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Qing, Z. (1995). The magnetized hydrogen plasma jet. Technische Universiteit Eindhoven.
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THE MAGNETIZED
HYDROGENPLASMAJET
CJP-DATA KONINKLIJKE BIBLIOTHEEK, DEN HÀAG Zhou Qing
The magnetized hydrogen plasma jet I Zhou Qing. -Eindhoven: Eindhoven University ofTechnology. - II 1. Thesis Technishe Universiteit Eindhoven.
ISBN 90-386-0097-6
PROEFSCHRIFf
ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr. J.H. van Lint, voor een commissie aangewezen door het College van Dekanen in het openbaar te verdedigen op
dinsdag 7 november 1995 om 16.00 uur
door
ZHOUQING geboren te Shanghai, China
Dit proefschrift is goedgekeurd door de promotoren prof.dr.ir. D.C. Schram en prof.dr. D.K. Otorbaev copromotor dr.ir. M.C.M. van de Sanden
Contents 1 1.1 1.2 1.3
2
2.1 2.2 2.2.1 2.2.2 2.3 3 3.1 3.23.2.l
3.2.2
3.2.3 3.2.4 3.3 3.4 3.4.1 3.4.2 3.5 3.5. l 3.5.2 4 4.1 4.1.1 4.1.2 4.2 4.3 4.4 5 5.1 5.2 5.2.1 5.2.25.2.3
5.3 Genera! introductionGenera! interest of hydrogen plasma Hydrogen plasma in this thesis Structure of this thesis
The ex panding hydrogen cascaded are plasma Cascaded are set up and are plasma
Expanding plasma Vacuum system
Magnetic field distribution
Different regimes of an expanding hydrogen cascaded are plasma Experimental characterization of a cascaded are
Diagnostic techniques Electric field in a cascaded are
Plasma conductivity and the electric field Electric field strength in a cascaded are Electron temperature in an argon are Channel narrowing effect in a hydrogen are Pressure distribution in a cascaded are Efficiency of a cascaded are
Definition of the efficiency of a cascaded are Power efficiency of a cascaded are
Dissociation degree of hydrogen in a cascaded are Definition of the mass dissociation degree
Experimental determination of the mass dissociation degree Determination of the electron density and temperature in an expanding plasma
Summary of Langmuir probe theory
Conditions for applying a Langmuir probe measurement Current-Voltage characteristic of a Langmuir probe Langmuir probe results in an expanding argon plasma Langmuir probe results in an expanding hydrogen plasma Plasma continuum emission
Atomie regime of an expanding hydrogen plasma Spectrum of atomie hydrogen
Hydrogen Balmer emission and absorption spectroscopy Experimental set-up
Emission spectroscopy Absorption spectroscopy
Hydrogen excited state densities in the atomie regime
l 2 3
5
5
7 7 9 11 15 15 17 17 19 2426
28
3232
33 35 35 36 41 41 42 4346
49
5255
55
56 56 58 61 635.5 5.6 5.7 5.8 5.8. l 5.8.2 6 6.1 6. l. l 6.1.2 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.3 6.3.1 6.3.2 6.3.3 6.3.4 7 regime
A collisional radiative model for an expanding hydrogen plasma Production of hydrogen molecular ions H2 +, H3 + and the hydrogen negative ion ff : a one dimensional flow model
Atomie hydrogen ground state density and dissociation degree of hydrogen plasma
Photodetachment of hydrogen negative ions Principle of photodetachment
Photodetachment experiment
Molecular regime of an expanding hydrogen plasma Hydrogen molecular energy levels
Rotational-vibrational structure of molecular hydrogen Rotational bands of a hydrogen molecule
Fulcher
a.
emission and gas temperature in an expanding hydrogen plasmaHydrogen Fulcher
a.
spctrumDetennination of rotational temperature Detennination of gas temperature
Excitation mechanism and gas temperature in an expanding hydrogen plasma
Dissociation degree in an expanding hydrogen plasma Optica! actinometry in a plasma
Kinetics of hydrogen excited states
Expression for the dissociation degree of hydrogen plasma Atomie hydrogen density and hydrogen dissociation degree Genera! conclusions Summary Samenvatting Acknowledgements N omenclatu re
67
71 74 77 80 80 81 88 88 8890
92
93 95 9596
99
99
101 i04 105 109 111 113 115 1161 Genera/ introduction
l.
Genera) introduction1.1 Genera! interest of hydrogen plasma
A hydrogen plasma is in genera! a mixture of hydrogen molecules, hydrogen atoms, free electrons and hydrogen atomie and molecular ions. In the Jast two decades, hydrogen plasmas have been widely used in different research and application fieids and have become a more and more promising research subject. In microelectronics industry, for example hydrogen containing plasmas have been utilized in the thin film deposition '· 2· 3, surface cleaning and passivation techniques 4· 5. Also it has been established that high quality diamond films are grown in a hydrogen diluted plasma, and that the atomie hydrogen present in these plasmas is essential for the quality 6. Apart from this, atomie hydrogen sources have been utilized in surface treatment of iron archaeological artefacts to protect the artefacts after the excavation against post-corrosion without inducing any surface damage 7.
The research of hydrogen plasmas has also a direct hearing to controlled thermonuclear fusion project aimed at energy production. The genera] idea of controlled thermonuclear fusion is first to create a deuterium and a tritium plasma, then to confine and heat this plasma with high density and high temperature to reach the fusion reaction. This is done commonly in a specially designed equipment, the so called TOKAMAK machine 8. Heating by injection of neutra! beams produced by neutralization of negative ions from a negative deuterium ion source has been suggested as a key technology to reach the plasma conditions needed for energy production by nuclear fusion.
In
this research field, the study of hydrogen plasmas are fundamental since deuterium and tritium are isotopes of hydrogen. The conclusions on hydrogen plasmas are easily generalized to deuterium and tritium plasmas. For example, the result of the development of a negative hydrogen ion source can directly be used in the design of a negative deuterium ion source. Therefore almost all basic research in this field starts with the investigation of hydrogen plasmas.Apart from the mentioned applications the study of hydrogen plasmas is also of fundamental interest. Since the hydrogen molecule is the simplest diatomic molecule, the experimental results of hydrogen plasmas are often used to test models of molecular plasmas in modern plasma physics. Furthermore, the experimenta\ results can provide a clear kinetic scheme for the hydrogen plasma itself, i.e. knowledge on the mechanisms of ionization and recombination, excitation and de-excitation, formation and quenching processes.
Hydrogen plasmas can be created in different ways, e.g. in DC gas discharges, RF plasmas, microwave plasmas or in a hollow cathode are 9• 10· 11 . To obtain more source strength, it can be also created at higher pressures, e.g. by a so called cascaded are 12, which is a kind of wall stabilized high electron density plasma and which is the subject of this thesis.
The research of an argon cascaded are at the Eindhoven University of Technology shows that the cascaded are is an ideal design to create a stable are plasma with high electron density as well as an expanding plasma for both plasma physics studies and the applied research 13• 14" 15. lt has been also shown that the expanding cascaded are plasmas have potential prospect in different application fields; e.g. using a cascaded are as a light source for spectroscopy 16, as a particle source for surface modification 17• silicon thin film deposition 18, carbon thin film deposition 5• 19 and passivative protection technique for archaeological artefacts 7 .
The original aim of this hydrogen project has been to develop a hydrogen particle source for the rising interest in hydrogen plasma applications. The plasma is first created in a cascaded are. The treatment plasma is obtained by the expansion of the are plasma into a low pressure vessel. The research in this project has been carried out for both the are plasma and the expanding plasma. The work of de Graaf 7 has been devoted to develop the hydrogen are source to obtain an expanding hydrogen plasma beam. Special attention has been given to the dynamics and kinetics of nonmagnetized hydrogen plasmas at moderate pressures (- 100 Pa). It was demonstrated that in hydrogen at these high pressure an anomalously high recombination occurs which leads toa very effective destruction of charges. In this thesis the lower pressure range (- 5 Pa) is explored in order to avoid or reduce this recombination. At these lower pressures collisional confinement is not effective and magnetic confinement of electrons and ions is needed to obtain a high density expanding plasma. Therefore this work can be seen as an extension of the thesis work of de Graaf 7 focusing on magnetized expanding argon/hydrogen (Ar/H2) plasmas at low pressure. Both the are plasma and the expanding plasma are further studied in this thesis work.
For a cascaded are plasma, the are parameters, such as the electric field, the pressure and the pressure gradient, the plasma temperature, the effective plasma radius, the efficiency and the dissociation degree are important. In an atomie hydrogen source, the atomie hydrogen density is deterrnined by the dissociation degree of the hydrogen plasma; the electric properties of the are can be studied by deterrnining the electric field and the electrical conductivity; the transport properties of the are can be studied by deterrnining the pressure and pressure gradient in the are 20. A part of this thesis deals with the experimenta\ determination of these are parameters. By varying the ratio of argon and hydrogen gas tlow, a pure argon as well as a pure hydrogen are plasma can be obtained. The study of both a pure (argon or hydrogen) plasma and of Ar/H2 plasma
mixture can give us insight in the transition behavior between a pure (argon or hydrogen) plasma and a plasma mixture.
For the expanding plasma, the work described in this thesis has shown that depending on op.erational conditions and magnetic field strength two specific regimes of the expanding hydrogen plasma can be obtained, which can be characterized by different emission characteristics. Based on the observed spectroscopie characteristics, we have
1 Genera/ introduc1ion 3
named these two specific regimes the "atomie" regime and the "molecular" regime. In this work, both the atomie and the molecular regimes are studied.
1.3 Structure of this thesis
This thesis deals with an Ar/H2 cascaded are plasma mixture and a magnetized low pressure expanding hydrogen plasma. Chapter 2 gives genera! information on the plasma set up (both the cascaded are set up and the expansion vessel). The atomie regime and the molecular regime of an expanding hydrogen plasma wil! be introduced in chapter 2. Chapter 3 is devoted to the cascaded are plasma, and in this chapter the experimental determination of the are parameters, such as the electric field, the electrical eonductivity, the pressure and the dissociation degree etc. wil! be described. In chapter 4, the diagnostic methods for the determination of the electron temperature and density in the expanding plasma wil! be discussed. The experimental values of the electron temperature and density are needed in the discussion of the kinetic seheme in the later ehapters. Chapter 5 deals with the atomie regime of an expanding hydrogen plasma. Based on the experimental results of the hydrogen atomie excited states population densities, the population mechanism in the atomie regime will be discussed in that chapter. Chapter 6 is devoted to the molecular regime. In this chapter, besides the primary plasma parameters in an expanding plasma, the determination of the gas temperature and the dissoeiation degree will be described. In ehapter 7, a genera] overview of the results obtained for the hydrogen are plasma and the expanding plasma will be given.
References
J.C. Knight; AIP Conf. Proc., Amer. Inst. of Physics, New York 31 296 ( 1975) 2 A.Triska, D. Dennison and H. Fritsche, Bull. Am. Phys. Soc. 20 392 ( 1976)
H. Borning, Plasma News Report, Research Institute of Plasma Chemistry and Technology, Carlsbad ( 1986)
V. Dan ie Is, Studies in Conservation 26 45 ( 1982)
V. Daniels, L. Holland and M.W. Pascoe, Studies in Conservation 24 85 (1979)
6 Diamond Films'94, Ed. by P.K. Baehmann, I.M. Buckley-Golder, J.T. Glass and M. Kamo, Elsevier (1994)
M.l. de Graaf, Ph.D. thesis, Eindhoven University ofTechnology, The Netherlands, ( 1994)
8 L.A. Artsimovich, Nucl. Fusion 12215 ( 1972)
9 H.O. Blom, C. Nender, S. Berg, H. Norstroem, Vacuum 38 813 (1988) 1
°
C.J. Mogab, A.C. Adams and D.L. Flamm, J. Appl. Phys. 49 3796 (1979)11 K. Suzuki, S. Okudaira, S. Nishimatsu, K. Usami and I. Kanomata, J Electroehem. Soc. 129 2764 ( 1982)
13 J.C.M. de Haas, Ph.D. thesis, Eindhoven University of Technology, The Netherlands, (1983)
14 G. M. W. Kroesen, Ph.D. thesis, Eindhoven University of Technology, The Netherlands, ( 1988)
15 M.C.M. van de Sanden, Ph.D. thesis, Eindhoven University of Technology, The
Netherlands, (1991)
16 A.T.M. Wilbers, G.M.W. Kroesen, C.J. Timmermans and D.C. Schram, Meas. Sci.
Technol. 1 1326 (1990)
17 J.J. Beulens, Ph.D. thesis, Eindhoven University of Technology, The Netherlands, (1992)
18 G.J. Meeusen, R.P. Dahiya, M.C.M. van de Sanden, G. Dinescu, Zhou Qing, R.F.G.
Meulenbroeks and D.C. Schram, Plasma Sources Sci. Techno!. 3 521 (1994)
19 A.J.M. Buuron, D.K. Otorbaev, M.C.M. van de Sanden and D.C. Schram, Phys. Rev.
E
19
1383 (1994)20 Zhou Qing, M.J. de Graaf, M.C.M. van de Sanden, D.K. Otorbaev and D.C. Schram, Rev. Sci. Instrum. 65 1469 (1993)
2 Expanding hydrogen cascaded are plasma 5
2. Expanding hydrogen cascaded are plasma
2.1 Caseaded are set up and are plasma
The cascaded are, which was first introduced by Maecker in 1956 1, is an example of a wall stabilised thermal plasma and is characterized by a high electron density 2· 3. With the advantage of a large range of operational conditions for pressure and current, the cascaded are has been widely used as a light source 4' 5· 6 or as a particle source in plasma applications and plasma fundamental studies 7· 8· 9• io, 11• 12.
The cascaded are used in this work consists of three main parts, namely cathode section, cascade plates section and anode section as shown in Figure 2-1. The function of each components of the cascaded are set up is given in Table 2-1. The plasma is
Figure 2-1
cathode section cascade plates section
anode section cascade plate cooÜng water e:t;it · cathode house
pleite
cathode ho/der
PVC spacer cooling water ent rance
Cascaded are set up.
initiated by the application of a high voltage pulse to the cathode (V""'""' 1 kV, fputu"' 1 s), and the are plasma is sustained by drawing a high current (30 - 100 A) bet ween the cathode tips and the anode at a lower voltage (100 - 200 V). The are plasma is always started using pure argon since lower power is needed to generale an argon plasma. By this procedure the lifetime of the cascaded are set up can be significantly extended. After the argon are becomes stable, the hydrogen concentration in the flow is slowly increased from 0% until 100% and a pure hydrogen are plasma is obtained through a transition from an argon are to a hydrogen are. The power needed to generale and sustain an are is determined by are length, or the number of the cascade plates. The
used.
Table 2-1 Components of the cascaded are set up (the subscript c means that the
cathode section cascade plates section anode section 1 d)
component 1s water coo e component viewing window gas entrance cathode house c cathode holder c cathode tip cascade plate c shielding ring vacuum seal anode plate c nozzle 6
~
..:.: '-' 4 ~ ~ 0 • • 0.. • • 2 ' material functionquartz plate checking the are and the cathode copper tube flowing gas into the are
copper cover for high voltage part copper holder of replaceable cathode tip thoriated tungsten emission of electrons
copper stabilization of wall temperature PVC spacer insulation of copper plates Viton 0 ring vacuum seal of each plates copper holder of replaceable nozzle copper exit of the are plasma
a pure hydrogen are--- •
•
•
•
•
•
a pure argon are
0 20 40 60 80 100
y (%)
Figure 2-2 Power needed to generale an Ar!H2 are plasma. Conditions: Iarc = 50 A,
Qw1al = 1.0 sim, Bo= 0 mT.
Figure 2-2 shows the input power needed to sustain an Ar/H2 are as a function of the hydrogen flow concentration y, which is defined as
2 Expanding hydrogen cascaded are plasma 7
As can be seen in Figure 2-2, to sustain a pure hydrogen are under the same operational
conditions Uurc = 50 A,
Q
=
1.0 sim) a factor of 2.7 more power is needed than to sustain a pure argon are.2.2 Expanding plasma
2.2.1 Vacuum system
Figure 2-3 shows the genera! set up of the experiment. The water cooling system
is not shown in this figure. The water cooling of the cascaded are and the magnetic coils
are separated in to two independent systems. The source gas with a pressure of 2 - 3· l 05 Pa passes first a gas filter and then enters the cascaded are set up. For safety reasons,
two hydrogen alarm systems are mounted near the gas battle and the vessel system. The
pressure in the vessel can be varied manually by the valve controller. For 0.5 sim gas flow the vessel pressure Pvessel can be varied in the range between 5 Pa to 100 Pa. The main parameters of the genera! set up are listed in Table 2-2.
hydrogen alarm
magnetic coils
<--,,--, ---'low pressure vessel
e
H, Ar
roots pump
Figure 2-3 Experimental set up (the power supply system and cooling water system
are not shown in this picture).
The are plasma is first generated in the cascaded are and then expands into a low pressure vessel (pvessel = 5 Pa). For the same flow and the same pumping capacity, the
length of the vacuum vessel 0.5 m
radius of the vacuum vessel 0.25 m
viewing window radius mass flow controller for Ar gas mass flow controller for H2 gas are current voltage 0.15m 0- 10 sim 0- 3 sim 0- 80 A 0-400V 50 -300 A 0-45 mT magnetic coil current
magnetic field strength
pumping capacity 600 m3s-1 (in case Pve.rsel = 5 Pa)
vessel pressure for both an argon are and a hydrogen are are approximately the same. However, the axial pressure gradient in the are, espeeially the pressure gradient at the position close to the nozzle is very much different for an argon are and a hydrogen are. Figure 2-4 shows the pressure at an axial position of 3 mm before the nozzle in an Ar/H2
plasma mixture as funetion of the hydrogen flow coneentration
y.
At that position the pressure of an argon are plasma is still about three orders higher than the vessel pressure, while in the hydrogen case the pressure at the same position is already close to the vessel pressure. This implicates that in the argon case, the plasma expansion starts after the nozzle. In the hydrogen case however, the are plasma has already started the expansion inside the are before reaching the nozzle. The pressure and the pressuregradient in a eascaded are will be discussed in more detail in chapter 3.
• - a pure argon are
3CXXJ •
•
•
•
•
a pure hydrogen arelCXXl Pvessel = 5 Pa
•
\
•
•
•
0 20 40 60 80 100 y (%)Figure 2-4 Pressure of an Ar!H2 plasma mixture, measured at an axial position of 3
mmfrom the nozzle (in the are) as afunction of the hydrogen concentration.
2 Expanding hydrogen cascaded are plasma 9
2.2.2 Magnetic field distribution
It has been observed that at elevated pressure expanding hydrogen plasmas show a strong recombination of hydrogen atomie ions 13 . This strong recombination can not be explained by atomie processes (cf. chapter 5). In pure argon plasmas, recombination has be shown to be a relatively weak process 7 · 14 . The anomalous recombination of H2
containing plasma is due to charge exchange of the atomie ion H+ with H2 molecules to form the molecular ion H/ which recombines fast by dissociative recombination 13. In order to avoid the recombination, the charge exchange between the primary H+ ions and H2 molecules has to be reduced which can be achieved by reducing the hydrogen molecule density. However, then the mean free paths become larger and diffusion now reduces the electron density. Therefore a magnetic field is applied to confine the expanding plasma and by this to reduce outward diffusion and thus to increase the plasma density 13 .
To obtain a magnetized expanding plasma beam, a magnetic coil is mounted in front of the cascaded are (cf. Figure 2-3). Under the approximation that the coil radius
R
is much larger than the coil wire diameter d, the magnetic field strength inside the vessel can be calculated as the magnetic field created by current rings (cf. Figure 2-5). The magnetic field at a position (x,y,z) can be expressed by law of Biot-Savart 15· 16
(2.2)
Under the assumption that the total thickness of the n coil winding is much smaller than R, i.e. n·d << R, all n current rings may be taken at the same space position dl (cf. Figure 2-5). The integration over all coil rings gives the magnetic field distribution. Figure 2-6
y dB - - . - - - ~ - - - . - - - - -(x, y, z) z x n
Figure 2-5 Magnetic field of current rings. R is the radius of the coil, n the number of rings, I the current.
coil current. As can be seen, the magnetic field strength reaches a maximum value of 45 mT at
z
= 0 cm and y = 0 cm, which is the exit of the nozzle. Figure 2-7 gives the magnetic field as function of thez
direction for different coil currentsIn.
50
45l.
;
.\····+·-··].;;~ ~.-.
.
·.·_1: ... ,." ..• 40 35 ç:;- 30g
25 al 50 -20Figure 2-6 Magnetic field strength in the expansion vessel in the downstream
direction. Ie= 250 A. Nozzle position: z
=
0 cm, y=
0 cm.50 40 G, 30
~
20 co 10 G2 0 -10 --- --0 JO 20 z (cm) 30 - -y=O cm ·--·-- y= IOcm y=20cm 40 50Figure 2-7 Magneticfield strength in the vessel. Group G1: Ie
=
250 A, group G2:2 Expanding hydrogen cascaded are plasma 11
2.3 Different regimes of an expanding hydrogen cascaded are plasma
As mentioned a magnetic field has been introduced to the expanding hydrogen plasma to allow operation at low pressure and thus to avoid the observed anomalous recombination. At the same time, the magnetic field has also a distinct influence on the spectra! appearance of the expanding hydrogen plasma jet. Three regimes can be distinguished depending on the applied magnetic field, which we define as the atomie regime, the intermediate regime and the molecular regime. The three regimes can also be reached by varying the pressure suggesting that confinement of the plasma plays an important role. Earlier work, e.g. of de Graaf 13 concentrated on the high flow and
pressure regimes. Therefore, the lower pressure in the vacuum vessel reached by decreasing the flow is the essential difference with the work of de Graaf n As we will see, this will have a large impact on the properties of the ex panding plasma jet.
Figure 2-8 and Figure 2-9 illustrate the hydrogen plasma and a typical emission spectrum of the regime at relatively large magnetic field. The main feature of this regime is that the plasma emits strong hydrogen Balmer lines. Especially in the blue region of the plasma jet (cf. Figure 2-8), there is no observable molecular spectrum in the measured wavelength range. Therefore we name this regime the atomie regime.
cascaded are
red region
blue region
low pressure background
Figure 2-8 Expanding plasma beam in the atomie regime. Main characteristic:. the blue region of the plasma jet emits only strong hydrogen Balmer lines. Conditions: larc = 50 A, QH, = 0.5 slm, Is = 250 A, Pmset = 5 Pa.
Figure 2-10 and Figure 2-11 illustrate the hydrogen plasma and a typical emission spectrum of the regime at relatively small magnetic field. The main feature of this regime is that in the measured wavelength range, not only hydrogen Balmer lines but also strong hydrogen molecular lines are observed. We name this regime the molecular regime. This regime is reached by decreasing the magnetic field (by lowering the coil current Is from 250 A to 50 A) continuously from the atomie regime. The regime observed at Is= 150 Ais the intermediate regime which is in between the atomie regime and the molecular regime.
5CXXl 8 0 0 4CXXl "' c:
~
ICXXl 300 400 500 wavelength (nm) 700Figure 2-9 Visible spectrum of the hydro gen plasma (atomie regime). 111rc = 50 A, QH,
=
0. 5 slm, Is = 250 A, Pveue/=
5 Pa.Table 2-3 Different regimes of an expanding hydrogen cascaded are plasma obtained
b >Y varymg e magnet1c 1e th . f Id
atomie regime intermediate regime molecular regime
plasma jet torch type beam with short red white beam long and narrow
a blue head and red with a sharp head white beam
body
spectrum only strong atomie clear molecular band strong molecular
lines appear in the observed lines and weak
spectrum atomie lines
low pressure background
Figure 2-10 Expanding plasma beam in the molecular regime. Main characteristic:
strong molecular lines emitted from the white bright plasma beam.
~
~
0 ~ è ·;;; c:: B c::2 Expanding hydrogen cascaded are plasma
ICXXXXl 8CXXX) 600X) 400XJ 2CXXX) 590 600 610 620 630 640 650 660 670 wavelength (run) 13
Figure 2-11 Visible spectrum of hydrogen plasma (molecular regime). larc = 50 A,
QH
=
0.5 slm, IB=
50 A, Pvessei=
5 Pa.The main observed characteristics of the defined regimes are listed in Table 2-3. The spectra of the hydrogen atomie and molecular regimes will be discussed in more detail in chapter 5 and chapter 6.
Figure 2-12 demonstrates qualitatively the operational conditions for different plasma regimes in this work. As is shown in the figure, the different regimes can also be reached by changing the vessel pressure. As has been stated, this suggests that the confinement of the plasma is a key element in the explanation of the phenomena appearing in the different regimes. In this experiment, we vary the magnetic field to reach the different plasma regimes at the same gas flow.
80 70 60 50 -;;;- 40 l'qt, .;.to ~ Er; "lQ· ('r. p.. 30 "'1e0':. ~· '.;it. e,,, -Qe
20 e~. 0e 10 rno/ecu/
ar
.
regime 0 5 10 15 20 25 30 35 40 B (mT)Figure 2-12 Operational conditions (pressure and magnetic field) for the different plasma regimes
1 H. Maecker, Z. Naturforch
lla
475 (1956)2 C.J. Timmermans, Ph.O thesis, Eindhoven University of Technology, The Netherlands ( 1984)
3 F.P. Incropera and E.S. Murrer, J. Quant. Spectrosc. Radiat. Transfer. 12 1369 (1972) 4 A.T.M. Wilbers, G.J. Meeusen, G.M.W. Kroesen and O.C. Schram, Thin Solid Films
204 59 (1991)
5 J.M. Bridges and W.R. Ott, Applied Opties 16 367 (1977)
6 H. Shindo and S. Imazo, J. Quant. Spectrosc. Radiat. Transfer. 23 605 ( 1980) 7 M.C.M. van de Sanden, J.M. de Regt and O.C. Schram, Phys. Rev. E 47 2792 (1993)
A. Gleizes, H. Kafruni, H. Dang Duc and C. Maury, J. Phys. D. Appl. Phys. 15 1031 (1982)
9 J.J. Beu lens, A.J .M. Buuron and O.C. Schram, Surf. Coat. Techno!. 47 401 (1991) 10 A.J.M. Buuron, J.J. Beulens, M.F.J. v.d. Sande, J.G. v.d. Laan and O.C. Schram,
Fusion Tech. 19 2049 (1991)
11 G.J. Meeusen, Zhou Qing, A.T.M. Wilbers and O.C. Schram, Proc. of Thin Film Phys. and Appl. SPIE 1519 252 (1991)
12 M. J. de Graaf, Zhou Qing, H.W.A. Tolido, M.C.M. van de Sanden and D.C.
Schram, J. High Temp. Chem. Processes 1 11 ( 1992)
13 M. J. de Graaf, R.J. Severens, R.P. Oahiya, M.C.M. van de Sanden and O.C. Schram, Phys. Rev. E 48 2098 (1993)
14 M. J. de Graaf, Ph.O thesis, Eindhoven University of Technology, The Netherlands
(1994)
15 J.O. Jackson, "Classica[ Electrodynamics", 2nd Edition, John Wiley & Sans, New York (1975)
3 Experimental characterization of a cascaded are 15
3. Experimental characterization of a cascaded are
To understand the physics and to optimize the operation of the cascaded are, it is necessary to characterize the cascaded are. Experimentally, a cascaded are can be characterized by basic are parameters, such as the current, the electric field, the pressure, the pressure gradient and the efficiency. Other are parameters such as the plasma temperature, the effective are radius and "the dissociation degree of the hydrogen are plasma can be derived from basic are parameters. In this chapter we will discuss the experiment which is used to determine the are parameters. The experiment described in this chapter is carried out for an Ar/H2 plasma mixture. By varying the flow ratio between the argon and the hydrogen gas, the study is extended from a pure argon are to a pure hydrogen are.
3.1 Diagnostic techniques
The determination of the axially resolved are parameters is realized by power balance and pressure measurements at several axial positions. The measuring devices used in this experiment are shown in Figure 3-1. In power balance measurement, the potential, the cooling water flow and the water temperature at different axial positions are measured so that the fraction of the total power obtained by the are plasma can be determined. The cooling water temperature is measured by a calibrated semiconductor temperature sensor (National Semiconductor, LM35DZ). The temperature sensor is glued to a copper made flow tube which is connected to the cooling water exit of each component of the cascaded are set up. The output of the temperature sensor is proportional to the measured temperature with a known offset. In the water temperature range of 0 to 100 °C, the measuring error of the temperature sensor is about
±
0.3 °C. In the stationary state, the cooling water and the copper made component reach a thermal equilibrium and the measured water temperature represents the temperature of the component of the are set up. Since the heat loss is determined by the temperature change of the water, the same type of temperature sensor is mounted at the cooling water inlet to measure the inlet water temperature.The cooling water flow is measured by a water flow transmitter (Honsberg rotation). A water flow transmitter consists of a propeller type rotor, a light source and a pin-diode. When water is passing the rotor, it will be forced to rotate. The pin-diode is then alternatively covered by the wing of the rotor and it thus generates an alternating signa! with a frequency which is proportional to the water flow rate. In this experiment, the cooling water flow is in a range of 10 - 15 ml per second and the corresponding measuring error is about 0.5 ml per second.
The potential at each component of the cascaded are set up is measured by a voltage divider. It reduces the potential proportionally to a value within a range of 0 - 10 V which can be sampled by an ND converter in a computer. The accuracy of the potential measurement is mainly determined by the stability of the plasma during the experiment, which is approximately 15 %.
To measure the pressure in a cascaded are, a small hole with a radius of 1 mm is drilled in the wall of each cascade plate. The exit of the hole is connected toa calibrated pressure sensor (ICS 13). The pressure sensor gives a potential signa! which is proportional to the measured pressure. Since there is no flow in the drilled small hole which connects the pressure sensor and the measured position, the measured pressure represents the pressure of the are plasma at the wall position. In the experiment, the uncertainty in the pressure measurement is about
±
50 Pa. Note that the pressure value measured at the end plate of the hydrogen are is uncertain since the pressure there is lower than the minimum detection limit.pressure sensor
~
potential measuring devicewater entrance
.:. fa
'
are .eb an nel
\
copper platevoltage divider
Figure 3-1 A schematic representation of the are parameter measuring set up (on one
cascade plate). MP: multiplexer card, FC: frequency counting card. The potential signals. measured by the_ temperature sensor, the pressure sensor
and the voltage divider are selected by a multiplexer card and then measured by an ND converter (PCL 718 lab-card). The signa] of the water flow transmitter is selected and
measured by a frequency counting card (PCL830 lab-card). The experimental results presented in the remainder of this chapter are based on this measuring set up and the measurements will be used to deterrnine important are parameters such as the temperature of the plasma and the dissociation degree of a hydrogen are.
3 Experimental characterization of a cascaded are 17
3.2 Electric field in a cascaded are
3.2.1 Plasma conductivity and the electric field
The electron temperature T, is one of the most important parameter of an
plasma. In genera!, T, is associated with the electric conductivity of the plasma.
Therefore the conductivity can be used to determine the electron temperature of a
plasma. In a cascaded are plasma, the conductivity is directly associated to the electric field. The electric field at an axial position z along the are channel is given by
E(z)
=
J,(z)cr[ n,(z), T,(z),f.(z)]
(3.1)in which jc(z) is the current density and cr[n,(z), T,(z),f,(z)] the electric conductivity of the plasma (in which f,(z) is the electron velocity distribution). In the case that the
electric field strength is homogeneous over the cross section of the are plasma, the
current density can be written as
j(r)
=~
=~=
cr(r)·
ES,g
rtr,ff(3.2)
in which S,ff is the effective cross section and r,ff the effective radius of the are plasma. Combining equation (3.1) and equation (3.2), the plasma conductivity in the are is then
cr[
n
,
(z), T,(z),f.(z)]
=1;" E
rtr,ff .(3.3)
According to Spitzer 1, the electron temperature T, in a fully ionized plasma with single ionized ions is associated with the electric conductivity in the plasma through:
(3.4)
in which T, is in eV and lnA is the Coulomb logarithm. The argument of the Coulomb
logarithm, A is 9 times the number of charged particles in the Debye sphere.
The relation of O"sp;1zer(T,, n,) vs. T, for n, = 1022 m·3 is given in Figure 3-2. The n, dependence of O"spi•zer is rather weak due to the square root relation in the Debye length and the logarithmic relation in the Coulomb factor; e.g. if n,
=
1021 m·', which is one order of magnitude lower than the value in LTE at 1 atmosphere for Spitzer curve in Figure 3-2, for the same T, value, O"spitzer differs only approximately than 10%.Apart from the Spitzer relation, T, in a Local Thermal Equilibrium (LTE) plasma can also be associated with the electric conductivity through the Frost relation 2 :
_47t·n,(z)·e2 J~w4·f.(z)d cr Fm." - 3k T ( ) . w
b. •
z
o Ven+ V.;(3.5)
in which wis the electron velocity, v,0 is the electron-neutral collision frequency and V,;
is the electron-ion collision frequency. Both Vw and v,; aren, and T, dependent. For a Maxwellian velocity distribution, <1Frosi as a function of T, is also shown in Figure 3-2 3. As can be seen from this figure, for T, ~ 10000 K, the difference between <1Fmsi and crspi1Zer is very small. It has to be pointed out that the Spitzer relation is only val id for an
ionization degree in a plasma Iarger than 1 %, i.e. when Coulomb collisions are dominant for the electrons.
8 7 6 --: 5 6
C:
4"'
0 cr Spitzer .- 3 ' - ' b 2~
0 4 6 8 10 12 14 16 Te ( x 1000 K)Figure 3-2 The plasma conductivity cr as a function of the electron temperature T, in an argon plasma in the case of a Maxwellian velocity distribution for electrons. - : Spitzer relation, n,
=
1022 m-3; · ···: Frost relation 3. p=
Ja5
Pa.
Figure 3-3 shows schematically the electric field distribution in a cascaded are.
In principle, the electric field in the cascaded are is dependent on both the axial position
z and the radial position r. However, in the centra) part of the plasma, the electric field is
approximately linearly dependent on the axial position. Therefore we can define the
electric field at the center of the channel by
E,(z) = -
d~~z)
(3.6)In the case that one of the two parameters of the effective are cross section r,ff or T, is known, the other can be estimated by the Spitzer relation or the Frost relation. In this experiment we determine T, for an argon are by assuming that the are radius is close to
3 Experimental characterization of a cascaded are 19
the channel radius and using the Spitzer relation for the considered argon are. The situation in Ar/H2 mixture and pure H2 is more complicated. Due to the large heat
conductivity of H2, the centra] are channel with high ionization degree narrows.
Therefore in hydrogen the radius of the conducting channel reff is substantially smaller
than the channel width rc1wnne1 and there are two unknown parameters (in this case, both
Te as wel 1 as r,ff are unknown). So we have to assume one of these parameters to be known. In this work for hydrogen, we use T, values from the results from the literature of modelling for the conditions which are similar to our experimental conditions.
anode side electron: current ~ -· - ' - .- _ . - --1.. - - - ~ - •- -, - ~ - ·- - · - --7- · · 2rcff 2rdianncl
:
' ' t
i
__
_
:
_,_r_,>/.:
"
.
ion currentl:J/
/insul:ilion..
·>T
-
&--- &--- &--- " " " ' zFigure 3-3 A schematical representation of the electric potential distribution zn a
cascaded are.
3.2.2 Electric field strength in a cascaded are
Figure 3-4 shows the potential and the electric field distribution at the center of
the cascaded are for argon and hydrogen respectively. As can be seen the measured
voltage drop in the cathode region is much larger than elsewhere in the are. This is due
to the strong constriction of the are spot at the cathode tip. The thoriated tungsten made
cathode tip ( there are three cathode tips in a cascaded are set up, cf. Figure 2-1) used in
the cascaded are has a very sharp head. The measured voltage drop between the
cathodes and the first plate (the plate close to the cathode,
z
= -24 mm) occurs in a veryshort range close to the sharp head of the cathode tips. The part between the cathode tips
and the first plate only shares a very small fraction of the total voltage drop between the
cathodes and the first plate. Therefore the potential distribution between the cathodes
and the first plate is very imhomogeneous and the electric field derived based on
equation (3.6) does not represent the real electric field between the cathodes and the first plate. At the anode, the situation is somewhat similar, because of the edge effect, the electric field derived based on equation (3.6) can not represent the real situation between the nozzle and the last plate (the plate close to the anode,
z
= 0).'"I
120 100 80.>
>
60 40 20 0 -20.__.~~~~~~~'---'-~'---'-~~ -30 -25 -20 -15 -10 -5 0 z (mm) 8000 ,..., 6000~
"1.1 4000 2000 o~~~~~~~~~~~~~ -25 -20 -15 -10 -5 0 z ( nun)Figure 3-4 Left: potential distribution over a cascaded are; right: electric field in a cascaded are. •: an argon are, Is
=
O; •: a hydrogen are, Is=
O;+:
a hydrogen are, Is=
250 A; z=
0: the anode position; z= -
27 cm: the cathode position. Conditions: Q = 1.0 slm, lurc = 50 A.As can be seen from Figure 3-4 except for the cathode and anode region, the
electric potential in the are is approximately linearly dependent on the axial position. Since each cascaded plate is electrically floating, it gets its potential through the are
plasma. Actually, close to the wall most of the potential drop occurs over the insulation ring. As a consequence, the electric field in the cathode and the anode regions of the cascaded are can not be derived simply from the potential difference; on the other hand in the cascade plate section (cf. Figure 2-1), the electric field at the center of the
cascaded are is close to the value determined by equation (3.6). This conclusion will be used later in all electric field related studies, e.g. the determination of T, of an argon are,
the effective are radius of a hydrogen are and the efficiency of the cascaded are etc.,
where we will only discuss the experimental results in the cascade plates section. Note that at the end of the hydrogen are the electric field strength differs for the high magnetic field case (the condition of the atomie regime) and the zero magnetic field case (the condition close to the molecular regime).
Figure 3-4 also shows that the electric field in a hydrogen are is higher than that
in an argon are. This is demonstrated more clearly from a measurement of the electric
field in an Ar/lh are mixture. In Figure 3-5 the electric field as a function of the hydrogen flow concentration y is given for three positions in the are. As can be seen from this figure, the electric field along the are is rather homogeneous and it becomes larger with increasing
y.
3 Experimental characterization of a cascaded are 21 70CfJ fiXjJ 5COO ,... E 40C()
•
(:,•
•
•
Ll.l 300'.)•
•
•
•
•
•
• •
2(XX)•••
•
IOCfJ•
•
0 0 20 40 60 80 100 y(%)Figure 3-5 Electricfield in an Ar/H2 are, •: z
=
-6 mm; •: z=
-12 mm;+: z=
-18mm. Condition: Q101al
=
QAr + QH,=
1.0 sim, larc=
50 A, Is= 0.The difference in electric field between an argon are and a hydrogen are is mainly due to narrowing of the are channel for hydrogen arcs. This is partly related to the difference in the diffusibility of argon and hydrogen. The diffusibility of hydrogen particles is much larger than that of argon particles since the mass of a hydrogen atom is much smaller than the mass of an argon atom (a factor of 40). Therefore the energy exchange between hydrogen particles and the channel wall is faster and more efficient than the energy exchange between the argon particles and the channel wal!. This means that the heat conductivity in case of hydrogen is large and the are plasma in case of hydrogen is more efficiently cooled by the presence of the wall. Ina more kinetic picture we can state that the association of the hydrogen atoms and the recombination of the hydrogen ions at the channel wal! cool the are too, both facts lower the charged particles temperature and density close to the wal!. As a consequence, the effective are width in hydrogen case becomes smaller: the are channel narrows 4 . This effect will be discussed in more detail in section 3.2.4. The narrowing of the are channel results in a smaller electrical conductance and this rises the electric field in the are. The higher the hydrogen concentration, the narrower the effective are width and the smaller the electrical conductance of the plasma channel. We can conclude from the measurements that in order to keep a hydrogen are running a higher electric field is necessary.
The influence of the plasma operational conditions on the electric field is analyzed for the are current, the gas flow rate and the magnetic field. Figure 3-6 demonstrates the are current influence on the electric field in an argon and a hydrogen are. lt is clear that the are current has only a small influence on the electric field.
4000 8000 3000 6000 ~ E 2000 4000
G
.
•
1 ""1•
•
1000•
.
•
•
2000 0 ~~~~~~~~~~~~~ O~~~~~~~~~~~-'--~w 20 30 40 50 60 70 80 20 30 40 50 Jare (A) 60 70 80Figure 3-6 larc influenee on the eleetrie field. left: a pure argon are,; right: a pure hydrogen are;•: z
= -
9 mm; •: z=
-15 mm. Conditions:Q
=
1.0 sim, IB=
0, Pvessel=
5 Pa.Following equation (3.2) the eleetrie field should be Jinearly dependent on the
are eurrent larc if the electrical conduetance of the plasma channel would be constant.
The fact that larc has only a small influence on the electric field clearly demonstrates that
the conductance of the plasma channel rises with increasing are current. In argon case this is mainly the result of an inerease of T, with larc. but it is also due to a widening of the are ehannel effective radius 5.
5000 4000 ~ 3000 E
è.
Ul 2000 1000.
•
0 0 Figure 3-7 8000 6000•
• •
4000•
1•
• •
•
•
• •
• •
• •
•
•
•
•
•
1 1 2000 1.
0 2 4 6 8 10 0 2 J 4QAr (sim) QH, (sim)
Gas flow influenee on the eleetrie field. left: a pure argon are,; right: a
pure hydrogen are;•: z
=
-6 mm;•: z=
-12 mm;+: z = -18 mm.3 Experimental characterization of a cascaded are 23
Figure 3-7 demonstrates the gas flow influence on the electric field in a pure argon are and a pure hydrogen are. In both argon and hydrogen, the electric field behaves rather similar with varying gas flow. The are current is fixed in these series and the total input power changes only slightly. The rising of the electric field with increasing gas flow is due to the fact that a larger electric field is necessary to keep the are running with the same temperature at large flows. In the next section, we will show that the temperature does not change much with varying gas flow.
2000 1500 ~ E 1000
•
è
•
L.t.l•
500 0 0 Figure 3-8 8000 6000 4000•
:
•
•
•
•
•
•
•
•
•
•
•
2000 50 100 150 200 250 0 0 50 100 150 200 250 Is (A) Is (A)The magnetie field influenee on the eleetrie field. left: a pure argon are,; right: a pure hydrogen are;•: z
=
-6 mm;•: z=
-12 mm;+: z=
-18 mm. Conditions: ajour plates are, larc=
50A.
Q=
1.0 sim, Pvesut=
5
Pa.The influence of magnetic field on the electric field is demonstrated in Figure 3-8. lt appears that the magnetic field has almost no influence on the electric field of the cascaded are. We can explain this by studying the magnetization of the plasma in the
are. The magnetization of a plasma can be characterized by the so called Hall parameter
H 6.
e •
H, =
D,·î,
(3.7)Here 'te is the average collision time for momentum transfer of electrons to ions and neutrals and
n
e
is the electron cyclotron frequency:(3.8)
r,
m,
in which r, is the electron cyclotron radius, v, the electron thermal velocity. In the case that the electron-ion collisions dominate the momentum transfer processes, the Coulomb col lisions determine the electron velocity distribution function. In this case 'te is equal to the collision time for electron-ion scattering perpendicularly to the magnetic field 6· 7· 8 which can be expressed as 6 :
1
=
1 _=
3.5 · l 011 ·JT!
' " Jn A ·n, (3.9)
with T, in eV and 't, in seconds. By combining equations (3.7), (3.8) and (3.9), the electron Hall parameter can be expressed as
6 2 · 1022 · B ·
fi!
H,
=
Q, . 't,;= .
'
lnA·n, (3. l 0)
For a plasma to be magnetized, the Hall parameter H, should be much larger than one:
H, >> 1. In this experiment Uarc
=
30 - 75 A,Q
=
0.5 - l.O sim, 80=
8 - 45 mT), n, isabout 4· 1021 m·3 (the lower limit in the argon are 9) and T, is about 1.5 eV. Therefore for an argon plasma H, is approximately 0.3 and the cascaded are plasma is not magnetized. The applied magnetic field does not change the radial distribution of the are plasma and variation of the magnetic field does not change the electric field distribution in the are.
For hydrogen plasmas the flow velocity is much higher especially close to the anode and the electron density is smaller (8· 1020 m·\ A marginal magnetization close to
the nozzle can not be excluded in this case. Since H, - l .5 for the same conditions as in the argon are operation, the influence of the applied magnetic field is limited.
3.2.3 Electron temperature in an argon are
In section 3.2.1 we have seen that the electron temperature T, in a plasma is
associated with the electrical conductivity of the plasma. From the measurements of the
electric field it is possible to determine T, in the plasma if the effective are radius is known. In this section we will use the results of the electric field determination in the previous section to determine T, in an argon are plasma. For argon, it has been shown that the ratio of the effective are radius and the radius of the channel is in a range of
r,Jlrchan11e1"' 0.90 - 0.98 for are currents between 30 A and 70 A 5. If we assume that r,ff is unaffected by the flow and magnetic field strength then the electron temperature can be estimated from the Spitzer relation using the results of the measurements of the
electric field.
Figure 3-9 shows the electron temperature of an argon are plasma for different are settings. The electron temperature is almost the same with varying argon flow -in a flow range of 0.5 sim to 10 sim. In section 3.4.2 we wil! show that the power efficiency
of an argon are increases with the gas flow. Although the input power remains approximately the same, the total power gained by the are plasma increases due to a
higher efficiency. On the other hand the power gained by the are plasma per unit gas
flow remains almost constant due to the linear dependence of the power efficiency on
3 Experimental characterization of a cascaded are 25
approximately the same. It has been reported that in the very small flow range (0 - 0.03 sim), T, drops slightly with increasing gas flow IO.
20 15
I .
I
. . I .
I
Q'§
:::::. 10 r-~ 5 0 0 2 4 6 10 QAr (shn) 20 15I
I
10I
5 0 20 30 40 50 60 70 80 Jan: (A) 20 15 •I
I
10 5 0 0 50 100 150 200 250 I8(A)Figure 3-9 Electron temperature in an argon cascaded are plasma. z = -15 mm;
Conditions: left: Iarc
=
50 A,h
=
0, middle: QAr=
1.0 sim, Is=
0, right:larc
=
50 A, QAr=
1.0 sim, Pvessel=
5 Pa.As can be seen from Figure 3-9, the electron temperature T, increases slightly with increasing are current larc· Again we can explain this using the power efficiency results in section 3.4.2. We will show there that the power efficiency of an argon are increases with increasing larc· Since the voltage drop over the are increases only slightly with increasing current (in an Iarc range of 25 A to 75 A, the voltage drop Vinpui changes approximately 10% ), we can assume V;"""' to be a constant to a first order approximation. In this case, the power efficiency of the are increases linearly with the
input power. In other words, the power gained by the are plasma increases with
increasing larc Since the gas flow is constant, T, in the are plasma rises with increasing
larc· On the other hand, the effective are width also rises slightly with increasing lan 5.
This factor leads to a reverse result since the larger r,.ff, the smaller the resistance of the are and thus the lower T" However, r,.ff changes only very slightly in argon case 5 and the T, dependence on larc is dominated by the power efficiency of the are.
The magnetic field has no influence on T, of the argon are under the experimental conditions, in agreement with the fact that the argon cascaded are plasma is not magnetized.
The accuracy of the T, results presented in Figure 3-9 depends on the stability of the are plasma (reflected by the variation of the potential at each plate, which in this experiment is about 15% ), the accuracy of the assumptions made using the Spitzer relation and the assumption of a flat T, distribution over the are cross section. It is estimated that the error in the presented T, values is smaller than 25%.
3.2.4 Channel narrowing effect in a hydrogen are
In the centra! part of an are plasma the ionization degree is high and Coulomb collisions dominate. In the previous section, we have used the T, -a relation (Spitzer relation) to determine T, in an argon are. In this section we will apply the same method to a hydrogen are, but for this case we wil! use the T, -
a
relation to determine the effective plasma radius.We mentioned in section 3.2.2 that the larger heat conductivity of hydrogen in comparison with argon cools the plasma more efficiently when it comes in contact with the wal!. As a result the temperature profile in a hydrogen are becomes smaller in width. The same effect also occurs for the eleetron density. This is known as the channel narrowing effect of a hydrogen are 4 .
To study the channel narrowing effect and to determine the effective width of a hydrogen are using the Spitzer relation, it is necessary to know the eleetron temperature in the hydrogen are. In this work we use results from a numerical model in literature 11 . The model is based on magnetohydrodynamic conservation equations (for continuity, momentum, energy), Maxwell equations and Ohm's law. The plasma conditions in these ealculations are close to our experimental eonditions 11 . The assumptions of the model are that the flow and the plasma in the cascaded are are stationary, subsonic and laminar.
20000 20000 15000 15000 ,..._ ~ 10000 10000 '-"' r-<" 5000 5000 0 0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 r (mm) r (mm)
Figure 3-10 Calculated T, in the middle of a cascaded are 11• Left: a pure argon are, right: a pure hydrogen are. - - - : larc
=
20 A, - : larc=
50 A,Conditions: Q
=
1.0 sim, la= 0, Larc=
6.0 cm.Furthermore, the radiation is emitted from the whole volume of the plasma and an external magnetic field is absent. Moreover, it is assumed that the radial temperature gradient is larger than the axial temperature gradient so that a boundary layer exists. The electron density in the are is determined by the balanee between ionisation and three-body recombination reaetions 11 .
3 Experimental characterization of a cascaded are 27
Figure 3-10 shows the T, values in a 60 mm long cascaded are calculated from the model 11 • The calculation shows that T, in the center of the plasma is approximately 1.3 eV for larc
=
50 A, which confinns the value of 1.4 eV from the previous section. As can be seen in an argon are, although T, is dependent on the are current, the radial profile of T, is rather flat and the minimum radius of the effective conducting plasma is approximately 0.9 x 2=
1.8 mm for larc=
50 A. This value for reff is close to the one that has been used in the previous section to find T, in an argon are. Note that in the model calculation it is assumed that there is no external magnetic field applied on the are. Inthe experiment, an external magnetic field is applied at the nozzle position of the are. However, we have shown that in the magnetic field strength range of B < 45 mT, the are plasma is not magnetized and the applied magnetic field does not influence the electrical properties of the are plasma. The comparison of the T, results in the experiment and in the calculations for an argon are also show that the resulting differences between the T,
values with and without a magnetic field are negligibly small. We will assume that also for the hydrogen are the differences in the T, values with and without a magnetic field are small, and the T, values presented in Figure 3-10 equal the T, values in the experiment. Assuming furthennore that the current profile has an effective radius r,ff, we can use the T, values from the model calculation to determine the effective are radius
reff·
For larc
=
50 A, the difference in the calculated T, values in the center of a pure argon are and a pure hydrogen are is smaller than 5 %. Therefore, we may assume that under the experimental conditions, T, is approximately the same for both the argon and the hydrogen are. This provides a method to study the channel narrowing effect in an Ar/H2 are mixture experimentally. Figure 3-11 demonstrates the channel narrowing effect in an Ar/H2 are mixture.2.0
LI.
1.5I
î
•
I
.._., 1.0•
I
it::•
._.o 0.5 0.0 0 20 40 60 80 100 y(%)Figure 3-1 1 Channel narrowing effect in an Ar!H2 are mixture as a function of the
hydrogenflow concentration. Conditions: Iarc
=
50 A, Qwwl=
/.0 sim,As can be seen from this figure, the effective are radius reff becomes smaller with increasing H2 flow concentration
y.
The main decrease of r,ff occurs at smal 1y
range (0 - 10% H2 in total flow) indicating that hydrogen plays a dominant role in the
physical cause for the channel narrowing. Therefore it can be concluded that hydrogen determines the profile of the are plasma. For
y
> 10%, r,ff decreases slowly with increasing y. lt is interesting that for a pure hydrogen are, r,ff determined in the experiment is approximately 0.9 mm which is very close to the radius of the T, profile presented in Figure 3-10 (for lun = 50 A). This supports for the experimental determination of T, or r,.ffusing the T, -cr
relation.The conductivity
cr
determined is an average value over the effective cross section (0 < r < r,ff) of the are plasma. Also the electron temperature is an effective value averaged over the effective cross section. The uncertainty in r,ff will be directly related to the uncertainty in T, which is estimated to be 15%.3.3 Pressure distribution in a cascaded are
The pressure in a cascaded are is determined by the conservation of mass, momentum and energy. The generalized Navier-Stokes equation for a plasma is given by
p (u·'V)u +Vp+ 'V.fl =j
x
B (3.11)in which p is the mass density, p = m0·(n0
+ n,);
n
the viscosity tensor; m0 the atommass and no+ n, the heavy particle density; u the plasma flow velocity and is given by (3.12)
in which wi is the drift velocity of the particle j. If all heavy particles have the same heavy particle temperature Th, the total pressure can be written as (Dalton's law):
(3.13)
in which j stands for all kinds of heavy particles such as atoms, ions and molecules with densities ni. The pressure measured at the channel wall is equal to the centra! total pressure including the contributions of ions and electrons. The radial component of Navier Stokes equation gives
"dplàr
= 0 as the radial components of the Lorentz term velocity are small. The inertial term and the Lorentz term gives a contribution of around100 Pa over 1 mm, which is significant for the last plate measurement in hydrogen in particular in the low magnetic field case.
Figure 3-12 gives the pressure p and the pressure gradient dp/dz in the cascaded are. The results show that both pand dp/dz in a hydrogen are are smaller than that in an
