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Submitted on 1 Jan 1979
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TWO DIMENSIONAL FOURIER SPECTRUM OF TURBULENT IONIZATION WAVES
J. Skàla, J. Kràsa, V. Peřina
To cite this version:
J. Skàla, J. Kràsa, V. Peřina. TWO DIMENSIONAL FOURIER SPECTRUM OF TURBU- LENT IONIZATION WAVES. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-587-C7-588.
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JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au no?, Tome 40, JuilZet 1 9 7 9 , page C7- 587
TWO DIMENSONAL FOURIER SPECTRUM OF TURBULENT IONIZATION WAVES
J. Skhla, J. Kresa and V . ~ e % n a .
I n s t i t u t of Physics, Czech. Academy of Science, 180 40 Prague 8, Na SZovance 2, CzechosZovakia.
The turbulence of unstable ionisation waves often takes place in the positive column of low current and low pressure discharge in noble gases. Experimentally, the neon discharge is abounding in various mechanisms leading to a loss of wave
coherence and to the onset of strong irregular wave motion t1, 2 3 .
Lately, a great attention was paid to experiments concerning correlation
function measurements of such turbulent ionisation waves. These measurements have shown that the correlation length L of a fully developed wave turbulence cafi be shorter than the mean wavelengths
X o
of the wave packets13, 41.
In the presented contribution, measurements on turbulent ionisation waves are referred for which a wave-number filter [ 5 ] was used with subsequent frequency analysis. Two-dimen- sional Fourier spectra F (k,~)) were obtained by this method.Th.e light emitted from the discharge tube I (x,t) was passing through the filter composed of the stripes, whose transparence changes along the axis as T-1/2(1
+
m cos(kx)), where m is the mo'dulation depth and 2 / is the wavenumber corresponding to th% wavelengthIf
of the stripes, see Fig. 1. The signal from photomultiplier P, representing the whole light, passing through is then proportional to the real part of the space Fourier spectrumif we assume the integration length L to be much larger than the correlation length L
.
The frequency spectrum of the signal (17 in a conventional frequency analyser is then proportional to the absolute value of the Fouriertransformation of the light fluctuations I (x,t). By changing the wavelength
Xf
of the filter a time-space Fourier s
spectrum F ( k , ~ ) on the o - k plane can be measured
The space filter was realized by a loop of the film, on which a system of hyperbolic stripes was transferred photografically. In this arrangement, wavenumber scale is proportional to the
1
Fig 2. Two-dimensional spectrum F(l/~,f) of the light fluctuations of positive column of the neon discharge ( p = 5.2Torr, Pig. 1. Experimental arrangement: i = 42 mA, tube diameter 0.6 cml.
D
-
discharge tube, L-
lens, P-
photo- h = 2 W /k and f = U/2%.multiplier, FA
-
frequency analyzer.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797284
Fig. 3 , Dispersion curve of the turbulent ionisation wave evaluated from Fig. 2.
Pig.
4.
The course of the maximum values of the spectrum Fmax(f) over the dispersion curve as function of the frequency.
vertical shift of the film. Another possibility for realization of the space filter is the use of two crossed lattices.
In this case, the wavenumber of moire' patterns is proportional to the angle between the both latticies. The advantage of this filter is in a more genuine sinusoidal shape of the transparence.
The measurements were made in a discharge tube with the internal
diameter 0.6 cm. The distance between the electrodes was 90 cm. The neon pressure was 5.2 Torr and the discharge current 42 mA. The measurements were performed in the part of the positive columrl, where the wave turbulence was stationary.
Fig. 2 shows a typical shape of the two-dimensional spectrum F(k,w) The dispersion curve w = W (k) which is taken to be the projection of the crest line of F(k,w) to the w - k plane is plotted in Pig.3. Another important function specifying the properties of turbulent ionisation waves is the crest height over the dispersion curve. As Fig.4 shows, the crest height exhibits an asymmetry with regard to the center wave mode for which F(k
,
u ) attains a maximum value. This in8ica?es the different properties of the turbulent ionisation wave in the region of lower and higher frequencies and wavenumbers.The shape o f the frequency and/or wavenumber spectrum itself at higher
frequencies or wavenumbers is markedly influenced by the second harmonics of the basic wave, the trace of which is visible in our case at the frequency 105 kHz Nevertheless the difference between the frequency spectrum and the wavenumber spectrum is mostly given by the asymmetry of F(k,wl along the dispersion curve.
The procedure as described above is thus suitable for an evaluation of the main characteristics of the light fluctuations caused by the turbulent oni is at ion waves moving down the positive column of the gas discharge.
References
[1] Perkin R.M., Krgsa J. And Pekdrek L . , J Phys D:
8
(1975) 161[2]Krgsa J.
,
Perkin R.M. and Pekdrek L., J Phys D:-
7 (1974) 2541[3]Grabec I, and Poberaj S., Plasma Phys.
11 (1969) 519
-
[4]
Krdsa J.,
Pesina V. and Rothhardt L.,
Proc, 13th I.C.P.I.G. Berlin 1977, p.287 [5] Skdla J., Czech. J.Phys.
a
(1973) 284[6] Bendat J
.
S. ,
Principles and applica- tions of random noise theory.Russ. Nauka, Moscow 1965[7) Kr6sa J. and PeFina V.
