TTHHÈÈSSEE

En vue de l'obtention du

DDOOCCTTOORRAATT DDEE LL’’UUNNIIVVEERRSSIITTÉÉ DDEE TTOOUULLOOUUSSEE

Délivré par l'Université Toulouse III - Paul Sabatier Discipline ou spécialité : Physique et ingénierie des plasmas de décharge

JURY

Mr Tong Bao LI, Professeur et académicien, Université de Tongji Shanghai (Président et Rapporteur) Mr Dunpin HONG, Professeur, Université de d'Orléans (Rapporteur)

Mr David BUSO, Maître de conférence, Université de Toulouse (directeur de thèse) Mr Georges ZISSIS, Professeur, Université de Toulouse (co-directeur de thèse)

Mr Dahua CHEN, Professeur, Université de Fudan Shanghai (co-directeur de thèse) Mr Rong Qing LIANG, Professeur, Université de Fudan Shanghai (examinateur) Mr Shaolong ZHU, Professeur, Université de Fudan Shanghai (examinateur)

Ecole doctorale : Génie Electrique, Electronique, Télécommunications

Unité de recherche : Laboratoire LAPLACE (UMR 5013) Directeur(s) de Thèse : David BUSO, Georges ZISSIS

Rapporteurs : Dunpin HONG, Tong Bao LI

Présentée et soutenue par Yang LIU Le 02 Juin 2010

Titre : Research on striations in low pressure rare gas and mercury discharge

Acknowledgement

Special gratitude goes to Prof. Dahua Chen. Thanks for his care and support on my

work and my life. I am not able to finish my PhD program without his considerable

aid and supervision.

Special gratitude goes to Prof. Georges Zissis, Associated Prof. David Buso for their

patient discussion and direction on my work. Also thanks for their bounteous help on

my life in France, which makes it easier for me to fninish my work there. Thanks for

their efforts during the preparation of thesis defence.

Appreciation also goes to Sounil, Robert, Anca and Jasmine. You are like my big

family in France. The parties, the activities we joined together became important

sources of happiness and enjoyment in France. You make my life in France colorful

and impressive.

I should also thank Zein, Mohamad, Hughes, Julliens, Marie, Xiao Yu, Feihu Zheng,

Dongchang Sun. You are all my good friends in France. Your accompanying is

important for me.

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Table of Contents Table of Contents .........................................................................................................1 Abstract 3 Chapter 1 Introduction.............................................................................................5

1.1 Striations in gas discharge.............................................................................................5

1.1.1 Background .......................................................................................................5

1.1.2 Early research on striations ...............................................................................6

1.1.3 Recent research on striations...........................................................................16

1.2 Striations in low pressure rare gas and mercury discharge .........................................20

1.2.1 Introduction to fluorescent lamps....................................................................20

1.2.2 Research on striations in low pressure rare gas and mercury discharge..........22

1.3 Efforts from the present thesis ....................................................................................25

1.4 Creative points ............................................................................................................26

Chapter 2 Experimental investigation on moving striations in low pressure rare gas and mercury discharge .......................................................................................34

2.1 Introduction.................................................................................................................34

2.2 Experiments ................................................................................................................34

2.2.1 Electrode heating.............................................................................................34

2.2.2 Spectra.............................................................................................................38

2.2.3 ICCD High speed imaging ..............................................................................49

2.2.4 Monochromator...............................................................................................52

2.3 Summary .....................................................................................................................59

Chapter 3 Introduction to simulation of low pressure gas discharge.................63 3.1 Introduction.................................................................................................................63

3.2 Category of models on low pressure gas discharge plasma ........................................64

3.2.1 Particle model..................................................................................................64

3.2.2 Kinetic model ..................................................................................................65

3.2.3 Fluid model .....................................................................................................65

3.2.4 Hybrid method ................................................................................................67

3.3 Examples: simulation on low pressure gas discharge plasma .....................................67

3.3.1 Simulation on variation of plasma parameters versus cold spot temperature .67

3.3.2 Quantitative simulation on high frequency low pressure rare gas and mercury

discharge 76

3.4 Summary .....................................................................................................................83

Chapter 4 Kinetic model on striation in low pressure Ar-Hg discharge............87 4.1 Introduction.................................................................................................................87

4.2 Model establishment and solution...............................................................................87

4.2.1 Governing equations and macroscopic parameters of plasma ........................87

4.2.2 Solution conditions..........................................................................................90

4.2.3 Numeric method..............................................................................................92

4.3 Results and discussion.................................................................................................94

4.4 Summary ...................................................................................................................103

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Chapter 5 Conclusion ...........................................................................................107 Appendix A Introduction to FEMLAB ..................................................................109 Appendix B Elastic and inelastic collision cross sections of Ar and Hg .............. 114 Appendix C Matlab code for the kinetic model (part) .......................................... 118 Acknowledgement ....................................................................................................127

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Abstract

Stratified discharge was fisrt discovered by Michael Faraday in 1930s. Research on

striations in low pressure gas discharge has witnessed considerable achievements.

Nevertheless, most of the works focused on pure rare gas discharge, research on

striations in AC discharge of gas mixtures still remains to be done. In the present

thesis, investigation on moving striations in low pressure rare gas and mercury

discharge is performed, where reasons and properties of this phenomenon are

explored. By doing this work, we hope that reasons for this phenomenon can be

discovered; properties of low pressure rare gas and mercury discharge can be better

understood. Thereby, this phenomenon can be removed from fluorescent lamps in the

future.

In our experiment, we collect emissive spectra of the lamp under different cold spot

temperature. We find that strong moving striations always coincide with substantial

ratio of rare gas radiation in total spectrum. Theoretical analyses reveal that moving

striations in low pressure rare gas and mercury discharge are incurred due to

dominance of stepwise ionization of rare gas atoms in ionization balance of the

plasma. Then we perform high-speed imaging to the lamp with an ICCD cameara and

find that moving striations only appear on the rising edge of lamp current. On the

falling edge, the discharge is uniform. This phenomenon is rarely mentioned in

previous works. We couple the ICCD cameara with a monochromator and record

emissive atomic lines in the working period of the lamp. Results demonstrate that on

the rising edge of lamp current, radiation from both rare gas atoms and mercury atoms

is strong; on the falling edge, radiation from both species become weak. Therefore,

we can expect that on the rising edge of lamp current, external electrical energy is

injected into the plasma, which causes excitation and ionization frequently happen.

During this periond, lack of mercury atoms may result in dominance of stepwise

ionization of rare gas atoms in ionization balance, which incurs moving striations.

In our theoretical investigation, electron response to spatially periodical electric field

in low pressure Ar-Hg discharge is examined in the framework of kinetic theory. The

simulation is based on non-local stead-state Boltzmann, which is numerically solved

with Crank Nicholson scheme. Simulation results depict in detail the distribution of

electrons with different energy in spatially periodical electric field and how non-local

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effect influences the discharge. The EEDF can be divided into two parts: bulb part and

tail part, which stand for slow electron and fast electron. These two kinds of electrons

have different response to electric field. Slow electrons almost drift along the electric

field, while fast electrons tend to collide with and pass their energy to Ar and Hg

atoms. Simulation also infers that macroscopic parameters of the plasma such as

normalized electron density, electron temperature, excitation frequency and ionization

frequency react anomalously to the electric field, which provides the necessary

motivation for the propagation of the fluctuation.

According to experimental and simulation results, major causes of striations come

from stepwise ionization of metastable rare gas atoms dominating ionization balance.

This leads to non-local EEDF, which enables amplification and propagation of

instabilities. Therefore, the feasible method to eliminate striations is to suppress

production of metastable rare gas atoms. This can be realized by increasing discharge

current, increasing Hg vapor pressure; and increasing discharge frequency.

This thesis bears creative points as follow:

1. Provide electrode heating current to the lamp to suppress disturbances in cathode

region; then proves that under the experimental condition, striations in low pressure

rare gas mercury discharge are not originated from cathode region.

2. ICCD high speed imaging reveals that striations only appear on the rising edge of

the light signal; on the falling edge, striations disappear.

3. Solve the Boltzmann numerically by Crank-Nicholson scheme and simulate

electron response to spatially periodic electric field in low pressure Ar-Hg discharge.

Motivation of propagation of striations is discussed.

Key words: moving striations, fluorescent lamp, low pressure rare gas and mercury

discharge, metastable rare gas atoms, stepwise ionization

No. of Chinese Library Classification: O534

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Chapter 1 Introduction

1.1 Striations in gas discharge

1.1.1 Background

Striations, or stratified instabilities, or ionization waves are the most common

phenomena in gas discharge [1].They are featured by bright and dark intervals along

the discharge axis (shown by Figure 1.1). Stratified discharge is first recorded by

Michael Faraday in the 1930s; after that striations in different gas discharges under

different conditions are discovered in succession [1].

Figure 1.1 Striations in Gas discharge

Stratified discharges can be categorized according to different criteria. If striations

come themselves, they are named self-excited striations. If they are induced by

artificial means, then they are called artificial striations. If the bright and dark

intervals do not move, then we name them as standing striations; otherwise, we call

them moving striations. For moving striations, if direction of the group velocity is

toward cathode, then we say that it is positive striation; otherwise, we say that it is

negative striation. According to the magnitude of group velocity, we can classify the

striations into slow type striation (p-type) and fast type striation (r and s-type).Table

1.1 shows the comparison between group velocity of different moving striations in a

Ne discharge, where the radius of discharge tube is 1 cm, filling gas pressure is 2 Torr

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and discharge current is 3.4 mA.

Table 1.1 Comparison between group velocity of moving striations in a Ne discharge

[1]

Type of Striations Group velocity (m/s)

p

r

s

231

1570

4520

Striations appear in many application fields and bring about negative influences. In

laser cutting, striations may cause coarse cutting [2]-[4]. In lighting industry, striations

seriously affect lighting effects; furthermore, the flickering frequency locates at

sensitive area of human eyes, which leads to visual fatigue [5].

1.1.2 Early research on striations

Research on stratified discharges has a history over more than a century. We consider

the period to be the early phase of research on striations, from the very beginning

when Faraday recorded striations for the first time until 1960s Pekarek published

reviewed papers [1] - [7] on striations. Most of the work during this time was mainly

concentrated on self-excited striations. Existing condition, properties and factors that

might influence stations consisted of the dominant part of the research. Theoretical

efforts were also made. Later, artificial striations gradually became interesting topics.

Measurement on properties of artificial striations and theoretical work were

performed.

Research on self-excited striations——Ranges of occurrence

Pupp has found that for a fixed filling pressure if discharge current was beyond a

certain value, striations in the plasma would disappear ([6], pp. 162). Therefore, he

depicted the curve for this critical current and filling pressure (Figure 1.2). This curve

is called the Pupp’s limit. From the figure we can see that critical current increases

when gas pressure decreases. They comply with the equation as follow:

/ci c p= 1.1

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where c is an empirical constant.

Figure 1.2 Pupp’s Limit

Zaitsev et al discovered that in Ne discharge there existed a special current-pressure

region (current less than 20 mA and pressure less than 6 Torr), where striations did not

appear ([6], pp.16). This region was entitled to be the Quiet Region. Achtergerg and

Michel depicted this region, which is shown in Figure 1.3. The part enclosed by dash

lines is the so-called quiet region. The solid lines mark the discharge condition for

striations with the same frequency. Michel et al also found this region in Ar discharge;

while Zaitsev discovered in He discharge the similar region ([6], pp. 166).

Figure 1.3 the Quiet region in Ne discharge depicted by Achterberg ([6], pp. 166)

Pfau investigated striations in hydrogen discharge and depicted the i – p limit (shown

by Figure 1.4) ([6], pp. 169). In the A area, observation with bared eyes came up with

uniform discharge, but instrument detection revealed it to be stratified. In the B area,

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standing striation often appeared, however sometimes, moving striations also

appeared. In the C area, the discharge is uniform. In pure nitrogen discharge, Pfau

found that the existing region of striations on the i – p plot was quite smaller. The size

of this region was very sensitive to the radius of discharge tube. Figure 1.5 presents

the existing region of moving striations in nitrogen discharge with tube radii of 0.55

cm and 1.55 cm.

Figure 1.4 Existing region of striations in hydrogen discharge with tube radius 1.1 cm. In area A there are moving striations; in area B there are standing striations; in area C

the discharge is uniform. ([6], pp. 169)

Figure 1.5 i – p limit of striations in nitrogen discharge（[6], pp. 170）

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Foulds witnessed self-excited moving striations in Hg discharge when vapor pressure

was less than 0.01 Torr. The striations were attenuated towards the direction of anode.

He thought that disturbance in cold spot might be the reason for the phenomenon ([6],

pp. 171). Bandelin excited artificial striations in Hg discharge and he found that the

instabilities were damped along the direction pointing to anode. Thereby, he

concluded that in Hg discharge, self-excited moving striations hardly came unless

there were disturbances in cathode region ([6], pp. 171).

Hakeem and Robertson have found that in alkali metal vapor discharge there were no

moving striations. Disturbances could be witnessed near anode region if strong anode

oscillation came into being. But these disturbances did not survive for long distances.

Rutscher and Wojaczek carried out research on gas mixtures. They witnessed obvious

decrease in Pupp’s limit in a Ne discharge dosed by a small amount of He. However,

if Ne and Ar were mixed with the ration of 1 to 4, then the Pupp’s limit of the

discharge exhibited no differences with that of pure Ar discharge ([6], pp. 172).

Gundermann found that adding little Ar to Ne led to significantly lower Pupp’s limit

and striations were suppressed ([6], pp. 173). Garscadden et al observed moving

striations in He-Ne laser. Its direction was from anode to cathode, its frequency was

about 380 kHz and its group velocity was 3.15×103 m/s, which was one order bigger

than those of normal rare gas discharges. This might be due to higher axial electric

field [8], [9].

Novak measured the distances between two bright intervals of striations (wavelength

of the striation) and the electric field in this region in low current rare gas discharge

[10]. He found that for a certain type of striation, the product ϕλ of its wavelength λ

and the electric field E was constant. We called it the Novak’s Law. Figure 1.6

presents the λ - E relation of different striations in a Ne discharge with filling pressure

1.0 - 5.5 Torr and discharge current 0.2 - 8.0 mA. From the figure we can see that no

matter the striations are fast or slow, they all obey the Novak’s Law well. Table 1.2

lists the ϕλ of the above Ne discharge and the deviations from the standard value. We

can tell that measured ϕλ deviates little from the standard value.

In rare gas discharge, striations always coincide with anode oscillation and their

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frequencies locate at the same band. Therefore, anode oscillation was once considered

to be the cause of striations. However, Pupp found in his experiment that striations in

positive column remained the same even if anode oscillation was removed with an

auxiliary electrode. This means that anode oscillation has nothing to do with striations

[1]. Later efforts by Rademacher and Cooper also proved that there were no essential

connections between anode oscillation and striations ([6], pp. 188).

Figure 1.6 Relation between wavelength and electric field in a stratified Ne discharge

Table 1.2 Novak’s measurement on striations in a Ne discharge

Type of striations ϕλ （V） Number of

points

Average

deviation (%)

Maximum

Deviation (%)

p

r

s

9.20

12.67

19.48

105

34

13

1.6

2.7

0.94

7

9

2

Most of gas discharge plasmas have negative resistance property. Therefore, a ballast

is needed to work with the discharge component. According to some research,

frequency of moving striation is not determined by circuit parameters. Nevertheless,

disturbances in circuit may be coupled to the plasma and become sources of

instabilities. Stewart testified the above point by his experiments ([6], pp. 190).

Lakatos and Bito considered the plasma as an equivalent LC series, and they deduced

the condition under which the plasma was free from the circuit disturbance ([6], pp.

191).

Striations are closely connected with dimension of discharge tubes, the closest of

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which is tube radius. Pupp found that fitting striation frequency f and filling pressure

p for discharges with different tube radii led to a curve deviating from most of the

data points. If fitting with frequency×radius (f×r) and pressure×radius (p×r), almost

all the data points locate on the same curve, which has no dependency on discharge

current ([6], pp. 191). Kenjo and Hatta observed striations in a cone discharge tube.

They found that wavelength of the striation had nothing to do with direction of

discharge current and filling pressure. It only depended on n-th power of tube radius

(n is between 1.5 and 2.0) ([6], pp. 193).

Besides tube radius, striations also depend on tube length. Gertzenstein and Potemkin

proposed that self-excited striations resembled a self-oscillating system. Only when

discharge gap was integral multiple of striation wavelength, might the oscillation in

the system result in positive feedback, by which the oscillation could survive.

Therefore, when discharge gap changed, wavelength of striation followed suit so that

the system could kept its positive feedback ([6], pp. 194).

Research on artificial striations——Theoretical research

Watanabe and Oleson tried to use continuous equations and diffusive equations of

electron and ion and disturbing method to infer wave number and frequency of

striations. They found that when charged particles slightly suffered from dipole

diffusion, striations might be incurred ([6], pp. 198).

Robertson used particle balance equations to deduce the cause of striations in DC rare

gas discharge. His equation system included electron, ion and metastable atoms.

Ionization balance not only took into account direct ionization of atoms from ground

state, but it also included stepwise ionization. According to the simulation results,

when there were no metastable atoms, local perturbation of electric field might cause

variation in ionization frequency, which would propagate along the direction of

electric field. This instability would be quickly damped due to dipole diffusion and

volume recombination. If there were metastable atoms, the instability might not be

easily attenuated and would be continuously propagated because these kinds of atoms

could be easily ionized. This could be the reason for the appearance of striations in

discharge ([6], pp. 200; [11]).

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Stewart deduced radial distribution of electron density in Ar discharge from electron

continuous equation and variable separation ([6], pp. 204): 2

20aa

DR RD AR

r rr

∂ ∂+ + =∂∂

1.2

where R is radial distribution of electron density, Da is dipole diffusive coefficient, A

is constant from variable separation. By assuming that electron density is zero at the

tube wall, the solution R(r) of the above equation follows 0-class Bessel function.

Compared the simulation with his measurement results, good agreement was found.

He then concluded that even if there was moving striation along the discharge axis in

the positive column, radial motion of electrons was dominant by dipole diffusion.

Pekarek researched propagation of pulse disturbance in plasma [1], [12]. In his

simulation, he assumed a local instantaneous perturbation in the plasma, which led to

variation of plasma density, electric field and electron energy in this region (shown by

Figure 1.7). He considered that ionization rate coefficient was function of electron

energy and charged particles were mainly lost by dipole diffusion. Then he got:

1

2( )

2( )a za z

n nD n A e n d

t zξα ξ ξ

∞ −+ ++ +

∂ ∂= + −

∂ ∂ ∫

1.3

where ' 1 0/Z b kT qϑα −= , '

1 1 0 0( / )A Z b kT a q Eϑ −= + , 'Zϑ was electron energy derivative

of ionization frequency. Figure 1.8 shows the solution of equation 1.3 in 15 ms after

perturbation. Anode is on the left and cathode is on the right. From the figure we can

tell that perturbation of ion density goes in the direction of anode, i.e. group velocity

points to the anode. Motion of phase has the opposite situation, the direction of which

points to the cathode. Wojaczek once pointed out that moving striations with small amplitude could be put

into the form as ( )i Kx te −Ω ([1]; [6], pp.226). He also found in his experiment that only

when the frequency of external excitation source was close to the frequency of self-excited moving striation, would artificial striation appear. Otherwise, local external disturbance would be quickly damped. This means that a dispersion curve may be used to describe the artificial striation. Wojaczek presented this relation as:

( , ) 0F K Ω =

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1.4 where k is wave number, Ω is frequency. Normally, these two parameters are negative, thereby can be put as:

K k id= + iω ϕΩ = +

1.5 where d is spatial amplification and φ the temporal amplification. In the range of discharge parameters in which moving striations of small amplitude are observed, the

following inequalities always hold:d k

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2 21 1

1 1 111

( ' ) ( ' )( , ) exp{ }cos[ ]

4 244

z t z tCS z t t k z t

g tb tB t

ω ω ψω ωπ

− −= − + − + −

1.7

Finally, putting all the conditions together, we can get dispersion curve of artificial

striation.

Figure 1.8 Development of pulse disturbance in 15 ms. Dashed lines correspond to later moment (0.01 ms later) than solid lines

Novak and Wojaczek excited artificial striation in Ne discharge in order to testify the

aforementioned dispersion theory. In their experiment, gas pressure was 1.9 Torr and

discharge current was 4.2 A. Figure 1.9 presents the measured wavelength-frequency

relation of the artificial striation.

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Figure 1.9 Wavelength-frequency relation measured by Novak and Wojaczek

Rutscher assumed that wave number k is function of frequency ω, i.e. ( )k f ω= . He

expanded this relation near the optimum frequency ω0 and finally obtained the

dispersion relation as follow:

20 0 0

0

1( ) ( )k k b

uω ω ω ω= + − + −

1.8

where k0, ω0, u0, b could be acquired through experiment. Figure 1.10 depicts

Rutscher’s dispersion curve of artificial striation ([6], pp. 241).

Figure 1.10 Dispersion curve of artificial curve calculated by Rutscher. The radius of

discharge tube is 2 cm, filling pressure is 1.4 Torr and discharge current is 5 mA.

Circles on the figure were measured wave number and frequency [6]

Other references on striations include: Lee and his colleague’s efforts on essence of

artifical striation [13]; Ewald and Duncan’s research on striations in the positive

column of low pressure gas discharge with magnetic field [14]-[16]; Drouet measured

electron temperature in striations [17]; Garscadden’s research on properties and

dispersion curve of striations in He-Ne laser [18]-[20]; Gentle’s experimental and

theoretical efforts on striations [21][22]; Munt’s simulation on striation propagation

[23]; Nakata’s research on striation dispersion [24]; Watanabe and Olesen’s efforts

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[25]; Takeyama’s measurement on striations in high frequency discharge [26][27].

1.1.3 Recent research on striations

In 1970s, as research on striations going deeper, scientists found that electron kinetics

became inevitable in analyzing reasons and mechanisms of striations [28]. Therefore,

kinetic theory was more and more involved in research of striations.

Rohlena et al composed an equation system with Boltzmann equation (BE) of electron

and fluid equations of metastable atoms and ions in order to describe the moving

striation in ne discharge [29], [30]. He found six solutions from the system which

corresponded to six different types of striations. Four of them then had been

discovered (three types were correlated with electron spatial resonance, the other one

were the result of spatial drift of metastable atoms).

Rayment measured temporal variation of the electron energy distribution function

(EEDF) of different types of moving striations (p, r and s type) in Ne discharge [31].

He found that under small discharge current, p, r and s-type striation came from the

spatial resonance of electrons. This mechanism also provided explanation to Novak’s

Law. Under big discharge current, colossal electron – electron (coulomb collision)

collision might weaken temporal variation of EEDF. Under this condition, striations

occur due to variation of ionization rate along with electron density.

Skoblo et al numerically solved the BE and simulated striations in 1 Torr Ne

discharge. They analyzed modulation depths of electron density, electron temperature

and other plasma parameters corresponding to different striations. Meanwhile, they

deduced s and p type moving striation; and they also proved that r type striation

resulted from electron spatial resonance [32].

Tsendin solved the BE in a spatially periodic electric field [33]. He put the problem

into space-total energy (kinetic energy + potential energy) phase space and assumed

that once electrons’ kinetic energy exceeded excitation level of atoms, electrons lost

their energy by inelastic collision with the atoms. That means there is a “black wall”

in the phase space, none of the electrons bore energy bigger than excitation level of

atoms. He found that the BE gave a spatially periodic solution under this condition

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and fast electrons exhibited non-local behavior. Therefore, he attributed appearance of

striations to this non-local effect of EEDF.

Golubovskii developed Tsendin’s theory: he dropped the “black wall” assumption and

solved the BE in a spatially uniform and spatially periodic electric field [34]. He

found that in the absence of channels of energy dissipation connected with energy loss

in elastic impacts and in the presence of several excited states, information about the

initial EDF injected in a field of arbitrary configuration, can be transmitted over an

unlimited distance. The process of the relaxation has the nature of undamped

oscillations. The introduction of channels of energy dissipation results in a damped

oscillatory relaxation character of the EDF injected into a uniform field and in the

establishment of a homogeneous EDF in this field. The relaxation of an EDF injected

into a spatially periodic resonance field (shown by Figure 1.11, where z is spatial

coordinate, ε is total energy of electron) results in the distribution function having

specific maxima which change in energy and coordinates along the resonance paths in

accordance with the potential distribution (the so-called bunching effect). This effect

can be used for the interpretation of EDF formation in S- and P-striations in inert gas

discharges at low pressures and currents [35]. He also pointed out that non-local effect

of EEDF might lead to phase difference between electron density peak and ionization

frequency nadir, which provided the necessary motivation for striations. In [36] and

[37], he researched the electron kinetics and density of excited atoms in s and p-type

striation. In [38], he simulated striations in intermediate pressure rare gas discharge.

In [39], he measured the temporal and spatial variation of axial and radial plasma

potential in s and p-type striations in low pressure Ne discharge. In [40], measurement

and simulation on the r striation in Ne discharge were performed. In [41], research on

s and p striation in Ne discharge based on kinetic theory was performed.

Signeger and Winkler devised a numerical method to solve the BE based on

Crank-Nicholson scheme [42].With this method hey performed detailed theoretical

investigation on s and p-types striation in DC glow discharge [43] [44]. They found

that the initial injected EEDF would evolve into a certain distribution, which was only

determined by the spatially periodic electric field. Changing the initial EEDF would

not influence the final distribution of the EEDF.

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Figure 1.11 The Phase space used by Golubovskii to solve the BE in [34]

Arslanbekov performed 2D simulation on moving striation in lower pressure DC Ar

discharge [45]. His model was based on continuous equations of all particles and

Poisson Equation. Rate coefficients and diffusive coefficients of electron were

beforehand obtained by solving BE. The simulation result is shown in Figure 1.12.

Arslanbekov thought that ionization frequency’s dependency on electron density was

the reason for the appearance of striation.

Figure 1.12 Simulation result of moving striation in DC Ar discharge [45]

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Siefert carried out diagnostics on electron density in a low pressure Ar discharge with

microwave technology [46]. The subject plasma presents self-excited striation.

According to the measurement, electron density in the positive column varied

periodically with time (shown by Figure 1.13) and peaks of electron density did not

coincide with that of the metastable Ar. Siefert supposed that stepwise ionization of Ar

atoms was the main reason for the self-excited striation.

Sukhinin and Fedoseev established a 1D self-consistent model of striation in a Ne

plasma [47]. The discharge pressure was 1.6 Torr, average electric field was 4 V/cm,

and discharge gap was 20 cm. Electron was described with kinetic theory, ions

followed the continuous equation and electric field obeyed the Poisson Equation. The

model did not take into account excited atoms. Results revealed that electric field and

particle density in striation evolved periodically in space. But the profile of these

parameters deviated from sinusoid. Departure from electric neutrality i.e. ( )i ei

n nn

− ranged between 100 and 0.001.

Figure 1.13 Temporal variation of electron density in low pressure Ar discharge

diagnostic by microwave technology by Siefert [46]

LEE et al researched mechanism of striations in PDP (Plasma Display Panel). They

thought that accumulation of charged particles on anode surface and non-local effect

of electron kinetics contributed together to the appearance of striation [48], [49].

Muraoka et al performed simulation on striations in PDP and results agreed quite well

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with previous experiments [50].

Recent research on striations also include: Feng He’s research on striations in

PDP [51] [52]; Iza’s research on formation mechanism of striations in PDP [53];

Ohe’s efforts [54]-[57]; Muraoka’s simulation on striations in PDP [58]; Nerushev’s

research on stratified spherical discharge[59]; Sergey’s efforts on striations in

spherical discharge [60]; Dinklage’s simulation on hysteresis in striations [61];

Kumar’s research on pillared striations in Ar surface wave plasma [62]; Shkurenkov’s

simulation [63]; Bae’s fluid model on striations in PDP [64]; and Yang’s research on

striations in PDP anode region [65].

In the year 2006, Kolobov summarized progresses in research on striations since

1970s [28]. He pointed out that our newly obtained insight into striation mainly came

from the development of electron kinetic theory and computer science. Meanwhile, he

called for attention to striations in some new modes of discharges such as DBD.

Kolobov thought that diagnostic on plasma through striation might be feasible since

electron density and ionization processes were all very sensitive to striation. Therefore,

in the future, striation might accord us with deeper understanding of plasma sources.

1.2 Striations in low pressure rare gas and mercury

discharge

1.2.1 Introduction to fluorescent lamps

In the year 1938, George Inman and his research group in GE invented low pressure

Hg vapor discharge lamp, i.e. linear tube fluorescent lamp. Afterwards performance of

this kind of lamp was greatly improved due to the development of science and

technology. Now, fluorescent lamps have become the most widely used light sources.

Fluorescent lamp can be classified according to many standards: judging by tube

shapes there are linear tube fluorescent lamps, compact fluorescent lamps, ring-like

fluorescent lamps; judging by tube radius, there are T12, T8, T5 and T2 lamps;

judging by working frequency, there are DC fluorescent lamps, low frequency AC

fluorescent lamps, high frequency AC fluorescent lamps; judging by discharge

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mechanism, there are electroded fluorescent lamps, inductively coupled fluorescent

lamps and DBD fluorescent lamps.

Figure 1.14 Inside a fluorescent lamp

The structure of linear tube fluorescent lamp is shown in Figure 1.14. The discharge

chamber is enclosed by a glass shell, inside which there fills rare gas and mercury. Hg

is the main player of discharge; while rare gas (Ar or Ar, Kr mixture) ensures the

necessary electrical properties. Discharge is excited by the electrodes located on the

both end of the lamp. UV radiation produced by the excited Hg atoms will be

transferred into visible light by the phosphor coated on the inner wall of the tube.

Early lamps often use calciumhalophosphate phosphor. It is less expensive but suffers

from low efficacy and low stability. Now triband phosphor becomes prominent due to

its high maintenance of flux, high efficacy and high color rendering. Correlated color

temperature of the lamp may also be changed by altering the composition of the

phosphor.

Fluorescent lamp has negative resistance property, therefore should be operated with a

ballast. Figure 1.5 presents typical working circuit of a fluorescent lamp driven by

line power. Because ignition of the lamp requires high voltage, there is no current

inside the lamp right after the switch is on. The line power is directly applied on the

starter. Afterwards a high voltage will be produced by the ballast on the both ends of

the lamp so that discharge is established. Once the lamp begins to work, starter will

stop working.

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Figure 1.15 Typical circuit of a low frequency AC operated fluorescent lamp

1.2.2 Research on striations in low pressure rare gas and

mercury discharge

Donahue and Dieke did research on striations in low pressure Ar-Hg discharge ([6],

pp. 172). Measurements were made, however, for only a few isolated mixtures

(saturated mercury vapor in 4 Torr argon and in 15 Torr of argon and neon, in tubes of

diameter 15 and 13 mm, respectively). Moving striations were found over the entire

range of investigation, up to 60 mA discharge current. No control was maintained

over the mercury partial pressure, and cataphoretic separation of gases was not

mentioned.

Oleson and Found observed the upper critical current for a discharge in 7 Torr argon

with saturated vapor pressure of mercury at 40 centigrade maintained in a water bath.

The critical current in this case showed a hysteresis effect, changing from 0.25 A

when approached from above (i.e., from the homogeneous condition) to 1.4 A when

approached from below ([6], pp. 172).

Rutscher and Wojaczek reported a stabilizing effect on the discharge (i.e., suppression

of the moving striations) due to the addition of mercury to discharge in the inert gases

in a tube of 14 cm diameter. In view of the measurements already discussed, such a

stabilizing effect must be strongly dependent on tube geometry ([6], pp. 172).

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Yoshimoto have deduced wave function of light intensity due to striation in an Ar-Hg

discharge. However, he did not give any numeric results ([6], pp. 202).

Van den Heuvel has done research on artificial striation in low pressure Ar-Hg

discharge [66]. The discharge tube is 0.6 m long with diameter 12 mm. Inside the tube

there fills 400 Pa Ar and saturated Hg. Figure 1.16 shows the experimental circuit.

The discharge tube is connected with a DC source. An oscillation source, an

adjustable resistor and a capacitor are connected in parallel with the discharge tube.

The oscillation source and capacitor are used to excite striation in the discharge. The

resistor can control the feedback from the external circuit. Light output from the lamp

is collected by a photomultiplier. Van den Heuvel found that in his experiment the

striation came from the current oscillation in cathode region. Feedback from the

external circuit played an important role in the formation of striation.

Figure 1.16 Circuit layout in van den Heuvel’e experiments [66]

Kajiwara and Anzai once investigated moving striations in low pressure Kr-Hg

discharge driven by 50 Hz 200 V AC source [67]. In their experiment, discharge tubes

were filled with 1 – 5 Torr Kr and saturated Hg. They measured wavelength,

frequency and other parameters of the striations under different cold spot temperature.

Table 1.3 summarized relation between frequency and wavelength of striations for

different Kr pressure. They put forward that Kr filling pressure and cold spot

temperature of the discharge tubes might shed important influences on striations.

Given the striation frequency’s relation with cold spot temperature and discharge

current, they categorized striations in their experiment into r-type moving striation.

What was noted also was that when striations appeared, excitation and ionization of

Kr became more frequency; radiation from Hg atoms became weaker.

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Table 1.3 Measurement of frequency and wavelength of striations under different cold spot temperature and Kr filling pressure by Kajiware et al [67]

Kr

pressure * 5 ℃ 10 ℃ 15 ℃ 20 ℃ 25 ℃ 30 ℃ 35 ℃

f(Hz) 200 250 280 380 550 690 900 1 Torr

λ (cm) 9.2 8.8 8.6 7.8 7.0 5.3 5.0 f(Hz) - 200 200 250 350 520 -

2 Torr λ (cm) - 7.5 7.3 7.0 6.0 4.7 - f(Hz) 200 220 240 280 340 560 -

3 Torr λ (cm) 6.2 6.2 6.0 5.5 5.0 4.8 - f(Hz) - - 200 210 250 420 -

4 Torr λ (cm) - - 6.1 6.1 5.5 4.4 - f(Hz) 200 200 200 200 200 240 500

5 Torr λ (cm) 4.0 4.0 4.0 4.0 4.0 4.0 3.8

Kajiwara and Sano measured moving striations in T8 fluorescent lamps under

different cold spot temperature [68]; they also analysed how striations were incurred

and propagated [69]. Kajiwara et al thought that when cold spot temperature was low,

Hg atom density inside the lamp went lower, which resulted in more electron collision

with Ar. Since Ar has much higher excitation and ionization level than Hg, higher

electron temperature was needed in order to sustain the discharge. Especially, under

AC condition, lamp current passed zero periodically and the lamp must restart. In this

period, disturbances might appear due to high electron temperature, thus became

source of instabilities.

Bian and Zhu deducted dispersion relation from particle continuous equations and

disturbing method, based on which wavelength, velocity, spatial amplification, and

temporal amplification were calculated under different cold spot temperature [70].

Experiments were also made to verify the calculation. Table 1.4 lists calculation

results.

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Table 1.4 Parameters of striations versus cold spot temperature calculated by Bian et

al

Cold spot

temperature

℃

Wavelength

cm

Wave

number

m-1

Velocity

m/s

Spatial

amplification

cm-1

Temporal

amplification

s-1

15 10 62.8 90.0 ~ 100 0.2 1800 ~ 2000

20 9.5 66 85.5 ~ 95 0.2 1710 ~ 1900

24 8.4 75 75.6 ~ 84 0.19 1436 ~ 1596

30 6.8 92.4 61.2 ~ 68 0.19 1162 ~ 1292

35 5.5 114 49.5 ~ 55 0.19 940 ~ 1045

40 4.1 153 36.9 ~ 41 0.19 701 ~ 779

Zhang and Zhu measured Hg atomic lines in the bright and dark parts of striations in a

T8 fluorescent lamp by using monochromator and photomultiplier. Correlated

theoretical analyses were also developed. According their results, bright parts of the

striations had higher electron temperature (difference of electron temperature between

bright part and dark part of the striation was about 900 K), higher electric field and

higher density of excited atoms [70].

Langer et al investigated variation of propagating speed of ionization waves versus

voltage and gas composition in a DC fluorescent lamp with serials of photomultipliers

[72]. Results revealed that negative charged particles accumulated on discharge tube

wall might strongly affected propagation of ionization waves. Different buffer gas

might also influence ionization waves: gases with smaller elastic collision cross

sections coincide with faster ionization waves.

1.3 Efforts from the present thesis

Research on striations has passed more than a century. Major efforts were poured in

pure rare gas discharge due to simple atomic structure and rich atomic data.

Fluorescent lamps are the most widely used light sources nowadays. They are based

on low pressure rare gas and mercury discharge, in which striations may also be found

sometimes, especially when current is low or ambient temperature is low. Compared

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with research works on striations in rare gas discharge, correlated efforts on rare gas

and mercury discharge appear to be minor. Experimental and theoretical work is

urgently needed. In the present article, we will make our efforts to clarify the reasons

for the appearance of moving striation in low pressure rare gas and mercury discharge.

New experimental and theoretical method will be used. We hope that we can gain

deeper understanding of low pressure rare gas and mercury discharge and make good

preparation for eliminating striations from fluorescent lamps.

In this thesis we will carry out experimental and theoretical research on moving

striations in a 50 Hz AC operated rare gas and mercury discharge lamp (A T8

fluorescent lamp ballasted by a magnetic gear). The first chapter of the article

introduces background and state of art of striations. In the second chapter, we will try

different methods to investigate properties of the striation in the experimental lamp

and try to find out the possible reasons for this phenomenon. In the first experiment,

extra heating current will be provided to the lamp to suppress disturbances in cathode

region. We will check if striations are incurred by disturbances in cathode region. In

the second experiment, we collect emissive spectra of the lamp under different cold

spot temperature. We will see how cold spot temperature may influence the striation.

In the third experiment, variation of striation in the working period of the lamp is

recorded by a high speed ICCD camera, based on which analyses will be made. In the

fourth experiment, a monochromator is coupled with the ICCD camera to collect

atomic radiation in the working period of the lamp. Then further analyze on the third

experiment will be performed. All the experiments were accomplished in LAPLACE,

University Paul Sabatier, France. The third chapter introduces commonly used plasma

models: single particle model, collisional-radiative model (CR model), fluid model

and kinetic model. Examples are also provided. The fourth chapter provides kinetic

explanation on striations. Electron response to spatially periodic electric field will be

investigated. In the final chapter, summary of the entire thesis will be given.

1.4 Creative points

This thesis bears creative points as follow:

1. Provide electrode heating current to the lamp to suppress disturbances in

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cathode region; then proves that under the experimental condition, striations

in low pressure rare gas mercury discharge are not originated from cathode

region.

2. Trigger the high speed ICCD camera with light output of the lamp and

record variation of striation in the working period of the lamp. It turns out

that striations only appear on the rising edge of the light signal; on the

falling edge, striations disappear. Couple the monochromator with ICCD and

trigger the system with light output of the lamp. Atomic radiation from the

lamp during the working period of the lamp is recorded.

3. Solve the Boltzmann numerically by Crank-Nicholson scheme and simulate

electron response to spatially periodic electric field in low pressure Ar-Hg

discharge.

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Chapter 2 Experimental investigation on

moving striations in low pressure rare gas

and mercury discharge

2.1 Introduction

Previous research on striations was mainly limited to DC pure rare gas discharge.

More often than not, discharge of gas mixtures and AC discharge did not become

subjects. Since nowadays fluorescent lamps are widely used and striations inside these

lamps not only bring unpleasant effects to lighting environment, but they also cause

visual fatigue [1][2], it is meaningful to find out reasons for these phenomena and try

to eliminate them.

In this chapter, we will try to look into moving striations in a 50 Hz AC operated

fluorescent lamp through different experiments. We will try to find out why striations

form and how they will behave inside the lamp. All the contents of this chapter have

been published in [3], part of the contents have been reported in the IEEE IAS annual

meeting in 2008 [4].

2.2 Experiments

2.2.1 Electrode heating

Under DC condition, stably operated fluorescent lamps have constant lamp voltage

and lamp current. Under 50 Hz AC condition, lamp voltage and current pass zero

every half period, shown as Figure 2.1. This is the essential difference from DC

operation. When lamp current passes zero, discharge inside the lamp becomes weak

and plasma density considerable decreases. The lamp should go for reignition, during

which cathode region may bear some disturbances due to sputtering [5]. Therefore,

this disturbance in cathode region can be sources of instabilities inside the lamp [6]

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and [7]. In this section, we will check this point.

What we should notice is that in low pressure rare gas and mercury discharge, there is

oscillation in anode region. According to [1], [6], this oscillation is not the reason for

striations.

Figure 2.1 Plot of lamp voltage and current of a 50 Hz, 58W linear tube fluorescent

lamp

1. Experimental Setup and method Figure 2.2 depicts the layout of experimental setup. A T8 fluorescent lamp is used as

discharge tube. The dimension of the tube resembles that of Philips TLD 36W/840.

Inside the lamp, there fill 400 Pa buffer gas (80% Ar and 20% Kr) and small amount

of Hg. The inner wall of the tube is coated with phosphor. A 50 Hz adjustable power

source is used to drive the lamp. A ballast and igniter are used to ignite and operate

the lamp. Light output of the lamp is collected by a photodiode and sent into an

oscilloscope. Two DC sources (shown by Figure 2.3) are employed to provide 400

mA heating current to the electrodes of the lamp so that disturbances in cathode

region can be suppressed.

When the experiment starts, we regulate the output of the power source to 150 V.

Moving striations appear and the cold spot temperature of the lamp is about 34

centigrade. Figure 2.4 tells the lamp voltage and light signal collected. We used “AC

coupling” in the oscilloscope; so the DC component of light signals was filtered out.

From the figure we can see that there is small amplitude of high frequency fluctuation

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superposed on the flickering of light output. This fluctuation comes from the striations

in the lamp. Detail information of the striations can be revealed by filtering light

signal.

Figure 2.2 Layout of experimental setup Figure 2.3 The DC source

Figure 2.4 Lamp voltage (blue) and light signal (yellow) from the photodiode

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Figure 2.5 Variation of striations versus lamp voltage with (a) or without (b) electrode

heating

2. Results and discussion

Figure 2.5 describes variation of the striations versus lamp voltage when electrodes

are or are not heated by the DC current. The striation signals are obtained by inputting

light signal from the photodiode into Origin software and performing 800 Hz

high-passing filtering. The reason for choosing 800 Hz high-passing filter is that

according to [10] and [11], frequency of the moving striation in the discharge is

bigger than 800 Hz.

From the above figures we can see that striations inside the lamp remain the same no

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matter electrode heating is provided or not. Therefore, we can come up with such

conclusion that moving striations inside the experimental lamp are not caused by

disturbances in cathode region. There is an intrinsic mechanism in the plasma, which

gives birth to and sustains this stratified instability, i.e. this is a kind of self-excited

striation.

2.2.2 Spectra

In this experiment, we use a cooling spray to cool down a part of the lamp to see how

cold spot temperature affects moving striation. In the cooled region, striations can be

clearly seen. We use spectrometer and light signal to respectively record the emissive

spectra and light output of the lamp. Meantime, a thermal couple is used to detect

temperature evolution with time. Then we can establish links between cold spot

temperature and striations.

1. Experimental setup and method

Figure 2.6 shows experimental setup of this section. Basic components of the

experiment such as discharge tube and ballast are the same as the previous section. A

thermal couple is attached to the cold spot of the lamp, which located close to the

center of the tube. The spectrometer used is USB2000, manufactured by Ocean Optics.

It can cover 200 nm – 1000 nm radiation with FWHM resolution of 1.5 nm. In our

experiment, the integration time of the spectrometer is fixed at 7 ms and each

measurement comes from average result of 30 measurements.

At the beginning of the experiment, keep the lamp normally operated for 15 min and

at this time cold spot temperature of the tube is 42 centigrade. The discharge is

uniform and there is no striation. Cool the region where the thermal couple is attached

(dark region in Figure 2.6). Right after cooling, the temperature of this region can

reach below 5 centigrade. Afterwards, the temperature gradually goes up and finally

becomes stable. We record the spectra and light signals when the temperature returns

to 16, 20.8, 25.4, 28.9 and 31 centigrade.

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Figure 2.6 Experimental setup for measurement of emissive spectra and cold spot

temperature of the lamp

2. Results and discussion

Figure 2.7 shows measured spectra under different cold spot temperature. Figure 2.8

(a) depicts variation of Hg vapor pressure and radiation of Hg 365 nm, Hg 435.8 nm

and Ar/Kr 811 nm versus cold spot temperature. Hg 365 nm line comes from

deexcitation from Hg 6-3D2, 3 to Hg 6-3P2. Hg 435.8 nm line results from deexcitation

from Hg 7-3S1 to Hg 6-3P1. Radiation of 811 nm comes from deexciation of Ar and

Kr 35

4 [ ]2

p to 23

3 [ ]2

s . The reason for choosing 365 nm and 435.8 nm atomic lines is

to avoid the remanence from the phosphor. From the figure we can see that under

higher cold spot temperature, Hg vapor pressure is higher and radiation from excited

Hg atoms is also higher. Radiation from the excited rare gas atoms is on the contrary.

When cold spot temperature gets lower, Hg radiation reduces substantially; while rare

gas emits more radiation.

Figure 2.8 (b) presents FFT of light signals collected by the photodiode. We can see

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that striation frequency ranges from 560 Hz – 580 Hz under cold spot temperature of

16 centigrade. Correlated amplitude is beyond 0.5. When the temperature climbs up to

20.8 centigrade, striation frequency comes to about 600 Hz; while amplitude goes

down to about 0.2. When the temperature rises to 25.4 centigrade, striation frequency

reaches 720 Hz and amplitude descends to about 0.15. As cold spot temperature

increases even higher, the FFT plot hardly tells information of striations. Frequency of

striations goes up when cold spot temperature goes up; and goes down when cold spot

temperature goes down. This coincides with phenomena in experiment [10]. In [12],

van den Heuvel et al witnessed striations moving faster than those in our experiments.

In their experiment, FFT results revealed that striation frequency located between 2

kHz and 3 kHz. That’s because striations that they observed were stirred up by

external sources and amplified by circuit loop, whose mechanism was different from

that of ours.

Figure 2.7 Spectra under different cold spot temperature

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Figure 2.8 (a)Variation of Hg vapor pressure and radiation of Hg 365 nm, Hg 435.8

nm and rare gas 811 nm versus cold spot temperature; (b) FFT of light output of the

lamp, peaks are marked by arrows

Figure 2.9 describes lamp current and light signals from the photodiode under

different cold spot temperature. From the figure we can see that when cold spot

temperature is low, striations seriously perturb light output of the lamp. Amplitude of

striation even overweighs flickering (shown by Figure 2.9 (a) and (b)). As cold spot

temperature goes higher, striations are attenuated, thus disturbances caused by them

are weaker. What we should also noticed is that profile of lamp current keeps the

same no matter what cold spot temperature is high or low. Only the RMS value

changes slightly, from 192 mA at 16 centigrade to 162 mA at 31 centigrade.

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(a)

(b)

(c)

(d)

(e)

Figure 2.9 Lamp current (purple) and light signals (yellow) under different cold spot

temperature; (a)-(e) correspond to cold spot temperature of 16, 20.8, 25.4, 28.9 and 31

centigrade

Another interesting phenomenon is that striations only appear in the cooled region of

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the tube. Discharge in the other region is uniform. This implies that either there are

sources of instabilities or lower damping factors in the cooled region, which agrees

with survival and propagation of striations. Such factors do not exist in the other part

of the tube. The above point can be indirectly proved by Figure 2.9. Because the

cooled region is in the middle part of the tube while lamp current is measured in the

circuit, undisturbed profiles of lamp current verify that disturbances in the cooled

region undergo substantial damping when they go to the both ends of the lamp so that

they are almost suppressed before arrival.

Combining Figure 2.8 and Figure 2.9 we will find that under low cold spot

temperature, striations are stronger; under high temperature, the situation goes to the

opposite. Kajiwara pointed out in his articles [10] and [11] that under low temperature

in Ar-Hg discharge, Hg coagulated and more Ar atoms participated in and presided in

the discharge. Because Ar had high excitation level (about 11.5 eV), considerable

participation of big amount of Ar atoms would consume more electron energy, which

might incur striations to the discharge. We use Bolsig+ [14] to simulate energy consumption of different reactive processes under different Hg vapor pressure. Basic

conditions involved in the simulation as follow: electric field 110 V/m, Ar density 1×1023 m-3, electron density 1×1018 m-3. Hg atom density can be calculated from the equation [13]:

7564ln( / 0.133) 30.804 0.8254ln( )Hg c

c

P TT

= − −

2.1

Major reactive processes of Ar involved in the simulation include: (1) elastic collision

between electron and Ar atom; (2) collisonal excitation of Ar atoms by electron; (3)

collisonal deexcitation of Ar atoms by electron; (4) collisional ionization of Ar atoms

by electron. The counterpart of Hg atoms consists of: (1) elastic collision between

electron and Hg atom; (2) collisional excitation of Hg atom to 6-3P0, 1, 2 by electron; (3) collisional deexcitation of Hg atom to 6-3P0, 1, 2 by electron; (4) collisional ionization of Hg by electron; (3) collisional ionization of Hg 6-3P0, 1, 2 atoms by electron. Cross sections of Hg are from [15] and those of Ar are from [14]. Part of

them is shown in Figure 2.10.

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Figure 2.10 Cross sections used for the Bolsig+ simulation

Simulation results are listed in Table 2.1. From the table we can see that under 42

centigrade, inelastic collision between electron and Hg atom takes up about 83% of

total energy; elastic collision between electron and Ar atom takes up about 17% of

total energy. When temperature gets down to 31 centigrade, Hg vapor pressure will be

decreased about 60% according to equation 2.1. Inelastic collision between Hg atom

and electron consumes about 72% of total energy; elastic collision between Ar atom

and electron is increased to about 26%; inelastic collision between Ar atom and

electron begins to come on the stage, which cost about 2% of total energy. When

temperature is cut down to 16 centigrade, energy balance in the plasma undergoes

significant change. Inelastic collision joined by Hg atoms costs about 44% of total

energy, thus handles over its dominance to electron-Ar collision, which consumes

about 56% of total energy. In this case, Ar is the major player in the discharge.

Table 2.1 Percentage of energy consumption in low pressure Ar-Hg discharge under

different cold spot temperature Cold spot temperature Tc

Collision 42 � 31 � 16 � Ar Elastic 17% 26% 45%

Ar Inelastic 3 × 10-1% 2% 11% Ar Subtotal 17% 28% 56% Hg Elastic 9 × 10-2% 5 × 10-2% 2 × 10-2%

Hg Inelastic 83% 72% 44% Hg Subtotal 83% 72% 44%

Given Figure 1.2 and Figure 2.11, if there is no Hg inside normal T8 fluorescent

lamps and the discharge is pure rare gas discharge, then the gas pressure (3 Torr) and

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discharge current (lower than 1 A) decide that the discharge locates in the unstable

region. Therefore, in low pressure rare gas and mercury discharge, the plasma always

tends to become stratified. However, this tendency is suppressed by the large amount

of Hg atoms. Once ambient temperature gets lower and Hg atom density is greatly

reduced, rare gas atoms will become important in energy balance (or ionization

balance) of the plasma, striations will appear. Rutscher and Wojaczek found that

adding mercury to rare gas might help to remove striations [17]. Lee et al also noticed

that low pressure Ar-Hg discharge had lower Pupp limit than pure Ar discharge [18],

which verify that Hg could uniformize the discharge.

Robertson had proved that in DC rare gas discharge, if stepwise ionization of rare gas

atoms dominated ionization balance, discharge could seldom stay uniform. Local

minor disturbances might be amplified and propagated; electrons and ions might

exhibit wave-like instabilities, i.e. striations [20]. Siefert has similar opinion as

Robertson. He measured temporal variation of electron density and metastable Ar

density in a stratified low pressure Ar discharge and concluded that metastable Ar

atoms would amplify small perturbations in the plasma. If these kinds of atoms could

be quenched quickly enough, disturbances in the plasma would not survive.

Furthermore, frequency of striation is correlated with quenching frequency of

metastable atoms [21].

Figure 2.11 p – I limit proposed by Oleson and Cooper for DC rare gas discharge

under different conditions [16]

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According to Siefert’s idea, we perform theoretical inference on disturbance

propagation in low pressure Ar discharge. We assume that ionization balance

comprises the following reactions:

*me Ar e Arυ+ → +

2.2

2* Ke Ar e e Ar++ → + +

2.3

ie Ar e e Arυ ++ → + +

2.4

* * quenchAr Ar Ar Ar eυ ++ → + +

2.5

where mυ is excitation frequency, 2K is rate coefficient of stepwise ionization, iυ is ionization frequency, quenchυ is quenching frequency.

Then variation of electron density ne and metastable Ar density nArm is as follows:

2( )e

e i amb e Arm Arm quench

nn n n K n

tυ υ υ∂ = − + +

∂

2.6

2Arm

e m e Arm Arm quench

nn n n K n

tυ υ∂ = − −

∂

2.7

We assume that there appears a small perturbation teαδ (α is temporal amplification) in the plasma. Then electron density and metastable Ar density can be put into

0t

e e en n eαδ= + and 0

tArm Arm Armn n e

αδ= + , where 0en and 0Armn are constants and stand for steady-state densities. Insert the two equations into 2.6 and 2.7, omit the

second order terms, then we obtain:

0 2 0 2( )t t t t t

e e i amb e Arm Arm e Arm quenche e n K e n K e eα α α α ααδ δ υ υ δ δ δ υ= − + + +

2.8

0 2 0 2t t t t t

Arm e m e Arm Arm e Arm quenche e n K e n K e eα α α α ααδ δ υ δ δ δ υ= − − −

2.9

Transform 2.8 and we get

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0 2 0 2( )Arm Arm

i amb Arm e quenche e

n K n Kδ δα υ υ υδ δ

= − + + +

i.e.

0 2 0 2( ) ( )Arm

e quench i amb Arme

n K n Kδ υ α υ υδ

+ = − − −

2.10

Transform 2.9 and we get

0 2 0 2Arm Arm Arm

m Arm e quenche e e

n K n Kδ δ δα υ υδ δ δ

= − − −

i.e.

0 2 0 2( )Arm

e quench m Arme

n K n Kδ α υ υδ

+ + = −

2.11

Divide 2.10 with 2.11, we get

0 2 0 2

0 2 0 2

( ) ( )

( )e quench i amb Arm

e quench m Arm

n K n K

n K n K

υ α υ υα υ υ

+ − − −=

+ + −

If metastable Ar atoms are quenched quickly enough (0 2e quenchn K υ

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due to large amount of metastable rare gas atoms while Hg can help hold in the

stratified instability by Penning collision (there is strong Penning effect between Ar

and Hg, weak Penning effect between Kr and Hg [19]). Furthermore, if there are a lot

of Hg atoms in the gas, Hg will preside in both ionization balance and energy balance

because of its lower excitation level and ionization level. Therefore, metastable rare

gas atoms have less possibility to be produced. This is another mechanism that may

prevent striation from occurring.

Arslanbekov and Kolobov simulated striations in a Ar discharge, where gas pressure

is 2 Torr, discharge current is 100 mA and discharge tube’s radius is 1 cm [22][23]. In

their model, ions, excited atoms and electron temperature were governed by fluid

equations. Electrons follow the semi-nonlocal description. Arslanbekov thought that

nonlinear change of excitation and ionization rate due to strong coulomb collision was

the major reason for striation. However, in normally operated fluorescent lamps, gas

pressure and discharge current are close to those in their simulation. Strong coulomb

collision can also be expected therein. Striations do not appear unless e.g. ambient

temperature is low. That means the point proposed by Arslanbekov only consists of

part of the mechanism that leads to striation. In other words, the existence of Hg helps

to suppress striations.

Tsendin attributed ionizing instabilities such as striations and anode oscillation to the

non-local effect of EEDF [24]. He gave a criterion to judge whether the EEDF is

non-local:

If electron energy relaxation length *λ is bigger than discharge tube radius R, then EEDF is non-local; where* El InElλ λ λ= , Elλ is electron energy relaxation length through elastic collision, InElλ is electron energy relaxation length through inelastic collision. Take Ar for example. Under similar discharge condition, elastic collision

between electron and Ar atom frequently happens. But energy exchange of each

collision is small. Therefore, energy relaxation length through elastic collision is long.

Inelastic collision between electron and Ar atoms also calls for long distance because

Ar’s excitation and ionization level are very high and electrons must be accelerated

for long enough distance to acquire necessary energy. Therefore, *λ is longer than discharge tube radius and EEDF is non-local. In rare gas and mercury discharge,

elastic and inelastic collision are respectively dominated by Ar and Hg atoms.

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