Observation of WaveLike Structures in Magnetized DC Dischargein Cylindrical Symmetry in Argon

Contrib. Plasma Phys. 46, No. 5-6, 361 – 366 (2006) / DOI 10.1002/ctpp.200610015

Observation of Wave-Like Structures in Magnetized DC Dis-charge in Cylindrical Symmetry in Argon

O. Bilyk, M. Holık, P. Kudrna, A. Marek, and M. Tichy ∗

Charles University in Prague, Faculty of Mathematics and Physics V Holesovickach 2, 182 00 Prague, CzechRepublic

Received 23 May 2005, accepted 10 February 2006Published online 9 June 2006

Key words Magnetron, fluctuations, Langmuir probe.

PACS 84.40.Fe, 52.25.Gj, 52.70.Ds

Wave-like structures in the dc discharge in cylindrical magnetron in conventional arrangement were investi-gated. Two Langmuir probes measured simultaneously fluctuations of floating potential. Power spectra wereevaluated according to the method developed in [1] to obtain frequency – wave number histogram. The mea-surements were carried out at the different external discharge parameters – pressure, discharge current andmagnetic field. Comparison with different theoretical description of fluctuations was performed to find outorigin of the instabilities in the cylindrical magnetron dc discharge.

c© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

Cylindrical magnetrons are nowadays widely used as technological systems e.g. for creating thin films of super-conductive or special magnetic properties. In the cylindrical magnetron the symmetry and homogeneity of themagnetic field simplifies both the theoretical and experimental investigations. In recent years strong efforts havebeen dedicated by several research groups to model the dc discharge plasma in cylindrical magnetron.

In former paper [2] there were performed Monte-Carlo simulations of radial charged particle transport in theE × B field in cylindrical magnetron. The model did not include the effect of stochastic oscillations. The modelshowed that at lower pressures the electrons from the cathode cannot reach the anode, while in experiment atsimilar conditions the discharge burnt (and stochastic oscillations were present).

From comparison of the results from 1D-PIC modelling with measured data from magnetron it followed thatthe model differed from the experimental data in determination of cathode fall at magnetic fields higher thanapproximately 20 mT (see [3]). Model predicted the cathode fall lower and nearer to the cathode than it wasfound in reality.

In our previous experimental studies we already reported the presence of fluctuations of the plasma potentialin cylindrical magnetron system [4, 5]. Fluctuations manifested themselves as an unwanted noise added to theLangmuir probe floating potential when measuring with the floating probe and in the increased noise of themeasured current when measuring the V-A probe characteristics.

It seemed very probable that in dc discharge plasma in cylindrical magnetron the stochastic fluctuations helpedthe transport of charged particles across the magnetic field. In this manner the research performed on a simple,small and cheap experimental magnetron system may be relevant for tokamak edge plasma research and in generalfor research on all fusion devices with magnetic confinement.

The aim was to study the properties of the fluctuations, to find conditions at which the fluctuations occurredin the magnetron system and to attempt to classificate them.

∗ Corresponding author: e-mail: [email protected], Phone: +00 420 221 912 305, Fax: +420 284 685 095

c© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

362 O. Bilyk, M. Holık, P. Kudrna, A. Marek, and M. Tichy: Observation of wave-like structures in . . .

2 Experimental setup

Experiments were carried out on the dc discharge cylindrical magnetron system depicted in Fig. 1. The mag-netron consists of cylindrical electrode mounted co-axially in the cylindrical vacuum vessel. In the conventionalarrangement this electrode serves as cathode. The grounded surrounding vacuum vessel serves as anode. In theinverted configuration the polarity is swapped, i.e. the electrode at the system axis is positive with reference to thecylindrical vacuum vessel, which remains grounded. The inverted configuration was used to gain the possibilityto reach higher power dissipated in the discharge because of much bigger cathode surface area.

A V

magnetic coils

glasswindow

anode

cathode

water coolingpower supply formagnetic coils

DC dischargepower supply(current mode)

Pirani and Penningvacuummeter

turbomolecular andmechanical pump

MKS flowcontroller

MKS Baratronpressure meter

measurement

radially movableLangmuir probe

cylindricalvacuumvessel

B

Oscilloscope

TEKTRONIX

working gasreservoir (Ar, Kr, Ne)

TDS 5032B

axially movableLangmuir probe

Oscilloscope

Agilent

54622A

Computer

cathode

anode

orientationof probes

Fig. 1 Experimental setup with cylindrical magnetron.

The diameters of the inner and outer electrodes (vacuum vessel) are 10 mm and 60 mm, respectively. Thelength of the discharge vessel is 120 mm. The discharge volume is axially constrained by means of two disc-shaped limiters, which are biased at the inner electrode potential. Magnetron system was constructed in high-vacuum technology. The pumping unit consists of the combination of the turbomolecular pump Leybold Turbovac150 and oil-free piston pump Leybold Eco-Dry M15. The ultimate pressure is in the order of 10−3 Pa. Thehomogeneous magnetic field is created by means of a couple of magnetic coils placed symmetrically in themiddle of the discharge vessel. The magnetic field is always parallel with the common axis of the system. Thehomogeneity of the magnetic field on the discharge axis was found to be constant within the precision of 1%.The current through the magnetic coils is also electronically stabilized so that it is insensitive to the change of the

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Contrib. Plasma Phys. 46, No. 5-6 (2006) 363

coil resistance due to warming up of the coils. To prevent overheating of both the coils and of the inner electrode,they are water-cooled. The discharge current is stabilized by a power supply Advanced Energy MDX 500 that isoperated in a constant-current mode. The magnetic field strength varied in experiments from 10 to 40 mT. Duringthe operation of the magnetron discharge the working gas (argon, krypton, neon) slowly flows through the systemwith the typical flow rate below 0.5 sccm. The flow is adjusted by the MKS flow controller.

The system was equipped with radially and axially movable Langmuir probes, whose positions were controlledby a micrometric screw. Holders of the probes are made of Degusit pipes and have special construction to avoidsputtering of the cathode material.

To investigate fluctuations of the floating potential within the discharge no bias voltage has been applied to theused Langmuir probes. The floating potential signal of both probes was sampled simultaneously using the digitaloscilloscope Agilent 54622A which had capacitance of oscilloscope probes 14 pF and the oscilloscope TektronixTDS 5032B, with probes capacitance 11.1 pF. Impedance of both probes was 10 MΩ.

From the oscilloscope Agilent 54622A samples were transferred to the computer via the GPIB interface, whileTektronix TDS 5032B is able to transfer samples directly to its hard drive over PCI bus.

3 Results and discussion

In Fig. 2 there are depicted frequency - wave number histograms for different positions between the anode and thecathode (rA is anode radius, thus r/rA is normalized radial coordinate; r/rA = 0.32 corresponds to the positionat the cathode and r/rA = 1 corresponds to the anode position). At the cathode the waves originate. They aresupposed to circulate around the cathode with constant frequency. Oscillations propagate in anode direction. Thispropagation proceeds with increasing phase shift.

Fig. 2 Frequency – wave number histograms at different positions between the anode and the cathode at 50 mA, 18 mT and7 Pa.

The histograms in Fig. 2 were evaluated according to the method described in [1]. Two simultaneouslymeasured floating potential signals from the probes were processed using fast Fourier transform method. Toreduce noise of the power spectra tens of measurements were averaged. The resulting frequency and phase shiftgives an information about correlation between the signals from both probes. In the histograms in Fig. 2 the grey



scale corresponds to the correlation between the probe signals – the darker is the area, the more correlated are thesignals at given frequency and wave number. The wave number was expressed at each frequency from the phaseshift between the probe signals and the known distance ∆x between the probes:

k(i) =argH

(i)2 (f) − arg H

(i)1 (f)

∆x. (1)

Using the wave number and the average spectral power density at the two probes [S(i)1 (f) + S

(i)2 (f)] the

histogram S(f, k) is built by the ensemble averaging the same way as in [1]. The range of (i) (number ofmeasurements the average spectrum was taken from) was typically 40.

The histograms in Fig. 2 have local maxima at certain frequencies. These peaks have also been observed inthe single frequency spectra and the frequency of the main peak (”first mode”) was studied in dependence onmagnetic field and pressure. The results are shown in Figs. 3 and 4.

Fig. 3 Dependence of the peak frequency on themagnetic field at different pressures.

Fig. 4 Dependence of the peak frequency on the pa-rameter B/p.

To answer the question, what type are the propagating waves, the peak frequencies were compared with the iongyro-frequency Ωi of Ar+ and Ar+2 . In this comparison only incidentally some peak frequencies corresponded tothe Ωi. Also, results were compared with other works ( [1, 6]).

The linear theory of E × B instability from the work of Weng et al. [6] was used at first. The frequencies ofE × B instability were calculated by analytical approximation (fitting) of the experimental dependence of theelectron density on the radial position at typical B = 20mT, p = 4Pa and I = 50mA in the magnetron.


Contrib. Plasma Phys. 46, No. 5-6 (2006) 365

The real part ωr of the frequency corresponding to axial mode number kz = 0 to 3 and azimuthal modenumber m = 0 to 3 is plotted in Fig. 5b. The imaginary frequency component ωi, which shows the growth rateof fluctuations is depicted in Fig. 5a. In the unstable case ωi must be positive otherwise the oscillations would bedamped.

a) b)

Fig. 5 a) the imaginary component ωi and b) the frequency of the real component ωr calculated from dispersion relationdeveloped by [6].

From figures it is seen that for m ≥ 1 the growth rate is positive while for m = 0 only the mode kz = 0 canbe present. The corresponding frequencies are in the order of several kHz. Although this E × B instability givestheoretically the characteristic frequencies in the same order as the measurements, it is not possible to fit the datato this theory. One of the discrepancies consists in the fact, that the experimental results can not be approximatedby

n1 = n1(r) exp(−iωt + imθ + ikz) and ϕ1 = ϕ1(r) exp(−iωt + imθ + ikz),because the dependence of k on radial position observed in our experiments is close to inverse proportionality

(see Fig. 5). In the calculation the values 0.24 and 116 were used for the cyclotron to collision frequency ratioΩi,e/νi,e for Ar+ ions and electrons respectively which corresponds to our experimental conditions B = 20mT

mT, p = 4 Pa. Those values lead to the ion mobility µi of 3.8 m2

sV and electron mobility µe of 8.1 · 104 m2

sV .

a) b)

Fig. 6 a) the imaginary component ωi and b) the frequency of the real component ωr calculated from dispersion relationdeveloped by [1]. Here ky represents azimuthal wavenumber in the slab approximation.

For further attempt to interpret the data the dispersion relation from the work by Martines et al. [1] was usedwhich follows from the theory of E × B density gradient instability [7]. The used parameters were: B = 20mT, E = −117 V/m, Te = 2 · 104 K, Z = 2.4 · 104, νi = 5.9 · 104 s−1, νe = 2.7 · 107 s−1, kx, ky = 1.The frequencies obtained at given conditions were in the order of several tens kHz and therefore well above themeasured values (see Fig. 6).



That apparent discrepancy between experiment and theory might be caused by smaller dimensions of themagnetron system, but also it might be an indication that the observed fluctuations are coupled with ionizationwaves. Ionization waves have been studied and described e.g. in [8].

The phase velocity of observed fluctuations was found in the range of the phase velocity for the ionizationwaves. From Langmuir probe measurements plasma potential was evaluated and these measurements show, thatthere is a sufficient electric field in the cathode fall region for creation of the ionization waves.

Also, when repeating measurements at the same conditions (at the same magnetic field, pressure and dischargecurrent) sometimes two frequencies or more for the same peak number were found. Different peak frequencymodes could be related to the different types of ionization waves.

4 Conclusion

Coherent modes were observed in the azimuth direction in the cylindrical magnetron dc discharge. Parameters ofthese wave-like structures were compared with other theoretical works to find their origin.

The exact classification of the type of the instability occurred in our magnetron did not succeed yet, althoughthe work brings new findings about the processes in magnetron dc discharge.

Acknowledgements The work was partially financially supported by the Czech Science Foundation, Grant No. 202/06/0776,202/04/0360, 202/03/H162, by project COST action 527.70, by the Faculty of Mathematics and Physics of Charles Univer-sity in Prague and by EURATOM. This work is also a part of the research plan MSM 0021620834 that is financed by theMinistry of Education of the Czech Republic. Thanks are also due to the University of Greifswald which provided us withthe cylindrical magnetron system.

References

[1] E. Martines, R. Cavazzana, G. Serianni, M. Spolaore, L. Tramontin, M. Zuin, and V. Antoni, Phys. of Plasmas 8, 3042(2001).

[2] J.F. Behnke, E. Passoth, C. Csambal, M. Tichy, P. Kudrna, D. Trunec, and A.Brablec, Czech. J. Phys., B49, 483 (1999).[3] P. Kudrna, M. Holık, M. Tichy, C. Csambal, and J.F. Behnke, Czech. J. Phys., 52/SA (2002).[4] J.F. Behnke, P. Kudrna, J. Rusz, and M. Tichy, Czech. J. Phys., 50/S3, 419 (2000).[5] P. Kudrna and E. Passoth, Contrib. Plasma Phys., 37, 417 (1997).[6] C I. Weng and C.S. Ma, Chinese Journal of Physics 13, 44 (1975).[7] E.J. Powers and P.B. Mumola, Plasma Phys., 13, 817 (1971).[8] L. Pekarek and V. Krejcı, Czech. J. Phys., 13, 881 (1963).


Observation of WaveLike Structures in Magnetized DC Dischargein Cylindrical Symmetry in Argon

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