونَات م انب سيا حبيث عصهد سيها َ هبه‬
‫االيوَات ان انبة م انب سيا يتظى االنكونَات سوف جزجبط باأليوٌ ان انب مما ي بب قهه جيار االنكونَات ان انبة نان هًا نييوَهات‬
‫ارو بة بايزكة حنو ايبيبة انربارية نذنا جححول ححصه ايبيبة يٍ ان انب اىل ارو ب جدرجييا‪.‬‬
‫نكهذنا ا نصحهائج انيهحث جهأثري جزكيهش االيهوٌ ان هانب ن ر هه حزارجهه عههم سهزعه هور ارو هات( ‪negative ion-dust‬‬
‫‪. acoustic‬‬