A. Komori et al- Helicon waves and efficient plasma production

8/3/2019 A. Komori et al- Helicon waves and efficient plasma production

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Helicon waves and efficient plasma productionA. Komori, T. Shoji,a) K. Miyamoto, J. Kawai, and Y. KawaiInterdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga,Fukuoka 816, Japan(Received 13 August 1990; acccepted 31 December 1990)Helicon waves generated by radio-frequency (rf) waves are experimentally demonstrated tohave the characteristics of Landau damping, as predicted theoretically, and fully ionizedplasmas are realized by this efficient coupling of rf powers to plasmas. Excited waves areidentified as a helicon wave by measuring wavelengths in the plasma along the magnetic fieldand comparing with the dispersion relation. Good agreement is found between experimentaland theoretical results.

I. INTRODUCTION II. THEORETICAL BACKGROUNDThe plasma production by radio-frequency (rf) wavesusing either inductive or capacitive coupling methods hasbeen well known to realize appreciable high density and tem-perature plasmas easily. Rather than simply relying on thelarge oscillatory electric fields of the antenna to accelerate

electrons to ionizing energies, resonant excitation methodshave been found to be more effective. Recent experimentsby Boswell et aLZ4 have shown that fully ionized pl asmaswhose density is higher than 1X 10 cme3 can be producedwith a special antenna to excite a helicon wave in a chamberof 10 cm in diameter and 120 cm in length with an rf power of180 W at 8.8 MHz and a confining magnetic field of 0.75 kG.It has been shown that wave properties are consistent withthose expected of helicon waves. Shoji has obtained almostthe same results with a different antenna from that used byBoswell et aLz4 In a theoretical analysis, Chen6* has sug-gested that the rate of energy absorption by wave dampingmay be due to Landau damping of the helicon wave that hasan electric field component parallel to the magnetic field.This can interact directly with electrons, and hence, pro-vides an efficient means for transferring energy to electronsthat subsequently suffer inelastic collisions in the column.Landau damping has been observed and is the main subjectof the present paper.

Helicon waves are known to be right-handed circularlypolarized electromagnetic waves, propagating along themagnetic field.s-lo The frequency w is in the range oftiCi Qw,


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We note that, up to here, K, k, andp are all real.Since the B, and j, lines of the helicon wave are more orless helical, an antenna of the helical shape, that is, a helicalantenna is considered to be able to excite the heli con wave bythe rfat the frequency oftiCi 40,


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cycle. The p lasma density n, is measured at t = 1.5 msecafter the oscillator is turned on at t = 0 msec with a boxcarintegrator with a gate width ofO.1 msec, while T, is obtainedin the afterglow plasma because T, of 4 - 6 eV at t = 1.5msec is considered to be affected by the rf wave.Radial profiles of plasma parameters are measured atz = 25 cm, and axial profiles are obtained in the range of 25cm


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.O

,

1 2B,(kG)

FIG. 6. Density n, as a function of B,, for PCr= 0.7 and 1.4 kW.

to b e adjusted at P,s below -0.4 kW, so that we cannotproduce the plasma in this Pti range.The &, d ependenceof n, is shown in Fig. 6 for Prf = 0.7and 1.4 kW. The electron density n, is roughly proportionalto B. in the region of B. 5 1 kG, although the slope of thecurve depends a little on P&. This ag rees qualitatively withthe relation between n, and B,, predicted in the dispersionrelation of the helicon wave. For quantitative agreement, themeasurement of the wavelength is, of course, required, asknown from Eq. (4). In the range of B,, 2 1 kG, n,, is con-stant independently of B. since the fully ionized pl asma isaccomplished. The radial n, profile is studied by changingB, at P,, = 1.4 kW, and the result is shown in Fig. 7. WhenB, is smaller than - 0.45 kG, the n, profile ar ound r = 0 cmhas a concave shape and the distance betwen two ridges isalmost equal to the inner diameter of the Pyrex tube. Byincreasing B,, the n, profile is varied drastically and be-comes peake d at r = 0 cm, as shown in Fig. 7. This dep en-den ce of the radial n, profile on B, may be explained by

FIG. 7. Dependenc e of radial n, profile on B,, at P,p = 1.4 kW.896 Phys. Fluids B, Vol. 3, No. 4, April 1991

, I I I ,

c\v).t5i022.cTi:

Wkxl;d$b 2.1x103

~~ 2.5x1 oi3t I , I I I 1

3

20 40 60 80 100z (cm)

FIG. 8. Tracing s of spatial variations of damped waves; Bdn,s are4.2 x lo- * kG cm, 3.5 X IO- kG cm, and 3.2~ lo- I4 kG cm3 from thetop.

taking account of the confinement of the plasma.h Basically,the heating and ionization will be localized near the walls,and so is the energy deposition. This causes he c oncave n,profile with the ridges at the inner-wall position of the Pyrextube. By increasing B,,, the energy confinement, which isdetermined by the end plate sheaths and the intensity of B,,may be better on the axis, leading to the appear ance of adense core.l3. Dispersion relation and damping of the helicon wa veThe phase and amplitude of the helicon wave as a func-tion of axial position z are obtained by interferometry withthe magnetic probe. Tracings of the spatial variations of thedampe d waves are shown in Fig. 8 at B. = 0.4 - 0.8 kG andPrf = 1.3 - 1.6 kW. An importan t point in the figure is thatthe wavelength is about half of the antenna length, and isvaried dependi ng on ne, strictly speaking, on BJn, as ex-pected from Eq. (4). This suggests hat the wavelength is notdetermined by the antenn a length, and is varied automatical-ly to provide the best coupli ng o r to satisfy the dispersi onrelation. We cannot obtain the dispersion relation directlysince the frequency of the oscillator is fixed, but the relationbetween n, and kB, can be obtained, and compared with thetheoretical prediction. Figure 9 shows the dependen ceof Iz,on kB, under various conditions of B,, P,,, andp. The experi-mental results represented by ope n circles are obtained in thelow-B, region, where n, does not saturate with the variationof B, and the relatively flat n, profile is obse rved inside thePyrex tube. The solid line represents n, given by Eq. (3);a = 2,5 cm and w/2n = 7 MHzare used. It is evident that n,is proportional to kB,, and there is relatively good agreementbetween the experimental and theoretical results, indicatingthat the observed wave obeys the dispersion relation of thehelicon wave.

Komori et at. 89 6

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-:Emu-bc

0 1 2 3kBe ( ldcm-kG)

FIG. 9. Dependen ce of n, on kB, under various conditi ons of B(,, P,,.,andp.

The most important point which is noticed in studyingthe relation between ne and k, is that 5 approaches @ byincreasing n, and keeping B, constant, and that n, has amaximum at S-G where the Landau damping rate maxi-mizes. In fact, the lowest tracing in Fig. 8 yields{=1.49-$atT,=3eVandw/2~=7MHz.Thissug-gests that the damping of the helicon wave can be explainedby Landau damping in our experiments. The variation of B,,makes it possible to change n, with keeping c at -8.The value of Im(k)/Re(k) can be also obtained fromthe tracing of the spatial variation of the damped wave. Fig-ure 10 shows the dependence of Im(k)/Re(k) on n,, ob-tained by changing Bo. The wave number k is kept constantto satisfy [ = fi, as mentioned above. The experimental re-sults are plotted by open circles. There is a tendency forIm(k)/Re( k) to decrease with an increase in n,. This ischaracteristic of Landau damping, and cannot be explainedby the collisional damping since Im(k)/Re(k) due to theresistivity depends little on n,, as known from Eq. (7). How-ever, for example, at n, = 2.5X 1013 cme3, the Landaudamping rate is about one third of the collisional dampingrate, and is about one-fourth of the measured damping rate.Landau damping is larger than the collisional damping inthe range of n, 5 7.2X lo* cmA3. Taking account of theseresults, both Landau damping and collisional damping areconsidered to occur at the same time in our n, range. Thesolid line shown in Fig. 10 represents the damping rate pre-dicted theoretically, which consists of the Landau dampingrate plus the collisional damping rate. Good agreement isfound between the experimental and theoretical results.V. CONCLUSIONS

Experiments reported here demonstrate the excitationof a helicon wave in a cylindrical magnetoplasma and theproduction of a fully ionized plasma. An axial wavelength

,- 3-0AY2 2-\Y? ,-

000 1 2 3ne ( 103cm-3 )

FIG. 10. Dependen ce of Im(k)/Re(k) on n,, obtained by changing B,, atP,, = 1.5 kW.

measured in the vacuum chamber indicates that the axialwavelength is not determined by the antenna length, but isautomatically varied depending on the density and the mag-netic field to satisfy the dispersion relation of the heliconwave. As the magnetic field is increased, the density in-creases according to the dispersion relation of the heliconwave, and the central core of the plasma becomes fully ion-ized at an appreciabl e t-f power with the optical emissionsbeing typical of Ar II. It is also shown that the density has amaximum at c( = w/kv,,, ) -&! where the Landau dampingrate maximizes, and that there is a tendency for Im(k)/Re( k) to decrease with an increase in the density. These arecharacteristic of Landau damping. However, both Landaudamping and collisional damping are considered to occur atthe same time in our densi ty range, since the collisionaldamping rate is larger than the Landau damping rate at den-sities above 7.2X IO* cmB3. There is good agreementbetween the experimental and theoretical damping rateswhen the theoretical damping rate consists of both the Lan-dau damping rate and the collisional damping rate. Landaudamping rather than the collisional damping is considered toplay an important role on the plasma production, becausethe resonant mechanism can accelerate electrons to ionizingenergies more efficiently.

ACKNOWLEDGMENTSThe authors wish to thank M. Tanaka for many illumi-nating discussions, and M. Fuji wara, N. Sato, and H. Ike-gami for their continuing encouragement.This work was supported by a Grant-in-Aid for Scientif-ic Research from the Ministry of Education, Science and

Culture of Japan.897 Phys. Fluids B, Vol. 3, No. 4, April 1991 Komori eta/. 897

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G. Lisitano, R. A. Ellis, Jr., W. M. Hooke, and T. H. Stix, Rev. Sci. In- pages. Airmail additional. Make checks payable to the American Institutestrum. 39,295 (1968). of Physics.R. W. Boswell, R. K. Porteous, A. Prytz, A. Bouchoule, and P. Ranson,Phys. Lett. A 91, 163 (1982).3R. W. Boswell, Plasma Phys. Controlled Fusion 26, 1147 ( 1984).4Z. Peiyuan and R. W. Boswell, Phys. Rev. Lett. 63.2805 (1989).sSeeAIP document No. PAPS-PFBPE-03-893-7 for 7 pages of WhistlerWave Plasma Production, by Tatsuo Shoji, Annual Review, Institute ofPlasma Physics, Nagoya University, Japan ( 1986), p. 67. Order by PAPSnumber and ournal reference from American Institute of Physics, PhysicsAuxiliary Publication Service, 335 East 45th Street, New York, NY10017. The price is $1.50 for each microfiche (98 pages) or $5.00 for pho-tocopies of up to 30 pages, and SO.15 or each additional page over 30

F. F. Chen, in Proceedings ofthe Second International Conference on PIas-ma Physics, Kiev 1987, edited by A. G. Sitenko (Naukova Dumka, Kiev,1987), Vol. 4, p, 321.F. F. Chen andC. D. Decker, Bull. Am. Phys. Sot. 34,212s (1989); F. EChen, Laser Part. Beams 7,551 ( 1989).%I. A. Lehane and P. C. Thonemann, Proc. Phys. Sot. London 85, 301(1965).9G. N. Harding and P. C. Thonemann, Proc. Phys. Sot. London 85, 319(1965).J P. Klozenberg, B. McNamara, and P. C. Thonemann, J. Fluid Mech.2;, 545 (1965).

898 Phys. Fluids B, Vol. 3, No. 4, April 1991 Komori eta/. 898

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A. Komori et al- Helicon waves and efficient plasma production