Glow Discharge Theory

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2002 Plasma Science and Fusion Energy InstituteJuly 22 August 2, 2002

DC Glow Discharge

Safety Rules

The DC Glow discharge tubes that you are building are designed to be safe. There are

numerous hazards associated with the equipment and it is critical that you are aware of these dangersand how to avoid them. Remember, you are taking this equipment back to your classroom. These

guidelines should ensure not only your safety, but that of your students.

Electrical Safety

The electricity generated by thepower supply used in these

experiments (3000 volts, 0.01 amperes) is LETHAL.

Always follow the safety rules!

1. The power supply must be OFF and unplugged when making any changes or

adjustments in the system (changing electrode distance, changing pressure, etc.)

2. Never work alone. If you are testing the equipment before a class, make sure that a

colleague is around and knows how to turn off the power supply in case of

emergency.

3. All of the electrical leads and connections must be insulated. NO EXPOSED

WIRES OR CONNECTORS

4. Make sure the power supply and the vacuum tube are properly and securely

GROUNDED at all times. Ensure that all connections are securely fastened.

5. The plastic cover is used to keep the electrode leads and connections to the power

supply away from the operator. It must remain on the tube at all times when

operating the equipment.

6. Never leave a turned-on power supply unattended. The power supply must be

under your control at all times even when turned-off.

7. Never walk away from an operating system.

8. Making changes and adjustments with one hand to make sure your full attention is

always on the task, and the current does not find a closed circuit through your

body.

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Vacuum Safety

The glass tube is aserious hazard if it breaks while under vacuum. The hardplastic cover not only provides electrical safety, it protects the glass from breaking.

1. The plastic cover must remain on the tube at all times!

2. Do not drop anything on the tube under vacuum.

3. Do not leave the system unattended.

4. Do not operate the vacuum system if the vacuum gauge is not functioning

properly. (gauge does not read a pressure less than atmosphere when the pump is

on)

5.While leak checking with ethanol is convenient it is critical to not do so with thepower supply turned on due to the flammability hazard.

I have read and understand the DC Glow discharge tube safety document and

operating instructions. I understand the various hazards associated with this

equipment and am confident that I can operate it in a safe manner both at PPPL and in

my classroom.

_____________________ ______________

Signed Date

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ANATOMY OF THE GLOW DISCHARGEANATOMY OF THE GLOW DISCHARGE

The glow discharge regime is characterized by a steady current between the electrodes and a

continuous light emission by the gas. The usual glow discharge conditions may have the potential

difference between the cathode and the anode of about 400 2000 Volts, the current in the milliamp

range. The cathode is made of conducting material that usually operates cold. For pressures of about100 mTorr (0.1 mm Hg) to 1 Torr (1 mm Hg) the discharge in a tube has the structure below:

Figure 1. Variations in the light intensity and color along the length of the a dc glow discharge

The structures shown above were first observed in the 1830s by Michael Faraday, and are sure to

provoke a series of questions from all observers. They are the variations of the light intensity along

the length of the discharge and their individual names are shown in the idealized diagram above.

The Cathode Region

The cathode region consists of the Aston dark space, the cathode glow, the cathode (Hittorf

Crookes) dark space, and the negative glow. The cathode region is the fundamentally important areamaintaining the glow discharge. The anode can be moved into the Faraday dark space and the

positive column will disappear without much effect on the other parameters of the discharge, but the

cathode region remains. Staring from the cathode surface and proceeding toward the anode, thediscussion below outlines the changes in the light intensity, the electric potential, the electric field,

and the total charge density in the discharge chamber.

An electron that is first emitted from a cathode has very low initial energy. It accelerates in a strongelectric field near the cathode but its collisions with the neutrals do not lead to ionization because the

electron energy is too low. Further from the cathode the field gets weaker, but the electron energy is

greater and more ionizing collisions take place. There is strong electron multiplication occurring inthis region, there are now many more electrons that can produce ionization and many positive ions.

The positive ions move toward the cathode, and the electrons are moving away from the cathode.

The electrons are tens of thousands of times less massive and more mobile than the ions, so theyPage 3 3


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leave the region leaving the ions behind. Therefore a positive charge density is created in the area

next to the cathode. Notice the positive net charge density in this region shown in the diagrambelow.

Figure 2. Net charge as a function of the distance from the cathode

The positive space charge affects the electric field. Looking from inside the gas chamber, the electric

field of the negative cathode combined with the field of the positive space charge, results in

decreasing field strength away from the cathode. The electric field decreases toward the negativeglow, and becomes very weak close to the edge of the negative glow. Note the relationship between

the changes in the electric field and the electric potential in this region.

Figure 3. Variations of the electric field and potential as a function of the distance from the cathodePage 4 4


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There are two types of electrons in the cathode region: the fast electrons accelerated in the cathodepotential and involved in ionizing collisions, and slow electrons freshly produced in the ionization

processes. The number of slower electrons is large in this area, and only the fastest ones are still able

to ionize. The total population in the negative glow region consists of electrons with energies above

the excitation minimum but below ionization potential, slow electrons produced in inelasticcollisions in the dark space, excited atoms, ions, and unaffected atoms. The electron energies

decrease away from the negative glow boundary. The running figures represent the changes in the

kinetic energy of the fast electrons.

Figure 4. Variations of the electron energy as a function of the distance from the cathode

Most voltage drop across the discharge occurs between the cathode and the boundary between the

cathode dark space and the negative glow.

Through the negative glow the electric potential is increasing slowly in the direction of the positivecolumn and the electric field is leveling off. The electrons are entering the Faraday dark space.

Maintaining the Steady Glow: Townsend Theory of the Cathode Region

The main role of the cathode region is maintaining the discharge. The cathode voltage drop that

develops in order to maintain the discharge can be estimated by the same argument as the Townsenddischarge and breakdown voltage. The cathode material and the cathode emission coefficient g are

extremely important for establishing the self-sustained glow.

Under certain conditions and for small current, cathode fall, dark space, and current density remainconstant when the current is increased. The discharge covers a progressively greater area of the

cathode to accommodate the increase in current. This is historically called the normal regime,

although it is not commonly used or observed. Once the entire cathode is covered by the discharge,a further increase in the current can be achieved by increasing the voltage difference between the

electrodes. Historically, this is called the abnormal regime, although this regime is what is

commonly referred to as the glow discharge.

A low pressure glow discharge will adjust the axial length of the cathode region, dc, so that the

minimum value of the product dcp is established,

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( ) ( )pd pdc min where (pd)min is the minimum breakdown parameter of the Paschen curve, and the cathode fall

voltage is given by

V Vc minand Vbmin is the breakdown voltage at the minimum of the Paschen curve. At the Paschen minimum,

the discharge maintains itself under the conditions of minimum cathode voltage fall and power

dissipation. The cathode fall potential, and hence the type of discharge produced are determined by

the material of the cathode, the type of gas, and the geometry of the system.

The electric field in the cathode region can be determined by observing the deflection of an electron

beam shot across the discharge column. By this and other methods it has been shown experimentallythat the electric field is proportional to the distance away from the cathode (x).

E = C(dc - x)That gives a quadratic relationship for the potential

V(x) = Edx = C dc x( )0

x

0

x

dx = C xdc x2

2

.

The potential at x = dc is called the cathode potential. Denoting the cathode potential Vc, the constantC = 2Vc/dc

2. Then

V(x) =Vcx 2dc x( )

dc2

and the field is

E(x) =dV

dx =2Vc dc x( )

dc2 .

This is exactly what must happen in the presence of a constant space charge distribution. From

Gausss law,

dE

dx=

eno

,

where n = Zni ne is the net charge density . From the equation for the electric field it follows thatthe net charge density

n = 2oVcedc

2 (particles/m3)

is a constant, positive net ion number density in the cathode region of the glow discharge.

The abnormal glow discharge

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The normally observed abnormal glow discharge occurs when the current is increased beyond the

value which the glow covers the whole cathode surface. A larger current then requires a cathode fallthat is greater than for a normal glow and increases to produce a greater current density. At the same

time the (pdc) value decreases away from the minimum of the Paschen curve. For constant pressure,

the dark space shrinks. The increase in current density means that considerable heating of the gas

occurs in the cathode dark space.

The Faraday Dark Space

Faraday dark space is the anteroom of the positive column and its properties are intermediate

between the negative glow and the positive column. The number of electrons decreases by

recombination and radial diffusion, the net space charge is very low, and the axial electric field isrelatively small. The electrons are slowly accelerating toward the positive column.

The Positive Column

The positive column is bounded on one side by the Faraday dark space and on the other by the anodeglow. Although it can be the largest part of the discharge, the positive column is not necessary formaintaining the discharge. The positive column can be extended by increasing the separation

between the electrodes or alternately the electrons can be moved close together so that the positive

column and even the Faraday dark space disappear. The discharge does not change in this procedure.

The positive properties of the gas in the positive column are the closest to those of plasma: it is

almost neutral overall with almost no electric field. Electric potential is almost constant throughout

the length of the column and that means that there is no net space charge distribution and very weakelectric field. The electric field is about 1 V/cm, just large enough to maintain the required degree of

ionization. The electron number density is typically 1015 to 1016 electrons/m3 in the positive column,

with an electron kinetic temperature of 1 to 2 eV. The gas in the glow discharge tube is not confinedin any way other than by the walls of the tube and therefore diffuses to the walls. High electron

mobility leads to more electrons moving out to the walls than ions. That produces a negative charge

on the walls and a slightly positive potential of the plasma, hence the name thepositive column.Once the walls become slightly negative, they repel additional electrons, the electrons slow down,

the ions catch up since they are attracted to the negative charge and the diffusion becomes

ambipolar. Once the voltage across the discharge is turned off, the plasma diffuses to the walls byambipolar diffusion.

Another manifestation of the plasma type of behavior of the positive column is its support of various

types of waves. Oscillations at microwave and ultrahigh frequencies (1010 108 Hz) are explained

as the electron plasma oscillations, and oscillations at lower frequencies (107 105 Hz) are usuallyattributed to ion plasma oscillations. At even lower frequencies, the oscillations may be the ion

acoustic waves or ionizations waves visible in the discharge as standing and moving striations.Moving or standing striations are traveling waves or stationary perturbations in electron number

density and temperature that occurs in partially ionized gasses. In their most usual form, moving

striations propagate to the anode (negative striations) or to the cathode (positive striations). Whenobserved at a specific point on the axis, the moving striations usually have frequencies from a few

hertz up to several tens of kilohertz.Page 7 7


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The waves you are most likely to observe are ionization waves. These are ion waves that have afrequency dependent on the electron temperature and on ion inertia. This is not surprising in plasma

since here the electromagnetic effects are combined with phenomena that in a regular gas are

determined by the particle collisions. When waves are set up at electron frequencies, ions are usually

not affected because of their large inertia. On the other hand the waves at ion frequencies willproduce both electromagnetic effects and density variations. The electromagnetic fields affect the

electrons, and so also the ions. Specific to the ionization waves is their dependence on the neutral

flows. The reason for this effect is that in ionization waves, there are variations not just in density ofions and electrons, but also in the electron temperature. This means that there are alternating regions

of higher and lower ionization rates. The expression of these variations can be seen as alternating

bands of light and dark.

Figure 5. Axial variations of the electron kinetic energy (temperature) in the positive column

The Anode Region

Anode Glow

The anode glow is a bright region at the anode end of the positive column. The anode glow is not

always present. This is the boundary at the start of the anode change is voltage.

Anode Dark Space

The anode attracts the electrons from the positive column and returns them to the external circuit.

The electrons approaching the anode form a negative space charge in the anode region. The electronscoming in from the positive column see the electric field of the anode decreased by the presence of

this space charge. This establishes the anode voltage change and the equilibrium flow of electronsthrough the anode.1

The Summary of the Axial Variations of the

Electric Potential and Electric Field Across the Discharge

1 The anode acts like a Langmuir probe in electron saturation regime.

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The running figures show the relative energy of the electrons in the various regions of the discharge.

Glow Discharge facts:

Electron energy determines the variations of light and dark regions Photon emission from electron impact excitation and ionization Air (photo) is pink and blue, helium is red and green

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WHAT IS A GLOW DISCHARGE?

Sections C-G are considered Glow Discharges

from Introduction to Electrical Discharges in Gases by S.C. Brown

Section Description

AB - Random

Bursts

Very low current and voltage. Discharge is not self-sustaining. Current is

measured in random bursts.

BC -

Townsend

Breakdown begins, current increases for a fixed voltage, visible light not

observed

CDE - Corona Voltage drops as current increases. Discharge begins to GLOW visibly.

EF - NormalGlow Voltage is constant as current increases. Discharge covers only a part of thecathode. Amount covered is proportional to current. Current density remainsconstant.

FG - AbnormalGlow

Entire cathode is covered with glow. Voltage increases as the current increases.

Past G - Arc Very high current, low voltage.

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Background Information

Vacuum and Pressure

Vacuum is measured using various units:

millimeter of mercury (mm Hg), in which one standard atmosphere (atm), at 0 oC, is equal to 760mm Hg. One mm Hg is called or equal to one Torr;

in the Si system: Pascal (Pa) defined as one Newton per square meter (N/m2)1 Torr = 133.32 Pa, and 1 mTorr = 0.13332 Pa

1 atm = 760 Torr = 1.0133 bar = 1.0133 x 105 Pa

Low vacuum - 760 - 10-2 TorrHigh vacuum - 10-2 10-6 Torr

Ultra high vacuum - 10-6 10-14 Torr

The quantity of interest is usually the number density defined as the number of particles per unit

volume, usually cubic meter or cubic centimeter. The pressure can be related to the number densityby the ideal gas law,

nkTp = ,

where kis Boltzmanns constant (1.381x10-31 J/K) and T is absolute temperature (in K).

At room temperature T = 300 K, the particle density measured in particles per cubic meter,

)Torr(px.)m(n 223 10223= .

This is the conversion between neutral number density in a vacuum system and the background

pressure in Torr at room temperature. The conversion depends on the temperature.

The Concept of Temperature

Temperature is a measure of the average kinetic energy per particle and depends on the

specific speed distribution of a particle species. Single-body particle species have three degrees offreedom, and from statistical mechanics their average kinetic energy equals their thermal energy:

kTmv2

3

2

1 2 = .

Temperature is a statistical concept and it is applicable when the interactions between the

particles allow the particle energies to be randomized. In an ideal gas for example, elastic collisions

between atoms allow for the transfer of kinetic energy between particles so that the system can reachthe most probable distribution of speeds. The units of temperature commonly used in plasma physics

reflect the close relationship between energy and temperature. To avoid confusion on the number of

dimensions involved, the energy corresponding to kT, not the kinetic energy that is used to denote

temperature. ForkT = 1 eV = 1.6 x1019 J, the temperature is T = 11,600 K, so the conversion factoris

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1 eV = 11,600 K

Velocity Distribution Functions

When plasma is in statistical equilibrium, the random speeds of particles are described by aMaxwell distribution of speeds:

==

1/2 2kT

mv-exp

2

4

d

d 2223

vkT

mn

v

n)v(f

/v

.

Here f v dv( ) is the number of particles that have speeds in the range from v to v + dv.

Below is a plot of this distribution for two temperatures:

The area under each curve is equal to the number of particles n:

( )

=0

d nnvf .

The arithmetic mean speed(average speed) ormean thermal speed, v , is given by

( )21

0

8d

1/

m

kTvvvf

nv

==

.

The average speed of electrons and ions in a more useful form, in m/s:

ee Tx.v510696=

and

= iiT

x.v 410561 ,

where Te and Ti are in eV and is the ion atomic mass number.

Example:

If the electron energy is Te = 3 eV and argon ions, = 40, are at at room temperature,Ti = 0.025 eV, ve = 1,160,600 m/s and vi = 390 m/s. Jet airlines travel at 200 m/s.

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V e l o c i t y , v0

Distributionfunction,

f(v)

T1

T2

> T1

T2

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There are several statistically meaningful characteristics of the particle velocity. The mean thermal

speed, v , the root mean square speed, rmsv , and the most probable speed, vm, are shown on the

graph below

Energy distribution functions.

Maxwell-Boltzmann energy distribution function;

( )f

kT kT( ) exp

/

/ /

=

2 1 2

1 2 3 2

where f()d is the number of particles having an energy between and + d. As before, k isBoltzmanns constant, and T is the electron temperature.

Plasma is characterized by the energy distributions of neutral particles, fn(), ions, fi(), andelectrons, fe().

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V e l o c i t y , v0


f(v)

Vm

Vr m s

V

M e a n e n e r g y

D i m e n s i o n l e s s e n e r g y , / k T

0 1 / 2 31 3 / 2 2


f(

)

M o s t p r o b a b l e e n e r g y

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The mean energy, , is

( )

=+ + +

= =1 2 01 3

2

... n

n n

f d kT

The assumptions for the Maxwell distribution:

1. The velocity distribution in the plasma is isotropic.

2. Inelastic collisions act only as a perturbation to the isotropy.

3. Effect of the electric field is negligible.

The Maxwell-Boltzmann distribution function describes the energy distribution of particles if the

particles are in either thermodynamic ofkinetic equilibrium. The thermodynamic equilibrium is notsatisfied for most coldplasmas, such asglow discharge. Electrons are accelerated near the cathode

in the glow discharge and stream away from the cathode violating the isotropic distribution of

velocity, and not achieving thermodynamic equilibrium. Kinetic equilibrium is a less stringentcondition, which allows energy flows in the medium and does not require that the medium radiate

like a black body. It requires only that the particle interaction is sufficient to achieve a Maxwell-

Boltzmann distribution of energy. A different distribution function is more applicable to a glow

discharge (positive column). This distribution has the following assumptions:

1. The electric field strength is low enough to disregard inelastic collisions, but is high

enough so that Te>>Ti.

2. Electrical field frequency is much lower than the collision frequency,


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where is the cross section for collision. Collision cross section is a measure of the probability that agiven collision (process) will occur. Collision cross-section depends on the particle temperature.

At low pressures, the effect of the long-range electromagnetic forces on the motion of charged particles

can be much stronger that the effect of the collisions between particles. This is the case of collisionless

plasma.

Glow discharge is a collision-dominated plasma, therefore studying the collision processes is very

important.

The sketches below show the difference in the motion of the particles in the ideal gas as compared to

the motion of charged particles in cold plasma. As shown in the sketches, the interacting chargedparticles move along curved trajectories between collisions.

Independent motion of molecules: Dependent motion of charged species:

B r o w n i a n m o t i o n o f

a n e u t r a l g a s m o l e c u l e

M o t i o n o f a c h a r g e d

p a r t i c l e i n a p l a s m a

Electron collisions with atoms

The most important type of an interaction in cold plasma is a collision between an electron and a neutralatom or molecule. This is due to the low degree of ionization in these plasmas.

Electrons are much faster than ions and neutrals: ve>> va, where veis the speed of an electron and va is

the speed of a neutral atom. The collision process is shown below, calculating the collision cross-

section. If an atom is considered simply as a hard sphere, the cross-section is = a2, as shown in thediagram.

The number of electron collisions per unit time orcollision frequency,, is given by

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e a en v=

where na in the density of neutral atoms or molecules and v is the electron velocity (average velocity).

The distance traveled between collisions, the mean free path of electrons, e,

e = (na)-1.

Collisions fall into two general categories: elastic collisions and inelastic collisions.

Electron-Neutral Elastic Collisions.

Energy transferred in an elastic collision can be calculated by standard high school methods. If is theangle between the relative velocity vector and the line joining centers, the energy transferred is

( )

E Em m

m m

t =

+1

1 2

1 2

2

4cos,

the maximum energy transferred is in a central collision:

( )E E

m m

m mt,max =

+1

1 2

1 22

4,

and the average transferred energy is

( )E E

m m

m mt avg , =

+1

1 2

1 22

2

The average energy transferred to an atom by an electron in an elastic collision, Et, is

E Em

Mt avg,= 1

2

where m and M are the electron and atom masses, respectively. For Ar atoms,

E

E

t 1

40 000,.

If an electron has an energy of about 200 eV, Et 0.005 eV that is much less than 0.027 eV theaverage energy of atoms at 300 oK.

Examples:

For electrons with energy of 15 eV the elastic cross-section with Ar is about 2.5x10-15 cm2

Concentration of atoms at 10 mTor is about 3.54x1014 atom/cm3, and the mean free path is about0.9 cm.

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Electron-Neutral Inelastic Collisions.

Any collision in which the internal energy of a particle is changed is inelastic.

Ionization.

Electron impact ionization:

e Ar e Ar + + 2

The minimum energy necessary to ionize an atom is its ionization potential. For Ar, H2, O2, and H2O theionization potentials are respectively, 15.76, 15.43, 12.06, and 12.6 eV. The graph below shows the

probability for an ionizing collision as a function of the electron impact energy. For a majority of gases

the maximum in the ionization efficiency versus electron energy lies between about 80 and 120 eV.

Excitation

Electron impact excitation (followed by radiation):

e Ar e Ar + +

Ar Ar h + A cross section can be evaluated using quantum mechanics but only qualitatively. The best way is to

determine it is experimentally. Excitation potential of Ar is 11.56 eV the first excited level of Ar. Ar

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excitation cross-section has a maximum at 21 eV. Excitation of atoms is followed usually by the

emission of light.

Other collisional processes.

Dissociation: e + O2 -> e + O + O

Dissociative ionization:

e + O2 -> 2e + O+ + O

Electron attachment:

e + O2 -> O2-

Electron recombination:e + O2

+ -> O2

TOTAL COLLISION CROSS-SECTION

The graph shows what type of collisions is most probable depending on the electron energy.

= i + ex + d + r+ ....

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A few words on Electricity and Magnetism or where the high school courses usually end

Maxwells equations in the absence of dielectric or magnetic materials:

Integral Form Differential form Differential Form In Onedimension (if useful)

E dA Qoarea

=

=Eo

dEdx o

=

, or d Vdx o

2

2 =

B dAarea

= 0 =B 0 dBdx

= 0

E dld

dt

B

path

=

= EB

t

B dl Id

dto o oE

path

= +

= +B jE

to o o

Maxwells equations in differential form in the absence of dielectric or magnetic materials are given

in the second column. The third column has Maxwells equations in differential form in one

dimension. It is often more convenient to write Maxwells equations in differential form. The changeto the differential form is based on a couple theorems from vector analysis. The two theorems are

listed below, but you can skip that part unless you find this particularly exciting.

Gausss Theorem or the divergence theorem:F dA FdV

volumearea

=

where = + +

x

ti

y

tj

z

tk and

= + +F

F

x

F

y

F

z

x y z

Stokess theorem: F dl F dAarealine

=

The electrostatic potential is defined as E V= or in one dimension, EdV

dx= in the direction of

the most rapid fall of the potential. This definition leads to a different differential statement of

Gausss law: d Vdx o

2

2 = . This form of Gausss law is used for calculating V(x), where x is the

distance from the cathode in glow discharge.

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Plasma Properties

The definition of plasma:

Plasma is a quasi-neutral gas of charged and neutral particles characterized by a

collective behavior.

It is evident from the definition that describing plasma involves describing electromagnetic,

statistical, and long-range effects in a collection of extremely disparate types of particles, neutralatoms or molecules, ions, and electrons.

In glow discharge plasmas electric field affects both electrons and ions, but it is only the electronsthat get hot. According to Newtons second law, acceleration a of a charged particle with a charge q

and mass m in an electric fieldE, is equal

m

qEa = .

The electron mass is at least 1,836 times less than an ion mass. Therefore, the electrical field willhave the largest effect on the electrons. They are accelerated to fast speeds and therefore are

considered hot.

CONDITIONS FOR PLASMA EXISTENCE:

Plasma exists when D >1.

If D e ev= then the electrons can maintain plasma neutrality, or ifee>1, where te is thetime between collisions

1. D > 1

3. e e>1

Plasma Frequency.

Large restoring forces will appear in plasma if the electric neutrality is disturbed for anyreason. These restoring forces are approximately proportional to the displacement, and thats a

condition for simple harmonic motion.

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Plasma Sheath: Interaction of Plasma with the Wall

Particles tend to settle at the bottom of a potential well, whether the system is gravitational or

electromagnetic. In other words, everything must roll to the bottom of a hole at a zero temperature.Plasma in kinetic equilibrium forms an atmosphere around a potential well with highest densities

at the lowest values of energy. In a glow discharge this situation applies to the potential difference

produced between the plasma and the walls of the container as shown in the diagram. The fastelectrons in the positive column quickly make their way to the wall while the plasma is forming.

When the positive column is happily all set up, the negative potential slows the electrons and speeds

up the ions. The hot electrons moving toward the wall also drag the positive ions with them.

The result is that for any given electron temperature of a positive column, the ions and electronsleave together in a process that does not result in a net current and is called an ambipolar diffusion.

Ambipolar diffusion is the movement of both ions and electrons through the gas.

Consider the surface build-up of charge. During the steady state condition, plasma must be in

equilibrium. For the pillbox shown in the diagram to be in equilibrium:

( ) ApppApzAnqE ddddd +=+where the first term is the electrical force and the second is the kinetic pressure term. From this

equation:

znqEp dd = and zkT

qEpd

p

d= .

Page 22 22

-- - - - - - - -

i n s u l a t i n g w a l l

s u r f a c e c h a r g e

nn

o

z

d F = p d A

d F ' = ( p + d p ) d An q d A d z

d z

p l a s m a


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The last equation can be integrated from the top surface of the plasma where z= 0,p =po, and V=

Vo to the positionzwithin the pillbox:

=p

op

z

zEkT

qp

0

dp

d.

Where kinetic temperature of electrons was used: nkTp =The electric field is:

z

VE

d

d=

and the kinetic pressure of a plasma and electron concentration in electrostatic field may be writtenas:

( )

=

kT

Vpp o

oVeexp and( )

=

kT

Vnn o

oVeexp

As shown in the diagram, electric field is established between the plasma and the walls of thecontainer. This electric field will repel the electrons and the plasma therefore is surrounded by anatmosphere of electrons that falls off exponentially toward the walls. The idea of the plasma density

falling off exponentially toward the higher electrostatic potential is essential to the discussion of

shielding and collective behavior of plasma.

Debye Shielding

Shielding effects are specific to plasmas and plasma types. The collective behavior and

quasineutrality manifest themselves in shielding effects.

Lets place a point charge q in a plasma. In free space this charge would create an electric field with apotential V given by

r

qV

04=

where r is the distance from the charge and o is the permitivity of free space, equal to 8.85x10 -12farad/m. In the case of plasma, one can use the Poissons equation

0

2

== EV

where is the space charge density in the plasma. When a charge is inserted in plasma, electronconcentration is changing fast while ion concentration stays the same at least initially. Therefore

( ))x(nne ei = .In the presence of potential Vand electron equilibrium (Boltzmann equation),

=

kT

eVexpnn e

'e (x) .

Substituting this equation in the previous one

Page 23 23


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( )

=

=

e

iei

kT

eVexp

en)x(nn

e

dx

Vd1

002

2

and assuming that eV/kT


25/37


The initial current densities to an electrically isolated substrate or wall

4

v=vvv eee

0

ee

eeen

d)(nej

=

and

ei

i j

en

j


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If the wall is at the floating potential, the electron flux

==

e

weoew,ee

'T

V

m

'eTnvn exp

8

44

1

The net current to the wall is zero

( ) 0== eieAI

Substituting, we can find the potential of the wall orthe floating potential:

=

ei

ieef

'Tm

'Tmln

'TV

2or

=

ie

eiefp

'Tm

'Tmln

'TVV

2

Example:

For Ar ions and Ti = 0.04 eV and Te = 2 eV, the voltage difference is about 15 V.

So an insulated substrate or a wall at a floating potential decreases the electron flux, does not change

the ion flux but increases the energy of ions that reaches the substrate.

Townsend Discharge

To produce a glow discharge, a potential difference can be applied between two electrodes.

The charged particles present in the background accelerate in the produced electric field and a very

small current may be registered. This current quickly saturates as the particles in the background areswept away. If the voltage is increased beyond the saturation point, the current begins to rise

exponentially.

The electrons initially produced by external ionizing radiation or some other source, are

accelerated in the electric field of the discharge tube. If the electric field is high enough, the

electrons can acquire enough energy to ionize another neutral atom before reaching the anode. Asthe electric field becomes stronger these electrons may themselves ionize a third neutral atom

leading to a chain reaction, or an avalanche of electron and ion production. This discharge regime is

called Townsend discharge.The average number of ionizing collisions that one electron makes as it travels one meter

along the electric field is called the Townsends first ionization coefficient . This gives the increasein current density that is proportional to the current density itself and hence an exponentialexpression for the current density

jea = jeced ,

where d is the distance from the cathode to the anode.

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In the absence of secondary emission from the cathode, eventually all the electrons produced reach

the anode and the discharge stops. There must be some secondary emission from the cathode. In thecase of a cold cathode, this is usually caused by ion bombardment.

jes = jic,

where is the secondary emission coefficient the number of electrons emitted per each ion strikingthe cathode.

The current at the cathode is equal to the total of the initial current produced by external

sources, the current produced by the ionization, and the current produced by the bombardment ofions. In the steady state, the ion current arriving at the cathode must equal the difference between

electron current arriving at the anode and the electron current at the cathode. This gives the electron

current at the anode

J Je

e

o

d

=

1 1( )At the breakdown potential Vb, the current might increase by four to eight orders of magnitude, andis limited by the internal resistance of the power supply. From the above expression, the breakdown

occurs when the discharge continues without the external source of current, that is when Jo = 0, butthat is only possible if the denominator is zero. The Townsend criterion is

e d = 1 , for


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ONE MORE LOOK AT THE GLOW DISCHARGE:

WHAT DOES IT HAVE TO DO WITH ALL THAT PLASMA

PHYSICS?

1. Glow discharge is an example of non-equilibrium plasma (as compared to

the thermonuclear plasmas or high pressure thermal plasmas). The

electrons are fast (hot), and the ions are slow (cold). Some ions accelerate to

high enough energy to eject electrons and ions from the cathode. Without

the electron emission from the cathode, the glow discharge cannot exist.

Some electrons are very fast as those in the cathode dark space and some

are much slower as the ones produced by ionization in the negative glow

and the positive column. If it wasnt for its nonthermal character, the

degree on ionization in the discharge would be insignificant.

2. Glow discharge is collision dominated plasma with electron-neutral

collisions playing the dominating role in most processes. The most

important collisions are the inelastic, exciting or ionizing collisions between

the fast accelerated electrons and the neutral atoms or molecules of the gas.

3. The glow discharge operates between three sheaths: two high voltage

sheaths, the cathode and the anode, and one wall potential the walls. The

energy transfer from the outside electric field to the electrons and ions in

the glow discharge occurs mostly in the cathode sheath. The potentials ofthe walls and the electrodes are shielded: within the bulk of the discharge

the electric field is very small. Shielding and the formation of sheaths are

plasma types of behaviors.

4. The glow discharge responds collectively to externally applied electric and

magnetic fields.

5. The plasma parameters of the discharge, such as the Debye length and

plasma frequency, must be considered when choosing diagnostic methods

such as Langmuir probes and microwave interferometry, and forinterpreting the results.

Bibliography

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1. Chen, Francis F. Introduction to Plasma Physics and Controlled Fusion, Volume 1, Second

Edition, Plenum Press, New York, 19842. Roth, J Reece Industrial Plasma Engineering, Volume 1, IOP Publishing Ltd, 1995

3. von Engel A. Electric Plasmas: Their Nature and Uses, Taylor & Francis Ltd, 1983

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BREAKDOWN EXPERIMENT

OPERATING INSTRUCTIONS

Glow discharge tubes have been designed for safe and effective classroom use. To insure long termsuccessful and accident free operation safety guidelines and operating instructions must be followed

at all times.

All teachers and students operating the glow discharge system must complete appropriate laboratory

safety training. The glow discharge system must be operated only under the supervision of a

qualified teacher.

Preliminary Systems Check:

1. First make sure that all the equipment has been properly turned off and disconnected, sincethe previous user may have made operational mistakes.

2. Adjust the separation between the electrodes if needed. Make sure that the separationbetween the electrodes and the pressure you are planning to achieve give a (pd) value that

needs a breakdown voltage less than 1500 V.3. With all power disconnected, check all the electrical connections and grounds. The tube

cables outer shell must be grounded, the body of the power supply must be grounded, and

the ground electrode must have a secure ground.4. Check all gas flow connections. If a gas cylinder is used, it must be closed at this time: the

shut off valve on the cylinder must be closed, the valves on and following the pressure

reducer must be off. The gas intake valve on the system must be closed whether it isconnected to a cylinder or not. The valve connecting the system to the vacuum pump should

be closed also.

5. Make sure the oil level in the pump is correct and the oil has been changed at the appropriate

time.

Turning on the System:

6. Turn on the vacuum gauge. Make sure that the reading makes sense for the atmosphericpressure of about 760 Torr (mmHg).

7. Turn on the vacuum pump following carefully the operating directions for the pump. Listen

for smooth healthy operating noise.8. Slowly open the valve connecting the vacuum pump to the system. Opening the valve slowly

is intended to avoid choking the pump. Watch the pressure gauge and listen to the pump.

Pump down as low as the pump allows, especially if working with a gas other than air, or ifoperating the system after some time of not being used.

9. If using a gas cylinder, follow all operating instructions provided with the cylinder! Open the

cylinder valve slowly and do not exceed the limit on the pressure reducer. Open the valve

after the pressure reducer. Make sure both gauges on the pressure reducer are within safeoperating limits.

10. Slowly open the gas intake valve and adjust the pressure to the desired value within the

interval of about 100 mTorr 2 Torr. Wait for the pressure to stabilize. You should be able tomaintain the pressure for several minutes prior to trying to strike the plasma.

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11. Double-check the electrical connections. Work with one hand. Turn on the power supply.

12. Increase the voltage in steps smaller than 40 Volts to avoid arcing. Watch the ammeter forthe breakdown condition. Avoid increasing the voltage far above the breakdown value to

avoid arcing. The plasma will exists at least within a couple hundred volts below the

breakdown voltage in most situations, so there is a lot of room for changing voltage safely.

Making Adjustments:

13. Before making any adjustments to the system, TURN OFF the POWER supply!

14. To change the pressure, adjust the gas intake valve and/or the valve connecting the system tothe pump, while monitoring the pressure gauge.

15. To strike a plasma again, follow steps 11 and12 above.

16. To change the distance between the electrodes, make sure the power supply is off anddisconnected. The vacuum pump may remain operating. Change the distance between the

electrodes. Check and adjust the pressure in the system.

17. To strike a plasma again, follow steps 11 and12 above.

Shutting Down:18. TURN OFF the POWER

19. Close main valve on the gas cylinder, if it was used. Close the valve after the pressurereducer.

20. Close the gas valve on the system.

21. Close the valve between the system and the vacuum pump.22. Turn off the vacuum pump following the pump operating directions.

23. Do not leave the system under vacuum unattended!

24. If not planning to use the system soon, disconnect the gas line and slowly bring the pressureup to the normal atmospheric pressure. If not planning to use the system for a while, turn off

the vacuum gauge.

25. Lock up the power supply and safely store all the components of the system when not in use!

Training Students:

All students operating the system must be under the supervision of a trained teacher. All students

must pass the safety training. To train students in operating the system,

2. Demonstrate the operating procedure several times.

3. Train the students to perform one step at a time, demonstrating and checking one step at a time.

4. The students should be required to write down the operating instructions for the system. Give thestudents a chance to correct their own operating instructions, and then assess the finished

product.

5. Supervise the students operating the system at all times!!

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1. The Vacuum SystemNote:The experimental work with glow discharge parallels the development of vacuum equipment. This is

reflected in the units used to measure pressure, with the older literature using millimeters of

mercury, and more recent work using Torr for characterizing vacuum and atmospheres for the

pressures above normal atmospheric pressure. Please see the Background section for unitconversions.

Experiment

Sketch the vacuum system include all valves and connections.

Check all valves and connections. Close the inlet gas valve completely. Make sure the valve to the

pump is also closed. Check the gauge connections and turn on the controller. The controller should

read close to the atmospheric pressure, 760 Torr (mmHg). With the valve to the pump closed, turnon the pump. Start opening the valve between the pump to the chamber. The gauge should start

showing a decrease in pressure. If pump is not choking, making loud noises, etc., slowly open thevalve completely. Pump the system for about 10 15 minutes or until the pressure read by the gauge

stops decreasing. The pressure should drop to about 200 mTorr. If the pressure remains in the Torrcheck for leaks with alcohol. This particular arrangement should hold vacuum quite well, so if the

pressure does not decrease, turn of the pump, let the pressure go back up to the normal atmospheric,

check all the seals and connections, and repeat the procedure again.

Record the lowest pressure youre able to achieve and the rate of pressure drop..

Vary slowly open the inlet needle valve. Observe the readings on the gauge. Practice maintaining

several pressure values in the 100 400 mTorr range.

Record a few pressure values youre able to maintain for several minutes.

Repeat this practice exercise but use both the inlet and the pump valves. Try achieving the same

pressures. What is different about the system in these two cases?

How does a convectron gauge work?

Curriculum Connection:

Suggest some ways to use the experiment, the notes, or any of the ideas in this

section to teach or illustrate the concepts of pressure, gas laws, andtemperature usually presented in chemistry or physics curriculum.

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2. Electrical system

Experiment

Make sure the power supply is turned off. Check the electrical connections. Make sure that the

power supply and the chamber are grounded properly (use the water pipes for the ground cable).

Sketch a diagram of the electrical system.

Adjust the pressure to be about 200 mTorr and the distance between the electrodes about 0.40 m.

Turn on the power supply. Slowly increase the voltage until breakdown is achieved, but do not

exceed 1000 V. Record the breakdown voltage, pressure, and the distance between the electrodes.


Suggest some ways to use the experiment or any of the ideas in this section to

teach or illustrate electrical circuits, circuit elements (resistors, capacitors,power sources), electrical conductivity, or any other topics or concepts you mayfind appropriate.

3. Must Try Breakdown

Experiment

Start with small separation between the electrodes of about 1 cm and increase the distance in steps of

about 2 cm. Try some longer distances, 10 cm, 20 cm, 30 cm. At each separation between the

electrodes determine the breakdown voltage and the current for several different pressures. Try

pressures from about 100 mTorr to under 1 Torr. Do not exceed 1000 V on the power supply.

Observe the discharge while taking measurements for very small distances. At these distances the

anode is touching or is inside the negative glow region. The discharge (if it occurs) under theseconditions is called an obstructed glow discharge. There is another possible factor responsible for the

rise in the breakdown voltage for pd decreasing beyond this point. The cathode dark space and some

part of the negative glow may be supplying the cathode with ionizing photons.

Plot the breakdown voltage as a function of (pd), pressure times the distance between the electrodes.

Determine the minimum breakdown voltage and the corresponding value of (pd)min.


Suggest some ways to use the experiment, or any of the ideas in this section toteach or illustrate the concepts of pressure and density, electric field voltagerelationship, behavior of charged particles in the electric field, elastic andinelastic collisions, or anything else except the meaning of life.

Page 33 33


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GLOW DISCHARGE EXPERIMENT

1. Observe the glow

Experiment

Observe the general appearance of the discharge and try to identify the main regions of thedischarge. Which of the regions are visible? Which of the regions seem to be absent? Why?

This may be good time to take a picture of the discharge or to make a sketch.

Establish a discharge at a stable pressure under 500 mTorr. What cathode regions are present? Does

the discharge cover the entire area of the cathode? If it does, the discharge is in what is called an

abnormal regime. The term is purely historical and most discharges in experiments and inapplications are usually in the abnormal regime. Measure and record the axial length of the cathode

(Crooks) dark space, and other visible regions.

Measure and record the length of the positive column.

Turn off the power supply. Change the distance between the electrodes, but keep the pressureexactly the same. Start the discharge again and repeat the measurements of the cathode region and

the positive column. Repeat the measurements three or four times.

Is the behavior of the cathode region the same as the positive column? What is happening to the

positive column? What distance between the electrodes makes the positive column disappear?

Suggest a mechanism to explain your observations.

Suggest a method or several methods to verify your ideas and to further compare the behavior of

the positive column and the cathode region.


Suggest some ways to use the experiment, the notes, or any of the ideas in thissection to teach or illustrate the concepts of energy, energy transfer,temperature, random versus organized behavior, the role of collision processes.

2. Pressure changes Cathode region

Notes:

Before pressure gauges were developed that gave continuous readings it was an accepted practiceto estimate the gas pressure by the length of the cathode dark space.

Experiment

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Vary the pressure and measure the length of the cathode dark space and also dc, the length of the

cathode region from the cathode to the beginning of the negative glow.

Develop a calibration curve for a pressure gauge based on the cathode dark space. Compare the

readings to the convection gauge. What is the accuracy and reproducibility of the cathode

manometer?

What processes could account for the observed relationship between the cathode dark space and

pressure?

Calculate the values of (pdc) for the measurements taken in this section. How do these values

compare to the (pd)min from the Paschen curve in the breakdown section of the experiment?

If ( ) ( )pd pdc min then V Vc min and is independent of other parameters of the discharge, such ascurrent. Suggest why that might be the case and also suggest the mechanism(s) by which this

condition may be violated by increasing the current.


Suggest some ways to use the experiment or any of the ideas in this section toteach or illustrate the concepts of pressure, mean free path, resistivity, themeaning of light and dark or any other topics or concepts you may findappropriate.

3. Voltage-Current Characteristic.

Experiment

Draw a circuit diagram for measuring the V-I characteristic of the glow discharge.

Starting with a discharge at about 100 mTorr and with the electrodes close enough so that there is no

positive column, take the voltage- current characteristic of the discharge. Take steps of about 50 Vand change the voltage over about 500 V range. While changing the voltage observe and record the

changes (if any) in the size of the features in the cathode region. Explain your observations. Repeat

with the positive column present. Graph the results and estimate the resistivity of the plasma. Doesthe resistivity depend on the current? Is this result consistent with visual observation of the glow?

Please provide a possible explanation.


Suggest some ways to use the experiment or any of the ideas in this section toteach or illustrate the concepts of circuits, ohms (or not so ) law, resistivity,electrical power use and dissipation, electrical lighting devices or any othertopics or concepts you may find appropriate.

Page 35 35


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4. Spectroscopy

Experiment

Record the spectra of the negative glow and the positive column. Compare the results and explain

the differences.

If an optical attachment is available, try to take the spectra from more localized regions in thedischarge. Give a qualitative explanation of the results.

Repeat the measurements with other gasses if available.


Suggest some ways to use the experiment or any of the ideas in this section to

teach or illustrate the concepts of energy, potential difference and electricalpotential energy, elastic and inelastic collisions, emission of photons, electronenergy states in atoms or molecules or any other topics or concepts you mayfind appropriate.

5. Observing striations

Experiment

Alternating regions of light and dark have appeared many times throughout the previousexperiments. The discharge conditions mentioned above, 100 mTorr, d = 0.40 m, probably have

them. If not, vary the pressure and voltage until you do see them.Slowly change the pressure and record your observations in as much detail as possible. Record yourobservations, measurements, and comments. Suggest a possible explanation of the observed effect.

Are the striations moving or standing? How can you find out?

Under what conditions do the striations change from standing to moving?

When the positive column looks uniform, is it really?

A photodiode can be used to investigate the behavior of the moving and standing striations. Connect

the diode to an oscilloscope, check for background reading, then check for a reading in a dim region

and in a bright region. How do the measurements compare to the background noise? If the signal-to-noise ratio is acceptable, then conduct measurements to investigate the nature of the striations. For

example, determine the frequency of the observed waves.


Suggest some ways to use the experiment or any of the ideas in this section toteach or illustrate the concepts of pressure, mean free path, temperature and

Page 36 36


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energy, waves of all sorts, the relationship between acoustic andelectromagnetic waves or any other topics or concepts you may findappropriate.

Optional: Try some other experiments.

For example, a Langmuir probe is available (might have to be used on a different glow discharge

apparatus), an antenna can be constructed, magnets are available and magnetic properties can be

investigated, a coil can be used to drive music waves through plasma.

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Glow Discharge Theory

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