Excitation of ion oscillations by beam-plasma interaction

EXCITATION OF ION OSCILLATIONS BY

BEAM-PLASMA INTERACTION

EXCITATION OF ION OSCILLATIONS BY

BEAM-PLASMA INTERACTION

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL DELFT OP GEZAG VAN

DE RECTOR MAGNIFICUS Dr.Ir. CJ.D.M. VERHAGEN, HOOGLERAAR IN DE AFDEUNG DER TECHNISCHE NATUURKUNDE, VOOR EEN COMMISSIE UIT DE

SENAAT TE VERDEDIGEN OP WOENSDAG 26 JUNI 1968 TE 16 UUR

DOOR ABRAHAM VERMEER ELEKTROTECHNISCH INGENIEUR GEBOREN TE HAARLEM

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DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOR PROF. DR. J. KISTEMAKER

This work was performed as part of the research program of the association agreement Euratom and the ' Stichting voor Fundamenteel Onderzoek der Ma-terie', (Foundation for Fimdamental Research on Matter) with financial support from the 'Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek' p u t c h Organization for Pure Scientific Research, Z.W.O.) and Euratom.

C O N T E N T S Chapter I Introduction

1.1 Objective 1.2 Historical survey

1.3 The presence of a magnetic field 1.4 Excitation mechanism 1.4.1. Beam-plasma interaction 1.5 Arrangement. References page 9 9 10 13 14 15 18

Chapter 11 Experimental Setup

2.1. Mechanical construction 2.2 The electron gun

2.3 The vacuum system 2.4 The magnetic field

References 21 21 24 26 26

Chapter III Diagnostic Methods

3.1 R.f. spectrum analysis

3.1.1 The Panoramic spectrum-analyser 3.1.2 The Lavoie spectrum-analyser 3.2 The antennae

3.2.1 Configurations of the measuring circuits 3.2.2 The Rogowski coil

3.3 Microwave cavity measurements 3.4 Electron temperature measurements 3.4.1 Description of the apparatus

References 28 28 29 30 30 31 34 37 43 45

Chapter IV Experimental Results 4.1 Beam-plasma system 4.1.1 The regimes of the system

4.1.2 The AC/DC mode of the electron gun 4.1.3 Data of the plasma system

50 51 51 52 53

page

4.1.4 The density of the p l a s m a 56 4.1.5 A simple calculation of the p l a s m a density 57

4.1.6 The electron t e m p e r a t u r e 60 4.2 The frequency s p e c t r u m 60 4.2.1 The instability a s a function of different p a r a m e t e r s 62

4.2.2 Wavelength m e a s u r e m e n t s 67 4.2.3 Azimuthal dependence 71

References

Chapter V Discussion of the Experimental Results 76

5.1 Introduction 76 5.2 Theory for the b e a m - p l a s m a interaction 78

5.2.1 The dispersion diagram 78 5.2.2 The calculated dispersion diagram 84

5.3 Growth r a t e s 85 5.4 The model of the partially filled wave guide 90

5.5 A comparison between theory and experimental r e s u l t s 93

5.6 Optimum conditions of the instability 94 5.7 The influence of the p a r a m e t e r s 97 5.8 Standing wave investigations 99

5.9 Multiple m o d e s 103 5.10 The azimuthal wave number 105

5.11 Cyclotron h a r m o n i c waves 106

References

Appendix A H I Appendix B 112

CHAPTER I INTRODUCTION 1.1. O b j e c t i v e

Of the v a r i o u s s t a t e s in which a p l a s m a may be, one which frequently o c c u r s i s when a beam of charged p a r t i c l e s i s travelling in a c e r t a i n direction through the p l a s m a . T h i s not only happens in g a s d i s c h a r g e s , in which directed e l e c t r o n - and i o n - b e a m s a r e p r e s e n t , but also in s e v e r a l p l a s m a e x p e r i m e n t s and in the c o s m o s .

In 1949 Bohm and G r o s s showed in a t h e o r e t i c a l study that instabilities may occur a s a r e s u l t of interaction between a beam of charged p a r t i c l e s and a p l a s m a . T h e s e a r e the so-called ' m i c r o i n s t a b i l i t i e s ' : they a r e distinctive since they a r e excited by collective Coulomb i n t e r a c t i o n s between g r o u p s of charged p a r t i c l e s behaving coherently. This in contradistinction to m a g -netohydrodynamic instabilities, w h e r e Coulomb collisions occur between the individual charged p a r t i c l e s .

2)

In 1958 Buneman pointed out the possibility of heating a p l a s m a by m e a n s of m i c r o i n s t a b i l i t i e s . T h e s e instabilities a r e v e r y important since in p l a s m a p h y s i c s methods a r e being sought to heat and confine p l a s m a s in a stable m a n n e r . In l i t e r a t u r e t h i s form of p l a s m a heating i s s o m e t i m e s called

3) 4)

'turbulent heating*. Russian i n v e s t i g a t o r s ' ' showed the possibility of the r e l e a s e of energy of an e l e c t r o n beam to a p l a s m a .

With the aid of an e l e c t r o s t a t i c energy a n a l y s e r , they m e a s u r e d the e n e r g y r e l e a s e of an e l e c t r o n beam to a p l a s m a and a value of 80 e V / c m was 5) found for the energy l o s s . In l a t e r e x p e r i m e n t s by SmuUin and Getty , Alexeff e t a l . ' a n d B a b y k i n e t a l . ' a strong heating of the p l a s m a was noticed.

In o r d e r to study the fundamental a s p e c t s of t h e s e collective pheno-m e n a in a p l a s pheno-m a without considering p l a s pheno-m a heating directly, a p l a s pheno-m a beam experiment was set up in the F.O.M. Institute for Atomic and Mole-c u l a r P h y s i Mole-c s (formerly: L a b o r a t o r y , for Mass-Separation) in A m s t e r d a m . The r e s u l t s a r e important among o t h e r things for the p l a s m a physics a s p e c t s

. . . 8) o c c u r m g m ion s o u r c e s ' .

In the experiment described herein a thin electron beam is injected into a tube filled with a low pressure gas. As a result of the ionization by the electron beam of the gas present, a plasma is excited (the so-called self-created plasma). Measurements were made of the oscillations occurring in this beam plasma system. The frequency spectrum of the measured insta-bilities can be divided into two categories ': namely the 'high' frequency spectrum, for which the oscillation frequencies are determined by the electrons and the 'low' frequency spectrum for which the influence of the ions dominates.

Whenever we refer in the following work to l.f. oscillations, we shall mean ion oscillations (for which the frequency range in our case is up to about 10 MHz) The term h.f. oscillations will signify electron oscillations (for which the frequency spectrum lies in the range of several hundred MHz to some kMHz). In this thesis we shall be concerned with l.f. oscillations in plasma beams and in particular with the interactions for which the frequencies lie in the neighbourhood of the ion plasma frequency co ..

1.2. H i s t o r i c a l s u r v e y .

In a plasma consisting of electrons, ions and neutral particles, a variety of oscillation phenomena can take place. When, in addition, the plasma is situated in a magnetic field then the modes of oscillation become particularly complicated ' .

Research in the properties of wave phenomena in plasma has been going on over the last 40 years or so. In the last 20 years, in particular, this research has become very important because of the advent of plasma physics. Historically the l.f. oscillations were observed earlier than the h.f. ones, presumably because of the fact that their experimental detection was simpler. Among the first to observe these l.f. oscillations were

Apple-12)

ton and West ' in 1923. In their glow discharge experiments oscillations took place in the frequency range of several kHz. The oscillations were of a pulsating character and only occurred when striations appeared in the glow discharge. They interpreted these oscillations as ion oscillations in the ionized gas.

The high electron velocities measured in a scattered electron plasma 13)

were presumed by Langmuir ' to be due to the presence of h.f. oscillations. 10

Some electrons, in fact, had a velocity which was higher than that corresponding to the voltage on the gas discharge tube. Langmuir was unsuccessful in his attemps to measure these oscillations. In 1926 Perming , however, suc-sessfuUy demonstrated the h.f. oscillations in a mercury discharge.

These oscillations, which had a frequency of about IkMHz, were detected 15)

by means of a tunable Lecherwiresystem. Tonks and Langmuir 'repeated these measurements and formulated a theory for the observed plasma os-cillations. The theory of Tonks and Langmuir can be viewed as the basis of further work in this field and embraces both ion and electron oscillations. A formula was developed for the frequency of ion oscillations for the case of a plasma of infinite extent. This formula was as follows:

OJ 2 2 - _ _ % i 1+-2 I . m . Pi i (1) /5' V l ^ e where 27r

P=~ir = the phase constant

A = wavelength of the disturbance

T o e = the electron temperature in K

V = P/cy = the adiabatic constant ui—. = • ,,^ = the ionplasma frequency

pi T ^

n. = the density of the ions in the plasma e = charge of a proton

Z = the charge number of the particles m. = mass of a ion

1

If the right hand side of the denominator in equation (1) is small with respect to unity, in other words if T is sufficiently high, we obtain

a, = a>p. (2) One can they say that the ion gas oscillates independently from the

move-ments of the electrons. This property is used in turbulent heating experimove-ments 5)

in which the electron gas is first strongly heated whereupon the ions are no longer effectively screened and can be heated successively.

On the other hand, if this term is large with respect to unity we find that

- 2 = -ph = - l ï ï ^ (3)

where v , = the phase velocity.

In this case the electron temperature is so low that the electron gas de-termines the ion oscillations. The waves which then occur in the plasma resemble in their behaviour the sound waves in a neutral gas and are therefore named ionic sound waves.

Although frequencies measured by Tonks and Langmuir were within the predicted range of ion plasma frequencies, they were not in complete agree-ment with the theoretical values.

Pardue and Webb ' were probably the first to observe oscillations for - 1 -2 which Q)~ o) .. In gas discharges in air:o(pressure 10 - 10 Torr) they found oscillations of the type given by equation (2) which agreed with theori-tical predictions, calculated from the cathode current and the pressure and the anode potential. They were not able to measure the density of their plasma, so that their measurements were still of a qualitative character. They also observed harmonics of the oscillations.

17^ 18^

Kojima et al. ' and also Garscadden ' made measurements in which the density of the plasma in the gas discharge was simultaneously observed. They discovered an ion oscillation the frequency of which was a function of density according to equation (2).

Ion waves at frequencies higher than the ion plasma frequency are also observed, which are an extension of the ionic sound waves given by equation (3).

19)

Sessler ' studied the behaviour of these ion waves generating them, by applying pulsed wave trains to a double grid, and detecting the response by an other pair of grids. He found a good agreement between the measured and calculated phase velocities of the ion waves, and, to a less extent, for the measured and calculated attenuation coefficient. This discrepancy could only partly be explained.

1.3 T h e p r e s e n c e of a m a g n e t i c f i e l d .

The previously mentioned experiments were all conducted without the presence of a magnetic field.

If, however, a magnetic field is present then (apart from the noise) one can expect the discrete frequency spectrum illustrated in figure 1.

AmpUtvidc a r b i t n r y units 10-B 6 tonic sound w a v e s f p i harm fni

"1'

Fig. 1.1. Survey of the oscillations obtained "' in plasma columns with a 2 —3 lor^itudinal magnetic field : B = O.lWb/m and P „ ^ 1 0 Torr, discharge

Q H e current density lA/cm . Relative amplitudes are approximate

f . = — and f = — , resp. the ion- and electron cyclotronfrequency.

i 6 f2. pi 2 e n. ₁ and IT I m . pe 0 1 ^ e^n e. « m ' _{o e}

resp. the ion- and electronplasma frequency.

m. = mass of ion, m = mass of electron, n. = ionplasma density, n = electron plasma density, B = strength of the magnetic field.

So far the most detailed research in this frequency spectrum have been conducted on the high frequency portion. A practical reason for this may be that the ion oscillations are in general weaker, due to the screening of the lighter electrons and therefore they are more difficult to observe.

20)

An article by Crawford and Kino gives a very good overall picture of the work which has been done on oscillations and noise with low pressure gas discharges.

As previously mentioned, our r e s e a r c h e s were r e s t r i c t e d to oscillations in a p l a s m a in the p r e s e n c e of a magnetic field for which the frequencies lay in the ion p l a s m a frequency region.

1.4. E x c i t a t i o n m e c h a n i s m .

The m a n n e r in which the e n e r g y was imparted to the oscillations was not considered in the work of Langmuir and Tonks. A mechanism m u s t have been available which enabled the oscillations to be generated and in s e l f s u s -tained, continuous oscillations a l s o a feedback mechanism m u s t have been available. R e s e a r c h e s in g a s d i s c h a r g e s have shown that t h e r e a r e s e v e r a l ways in which ion oscillations could be generated. It i s to be noted that the ion oscillations m o s t l y o c c u r r e d in the p r e s e n c e of a strong backgroimd of n o i s e . T h i s noise often shows a large i n c r e a s e at low frequencies while at higher frequencies (above s e v e r a l MHz) the background noise d e c r e a s e s sharply. In a r c d i s c h a r g e e x p e r i m e n t s of the hot cathode t3rpe a minimum potential in front of the cathode i s found. In t h i s potential minimum the trapped ions

21) 22) can make oscillations. E m e l e u s and Daly , and Zollweg and Gottlieb '

used this phenomenon to explain the ion oscillations they obtained. The l a t t e r a l s o put forward a theory which gave good agreement with the m e a s u r e m e n t s .

23)

Another explanation h a s been given by Hernqvist ' . He maintains that, with a s p a c e - c h a r g e n e u t r a l i s e d e l e c t r o n beam, the ion-sheath n e a r the anode can modulate the secondary e m i s s i o n c u r r e n t from the anode due to bombardment of the beam e l e c t r o n s and in this way can sustain any o s c i l l a -tions which m a y be p r e s e n t . He d e m o n s t r a t e d experimentally that secondary e m i s s i o n from the anode provided the n e c e s s a r y feedback m e c h a n i s m .

24)

Gabovich et al. foimd that the existence of an ion sheath aroimd the receiving dipole was e s s e n t i a l for the detection of the p l a s m a ion oscillations. They verified that the maximum of the resonance peak o c c u r r e d when the r a d i u s of the sheath was approximately equal to the w a v e l e r ^ h of the p l a s m a ion oscillations. However the e x p e r i m e n t s were not conclusive a s to whether the ion sheath affected the detection of oscillations by the probe o r that the sheath itself c r e a t e d oscillations.

1.4.1. B e a m - p l a s m a i n t e r a c t i o n , 25)

In 1948 Pierce ' demonstrated in a theoretical article that an electron stream going through an ion cloud may give rise to fluctuations in the electron beam. The motive for this investigation was the occurrence of instabilities in travelling wave tubes caused by the interaction of the electrons of the electron beam with the ions due tot the ionization of the residual gas in the tube. These oscillations can be explained by a mechanism whereby the space charge waves on the electron beam excite the plasma waves in the plasma. The principle is identical to that of a travelling wave tube am-plifier, in which the electron waves on the beam start interaction with the travelling waves aloi^ the helix to reinforce the amplitude of the latter. The condition for the interaction between the beam- and plasma waves is that their phase velocities are about the same. Under these conditions there is a strong coupling and energy release between the two waves - the plasma acts as the heUx in a travelling wave tube amplifier and hence as a slow wave circuit.

The beam plasma experiments mentioned in literature can be divided into two categories, namely those which make use of electron beams and those which use ion beams. However, so far, little work has been done on beam plasma interaction with ion beams. The work of Etievant ' and his co-workers can be mentioned in this respect,

The experiments can also be divided into pre-modulated beams and non pre-modulated beams. In the absence of pre-modulation the oscillations start from the fluctuations which are present in the background noise of the beam plasma system. As far as the pre-modulation of ion waves in an electron beam-plasma system is concerned, no cases appear to have been mentioned so far in literature. It should be pointed out, that on account of the low frequencies of the ion oscillations and the high velocity of the electron beam effective modulation at the frequencies of the ion oscillations is not an easy matter. This is due to the fact that the period of an oscillation is long compared to the transit time of the beam electrons across the modulation gap. This problem is much simpler for ion beams. Experimentson beam-plasma

inter-27)

action were reported by Kornilov et al. ' who claimed (without going into detail) oscillations at the ion plasma frequency in a beam-plasma system. Measurements on a pulsed beam-plasma system of high plasma density

were done by Hsieh '. Two distinctive frequency ranges of the r.f. spectrum were foimd, of which the higher one belongs to the electron oscillations. Hsieh concentrated himself on the lowestpart (30 - 600 MHz) of the spectrum, which he could indicate as ion oscillations. However, he does not offer a

29)

theoretical explanation. Lielaerman and Bers pointed out that the mea-surements of Hsieh might be explained by beam-plasma interaction. They showed that under his experimental conditions the interaction between the slow-cyclotron wave on the beam and the plasma could excite the observed ions oscillations. These suggestions were not checked by wavelength measure-ments.

30)

Kato et al. ' explained their measurements done on a mercury discharge in terms of beam-plasma interaction (taking into account the velocity dis-tributions of the beam and plasma electrons). In this way they could explain why the measured frequency had a somewhat higher value outside the beam than inside.

In this thesis, a beam-plasma experiment will be described in which plasma oscillations of the ions were observed at frequencies below 10 MHz. The measurements were done on a thin beam-plasma system, in an axial B-field. The experiment is D.C. operated.

1.5 S u m m a r y .

Chapter II gives a description of our experimental set-up and Chapter III of the methods of measuring. Use was made of r.f. spectrum analysers, while the plasma density measurements were made with the aid of a microwave cavity. The temperature of the plasma electrons was measured by a Langmuir probe. Chapter IV lists the measurements performed.and the results obtained, The behaviour of the studied interaction is considered as a function of dif-ferent parameters, such as the beam current and -voltage, and the magnetic field. Results of wavelength measurements are also given. In this chapter data can be found about the beam-plasma discharge on which the measure-ments are performed.

In the first four sections of Chapter V, the theory of the beam-plasma interaction needed for the explanation of our measurements is dealt with. The dispersion diagram of a simplified model of the system is given and

the growth rate for the studied interaction peak is calculated. We assume a homogeneous beam plasma system which fills a hypothetical wave guide, the radius of which is equal to the beam radius. The reasons for using this model are given. A discussion is given of the high value of the transversal wave number p, as compared to the axial wave number k, which occurs in thin electron beams for Interactions in the neighbourhood of c^ ..

In the second part of the last section an interpretation and discussion of the experimental results are treated, with the aid of the theory.

Formulae are given throughout in rationalised M.K.S. units. For thé technical data and in the graphs sometimes other units are used.

References to Chapter I.

1) D.Bohm and E.P.Gross. Phys.Rev. 75 (1949) 1851. Phys.Rev._75 (1949) 1864. 2) O.Buneman. Phys.Rev.Letters, J.. (1958) 8.

3) F.Karchenko, Ya. B. Fainberg, R.M.Nikolaev, E.A. Komilov, E.A.Lutsen-ko, and N.S. PedenE.A.Lutsen-ko, Sov, Phys, JETP 11, (1960) 493.

4) A.K.Berzin, G,P.Berezina, L.I.Bolotin and Ya.B.Fainberg.

J. of Nucl. Energy C. 6, (1964) 173. 5) L.D.SmuUin and W.D.Getty Phys.Rev.Letters,^, (1962) 3.

6) LAlexeff, R.V. Neidigh, W.F.Peed, E.D.Shipley and E.G.Harris. Phys. Rev, Letters, 10, (1963) 273,

7) M.V.Babykin, P.P.Gavrin, E.K.Zavoiskii, L.LRudakov and V.A.Skoryupin Sov. Phys. JETP, 16, (1963) 295.

8) J.Klstemaker, P.K.Rol and J.Politiek.

NucL Instr. and M e t h . ^ , (1965) 1. 9) A.Vermeer, H.J.Hopman, T.Matitti and J.Klstemaker.

Proc. Vllth Conf. on Phenomena in Ionized Gases, Belgrade 1965, VoL n, p. 386. 10) T.H.Stlx, The theory of Plasma Waves. McGraw-Hill

Book Comp, Inc., 1962. 11) W.P.Allis, S.J.Buchbaum and A.Bers.

Waves in anisotropic plasmas.

M.I.T. P r e s s Cambridge, Massachusetts, 1963.

12) E.V. Appleton and A.G.West. PhiL Mag. 45, (1923) 879. 13) LLangmuir, Phys.Rev. 26, (1925) 585, 14) F.M.Penning. Physica J , (1926) 241, 15) L,Tonks and LLangmuir, Phys,Rev, ^ , (1929) 195, 16) L,A,Pardue and J.S,Webb, Phys.Rev. 32, (1928)946. 17) S.Kojima, S.Hagiwara and K.Takayama,

Proc. Vlth Conf. on Ionization Phenomena in Gases Munchen, 1961. Vol. 1, p. 471. 18) A.Garscadden, Phys.Letters,^, (1962) 224.

19) G.M.Sessler. J.Acoustical Soc. of Am, 42, (1967), 360, 18

20) F.W.Grawford andG.S.Kino.Proc. IRE Vol. 49, (1961), 1767.

21) K.G.Emeleus and N.R.Daly. Proc.Phys.Soc. (London) 69B, (1959) 114. 22) R.J.ZollwegandM.GottUeb.J.AppLPhys., 32, (1961) 890.

23) K.G.Hernqvist. J.Appl,Phys., 26, (1955) 544. 24) M,D,Gabovich, L.L.Pasechnik and V.G.Yazeva.

Sov.Phys, JETP, 11. (1960) 1033, 25) J.R.Pierce, J.Appl.Phys., 19. (1948) 231. 26) M.Perulli, C.Etievant and E.Lutaud,

Proc. Vnth Int. Conf. on Phenomena in Ionized Gases, Beograd 1965, VoL n , p. 409; 27) E.A. Kornilov, O.I.Kovpik, Ya.B.Fainberg and L F.Khar chenko.

Sov.Phys.Techn.Phys. J^, (1966), 1064. 28) Hsien Yuen Hsieh. Experimental Study of BeamPlasma D i s c h ^

-ge. Thesis M.LT., 1964. 29) M.A.Lieberman and A.Bers.

Quarterly Progress Report No. 81, April 15, 1966, M.LT., Cambridge, Mass.

30) K.Kato, K.Matsura and M.Yoseli.

Photograph of the experiment:

On top of the frame construction the magnetic coils and the vacuum vessel are placed. On the right hand side a part of the pumping section is visible. The electron gun, which is on the other side, was removed at the moment of taking the photograph. In front there are the two spegtrum analysers and one of the x-y recorders. The power supplies, controls etc, are put in cabinets which are moimted in the shown rack.

CHAPTER II EXPERIMENTAL SET UP

An experiment was performed in which an unmodulated electron beam was injected axially, by means of an electron gun, into a stainless steel tube. The beun creates its own plasma by ionization of the neutral gas with which the vessel is filled. All measurements were done in the so-called first regime ' of the beam-plasma system, i,e. a quiet, barely visible plasma, which is unstable only in narrow frequency regions.

In the following paragraphs a description of the experimental set up will be given.

2.1 M e c h a n i c a l c o n s t r u c t i o n .

The experimental layout is shown in fig. 2.1 and consists of a tube of non-magnetic stainless steel (inside diameter 8 cm), with an electron gun at one end and at the other a tube leading to the pump section. The tube is built up of easy changeable sections of 20-30 cm. In each section there are holes for inserting probes, microwave equipment, etc.

Electron gun 10nun cavity Coils Uicuumgauga

•"•2) ''(/) 0'« 0''

X

n

X

1

Fig. 2.1. Schematic diagram of the experimental device

i, , i , i , i and i are currents in different electrodes, measured with the _{k e p w a} indicated meters.

There are windows along the tube which make it possible to view the plasma column; they are also a help in adjusting the probes to the right position inside the beam-pla:sma system. For fixing these Pyrex windows, use was made of 1" Edwards vacuum couplings connected sideways to the tube. The advantage of this flexible system of sections is that dif-ferent test sections (for example a microwave cavity) can be prepared beforehand without interrupting the progress of the measurements. The sections have plain flanges on both side sand are clamped together by a clam-ping ring construction. An O-ring fixed in a metal ring for correct positioning serves as a vacuum seal. It is also possible to put insultating rings between the sections in which case the wall current of the tube can be measured. The r.f. signals caused by the beam-plasma system were detected by small antennae in the form of probes and fed into a spectrum analyser or an oscilloscope. The probes used were either single or double Langmuir probes. The small unshielded Langmuir probes (diameter 0.1 mm, length 15 mm) were placed inside the beam. Because of bombardment by the beam-electrons the tungsten wire of the probe may become red- or even white-hot. To prevent damage, the probe-wires were fixed into a small block of boron nitride instead of glass (see fig. 2.2).

Fig. 2.2 shows a schematic drawing of the probeholder with a probe antenna. By means of a knob (f), the probe could be moved into radial di-rection and by nuts (g) it was possible to move the probe slightly in a transverse direction around point A. The components of the probeholder are explained in the caption of fig. 2.2.

Inside the tube, as is shown in fig. 2.1., an axially movable probe is present, which can be used to observe growing waves or standing wave patterns. Instead of a dipole inside the beam, we used a Rogowski coil and placed it around the beam (see fig, 2.1). A Rogowski coil was used because in our case it was difficult to move the dipole probe along the axis keeping exactly the same position inside the beam, which was a r e -quirement for correlating the measurements at different times.

The Rogowski coil had a large diameter (3 cm) and could be moved from 30 to 90 cm. In fig. 2.1. inside the tube the starting point of the

cm-scale is indicated by 'O'. Also the stainless steel collector at which the electron beam ended could be moved over the same distance.

Fig. 2.2. Drawing of the probeholder

(a) probe, timgsten wire diameter = 0.1 mm, lenght = 1-2 cm (b) boron nitrate insulation

(c) coaxial cable (d) stainless steel tube (e) bellows

(f) knob to move the probe up and down accurately (g) nut to move the probe into the cross-section plane (h) O-rings.

Fig. 2.3 shows the mechanical construction for moving the probe-holder and the collector inside the tube. The movable probeprobe-holder slides along 2 copper bars, and can be moved by a metal string via a rotating drum. The output from the probe goes via a coaxial cable to a BNC con-nector. To avoid kinks in this cable it is lead round a weighted pulley as shown in the figure. The position ofthe collector can be adjusted by means of a tooth-wheel and a tooth-rack. Both the probe and the collector are moved by small electric motors. Toavoidabreakdownwheneither the probe or collector reach their end positions the small motors are switched off by a micro switch, after which the motors can only be run in the opposite sense.

When making standing wave measurements the movable probe is used very frequently and experience showed that the risk of damaging one of the radial probes or of bouncing against the collector is rather great. For this reason an outsifle simulator was constructed from which the position of the movable probe could be observed. Clip-on tags could be placed on the simulator which would stop the movement ofthe moving probe when it arrived at the desired position. This simulator was excited by a Bowden cable which was connected at one end to the extension piece of the motor axis as fig. 2.3 shows. A cm-scale on the simulator made it easy to find out the right position of the probe. Synchronization of the x-axis of the x-y recorder with the position of both the movable probe and the collector is effected by means of a potentiometer coupled with the axis of the small electromotors. A p.s.a. is connected to the potentiometer, so that the voltage going to the x-y recorder between the slider and one end of the potentiometer is linearly dependent on the position of the probe.

For scaling purposes a resistor, adjustable in fixed steps, is available.

2.2 T h e e l e c t r o n gun

The electron gun consists of a hairpin tungsten cathode of 0.1 cm diameter and an electrode system. The electrode system is, as far as the dimensions are concerned, as copy of the accelerating system of the electron gun of a Philips travelling wave tube. Fig. 2.1 shows the electrical circuit with the meters used for measuring the various currents. The filament is connected to a 50 Hz power supply. The maximum permissible filament current is 60A, in which case the filament voltage is about 4.5 Volts.

The acceleration voltage could be regulated between 500 to 3000 Volts. At still higher voltages sparking occurs inside the electron gun. The maximum available beam current is about 30 mA, and the beam diameter is approxi-mately 2-3 mm. In fig 2.4. across-sectional view of the electron gun is shown.

Fig. 2.4. The electron gun. (1) end plate

(2), (3) electrodes (4) carbon hood (5) glass tube

(6) Wehnelt cylinder (water cooled) (7) radiation shield

(8) axial adjustment ring

(9) filament holder (water cooled)

To avoid damage due to vibrations of the filament in the magnetic field, caused by the Lorentz force, the filament is magnetically shielded. The Wehnelt cylinder (6), which is made of soft iron serves as a magnetic shield. Due to this screening the B-field at the top of the filament has a maximum

—3 2

value of about 20 Gauss. (2.10 Wb/m ). The Wehnelt cylinder is water-coo-led and has a carbon hood (4) inside (just above the filament) to withstand the high temperatures there. The cathode has more or less a Pierce con-figuration and its filament can be moved axially by means of a ring (8)

to obtain the optimum conditions. To get an electrical field free space between electron gun and collector, an earthed end plate (1) with a central hole (diameter 1 cm) is put at the end of the gun. The gun is placed inside a Pyrex tube to insulate it from the metal tube (see fig. 2.1.).

2.3. T h e v a c u u m s y s t e m .

The tube of the interaction chamber is connected to a pump section consisting of 2 Edwards F 603 oil diffusion pumps, each with a pumping capacity of 600 l / s e c . (see fig. 2.1.) The diffusion pump next to the inter-action chamber is provided with a liquid nitrogen baffle. The other pymp is provided with a water-cooled one. The backing vacuum is delivered by an Edwards 1SC450 rotating vacuum pump. The background pressure

_7

obtained is2,10 Torr, All measurements were performed in helium at p r e s --5 - 3

sures in the range 5,10 to 10 Torr, The required pressure can be adjusted by means of an adjustable leak. During the measurements the pumping was continuous, mostly at low pumping speeds, the diffusion pumps being throttled by means of their butterfly valves. The pressures during the measurements was measured by a Bayard-Alpert ionization gauge. The backing pressure was indicated by an LKB Pirani vacuum meter.

The total vacuum system could not be baked.

2.4 T h e m a g n e t i c f i e l d .

The axial B-field is obtained by the use of 10 magnetic coils. These coils are wound with Povin D wire (lEf = 3 mm, N = 250 windings). Fig. 2.5 indicates how the coils are situated along the interaction chamber, and also shows the dimensions.

The power supply for the coils, which are all in series, is a D.C. shunt generator (llOV, 110 A.). The strength of the B-field can be regulated by varying the shunt current of the generator. Fig. 2.5 also shows the homogeneity of the B-field: this is better than + 1% along the axis and was achieved by putting thin iron strips inside the coil diameter. At the gun side the B-field drops down very cpiickly for the reason explained

—2

above.The strength ofthe magnetic field is 27 Gauss/Amp. (27.10 Wb/m2 Amp) with a maximum value of about 1500 Gauss. Since the coils are not water-26

B-fi*ld (Arbitrary units) 1 S 0 -100 SO-Magnetic coil

1

]\1

Fig. 2.5. The magnetic field

cooled, working at the maximum B-field is only possible for periods of about half an hour. In practice this was not a disadvantage.

References to Chapter n

CHAPTER III DIAGNOSTIC METHODS

In this chapter the measuring techniques used in our experiment will be described. In some cases use could be made of commercially available appa-ratus, like spectrum analysers. In other cases new methods had to be devel-oped as, for instance, for the measurement of the small frequency shift of the microwave cavity and of the small Langmuir probe currents.

3.1 R.f. s p e c t r u m a n a l y s i s .

The r.f. signals caused by beam-plasma interaction have a fluctuating, non-discrete character, as time resolvedmeasurements show. To detect these signals two methods are possible. One is to use a spectrum analyser, the other to use an oscilloscope. Both methods have been used. With the spec-trum analyser, which has a narrow bandwidth, we integrate the signals from the plasma (which are not constant in amplitude and frequency) over a longer time period. The signal at the output of the analyser is D.C. rectified. By using an oscilloscope we measure the time-resolved signals.

Use is made of two different types of spectrum analysers, i.e. a Panor-amic spectrum analyser for the frequencies below 23.5 MHz and a Lavoie spectrum analyser for the high frequency part of the spectrum up to about 2000 MHz. The spectrum analysers, which are in the first instance developed for testing electronic- and radar equipment, can display on their scope screen a frequency spectrum of an adjustable frequency width.

In our measurements we preferred to have the frequency spectra plotted on an x-y recorder. Thishasthe advantage of having the spectra on an enlarged scale, which allows calibration of the spectra. Apart from this the sen-sitivity of the measurements is also higher. The time required for scanning one spectrum is about 1.5 minutes. However, in order to search the instabil-ities more rapidly, the spectrum was often scanned on the scope screen of the analyser.

In order to make the spectrum analyser available for use as a monochrom-ator (term adopted from the optical spectroscopy), we made some mechanical modifications. The frequency dial of the analyser is driven by a small motor instead of manually. To avoid mechanical damage in the connection of the motor and analyser a slip-coupling is provided. At the same time a mechani-cally coupled potentiometer is turned aroimd, which provides a voltage to the x-axis of the x-y reccfrder, which is ssmchronized in this way with the fre-quency scale of the analyser. This is the same procedure as is shown in Fig. 2.3. By means of a calibrated frequency ruler, which has the length of the recorded spectrum, the recorded frequency spectra are easily measured out.

3.1.1. T h e P a n o r a m i c s p e c t r u m - a n a l y s e r .

This analyser is used for our research at the low frequencies and has" two frequency ranges: 0-10.5 MHz and 10.5-23.5 MHz. The operation of the analyser is based on the so-called superheterodyne principle. The electronic scanning i s achieved by sweeping the local oscillator (L.O.) with a sawtooth voltage which is also applied to the horizontal deflection plates of the oscilloscope. The displayed frequency spectrum on the scope screen is adju-stable between 0 and 3 MHz. In Fig. 3.1 an electronically scanned spectrum displayed on the scope screen is exposed. The picture shows a noise mountain starting at a low frequency and an interaction and a harmonic. The symmetry with respect to zero frequency is caused by an apparatus effect.

Amplitude

Freq.

In fig. 4.7 a spectrum recorded on the x-y recorder is shown. The bandwidth of the spectrum-analyser, or, in other words, its resolution is determined by a crystal filter and is adjustable between 200 Hz and 1 kHz. The minimum detectable signal at the input resistance of 50fi is 20 fiV, by a signal to noise ratio S/N = 1. The accuracy ofthe frequency measurements is about 3%.

3.1.2 T h e L a v o i e s p e c t r u m - a n a l y s e r .

For some measurements the Lavoie analyser is used to study the high frequency cyclotron waves on the electron beam which excite the low frequency ion waves. The principle of the Lavoie spectrum-analyser is the same as of the Panoramic spectrum-analyser, with the exception that its frequency ranges from 10 MHz to 40 kMHz, divided into different frequency ranges. Because, with the higher frequency ranges, use is made of the harmonics of the local oscillator (up to the 20th harmonic), in scanning the frequency spectrum many beats of the input signal appear and this makes interpretation difficult. However this analyser is very useful up to 2000 MHz, because only the first harmonics of the local oscillator are used. The sensitivity is dependent on the frequency range and the bandwidth, between 70-85 dbm. (dbm = power in db below 1 mW). For the bandwidth two fixed values B = 10 kHz and 50 kHz can be chosen.

3.2 T h e a n t e n n a e

The signals from the beam-plasma system were picked up by means of antennae of which different types were used, i.e. single- and double dipole an-tennae and Rogowski coils. Fig. 2.2 gives an example of the single dipole anten-na (often called probe). It is also possible to use this antenanten-na as a Langmuir probe for the density measurements. Because the r.f. fields outside the thin beam-plasma system drop down quickly, the probes were put nearly always inside the beam, sometimes just outside the beam. This in contrast to the measurements at the interactions of the electron waves, when the sig-nals are easily detectable inside the whole tube. The wavelength in free space of the measured 'radiation' ofthe instabilities of the beam-plasma system is, for the low frequencies (MHz range), considerably greater than the

dimensions of the tube. So the antennae a r e put in the so-called quasi-stationary E.M.-field of the radiation of the instabilities.

3.2.1 C o n f i g u r a t i o n s of t h e m e a s u r i n g c i r c u i t s .

In Fig. 3.2 t h r e e configurations indicated with a),b) and c) a r e shown and the p a r t s a r e explained in the caption of the figure. With configuration b) we determine the wavelength of the interaction by m e a s u r i n g the phaseshift between the two r.f. signals of a double probe. The p r o b e s were placed at a short distance d (d = 2 - 8 mm) along the beam and a r e connected via two f i l t e r s Tf and F and an amplifier A to a double beam oscilloscope.

a) b) c)

collector

e-gun

F * A to dualbcam scope

Fig. 3.2 Schematic of the c i r c u i t s used for m e a s u r i n g the signals from the p l a s m a . P = probe P h = probe holder Tf = tunable filter F , = low p a s s filter A - amplifier F = band p a s s filter (1-5 MHz) R = matching r e s i s t o r LO = local o s c i l l a t o r M _{m i x e r}

F o r wavelength m e a s u r e m e n t s the use of tunable f i l t e r s with a n a r r o w bandwidth i s a n e c e s s i t y because only then can the condition that both r.f. s i g n a l s have the same frequency be r e a l i s e d . In Fig. 3.3 the scheme of the tunable filter i s shown. It c o n s i s t s of a bandfilter with 5 frequency r a n g e s .

The bandfilter can be tuned on the desired frequency by means of the variable condensers C- and C», which have a common shaft. The bandwidth ofthe filter depends on the frequency range and is between 250-750 kHz. Other data of this bandfilter are given in the caption of Fig. 3.3.

I 3.91(0 1 Fig. 3.3 Bandfilter.

Coils: L = L '; L = L ' etc. are magnetically coupled and have90, 54, 33, 18 and 10 windings respectively. Dia. wire .15 mm.

C = C„, coupled variable condenser, 45-450 pF; S , S ' and S are switches.

OSC = standard oscillator

Frequency ranges: 1. 1-1.5 MHz, 2. 1.5-2.3 MHz, 3. 2.3-3.5 MHz 4.3.5-5.3 MHz 5. 5.3-8 MHz.

The procedure to measure the wavelength of an interaction was as follows. First the interaction peak was plotted for both probes on the x-y recorder. Care was taken that both probes were in the same position inside the beam, so that the plotted signals of the double probe were the same in amplitude and frequency. Then the double probe was connected to the bandfilter s instead of to the Panoramic analyser (See Fig. 3.2 ^)). By means of Sg the bandfilter (See Fig. 3.3) could be switched to a standard oscillator the fre-quency ofwhichwasmadethe sameasthe frefre-quency ofthe maximum amplitude of the peak. Both bandfilters were tuned to resonance and the small phaseshift between both sinusoidal signals on the scope screen caused by the presence of small differences between both circuits was trimmed out by changing the condenser of one of the bandfilters a little.

frequency width of the interaction peak, the equality of both filter circuits is checked. When this is correct, the circuit is ready for the measurement when switch S„ is put into the probe position. Attention was paid to the fact that the coaxial cables to the probes had the same lengths as those to the standard oscillator, thus avoiding an uncontrolled phase shift in the measuring circuit. By triggering the probe on the guriside at the maximum amplitude of the peak we obtained two qua si-stationary sinusoidal time resolved signals on the screen of the oscilloscope. The low noise amplifier A (max.gain = 100) was put into the circuit to obtain a high signal at the input of the scope by which the trigge-ring has a good stability.

In order to measure the phase differences between two signals at the same a)

place, we made use of the circuit of Fig. 3.2 '. The two probes are placed diametrically or at an angle to one another. From the measured phase shifts the azimuthp.l dependence of the electric fields can be determined. The r.f. signals ofthe cyclotron harmonic waves on the beam, which have frequencies above 100 MHz, are not directly detectable with the dual beam oscilloscope Tektronix 551. We measured these signals by transforming down their fre-quencies with the aid of a Hewlett-Packard INIixer 10514A, which is suitable

c) for frequencies up to about 600 MHz. The circuit is shown in Fig. 3.2 '. The r.f. signal of the probe is mixed with the timable local oscillator signal (LO) by means of mixer M. The signal with the transformed frequency is applied to filter F , which has a pass-band of 0-5 MHz. This pass-band of the filter, which is smaller than the 30 MHz bandwidth of the oscilloscope, gives a higher frequency resolution and a better discrimination against spurious signals. These filters were also applied for the low frequency measurements as is shown in Fig. 3.2. '.

The filters have the advantage that the frequency band in which the measure-ments were made is well defined, so that interference can be avoided and the quality of the observations improved. The application of a high-pass filter, with a cut-off frequency of about 1 MHz, appears to be especially useful for the suppression of both the 50 Hz component due to the filament of the elec-tron gun, and signals in the region of the ionic sound waves.

We developed the pass-band filters following the filter theory found in many textbooks '. In Figures 3.4 and 3.5 the circuits of the low-pass and high-pass filters are shown. For electrical screening the filters are

enclosed in a copper box and e v e r y filter section i s put into a s e p a r a t e c o m p a r t m e n t of the box. The coils a r e wound on p e r s p e x c o r e s . The input impedance of each filter i s 50n if it i s loaded with the same r e s i s t a n c e .

1.1 11H 1.8M.H 2.6tiH 4.3nF f> |1.7nH i 7 9 ^ l H =pi.3nF l l . 7 | i H Q38nF 0.13nF / • 23nF l9nF

HI—rHI

Fig. 3.4 L o w - p a s s filter Fig. 3.5High-pass filter

Both f i l t e r s can be interconnected; in that c a s e we get a pass-band between about 1 MHz and 5 MHz a s i s plotted in Fig. 3.6.

"out 1000-5 0 0 -

r

Fig. 3 . 6 . Frequency c h a r a c t e r i s t i c of both f i l t e r s in s e r i e s .

3.2.2 T h e R o g o w s k i c o i l .

Instead of detecting the instabilities by their e l e c t r i c fields, it i s a l s o possible to m e a s u r e their magnetic fields. In some c a s e s this can give the advantage of l e s s disturbance of the system by the ahtenna. We used an axially movable Rogowski (or toroidal) coil in o u r ' r e s e a r c h to detect standing wave p a t t e r n s inside the interaction space (See F i g s . 2.1 and 2.3). To get reliable r e s u l t s when making standing wave m e a s u r e m e n t s it i s n e c e s s a r y to keep the antenna in the same position relative to the p l a s m a system during the movement of the probe. With a dipole antenna t h i s a p p e a r s to be very difficult in our thin b e a m - p l a s m a system. But such a condition was easily r e a l i s e d with a Rogowski coil of a l a r g e d i a m e t e r in c o m p a r i s o n to the p l a s m a .

A r e q u i r e m e n t for the Rogowski coil i s that i t s amplitude frec[uency c h a r a c t e r -i s t -i c , by a constant p r -i m a r y c u r r e n t , -i s almost flat -in the m e a s u r -i n g r a n g e . We designed a Rogowski coil with an a i r core because a magnetic c o r e would disturb the axiai B-field (see Fig. 3.7 '). The frequency dependence of such a coil can be d e t e r m i n e d by a simple calculation. The induced E.M. F. in the Rogowski coil i s :

d(D

u _{n dt} (1) (here also the radiation E.M. field i s neglected)

d» = BS, the magnetic flux in Weber H B = /u H, the magnetic induction n fi = magnetic p e r m e a b i l i t y of free S

space

magnetic field strength number of windings on the coil the. surface of c r o s s - s e c t i o n of the coil Amplitude (Arbitrary units) 20 1 0 0 -c t

1

1 1

^^h

b) Frequency c h a r a c t e r i s t i c of the Rogowski coil. The f i r s t law of Maxwell s t a t e s i = ^ H . d l (i = the axial a.c. c u r r e n t ,

a)

see Fig. 3.7 '), which gives in our c a s e i = 2 TTHR (R = the average r a d i u s of the coil). If we a s s u m e a sinusoidal dependence of time for the c u r r e n t i = r e •''"*, we find for the induced E . M . F . in the coil:

/( r&w i e ' o

2;TR

ja>t

Let u s look now at the equivalent circuit of the Rogowski coil and i t s e x t e r n a l load (see Fig. 3.8). In t h i s figure the self-inductance and r e s i s t a n c e

E.M.R u @

F i g . 3.8 E l e c t r i c a l c i r c u i t o f t h e Rogowski coil. L = 25 ;<iH; R^ = 5 0

Rg = 50D

of the coil i s r e p r e s e n t e d by L and R... The external load of the Rogowski coil i s r e p r e s e n t e d by a capacitance C . and a r e s i s t a n c e R^, The capacitance C . i s due to the coaxial c a b l e , and the input capacity of the connected filter and R„ i s the matched load of the external c i r c u i t , which i s 50ii. We made our design in such a way that /a)C- > > R „ and CÜL » R - » R in our frequency range of 1 to 10 MHz. In that c a s e the output voltage U i s given by:

•^2 - ^ 2 v ^ ^ n S , . ^ !

U - • u=: . —Ü =: constant x i /3\

joiL jwL 47tR ' which i s only dependent on the c u r r e n t i, and independent of the frequency.

Fig. 3.7 ' shows the obtained frequency c h a r a c t e r i s t i c which i s r a t h e r flat between 1 and 10 MHz. At higher frequencies the amplitude r i s e s due to a resonance at 30 MHz caused by the p a r a s i t i c capacitance Cg of the windings of the coil. The coil was c o n s t r u c t e d with one winding layer of 500 t u r n s . Use of a multiple layer coil would give r i s e to p a r a s i t i c r e s o n a n c e s within the frequency range o f t h e m e a s u r e m e n t s .

Another application of the Rogowski coil was to detect fluctuations in the collector c u r r e n t by placing it round the collector lead. T h e s e fluctuations c o r r e s p o n d with the fields of the instabilities inside the interaction space a s fig. 3.9 shows.

Amplitude

Rogowski Coil _Con

Bo Vh PH, k ditions : s UO Gauss = 1.0 kV = 8.4 lO'Sorr ^ i.l mA 1.0 — I — 2.0 —\ _{3.0 f(MHz)}

Fig. 3.9 The frequency spectrum, measured with a Langmuir probe inside the plasma, with a Rogowski coil around the collector wire. The peaks are plotted in a negative sense.

In this figure a spectrum is exposed, which i s measured with a (iipole probe inside the tube and a Rogowski coil around the collector. Both spectra are identical. The amplitude 'dip' at zero frequency is due to an apparatus effect,

2)

3.3 M i c r o w a v e c a v i t y m e a s u r e m e n t s .

A well-known technique developed at M.I.T. .by Brov/n et al, "' for measuring the electron density of a plasma is to place the plasma in a

suitable cavity. The shift of resonance frequency of the cavity is related to the density of the plasma. In our case we put a 1 cm cavity inside the interaction chamber. The beam was directed through the two holes of the cavity (see fig. 3.10 '). The derivation of the relation between the frequency shift and the density is based on a perturbation theory, in which it is assumed

2 2

that oj « <t) (b) = the electron plasma frequency, M = the oscillator

fre-r P

quency) and that influence of the plasma on the cavity is rather weak. These conditions can be realised by choosing a convenient frequency for «< and by making the dimensions of the cavity such that the volume of the plasma inside

iris a s * Wavcgulds J ' l

HiiiiiBiiiiliiM'*"'

4:1'

Fig. 3.10 ' T h e 1 cm microwave Fig. 3.10 ' Sketch of the density cavity for the density m e a - profile. s u r e m e n t s .

The p e r t u r b a t i o n theory s t a t e s for the frequency shift Aco o f t h e cavity, due to the p r e s e n c e of plasma:

2u)t ƒ

o CAV

aE^ d V / J E'' dV

o o (4) with the following

e x p r e s s i o n for the complex conductivity:

2 ne 2m ( 1+r - j ( l - r ) 0 j ( l - r ) (1+r) 0 0 0 2p I r ' i>Q+U<^t _"'c> P = V + c ]<^ (5)

E i s the microwave field in the absence of the p l a s m a and V p r e s e n t s the o

volume of the cavity. The motion of the ions i s negligible and the number of collisions p e r s e c . between the e l e c t r o n s and n e u t r a l s i s given by the collision frequency v . The r e a l p a r t offer instance (4) gives the fretjuency change c a u sed by the p l a s m a inside the cavity (see ref. 2). In t h e p r e s e n c e of a m a g -netic field the behaviour of the p l a s m a i s anisotropic, e x p r e s s e d in the conductivity t e n s o r (see eq. 5), which i s a function of the B-field. In g e n e r a l t h i s complicates u s e of the cavity a s a m e a s u r i n g i n s t r u m e n t , but t h i s can be avoided by choosing a cavity mode in which the e l e c t r i c field inside i s p a r a l l e l

to the axial B-field. Then the e l e c t r o n motion due to the e l e c t r i c field i s not influenced by the magnetic field, i . e . of the conductivity t e n s o r a, only the component in the axial direction m u s t be u s e d , thus simplifying the calculation considerably. Calculations give an e x p r e s s i o n of the form:

Af = en (6) (in this calculation v « « ^

e c

i s neglected).

The constant c depends on the profile (see fig. 3.10 ' of the p l a s m a . The following v a l u e s for c w e r e calculated for different a s s u m e d profiles

3)

of the p l a s m a , n i s the density on the a x i s . a)

n = n for o < r < r , r, = r a d i u s of the holes in o h h

. ^ ^Ti the cavity

n = o for r, < r < R •' h

9

c = 2.90 X 10 R = the r a d i u s of the cavity = 8.75 m m . b) 5 521-n = 521-n J ( ' „ ) for o < r < r * w h e r e r * (3.8 mm) i s the J, ^ value of r at which n = o for r * < r < R 5 521. Q J ( ' „ ) h a s i t s first z e r o . c = 2.33 X 10^ O K 5 52r

" = «^o Jo ( ^ ) ^'^[^'''^] *°" "h<^<^*

The differences in the calculated v a l u e s for c do not exceed 30%. We

can expect that p l a s m a l o s s e s inside the cavity due to diffusion will lower the p l a s m a density. As the p l a s m a density in the interaction c h a m b e r

between cavity and collector m u s t be m e a s u r e d we chose the highest value 9

for c = 2.9.10 for our m e a s u r e m e n t s .

It i s possible to d e t e r m i n e Af by photographing on one p i c t u r e the r e s o n a n c e c u r v e of the cavity with both ' p l a s m a off and ' p l a s m a on'. T h i s method was used in the f i r s t instance but had the disadvantage that it was r a t h e r difficult to r e a d the frequency shift from the p i c t u r e . The r e a s o n for

this is that in our experimental range the plasma density, between 10 - 5.10 electrons/cm ,gives rather small frequency shifts At, which were not always easy to determine. Also the noise on the resonancecurve, when the plasma was on, gave some trouble from time to time.

In ordertomeasurethese small frequency shifts more easily we developed another method ' , which will be described here. This method gave more accurate and quicker results.

1cm cavity collector

1 I

Q

II detector

J

<£>

Fig. 3.11 The microwave circuit for the density measurements of the plasma, In Fig. 3.11 the microwave circuit for the density measurement is shown. An 8 mm klystron (EMI 9646), tuned to the resonance frequency ofthe 1cm cavity (TM 020 mode) is swept in its mode around the resonance frequency by means of a sawtooth voltage applied to the repeller of the klystron. The reflected signal from the cavity, measured with a microwave detector, contains the resonance curve of the cavity superimposed on the signal of the klystron mode. The signal from the microwave detector is connected to oscilloscope I and II. On oscilloscope II the whole klystron mode and 40

the resonance curve of the cavity are displayed for checking and calibration purposes as will be explained further on. However, on oscilloscope I only the top of the resonance curve is made visible, because we are interested merely in the shift ofthe resonance curve. This shift is easiest observed when we look at a part of the top of the resonance curve, which can be made arbitrarilysharpbyincreasingthesensitivity of the oscilloscope (see Fig. 3.13). The method for measuring small shifts of the resonance frequency of the cavity will now be explained with the help of Fig. 3.12. In the circuit of Fig. 3.11 the sawtooth voltage for the klystron is delivered by the sawtooth gene-rator of oscilloscope n , through its terminal 'sawtooth out' (see Fig. 3.12 '), This sawtooth generator is triggered in the triggering mode 'line', consequent-ly once in every period of the mains the sawtooth voltage appears. Because the sawtooth voltage is supplied by a separate generator, the resonance curve i s again shown on beam A of oscilloscope I during flyback of the sawtooth of scope II (Fig. 3.12 '). Beam A of oscilloscope I has a slower time base (see Fig. 3.12*'^).

However, the resonance curveisnow compressed toa spike due to the very short flyback time ofthe sawtooth generator. As the plasma is switched on, the resonance curve shifts,butthe position ofthe spike remains the same, because the displacement of the spike is negligibly small and is not visible.

A Tektronix 555 dual beam oscilloscope, which has two independent time bases, gives the possibility of using the spike as a marker. The Tektronix 555 oscilloscope has, amongst other features, the possibility to trigger beam B on the trigger input of beam A, after a variable time delay, adjustable by a ten-turn potentiometer (Helipot). Therefore, by triggering beam B at time t

c)

(see Fig. 3.12 ') only the spike can be made visible on beam B by choosing e)

a convenient time base for this beam (Fig. 3.12 ' ) . By varying the point of time t by means ofthe Helipot, the spike on beam B can be shifted manually over the oscilloscope screen. By putting the marker on top of the resonance curve (see Fig. 3.13) in the case of'plasma off and by replacing it in the case of 'plasma on' the value of the frequency shift can be read accurately on the dial of the Helipot. In order to make only the resonance curve visible on beam A of oscilloscope I, we adjusted the time base in the position of '5x magnified' (see Figs. 3.12 ' and 3.13). The time bases of oscilloscope I can be chosen so as to make, for instance, one division on the screen of I correspond to 100 divisions on the scale of the Helipot.

fly.

back time (msec)

0 1 |1 '"^^ 20 sawtooth voltage of scope I I

(a) ,

I

time (msec)

0 I I 2

sawtooth voltage for beam A of scope I (b) I time '1 (c ) beam A of scope I \ \ / / time resonance \ / ; . curve \ V y

(d) beam A of scope I (Sxmagnified)

spike time

(e) beam B of scope I. delayed triggered at lime t^

Fig. 3.12 The signals on the screen of oscilloscope I.

resonance curve of the cavity without plasma; - . - . - . - . - . - . - . - . - . - resonance curve of the cavity with plasma. The frequency calibration was carried out by means of the calibrated microwave cavity F. The relation between the freipency of the klystron and the repeller voltage is Unear if the middle part of the klystron mode is used. So the resonance curve of the 1 cm cavity was adjusted in this part of the klystron mode.

To assure that due to drifting of the klystron the resonance curve does not come into the non-linear part of the mode, the klystron mode and the resonance curve are displayed on oscilloscope II. In this way any drift in the klystron frequency is immediately visible and can be easily corrected. In addition this picture is used for frequency calibration of the screen of V by shifting the dip of cavity F over a known frecpiency interval over the screen. The frequency calibration of oscilloscope I is then simply done by

multipli-cation with the ratio of time base speeds of I and II. The minimum detectable frequency shift with the 1 cm cavity was 0.15 MHz, which corresponds in

7 3 tlüs case with a plasma density of about 5.10 elec/cm .

upper beam; ImV/div. lower beam: 5mV/div. 1 division = 1.3 MHz

Fig. 3.13 Resonance curves in the situation plasma 'on' and plasma 'of with the markers.

In order to avoid unstable triggering, which can be caused by noise coming from the plasma, oscilloscope H was triggered on'line' and I on the 'gate out' of n , which delivers a high output voltage of about 30 V. Thus, an absolutely stable resonance curve on the oscilloscope in both the situations 'plasma on' and 'plasma off was obtained as is shown in Fig. 3.13.

3.4 E l e c t r o n t e m p e r a t u r e m e a s u r e m e n t s ,

The electron temperature of the plasma has been determined by means of a Langmuir probe, which is a small cylindrical wire with a diameter of 0.1 mm. The theory of such probes, to obtain from the probe characteristic (probe current i versus probe voltage Vp), the plasma temperature and

P 5^ density was developed in 1923 by Langmuir '. The made assumptions in this theory are that the dimensions of the probe and of the space-charge sheath

and electrons. In the presence of a magnetic field the mean free path of charged particles, especially that of electrons decreases, so reliable inter-pretation of a probe characteristic becomes rather difficult '. Especially the electron current,part of the probe characteristic can be strongly changed depending on the strength of the magnetic field. Fortunately, if the magnetic field does not exceed a few kilo gauss, the part of the probe characteristic in which the ion current predominates, is not deformed. This is illustrated in Fig. 3.14, which gives an exemple of a Langmuir probe characteristic with and without a magnetic field. The strength of the magnetic field was in this

2

case 500 Gauss (0,05 Wb/m ). The picture shows the strong reduction in the electron current due to the magnetic field. The electron temperature can then be calculated by the so-called retarding field method. We used this method for our calculation of electron temperatures, taking the part of the probe characteristic around the floating potential of the plasma. We calculate T from the following formula:

-eV

ig = const.exp. ^ ^ ' (7) e

in which i is the electron current and V the probe potential. It i s possible to find i by point-by-point subtraction of the ion current 1. from the probe current By plotting In i against the probe potential V , we get a straight line,

e p The cotangent of the slope is proportional to the electron temperature which can be calculated because the proportionality constant is known. Since the plasma density in our case is low and the probe used is small ( 0 = 0,1 mm) in order to minimize the disturbing effects on the plasma, the ion saturation current is very small (a few microamps.) Because the plasma parameters are not completely constant in time, we need a method which scans the small currents of the probe characteristic in a short time. However, in this case a few difficulties arise.

When the probe characteristic is scanned rapidly, currents of the same order of magnitude as the probe current may flow, due to the capacitance between probe and plasma (sheath effect) and to the capacitance of the probe cable. It is not possible to take into account the effect of the probe capa-citance, because the capacitance is unknown and changes with the probe potential. The probe current is derived from the voltage across a resistor

*, lOOTT^ ' 55v

n

V'

r^

r"

il

1

Fig. 3.14 Oscillogram of the whole probe characteristic for a cylindrical probe. Upper curve: without magnetic field; lower curve: with magnetic field. At points E and E' the probe starts arcing. of known value. As the probe current to be measured is small, one needs a large resistance to obtain a measurable signal. The voltage drop across the measuring resistor can be measured by connecting it to the differential input of an oscilloscope. As the probe voltage changes by ten or more volts and the voltage drop across the resistor is small, one needs a differential input with a high common mode rejection over the frequency band concerned.

Another important point is that the differential amplifier must be connected to the measuring resistor so that the high discrimination factor is not disturbed by unbalance effects at the inputs. To meet these demands, we found a solution by using a battery powered transistor amplifier with small input and output impedances. (See also Ref. 7). It was then possible to scan the probe characteristic in a time of 1 msec without any trouble. For shorter periods of time the influence of the parasitic capacitance between probe and plasma appeared significant.

3.4.1 D e s c r i p t i o n of t h e a p p a r a t u s .

The measuring circuit will be explained with the help of block diagram figure 3.15. The probe characteristic is scanned by the external sawtooth tension of the oscilloscope, while this characteristic is displayed on the same oscilloscope.

The inner conductor of the coaxial cable is connected to the probe. The outer conductor, which screens the probe lead against disturbances, makes no contact with the plasma. Around the probe there is a positive or

Plasma '.(Shuth Prob» cable Cl Ri ' ^ Transistor amptif. ^ -o D'rff. -o amplif.

Fig. 3.15. Block diagram.

0:

₁

Sawtooth output

negative space-charge sheath, depending on the potential difference between the probe and the plasma. Capacitor C separates the potential of the plasma from the input of the amplifier. When the sawtooth i s free running, capacitor C charges itself to the floating potential of the plasma and the probe characteristic is scanned around the floating potential. The measuring r e s i s -tor R.. connects the output of the transis-tor amplifier to the input. With this feedback we obtain a stable and low value of the input impedance, Rj/(A + 1) + R„, as can be easily derived. A is the voltage amplification factor of the amplifier. When A is very high, this input impedance is very low, so the influence of the parallel capacitance of the probe cable plays a negligible role. Also, in this case the voltage between points c and b becomes very low. Sometimes one simply indicates this by sajdng that point c is virtually grounded . The current in the measuring resistor R.. is then the same as the probe current, because the current going into the input of the amplifier is completely negligible. At the same time this feedback decreases the output impedance of the amplifier to a low value, by which unbalance effects at the inputs of the differential amplifier are avoided. In Figure 3.16 the electronic circuit ofthe amplifier is shown.

The probe is connected to point a. The capacitor C- corresponds to the one in Figure 3.15. To avoid damage of transistor T because of transient voltages, a small current-limiting resistor Rg and a diode D prevent the base from becoming negative. To explain the amplifier, we first think of transistor To as a resistor R. The combination of transistor T- and T„ then gives a high voltage amplification of about 5000. The reason for this high factor is the existence of capacitor C„. We can describe this in the follow-ing terms. Transistor Tg acts as an emitter follower. By means of capacitor