Experimental evidence of three-wave coupling on plasma turbulence

Abstract

Experimental evidence of the nonlinear nature of the broadband edge fluctuations has been obtained in edge turbulence in the Advanced Toroidal Facility torsatron. Whereas little nonlinear wave interaction is found in the scrape-off layer region, three-wave coupling is enhanced in the plasma edge region (r < tfshear). The degree of three-wave coupling strongly depends on the plasma conditions; it decreases in the temperature range (T e~ 10 eV) where the ionization rates depend strongly on T e suggesting a link between ionization source and turbulence. PACS numbers: 52.35.Mw, 52.35.Ra, 52.55.Fa Transport through broadband turbulence is an important loss mechanism for particles and energy in the plasma edge. Understanding the origin of the broadband edge fluctuations remains thus one of the key issues confronting fusion research. Many theoretical models explain the broadband fluctuation spectra on the basis of quadratically nonlinear mechanisms (i.e., three-wave interactions) which redistributes the energy supplied to the fluctuation spectrum by multiple instabilities present in the edge plasma region [1]. However, no experimental evidence of considerable wave-wave coupling of the broadband turbulence has been reported so far.Whereas the standard linear spectral analysis (power spectrum) provides experimental information on the amplitude and phase behavior of the individual Fourier component and about the transport induced by fluctuations [2,3], it does not give any information about the coupling among different spectral components. The use of the bispectral analysis allows one to discriminate between waves spontaneously excited by the plasma and those generated by the former by nonlinear coupling [3][4][5][6]. Nonlinear mode coupling of low m modes has been recently reported in the MST reversed field pitch [7]. Coupling between long-wavelength mode and small-scale turbulence has been recently reported in the TEXT tokamak [81.The present Letter shows the first direct evidence that quadratic interactions play an important role in the broadband edge fluctuations of a toroidal device.The bicoherence spectrum has been computed to study the strength of the three-wave coupling contributing to the characteristics of edge fluctuations in the Advanced Toroidal Facility (ATF) (/=2, M = 12 field period torsatron with /?=2.1 m and a =0.27 m). Edge turbulence was studied using Langmuir probes and the experimental techniques described elsewhere [9,10]. Edge fluctuations have been characterized by the Langmuir probe ion satu-ration current, I s ^ n e (T e ) 1/2 , and by the floating potential, <t>f = <P P -aT e , where (/> p is the plasma potential, T e is the electron temperature, and a« 3 for hydrogen plasmas [11].The experiments were performed in electron-cyclotron-resonance heating (ECRH) plasmas with heating power PECRU ~ 200 kW, average electron density n e ~(4-6)xl0 12 cm" 3 , stored energy S E ~ 1 kJ, and magnetic field 5 = 1 T. The signals were digitized at 1 MHz, using a 10 bit, 16 kbyte/channel digitizer. Nonlinear a...

Drift waves and transport

“…(85) have been developed (Kim and Powers, 1978). An example from the torsatron stellarator edge fluctuation data confirming the importance of the quadratic mode coupling components is given by Hidalgo et al (1993). The condition for self-trapping is that the amplitude of a disturbance be just above the mixing length level corresponding to Eq.…”

Third-Order Spectral Techniques for the Diagnosis of Motor Bearing Condition Using Artificial Neural Networks

“…Each B B ðf t Þ represents the fraction of the total power at frequency f t ð¼ f x þ f y Þ which is due to interactive coupling at frequencies f x and f y . B is the number of points used on either (because of bispectrum symmetry) of the f x or the f y frequency axes [14,15].…”

Technique for the experimental estimation of nonlinear energy transfer in fully developed turbulence

“…Recently, many experiments have used bispectral analysis to demonstrate that three-wave coupling processes are important in fluids 14,15 and plasmas. [1][2][3][4][5][6][7][8] This three-wave coupling term can be theoretically derived from the convective derivative ͓i.e., ͑ ជ -"͒ ជ , where ជ is the flow velocity͔ in neutral fluids or the polarization drift and ẼϫB drift convection in plasmas. 3 To make quantitative estimates of the linear growth rate and the energy cascade rate between waves for fully developed turbulence, we consider the nonlinear drift wave coupling equation written in the form 3…”

“…Recently, bispectral analysis has emerged as a way to experimentally estimate the linear growth rate and nonlinear energy transfer [1][2][3][4][5][6][7][8] in fully developed plasma turbulence, and thereby provide a more direct tool for mode identification compared to early transport experiments, which relied on indirect comparisons to theoretical expectations. 3 Bispectral analysis, which measures the amount of phase correlation between three spectral components, is used to investigate nonlinear wave-wave interactions.…”