2D turbulence structure observed by a fast framing camera system in linear magnetized device PANTA

Two dimensional turbulence observed in the linear magnetized device PANTA is studied using a visible high speed camera system. When the fluctuation component are decomposed with Fourier-Bessel expansion, complex density fluctuations are recognized as the superposition of the several mode having low mode number, e.g., m = 1, 2, and 3. The phase relations between waves indicate that they are non-linearly coupled.


Introduction
Mesoscale structures, such as the zonal flow and the streamer play important role in the drift-wave turbulence. The interaction of the mesoscale structure with the turbulence is a key to understand the structural formation of turbulence and the turbulence-driven transport in the magnetically confined plasmas. In a cylindrical magnetized device, the interaction of the streamer and the drift wave has been found [1]. In that study the spatial shape of the streamer-like structure were obtained by using the bispectrum analysis with a fixed probe array and a movable probe system. Statistical nature of the mesoscale structure can be studied by this method. However, if the dynamic wave-wave interaction can be observed directly, our understanding of the turbulence will be improved further. For this purpose, direct visualization of the turbulence with a high-speed camera system was performed. The analytical procedure and initial results are presented in this article.

Experimental Setup
A fast framing camera system observing the cylindrical plasma through an end port of the PANTA device is schematically shown in figure 1(A). If the perturbation is aligned to the magnetic field lines, two dimensional turbulent structures can be observed from this arrangementIt is noted that when we observed the plasma column perpendicularly, the mode structure is well aligned to the magnetic field lines. The parameters of the target plasma is the following; T e ~ 3 eV, n e ~ 1 × 10 19 m -3 , T i ~ 0.3 eV, B = 900 G, the neutral pressure P n = 0.8 m Torr, the minor radius a ~ 6 cm and L = 4 m. Helicon source (7 MHz, 3 kW) is used to generate plasma. No filter was used for the camera. Since the electron temperature is several eV, line emission of Ar I is the dominant component of the visible image. Its intensity is sensitive to the local electron density fluctuations and local electron temperature fluctuations. A sample image is shown in figure 1 imaging data and the ion saturation current measure by a probe tip of 64 pin system. High-coherence region is well localized so that the local density / temperature perturbation can be estimated from the visible emission intensity. It is confirmed that the spatial / frequency spectra measured by ion saturation using the probe system is quite similar to that by 2D visible measurement described in detail in Section 3. It is thus reasonable we assume that the fluctuation of the light emission density fluctuations having low mode number. .

Analysis and Initial Results
Fluctuating component of the visible emission g(r, θ) is decomposed to orthogonal components by the Fourier-Bessel expansion method [2] as, where is the l-th zero point of the m th order Bessel function (z).
Decomposition is performed where emission light is strong. The boundary is shown by the red r=1.0 circle in figure 1(B). Since the Fourier-Bessel series are orthogonal, it is quite easy to obtain the coefficients and . Error in the decomposition is estimated to less than 5% when m max = 4 and l max = 10 are assumed. If we combine coefficients and to complex coefficient = + i , represents the magnitude of mode with phase information. Complex amplitude at a minor radius r with a mode number m can be written from the integral as, Using the Fourier transform , rotary spectrum S(ω, m) [3] can be defined as S(ω, m) = <Z* Z>.
Rotary spectrum with m =1, 2 and 3 are shown in figure 2. There are many sharp peaks, labelled by f 1 , f 2 , , in broad spectra. It is noted that the m = 2 and m = 3 components are not strong in the core region. Those spectra in the edge region (e.g., ρ = 0.8) are quite similar to the spectra estimated with the multi-pin probe array data [1].    There is a time period where the two phases are locked between each other (Shaded region of figure 4(B)). That is the reason finite bi-coherence between mode A and mode B is observed. The amplitude of the mode B is larger when the two phases are locked (figure 4(C)). It is possible that the mode B is produced from the mode coupling of the mode A. Many peaks in the rotary spectra might be caused by this kind of wave-wave coupling of the fundamental mode. It is noted that from the time evolution of the phase difference ( figure 4(B)), there is a period where the two waves are unlocked, as well. Therefore, the wave-wave coupling process is found to be not simple steady process but a kind of intermittent process.