- Email: [email protected]
Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma
G Model
ARTICLE IN PRESS
FUSION-9007; No. of Pages 8
Fusion Engineering and Design xxx (2017) xxx–xxx
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma B. Kakati ∗ , S. Pradhan ∗ , J. Dhongde, P. Semwal, K. Yohan, M. Banaudha, SST-1 team Institute for Plasma Research, Bhat, Gandhinagar 382 428, Gujarat, India
h i g h l i g h t s • Anomalous particle transport during the high MHD activity at SST-1. • Electrostatic turbulence is modulated by MHD activity at SST-1 tokamak. • Edge floating potential fluctuations shows poloidal long-range cross correlation.
a r t i c l e
i n f o
Article history: Received 9 July 2016 Received in revised form 8 November 2016 Accepted 28 December 2016 Available online xxx Keywords: Tokamak plasma MHD Plasma confinement Particle transport Plasma diagnostics
a b s t r a c t Plasma edge transport characteristics are known to be heavily influenced by the edge fluctuation induced turbulences. These characteristics play a critical role towards the confinement of plasma column in a Tokamak. The edge magnetic fluctuations and its subsequent effect on electrostatic fluctuations have been experimentally investigated for the first time at the edge of the SST-1 plasma column. This paper reports the correlations that exist and is experimentally been observed between the edge densities and floating potential fluctuations with the magnetic fluctuations. The edge density and floating potential fluctuations have been measured with the help of poloidally separated Langmuir probes, whereas the magnetic fluctuations have been measured with poloidally spaced Mirnov coils. Increase in magnetic fluctuations associated with enhanced MHD activities has been found to increase the floating potential and ion saturation current. These observations indicate electrostatic turbulence getting influenced with the MHD activities and reveal the edge anomalous particle transport during SST-1 tokamak discharge. Large-scale coherent structures have been observed in the floating potential fluctuations, indicating longdistance cross correlation in the poloidal directions. From bispectral analysis, a strong nonlinear coupling among the floating potential fluctuations is observed in the low-frequency range about 0–15 kHz. © 2017 Elsevier B.V. All rights reserved.
1. Introduction In general, the plasma turbulence refers to the microscopic random fluctuations in particle density, temperature, potential and magnetic field. These fluctuations are generally driven by radial gradients that exist in the plasma density and temperature [1]. Plasma turbulence and transport properties, especially at the edge region are known to influence the overall plasma confinement characteristics in a tokamak. Turbulence, in fact is one of the primary reason attributed towards the anomalous particle and energy transport in a tokamak [1–4]. The magnetic and electrostatic fluctuations
∗ Corresponding authors. E-mail addresses: [email protected] (B. Kakati), [email protected] (S. Pradhan).
that lead to magnetic and electrostatic turbulence at the tokamak edge are known to drive the plasma turbulences [5,6]. These magnetic fluctuations further reduce the plasma performances. They limit relevant parameters like poloidal beta due to the change of plasma profiles [7]. The magnetic transport due to magnetic fluctuations is not large enough as compared to electrostatic transport in tokamak plasma. The edge plasma transport is primarily driven by electrostatic fluctuations [7]. Several efforts have been put towards understanding the plasma transport and turbulence behaviour in the last decades in tokamak plasmas. Presence of large-scale magneto-hydrodynamic (MHD) instabilities and small-scale turbulence are generally present at a sufficient to result in the anomalous particle transport in tokamak devices [8]. In presence of strong toroidal magnetic field, the timevarying radial electric field drives the E x B drift flows in poloidal direction. Such plasma flow is termed as zonal flow (ZF). In the
http://dx.doi.org/10.1016/j.fusengdes.2016.12.041 0920-3796/© 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS
2
B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
context of the tokamak configuration, the ZFs are radially localized potential perturbations which are toroidally and poloidally symmetric. Such plasma flows are generated due to the radial turbulent transport of poloidal momentum, i.e. the Reynolds stress [9]. In toroidal confined tokamak plasmas, two types of ZFs have been observed, i.e. a low-frequency zonal flow (LFZF) with nearly zero frequency and a geodesic acoustic mode (GAM) with higher frequency [9]. The plasma turbulence is expected to be in a selforganized state mediated by zonal flows [10]. The MHD phenomenon is another important topic for fusion community. MHD instabilities are considered as dangerous phenomena as they lead to destruction of magnetic surfaces and termination of plasma discharge. The MHD influences the sheared radial electric field within the plasma column. Depending on the strength of the MHD behaviour, the magnetic oscillations (MHD activity) change the plasma density, electron temperature and plasma potentials which in turn influence the electrostatic fluctuations [3]. The anomalous transports, together with MHD instabilities control the plasma confinement and overall plasma performance. It is observed and reported by different researcher that the radial electric field suppress the MHD activity which in turn improves the plasma confinement in tokamak [11–13]. The correlation between the magnetic oscillations and electrostatic turbulence is not significant [1] in many tokamak devices. However, the correlation between the magnetic oscillations and the electrostatic turbulence turns to be relevant in new highconfinement regimes achieved in tokamaks [14–16]. The studies on reversed field pinch (RFP) show that the electrostatic fluctuations are influenced by the magnetic fluctuations [5,6]. B. J. Ding et al. [7] have reported the edge density and potential fluctuations having high correlation with magnetic fluctuations; and the resulting mode spectra being similar to those of magnetic field fluctuations. These strongly indicate that, the electrostatic fluctuations are primarily caused by electromagnetic turbulence. In recent years, particular attention has been paid to the coherent structures in plasma turbulences. In fusion and non-fusion plasmas, the transport processes mostly contains the short range correlations, rather than long-range correlations. Recently, several authors [17–20] have reported the observations of long-range correlation and self-similarity in plasma edge fluctuations in the so called “mesoscale” range. These are larger than turbulence decorrelation time and plasma confinement time in many tokamak devices [17–20]. It has also been reported by many authors that the presence of the long-range correlation and self-similarity can be easily understood if the self-organized criticality (SOC) dynamics play a dominant role in the plasma transport processes [17–22]. Different statistical analysis techniques have been extended to identify the existence of long range correlations and self-similarity in plasma fluctuation [23]. G. S. Xu et al. [10] observed the poloidal long-distance correlations and have reported about 40% coherence at the poloidal distance (31.4 mm) that is nearly three times of the turbulence decorrelation length at HT-7 tokamak. Despite of the huge efforts on these aspects in the last decades, many features of plasma transports are still to be understood. Thus, more careful investigations are still necessary for better controlling of plasma confinement in tokamaks. Recently, the edge density and potential fluctuations and their correlation with magnetic fluctuations have been studied at Steadystate Superconducting Tokamak-1 (SST-1) tokamak. SST-1 is a medium sized tokamak having large aspect ratio with a major radius of 1.1 m and a plasma minor radius of 0.2 m with elongation of 1.7–1.9 and triangularity of 0.5–0.7 [24]. The recent experimental observations show a high correlation of edge density and potential fluctuations with that of the magnetic fluctuations. The cross correlation and coherence between the electrostatic fluctuations measured at different poloidal locations have been carried
Fig. 1. (Colour online) (a) Top view of SST-1 tokamak and (b) schematic of Langmuir probe arrangement.
out under this investigation. These events have also been studied with synchronized MHD activities as observed experimentally in SST-1 early plasmas. The remaining sections of this paper have been organized as follows. In Section 2, the experimental set-up, methodology and the diagnostic tools are described in detail. Section 3 summarizes the results and their physical interpretations. Finally, the present work has been concluded in Section 4. 2. Experimental assembly and methodology The present studies have been carried out in SST-1 tokamak over a large number of repeatable shots under identical plasma conditions. However, under this investigation two representative plasma shots (shot no 7799 and 7873) have been discussed. The top view of SST-1 tokamak and schematic of Langmuir probe arrangement is shown in Fig. 1(a) and (b). The SST-1 tokamak is operated in limiter configuration with a central field of 1.5 T. Graphite tiles have a density of 1.82 g/cm3 and a porosity of about 9.00% is used as limiter materials. Sixteen (16) toroidal field (TF) superconducting coils are used to produce the required toroidal field. A pair of vertical field coils placed symmetric to Z = 0 plane is used to provide the necessary equilibrium field to the plasma column formed [23]. In SST-1, the plasma is initiated with the help of ECH preionization, employing a 42 GHz Gyrotron in fundamental mode followed by the Ohmic transformer [25]. At present, plasma currents are produced in excess of 100 KA extending in durations up to ∼500 m s in a repeatable fashion. The plasma is confined within the two poloidal limiters. In the present report, two identical plasma shots (shot no 7799 and 7873) in terms of plasma duration and current have been chosen to study the edge parameters and its correlation with MHD. The plasma current reaches a maximum value
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
3
Fig. 2. Time evolutions of plasma discharge (a) for plasma shot no 7799, (b) for plasma shot no 7873.
of 86 kA with plasma duration of ∼280 ms for shot 7799 and 90 kA with plasma duration of ∼280 ms for shot 7873. The magnetic fluctuations are detected using eight (8) discrete in-vessel Mirnov coils. The corresponding electrostatic and density fluctuation generated at the plasma edge due to the MHD activities are detected using a set of Langmuir probes. The probes are mounted at 5.0 mm behind the outboard limiter to measure the edge plasma density, electron temperature, fluctuation of edge density in terms of ion saturation current and fluctuation of floating potential. The probes are arranged in poloidal direction at the same magnetic flux tube. The Langmuir probe marked with LP1 and LP3 are single cylindrical Langmuir probe with a tungsten tip having dia 1.0 mm and length 3.0 mm whereas the middle probe LP2 consist of three cylindrical tips having dia 1.0 mm and length 3.0 mm. The distance between the LP1 and LP2 (central tip) or LP2 (central tip) and LP3 is 80.0 mm. The distance between the each probe tip of LP2 is 4.0 mm. The probe tip separations are much larger than the Debye length (correspondingly its sheath thickness) of edge plasma parameters. At SST-1, the edge density and temperature are calculated from I–V characteristics of the Langmuir probe for the duration where the plasma current shows almost plateau nature. The plasma density is calculated from the ion saturation current whereas the electron temperature is calculated below the floating potential of the I–V characteristics using the procedure as adopted by different researchers [26–28]. The plasma density is of the order of 1016 /m3 where as the electron temperature is ∼10 eV for the shot no 7799 and 7873. Langmuir probe and Mirnov coil data are digitized at 100 kilosamples per second respectively. The Langmuir probe data are sampled with 16-bit resolution whereas Mirnov coil data are sampled with 14-bit resolution using a multichannel digitizer.
3. Experimental observation and discussion The observations are carried out on the SST-1 tokamak with two circular poloidal limiters, which are toroidally separated by 180◦ . The time evolution of plasma discharge for shot no 7799 and 7873 are shown in Fig. 2(a) and (b). The plasma current grows rapidly at the initial stage and shows an almost plateau nature for a short duration before it start decaying. Some clearly visible MHD activities during the plasma discharge are observed from Mirnov signals in both the shot. Initially, the MHD perturbations are occurred at the plasma core and rapidly propagate outwards. In shot no 7799 [shown in Fig. 2(a)], it is
observed that the high MHD activity grows at different stages during the plasma discharge. For shot no 7799, the high MHD activities are found between 105–155 ms, 205–213 ms and 253–282 ms where the fluctuation of the Mirnov signals (i.e. magnetic fluctuations) is large compared to that in other region. The effect of MHD activity for discharge duration 105–155 ms is very prominent. Thus, the effect on edge floating potential fluctuation and ion saturation fluctuation for the above duration is only addressed in this report. It is seen that the magnetic fluctuations are diminished with an abrupt fluctuation at the end. The abrupt magnetic fluctuation leads to a sharp fall of plasma current at a rate of 2.4 MA/s. After 155 ms, the magnetic oscillation reduces and the plasma current decays gradually at a slower rate of 0.3 MA/s till the next MHD activity. The floating potential and ion saturation current fluctuation shows almost identical behaviour with magnetic fluctuation. Some irregular fluctuations both in floating potential and ion saturation current are observed during high MHD activity. The standard deviation of the floating potential is found to be around 65% for LP2 (for ion saturation ∼60%) during the high MHD activity which is much higher than the standard deviation of floating potential (∼10%) and ion saturation (5%) at low MHD. It is found that the amplitude of ion saturation current (i.e. plasma density) fluctuation is slightly lower as compared to the floating potential fluctuation. The edge density fluctuation is directly proportional to the ion saturation current fluctuation (the temperature fluctuations are not taken into account and considered as negligible) [3,21]. Thus, from Fig. 2(a) and (b), it is clear that the edge density fluctuation also shows the identical behaviour during high and low MHD activity. The increase in magnetic fluctuation increases the floating potential and ion saturation current fluctuation during high MHD activity. It indicates an anomalous particle transport during the high MHD activities. The similar behaviour in magnetic and electrostatics fluctuation indicates that the electrostatic turbulence is modulated by Mirnov oscillations i.e. MHD activity at SST-1 tokamak. Such kind of electrostatics fluctuation driven by magnetic fluctuation is observed by many authors during the tokamak discharge [29–32]. In the present manuscript, the edge turbulence behaviour is mainly described on basis of the floating potential fluctuations only. For clear representation, the enlarged view of electrostatics fluctuation during low and high MHD for shot no 7799 is shown separately in Fig. 3. The discharge duration between 90 and 100 ms is considered as low MHD region where magnetic fluctuation is com-
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS
4
B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
Fig. 3. Floating potential fluctuations for shot no 7799.
paratively low. On the other hand, the discharge duration between 110 and 120 ms is considered as high MHD region where, magnetic fluctuation is comparatively high. Similar behaviour is observed for shot no 7873. For shot no 7873, it is observed that the magnetic oscillations starts increasing at t = 108 ms and stays high until t = 160 ms. The high MHD activity significantly alters the floating potential for the above plasma discharge duration. The normalized volume average beta for shot no 7799 is shown in Fig. 4. The volume average beta is calculated from diamagnetic loop and compensating loop data. It shows that the volume average beta is almost constant for the duration of ∼90–160 ms when the plasma current shows almost plateau nature. A power spectral analysis is carried out to quantify several statistical properties of the turbulent fluctuations at the plasma edge. The spectrogram of the Mirnov signal and floating potentials for shot no 7799 and 7873 are shown in Figs. 5 and 6. In the spectrograms, the oscillation frequencies are plotted against the discharge duration and the corresponding power spectral densities (in arbitrary units) are plotted in a colour scale. The spectrogram is constructed using MATLAB by considering the window length and DFT (discrete Fourier Transform) length of 128 points for a signal duration of 350 ms with a sampling frequency of 100 kHz. The total number of used sample points is 35, 000. The spectrogram for Mirnov oscillations is shown in Fig. 5(a) for shot no
Fig. 4. The volume average beta (normailized) during SST-1 tokamk discharge.
Fig. 5. (Colour online) Spectrogram for shot no 7799 (a) Mirnov signal, (b) Floating potential.
7799 where the periods of magnetic activity associated with peaks of the power spectral density is clearly visible. It is seen that the intense burst on magnetic oscillation is started at ∼105 ms with a sharp line and it extends up to ∼158 ms with a dominant frequency at ∼6 kHz. It has at least two overtones corresponding to higher harmonics of the dominant frequency. The spectrogram of floating potential fluctuation (shown in Fig. 5(b)) is also shown similar behaviour with magnetic fluctuation. An intense burst on floating potential fluctuation with a sharp line is appeared almost at the same discharge duration with a dominant frequency at ∼6 kHz. For shot no 7873 (shown in Fig. 6), the intense burst with a sharp line in the spectrogram of magnetic fluctuation have appeared for the discharge duration of 108–160 ms. Similar behaviour of electrostatic fluctuations have been observed for the identical discharge duration [32]. It indicates that the high MHD activity synchronizes with the electrostatic fluctuation during SST-1 plasma discharge. Such synchronization between the electrostatic and magnetic fluctuation had also been observed at TCABR tokomak during the plasma operation [3,32].
Fig. 6. (Colour online) Spectrogram for shot no 7873 (a) Mirnov signal, (b) Floating potential.
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
5
Fig. 7. The poloidal mode structure for shot no 7799.
In our present observation, the time evolution of poloidal modes associated with the MHD activity is evaluated using singular value decomposition (SVD) technique. The SVD is applied to tokamak Mirnov signals to identify MHD activities in the plasma [33]. It is observed in our recent observations that the poloidal MHD mode changes with the MHD growth. From the temporal evolution of mode structure, the m = 1–3 are observed as poloidal MHD modes for plasma shot 7799 and 7873. In both the plasma shot, m = 2 is found as a dominant poloidal MHD modes. The spatial structure represented by polar plot for the duration of 144–146 ms is shown in Fig. 7 which shows clearly m = 3 mode associated with the MHD activity. The role of MHD activity on radial electric field is studied during the plasma discharge. The radial electric field influences the plasma parallel flow through the Er × B force. A negative electric field clearly generates a force component anti-parallel to the plasma current [34]. The floating potentials measured by Langmuir probes are used to calculate the radial electric field. The time trace of Er = −∇ Vf (Assuming the impact of ∇ Te is negligible) during the MHD activity is studied for both the plasma shot. In SST-1, a negative radial electric field is observed during the tokamak discharge. It is observed that the MHD activity dramatically changes the radial electric field profile (see Fig. 8). It is observed that the high MHD activity which leads to a high magnetic fluctuation at the end changes the radial electric field from negative to positive value. V. Rozhansky et al. [35,36] reported such observations on radial electric field at TUMAN–3 M tokamak during the onset of MHD activity. Statistical analysis techniques are used by many authors to study the existence of long range correlations and self-similarity in edge plasma fluctuations [21,23,37,38]. The two-point cross correlation method is used in our present study to investigate the
Fig. 8. Radial electric field profile during MHD activity for plasma shot 7799.
Fig. 9. (a) Cross power spectrum and (b) coherence spectrum for shot no 7799.
correlations between two fluctuating signals in poloidal direction. The distance between the two probes LP1 and LP2, which are used to measure the floating potential signal is around 8.0 cm. The distance between the probes is much larger than the turbulence decorrelation length (close to 1 cm) [21]. The edge floating potentials measured by the Langmuir probe for both the plasma shot are used to study the cross correlation and coherence. The Langmuir probes are radially located at the same distance from the core of the plasma. The cross power spectrum of two time varying signal X(t) and Y(t) can be written as [39]; PXY = |PXY (f )|eiXY (f )
(1)
Where |PXY (f )| is the cross-amplitude spectrum which is given by PXY = X(f )Y (f )
(2)
Here X(f) and Y(f) are the Fast-Fourier-Transform (FFT) of two time varying signal X(t) and Y(t). The XY (f ) is the phase spectrum which is given by XY (f ) = Y (f ) − X (f )
(3)
The coherence spectrum measures the degree of mutua1 coherence between two time varying signals. The coherence spectrum is defined as follows: CXY (f ) =
|PXY (f ) | [PXX (f ) PYY (f )]
1⁄2
(4)
Here, PXX and PYY are the auto power spectra of the signals. In the present work, the cross power spectrums of floating potential signals are generated with the help of MATLAB and digitized for total 32768 numbers of FFT points at 100 kHz sampling frequency considering 50 points as non-overlapping points. The cross power spectrum and coherence spectrum of the two signals are depicted in Fig. 9(a) and (b) for shot no 7799 respectively. The identical cross power and coherence spectrum are observed for shot no 7873 as well. From the auto power spectra of the signals, it is found that the fluctuation levels of both the signals are close to each other. It confirms that the probe tips are approximately located in the same flux surface. In the low frequency range below 10 kHz, two peaks are observed in cross power and coherence spectrum (see Fig. 9). The peak around 6 kHz is associated with the MHD mode, it exhibits strong long-distance correlation and coherence. The MHD modes belong to the macroinstability that normally has a long poloidal wavelength. The associated perturbations are generated at the
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS
6
B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
Fig. 10. The poloidal wave number spectrum.
core of the plasma, propagating outward. Almost 40% coherence between the floating potential signals is observed in this frequency range in our case which is matching with the result, observed by G. S. Xu et al. [10] at HT-7 tokamak. Another peak is observed at the low frequency region, which is close to zero frequency and it quickly decayed. The similar zero-frequency peak in the potential fluctuations was also detected in HT-7 superconducting tokamak [21] and in a helical device [40]. The zero-frequency peak was considered to be associated with the zonal flows. For plasma shot 7799 (shown in Fig. 9), a broad band fluctuation, peaking at ∼35 kHz is observed above 15 kHz. G. S. Xu et al. [21] reported that such high frequency fluctuation have been generally associated with the drift-wave of the plasma. The zonal flows are believed to be a general feature of toroidal turbulence [41,42]. The existences of zonal flows can be obtained from the measurements of edge density and potential fluctuations. Phase contrast imaging measurements have observed a turbulent structure in the density field with a finite radial wavelength, and k ≈ 0, as predicted by theory and it indicating at the existence of zonal flows [43]. In order to support the identification of zonal flow, the poloidal wave number has been estimated, which have been shown in Fig. 10. The poloidal wave number is estimated using the following relation k (f ) =
xy (f )
(5)
Where xy is the phase difference between signal x and y and is the poloidal distance between x and y. It is seen that the poloidal wave number in the low frequency region is close to zero. It supports the possibility of presence of some low-frequency large-scale potential structures [21]. Such low frequency peak (∼0 Hz) in the potential fluctuations with k ≈ 0 is detected in different devices, which is considered to be associated with the zonal flows. Thus, the zero frequency peak is considered as zonal flow in our present work. Bispectral analysis is a powerful signal processing technique to study the nonlinear interactions among the fluctuating quantities. It has been applied to various plasma experiments to study the nonlinear interaction [44–47]. To study the nonlinear coupling, bispectral analysis of the edge floating potential fluctuation data is carried out in the present work. The bispectrum is the third order cumulant spectrum and is defined as Bˆ (f1 , f2 ) = Y (f1 ) Y (f2 ) Y ∗ (f3 )
(6)
Fig. 11. (Colour online) (a) 3-D plot and (b) 2-D plot of auto-bicoherence of edge floating potential fluctuation for shot no 7799.
where Y(f) is the Fourier component of the observed time series y(t), f is the frequency, and f3 = f1 ± f2 . The asterisk indicates the complex conjugate. Such bispectrum, composed of the Fourier components of the same time-series, is referred to as auto-bispectrum, whereas the bispectrum composed of different time series is referred to as cross-bispectrum. The cross-bispectrum is defined as Bˆ (f1 , f2 ) = X (f1 ) Y (f2 ) Z ∗ (f3 )
(7)
where X(f) and Z(f) are the Fourier components of the observed time-series x(t) and z(t), respectively. Qualitatively, the occurrence of three-wave interaction is investigated by measuring the squared bicoherence which is defined as bˆ 2 (f1 , f2 ) =
|?B (f1 , f2 ) | 2
2 2
|Y (f1 ) Y (f2 ) | |Y ∗ (f3 ) |
(8)
In the present work, the 3-D and 2-D plot of auto-bicoherence of floating potential fluctuation is shown in Fig. 11(a) and (b) . The time-domain window to be applied to each data segment is Hanning window. The used samples per segment are 1000 considering 50 points as overlapping points. It is seen from Fig. 11(a) and (b) that a strong nonlinear coupling among the floating potential fluctuations exists in the lowfrequency range about 0–15 kHz. But at higher frequency range, the nonlinear coupling among the fluctuating quantities is not significant. A detail studies on nonlinear coupling among the edge floating potential and density fluctuation using bispectral analysis are under progress which will be reported soon. The horizontal plasma displacement has been studied during these MHD activities. The horizontal plasma displacement for the entire discharge duration is shown in Fig. 12(a) for plasma shot 7799. The plasma column is normally required to be held at a stationary position for the above arguments to be valid. In-vessel flux loop and magnetic probes have been used to measure the horizontal plasma displacement during tokamak discharge. It is seen that initially plasma is produced almost at the centre and as the plasma
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
7
the different plasma turbulence mechanism. Some irregular fluctuations both in floating potential and ion saturation current have been observed during high MHD activity. During the high MHD activity, the standard deviation of the floating potential is found to be around 65% (for ion saturation ∼60%), which is much higher than the standard deviation of floating potential (∼10%) and ion saturation (5%) at low MHD region. Recent experimental observation shows that the electrostatic turbulence is modulated by Mirnov oscillations i.e. MHD activity at SST-1 tokamak. The high MHD activity synchronizes with the electrostatic fluctuation during SST-1 plasma discharge. It is found that the MHD activity modifies the radial electric field significantly. It is observed that the plasma turbulence is dominated by low-frequency and long-wavelength fluctuations. The cross power spectra show three distinct peaks around zero frequency which is associated with the zonal flow. The peak around 6 kHz is associated with the MHD mode and a broad band fluctuation above 15 kHz is associated with drift wave. Some large-scale coherent structures observed in the recent experiments, which indicate the long-distance cross correlation in the poloidal direction. These observations would serve as critical inputs towards the improvement of confinement characteristics of SST-1 plasma column. References
Fig. 12. (a) The horizontal plasma position during plasma discharge; (b) Enlarge view of horizontal plasma position during low and high MHD.
current increases, the plasma slowly moves toward the inboard side at SST-1 tokamak. While the plasma current shows almost a plateau nature, the horizontal plasma displacement is unchanged. For clear representation, the enlarged view of horizontal plasma displacement during low and high MHD is shown separately in Fig. 12(b). It is seen that the horizontal plasma position almost remains same during the MHD activity at SST-1 tokamak. Only ∼2.0 mm horizontal displacement during the MHD activity is observed at SST-1 tokamak discharge, which is within the experimental error bar. After the MHD activity, the plasma moves quickly towards the outboard side. Similar behaviour of horizontal plasma displacement have also been observed for shot no 7873. Thus, the above analyses have been carried out when the plasma column remains unchanged including its equilibrium characteristics. 4. Conclusions In the recent observations, some spontaneously generated MHD activities have been observed at SST-1 tokamak plasmas. The experimental results strongly validates the electrostatic fluctuation induced the plasma transport properties are associated with
[1] G.D. Conway, Plasma Phys. Control. Fusion 50 (2008) 124026. [2] W. Horton, Rev. Mod. Phys. 71 (1999) 735. [3] Z.O. Guimaraes-Filho, G.Z. dos Santos, I.L. Lima, R.L. Caldas, Nascimento I.C. Viana, Yu. K. Kuznetsov, J. Phys.: Conf. Series 246 (2010) 012014. [4] C. Hidalgo, M. A. Pedrosa, B. Goncalves, New J. Phys., (2002) 4 (51). 1–51.12. [5] S. Mazur, P. Nordlund, J.H. Brzozowski, J.R. Drake, K.D. Zastrow, Nucl. Fusion 34 (1994) 427. [6] P.R. Brunsell, Y. Maejima, Y. Vagi, Y. Hirano, T. Shimada, Phys. Plasmas 1 (1994) 2297. [7] B.J. Ding, G.L. Kuang, J.F. Shan, G.S. Xu, M. Song, B.N. Wan, Y.P. Zhao, J.G. Li, Plasma Phys. Control. Fusion 46 (2004) 1467–1478. [8] S. Coda, M. Porkolab, K.H. Burrell, Phys. Rev. Lett. 86 (2001) 4835. [9] D.F. Kong, et al., Nucl. Fusion 53 (2013) 123006. [10] G.S. Xu, B.N. Wan, M. Song, J. Li, Phys. Rev. Lett. 91 (19) (2003) 125001. [11] I.C. Nascimento, et al., Nucl. Fusion 47 (2007) 1570–1576. [12] F. Wagner, et al., Phys. Rev. Lett. 49 (1982) 1408. [13] I.C. Nascimento, et al., Nucl. Fusion 45 (2005) 796. [14] K.H. Finken, T.E. Evans, D. Reiter, K.H. Spatschek, W. Suttrop, Nucl. Fusion 48 (2008) 024001. [15] M.Z. Tokar, T.E. Evans, R. Singh, B. Unterberg, Phys. Plasmas 15 (2008) 072515. [16] M.J. Schaffer, J.E. Menard, M.P. Aldan, J.M. Bialek, T.E. Evans, R.A. Moyer, Nucl. Fusion 48 (2008) 024004. [17] B.A. Carreras, et al., Phys. Plasmas 7 (2000) 3278. [18] B.A. Carreras, et al., Phys. Plasmas 5 (1998) 3632. [19] B.A. Carreras, et al., Phys. Plasmas 6 (1999) 1885. [20] B.A. Carreras, et al., Phys. Rev. Lett. 80 (1998) 4438. [21] G.S. Xu, B.N. Wan, W. Zhang, Q.W. Yang, L. Wang, Y.Z. Wen, Phys. Plasmas 13 (2006) 102509. [22] P.H. Diamond, T.S. Hahm, Phys. Plasmas 2 (1995) 3640. [23] C.X. Yu, M. Gilmore, W.A. Peebles, T.L. Rhodes, Phys. Plasmas 10 (2003) 2772. [24] Y.C. Saxena, S.S.T.-1 Team, Nucl. Fusion 40 (6) (2000) 1069. [25] J. Dhongde, M. Bhandarkar, S. Pradhan, S. Kumar, S.S.T.-1 Team, Fusion Eng. Des. 108 (2016) 77–80. [26] P.C. Stangeby, Plasma Phys. Control. Fusion 37 (1995) 1031–1037. [27] R.A. Pitts, Plasma Phys. Control. Fusion 32 (1990) 1237–1248. [28] G.F. Matthews, Plasma Phys. Cotntrol. Fusion 36 (1994) 1595–1628. [29] M.V.A.P. Heller, R.M. Castro, Z.A. Brasılio, I.L. Caldas, R.P. Silva, Nucl. Fusion 35 (1995) 59. [30] P. Devynck, et al., Plasma Phys. Control. Fusion 47 (2005) 269. [31] M.V.A.P. Heller, I.L. Caldas, A.A. Ferreira, E.A.O. Saettone, A. Vannucci, J. Plas. Phys. 73 (2007) 295. [32] Z.O. Guimaraes-Filho, I.L. Caldas, R.L. Viana, M.V.A.P. Heller, I.C. Nascimento, Y.K. Kuznetsov, R.D. Bengtson, Phys. Plasmas 15 (2008) 062501. [33] J.S. Kim, D.H. Edgell, J.M. Greene, E.J. Strait, M.S. Chance, Plasma Phys. Control. Fusion 41 (1999) 1399–1420. [34] M. Dreval, C. Xiao, D. Trembach, A. Hirose, S. Elgriw, A. Pant, D. Rohraff, T. Niu, Plasma Phys. Control. Fusion 50 (2008) 095014. [35] V. Rozhansky E. Kaveeva and M. Tendler, 35th EPS Conf on Plasma Phys., Hersonissos, (9–13 2008) Vol. 32D, P-5.020. [36] L.G. Askinazi, V.E. Golant, V.A. Kornev, S.V. Lebedev, A.S. Tukachinsky, M.I. Vildjunas, N.A. Zhubr, Plasma Phys. Control. Fusion 48 (2006) A85–A91. [37] J.A. Krommes, M. Ottaviani, Phys. Plasmas 6 (1999) 3731. [38] V. Antoni, V. Carbone, R. Cavazzana, et al., Phys. Rev. Lett. 87 (2001) 045001.
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS
8
B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
[39] M. Vittoria, A.P. Heller, R.M. Castro, I.L. Caldas, Zoezer A. Brasilio, Ruy P. da Silva, T.B.R.-1 Team, Braz. J. Phys. 23 (3) (1993) 273. [40] A. Fujisawa, et al., Phys. Rev. Lett. 93 (2004) 165002. [41] S. Coda, M. Porkolab, K.H. Burrell, Phys. Rev. Lett. 86 (2001) 4835. [42] G.W. Hammett, et al., Plasma Phys. Controlled Fusion 35 (1993) 973. [43] G.R. McKee, R.J. Fonck, M. Jakubowski, K.H. Burrell, K. Hallatschek, R.A. Moyer, D.L. Rudakov, W. Nevins, G.D. Porter, P. Schoch, X. Xu, Phys. Plasmas 10 (2003) 1712.
[44] [45] [46] [47]
Y. Nagashima, et al., Plasma Phys. Control. Fusion 49 (2007) 1611–1625. Y. Nagashima, et al., Plasma Phys. Control. Fusion 48 (2006) A377–A386. G.S. Xu, B.N. Wan, M. Song, Phys. Plasmas 9 (1) (2002) 150. E.J. Powers, IEEE Trans. Plasma Sci. PS-7 (2) (1979) 120.
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
ARTICLE IN PRESS
FUSION-9007; No. of Pages 8
Fusion Engineering and Design xxx (2017) xxx–xxx
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma B. Kakati ∗ , S. Pradhan ∗ , J. Dhongde, P. Semwal, K. Yohan, M. Banaudha, SST-1 team Institute for Plasma Research, Bhat, Gandhinagar 382 428, Gujarat, India
h i g h l i g h t s • Anomalous particle transport during the high MHD activity at SST-1. • Electrostatic turbulence is modulated by MHD activity at SST-1 tokamak. • Edge floating potential fluctuations shows poloidal long-range cross correlation.
a r t i c l e
i n f o
Article history: Received 9 July 2016 Received in revised form 8 November 2016 Accepted 28 December 2016 Available online xxx Keywords: Tokamak plasma MHD Plasma confinement Particle transport Plasma diagnostics
a b s t r a c t Plasma edge transport characteristics are known to be heavily influenced by the edge fluctuation induced turbulences. These characteristics play a critical role towards the confinement of plasma column in a Tokamak. The edge magnetic fluctuations and its subsequent effect on electrostatic fluctuations have been experimentally investigated for the first time at the edge of the SST-1 plasma column. This paper reports the correlations that exist and is experimentally been observed between the edge densities and floating potential fluctuations with the magnetic fluctuations. The edge density and floating potential fluctuations have been measured with the help of poloidally separated Langmuir probes, whereas the magnetic fluctuations have been measured with poloidally spaced Mirnov coils. Increase in magnetic fluctuations associated with enhanced MHD activities has been found to increase the floating potential and ion saturation current. These observations indicate electrostatic turbulence getting influenced with the MHD activities and reveal the edge anomalous particle transport during SST-1 tokamak discharge. Large-scale coherent structures have been observed in the floating potential fluctuations, indicating longdistance cross correlation in the poloidal directions. From bispectral analysis, a strong nonlinear coupling among the floating potential fluctuations is observed in the low-frequency range about 0–15 kHz. © 2017 Elsevier B.V. All rights reserved.
1. Introduction In general, the plasma turbulence refers to the microscopic random fluctuations in particle density, temperature, potential and magnetic field. These fluctuations are generally driven by radial gradients that exist in the plasma density and temperature [1]. Plasma turbulence and transport properties, especially at the edge region are known to influence the overall plasma confinement characteristics in a tokamak. Turbulence, in fact is one of the primary reason attributed towards the anomalous particle and energy transport in a tokamak [1–4]. The magnetic and electrostatic fluctuations
∗ Corresponding authors. E-mail addresses: [email protected] (B. Kakati), [email protected] (S. Pradhan).
that lead to magnetic and electrostatic turbulence at the tokamak edge are known to drive the plasma turbulences [5,6]. These magnetic fluctuations further reduce the plasma performances. They limit relevant parameters like poloidal beta due to the change of plasma profiles [7]. The magnetic transport due to magnetic fluctuations is not large enough as compared to electrostatic transport in tokamak plasma. The edge plasma transport is primarily driven by electrostatic fluctuations [7]. Several efforts have been put towards understanding the plasma transport and turbulence behaviour in the last decades in tokamak plasmas. Presence of large-scale magneto-hydrodynamic (MHD) instabilities and small-scale turbulence are generally present at a sufficient to result in the anomalous particle transport in tokamak devices [8]. In presence of strong toroidal magnetic field, the timevarying radial electric field drives the E x B drift flows in poloidal direction. Such plasma flow is termed as zonal flow (ZF). In the
http://dx.doi.org/10.1016/j.fusengdes.2016.12.041 0920-3796/© 2017 Elsevier B.V. All rights reserved.
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS
2
B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
context of the tokamak configuration, the ZFs are radially localized potential perturbations which are toroidally and poloidally symmetric. Such plasma flows are generated due to the radial turbulent transport of poloidal momentum, i.e. the Reynolds stress [9]. In toroidal confined tokamak plasmas, two types of ZFs have been observed, i.e. a low-frequency zonal flow (LFZF) with nearly zero frequency and a geodesic acoustic mode (GAM) with higher frequency [9]. The plasma turbulence is expected to be in a selforganized state mediated by zonal flows [10]. The MHD phenomenon is another important topic for fusion community. MHD instabilities are considered as dangerous phenomena as they lead to destruction of magnetic surfaces and termination of plasma discharge. The MHD influences the sheared radial electric field within the plasma column. Depending on the strength of the MHD behaviour, the magnetic oscillations (MHD activity) change the plasma density, electron temperature and plasma potentials which in turn influence the electrostatic fluctuations [3]. The anomalous transports, together with MHD instabilities control the plasma confinement and overall plasma performance. It is observed and reported by different researcher that the radial electric field suppress the MHD activity which in turn improves the plasma confinement in tokamak [11–13]. The correlation between the magnetic oscillations and electrostatic turbulence is not significant [1] in many tokamak devices. However, the correlation between the magnetic oscillations and the electrostatic turbulence turns to be relevant in new highconfinement regimes achieved in tokamaks [14–16]. The studies on reversed field pinch (RFP) show that the electrostatic fluctuations are influenced by the magnetic fluctuations [5,6]. B. J. Ding et al. [7] have reported the edge density and potential fluctuations having high correlation with magnetic fluctuations; and the resulting mode spectra being similar to those of magnetic field fluctuations. These strongly indicate that, the electrostatic fluctuations are primarily caused by electromagnetic turbulence. In recent years, particular attention has been paid to the coherent structures in plasma turbulences. In fusion and non-fusion plasmas, the transport processes mostly contains the short range correlations, rather than long-range correlations. Recently, several authors [17–20] have reported the observations of long-range correlation and self-similarity in plasma edge fluctuations in the so called “mesoscale” range. These are larger than turbulence decorrelation time and plasma confinement time in many tokamak devices [17–20]. It has also been reported by many authors that the presence of the long-range correlation and self-similarity can be easily understood if the self-organized criticality (SOC) dynamics play a dominant role in the plasma transport processes [17–22]. Different statistical analysis techniques have been extended to identify the existence of long range correlations and self-similarity in plasma fluctuation [23]. G. S. Xu et al. [10] observed the poloidal long-distance correlations and have reported about 40% coherence at the poloidal distance (31.4 mm) that is nearly three times of the turbulence decorrelation length at HT-7 tokamak. Despite of the huge efforts on these aspects in the last decades, many features of plasma transports are still to be understood. Thus, more careful investigations are still necessary for better controlling of plasma confinement in tokamaks. Recently, the edge density and potential fluctuations and their correlation with magnetic fluctuations have been studied at Steadystate Superconducting Tokamak-1 (SST-1) tokamak. SST-1 is a medium sized tokamak having large aspect ratio with a major radius of 1.1 m and a plasma minor radius of 0.2 m with elongation of 1.7–1.9 and triangularity of 0.5–0.7 [24]. The recent experimental observations show a high correlation of edge density and potential fluctuations with that of the magnetic fluctuations. The cross correlation and coherence between the electrostatic fluctuations measured at different poloidal locations have been carried
Fig. 1. (Colour online) (a) Top view of SST-1 tokamak and (b) schematic of Langmuir probe arrangement.
out under this investigation. These events have also been studied with synchronized MHD activities as observed experimentally in SST-1 early plasmas. The remaining sections of this paper have been organized as follows. In Section 2, the experimental set-up, methodology and the diagnostic tools are described in detail. Section 3 summarizes the results and their physical interpretations. Finally, the present work has been concluded in Section 4. 2. Experimental assembly and methodology The present studies have been carried out in SST-1 tokamak over a large number of repeatable shots under identical plasma conditions. However, under this investigation two representative plasma shots (shot no 7799 and 7873) have been discussed. The top view of SST-1 tokamak and schematic of Langmuir probe arrangement is shown in Fig. 1(a) and (b). The SST-1 tokamak is operated in limiter configuration with a central field of 1.5 T. Graphite tiles have a density of 1.82 g/cm3 and a porosity of about 9.00% is used as limiter materials. Sixteen (16) toroidal field (TF) superconducting coils are used to produce the required toroidal field. A pair of vertical field coils placed symmetric to Z = 0 plane is used to provide the necessary equilibrium field to the plasma column formed [23]. In SST-1, the plasma is initiated with the help of ECH preionization, employing a 42 GHz Gyrotron in fundamental mode followed by the Ohmic transformer [25]. At present, plasma currents are produced in excess of 100 KA extending in durations up to ∼500 m s in a repeatable fashion. The plasma is confined within the two poloidal limiters. In the present report, two identical plasma shots (shot no 7799 and 7873) in terms of plasma duration and current have been chosen to study the edge parameters and its correlation with MHD. The plasma current reaches a maximum value
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
3
Fig. 2. Time evolutions of plasma discharge (a) for plasma shot no 7799, (b) for plasma shot no 7873.
of 86 kA with plasma duration of ∼280 ms for shot 7799 and 90 kA with plasma duration of ∼280 ms for shot 7873. The magnetic fluctuations are detected using eight (8) discrete in-vessel Mirnov coils. The corresponding electrostatic and density fluctuation generated at the plasma edge due to the MHD activities are detected using a set of Langmuir probes. The probes are mounted at 5.0 mm behind the outboard limiter to measure the edge plasma density, electron temperature, fluctuation of edge density in terms of ion saturation current and fluctuation of floating potential. The probes are arranged in poloidal direction at the same magnetic flux tube. The Langmuir probe marked with LP1 and LP3 are single cylindrical Langmuir probe with a tungsten tip having dia 1.0 mm and length 3.0 mm whereas the middle probe LP2 consist of three cylindrical tips having dia 1.0 mm and length 3.0 mm. The distance between the LP1 and LP2 (central tip) or LP2 (central tip) and LP3 is 80.0 mm. The distance between the each probe tip of LP2 is 4.0 mm. The probe tip separations are much larger than the Debye length (correspondingly its sheath thickness) of edge plasma parameters. At SST-1, the edge density and temperature are calculated from I–V characteristics of the Langmuir probe for the duration where the plasma current shows almost plateau nature. The plasma density is calculated from the ion saturation current whereas the electron temperature is calculated below the floating potential of the I–V characteristics using the procedure as adopted by different researchers [26–28]. The plasma density is of the order of 1016 /m3 where as the electron temperature is ∼10 eV for the shot no 7799 and 7873. Langmuir probe and Mirnov coil data are digitized at 100 kilosamples per second respectively. The Langmuir probe data are sampled with 16-bit resolution whereas Mirnov coil data are sampled with 14-bit resolution using a multichannel digitizer.
3. Experimental observation and discussion The observations are carried out on the SST-1 tokamak with two circular poloidal limiters, which are toroidally separated by 180◦ . The time evolution of plasma discharge for shot no 7799 and 7873 are shown in Fig. 2(a) and (b). The plasma current grows rapidly at the initial stage and shows an almost plateau nature for a short duration before it start decaying. Some clearly visible MHD activities during the plasma discharge are observed from Mirnov signals in both the shot. Initially, the MHD perturbations are occurred at the plasma core and rapidly propagate outwards. In shot no 7799 [shown in Fig. 2(a)], it is
observed that the high MHD activity grows at different stages during the plasma discharge. For shot no 7799, the high MHD activities are found between 105–155 ms, 205–213 ms and 253–282 ms where the fluctuation of the Mirnov signals (i.e. magnetic fluctuations) is large compared to that in other region. The effect of MHD activity for discharge duration 105–155 ms is very prominent. Thus, the effect on edge floating potential fluctuation and ion saturation fluctuation for the above duration is only addressed in this report. It is seen that the magnetic fluctuations are diminished with an abrupt fluctuation at the end. The abrupt magnetic fluctuation leads to a sharp fall of plasma current at a rate of 2.4 MA/s. After 155 ms, the magnetic oscillation reduces and the plasma current decays gradually at a slower rate of 0.3 MA/s till the next MHD activity. The floating potential and ion saturation current fluctuation shows almost identical behaviour with magnetic fluctuation. Some irregular fluctuations both in floating potential and ion saturation current are observed during high MHD activity. The standard deviation of the floating potential is found to be around 65% for LP2 (for ion saturation ∼60%) during the high MHD activity which is much higher than the standard deviation of floating potential (∼10%) and ion saturation (5%) at low MHD. It is found that the amplitude of ion saturation current (i.e. plasma density) fluctuation is slightly lower as compared to the floating potential fluctuation. The edge density fluctuation is directly proportional to the ion saturation current fluctuation (the temperature fluctuations are not taken into account and considered as negligible) [3,21]. Thus, from Fig. 2(a) and (b), it is clear that the edge density fluctuation also shows the identical behaviour during high and low MHD activity. The increase in magnetic fluctuation increases the floating potential and ion saturation current fluctuation during high MHD activity. It indicates an anomalous particle transport during the high MHD activities. The similar behaviour in magnetic and electrostatics fluctuation indicates that the electrostatic turbulence is modulated by Mirnov oscillations i.e. MHD activity at SST-1 tokamak. Such kind of electrostatics fluctuation driven by magnetic fluctuation is observed by many authors during the tokamak discharge [29–32]. In the present manuscript, the edge turbulence behaviour is mainly described on basis of the floating potential fluctuations only. For clear representation, the enlarged view of electrostatics fluctuation during low and high MHD for shot no 7799 is shown separately in Fig. 3. The discharge duration between 90 and 100 ms is considered as low MHD region where magnetic fluctuation is com-
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS
4
B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
Fig. 3. Floating potential fluctuations for shot no 7799.
paratively low. On the other hand, the discharge duration between 110 and 120 ms is considered as high MHD region where, magnetic fluctuation is comparatively high. Similar behaviour is observed for shot no 7873. For shot no 7873, it is observed that the magnetic oscillations starts increasing at t = 108 ms and stays high until t = 160 ms. The high MHD activity significantly alters the floating potential for the above plasma discharge duration. The normalized volume average beta for shot no 7799 is shown in Fig. 4. The volume average beta is calculated from diamagnetic loop and compensating loop data. It shows that the volume average beta is almost constant for the duration of ∼90–160 ms when the plasma current shows almost plateau nature. A power spectral analysis is carried out to quantify several statistical properties of the turbulent fluctuations at the plasma edge. The spectrogram of the Mirnov signal and floating potentials for shot no 7799 and 7873 are shown in Figs. 5 and 6. In the spectrograms, the oscillation frequencies are plotted against the discharge duration and the corresponding power spectral densities (in arbitrary units) are plotted in a colour scale. The spectrogram is constructed using MATLAB by considering the window length and DFT (discrete Fourier Transform) length of 128 points for a signal duration of 350 ms with a sampling frequency of 100 kHz. The total number of used sample points is 35, 000. The spectrogram for Mirnov oscillations is shown in Fig. 5(a) for shot no
Fig. 4. The volume average beta (normailized) during SST-1 tokamk discharge.
Fig. 5. (Colour online) Spectrogram for shot no 7799 (a) Mirnov signal, (b) Floating potential.
7799 where the periods of magnetic activity associated with peaks of the power spectral density is clearly visible. It is seen that the intense burst on magnetic oscillation is started at ∼105 ms with a sharp line and it extends up to ∼158 ms with a dominant frequency at ∼6 kHz. It has at least two overtones corresponding to higher harmonics of the dominant frequency. The spectrogram of floating potential fluctuation (shown in Fig. 5(b)) is also shown similar behaviour with magnetic fluctuation. An intense burst on floating potential fluctuation with a sharp line is appeared almost at the same discharge duration with a dominant frequency at ∼6 kHz. For shot no 7873 (shown in Fig. 6), the intense burst with a sharp line in the spectrogram of magnetic fluctuation have appeared for the discharge duration of 108–160 ms. Similar behaviour of electrostatic fluctuations have been observed for the identical discharge duration [32]. It indicates that the high MHD activity synchronizes with the electrostatic fluctuation during SST-1 plasma discharge. Such synchronization between the electrostatic and magnetic fluctuation had also been observed at TCABR tokomak during the plasma operation [3,32].
Fig. 6. (Colour online) Spectrogram for shot no 7873 (a) Mirnov signal, (b) Floating potential.
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
5
Fig. 7. The poloidal mode structure for shot no 7799.
In our present observation, the time evolution of poloidal modes associated with the MHD activity is evaluated using singular value decomposition (SVD) technique. The SVD is applied to tokamak Mirnov signals to identify MHD activities in the plasma [33]. It is observed in our recent observations that the poloidal MHD mode changes with the MHD growth. From the temporal evolution of mode structure, the m = 1–3 are observed as poloidal MHD modes for plasma shot 7799 and 7873. In both the plasma shot, m = 2 is found as a dominant poloidal MHD modes. The spatial structure represented by polar plot for the duration of 144–146 ms is shown in Fig. 7 which shows clearly m = 3 mode associated with the MHD activity. The role of MHD activity on radial electric field is studied during the plasma discharge. The radial electric field influences the plasma parallel flow through the Er × B force. A negative electric field clearly generates a force component anti-parallel to the plasma current [34]. The floating potentials measured by Langmuir probes are used to calculate the radial electric field. The time trace of Er = −∇ Vf (Assuming the impact of ∇ Te is negligible) during the MHD activity is studied for both the plasma shot. In SST-1, a negative radial electric field is observed during the tokamak discharge. It is observed that the MHD activity dramatically changes the radial electric field profile (see Fig. 8). It is observed that the high MHD activity which leads to a high magnetic fluctuation at the end changes the radial electric field from negative to positive value. V. Rozhansky et al. [35,36] reported such observations on radial electric field at TUMAN–3 M tokamak during the onset of MHD activity. Statistical analysis techniques are used by many authors to study the existence of long range correlations and self-similarity in edge plasma fluctuations [21,23,37,38]. The two-point cross correlation method is used in our present study to investigate the
Fig. 8. Radial electric field profile during MHD activity for plasma shot 7799.
Fig. 9. (a) Cross power spectrum and (b) coherence spectrum for shot no 7799.
correlations between two fluctuating signals in poloidal direction. The distance between the two probes LP1 and LP2, which are used to measure the floating potential signal is around 8.0 cm. The distance between the probes is much larger than the turbulence decorrelation length (close to 1 cm) [21]. The edge floating potentials measured by the Langmuir probe for both the plasma shot are used to study the cross correlation and coherence. The Langmuir probes are radially located at the same distance from the core of the plasma. The cross power spectrum of two time varying signal X(t) and Y(t) can be written as [39]; PXY = |PXY (f )|eiXY (f )
(1)
Where |PXY (f )| is the cross-amplitude spectrum which is given by PXY = X(f )Y (f )
(2)
Here X(f) and Y(f) are the Fast-Fourier-Transform (FFT) of two time varying signal X(t) and Y(t). The XY (f ) is the phase spectrum which is given by XY (f ) = Y (f ) − X (f )
(3)
The coherence spectrum measures the degree of mutua1 coherence between two time varying signals. The coherence spectrum is defined as follows: CXY (f ) =
|PXY (f ) | [PXX (f ) PYY (f )]
1⁄2
(4)
Here, PXX and PYY are the auto power spectra of the signals. In the present work, the cross power spectrums of floating potential signals are generated with the help of MATLAB and digitized for total 32768 numbers of FFT points at 100 kHz sampling frequency considering 50 points as non-overlapping points. The cross power spectrum and coherence spectrum of the two signals are depicted in Fig. 9(a) and (b) for shot no 7799 respectively. The identical cross power and coherence spectrum are observed for shot no 7873 as well. From the auto power spectra of the signals, it is found that the fluctuation levels of both the signals are close to each other. It confirms that the probe tips are approximately located in the same flux surface. In the low frequency range below 10 kHz, two peaks are observed in cross power and coherence spectrum (see Fig. 9). The peak around 6 kHz is associated with the MHD mode, it exhibits strong long-distance correlation and coherence. The MHD modes belong to the macroinstability that normally has a long poloidal wavelength. The associated perturbations are generated at the
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS
6
B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
Fig. 10. The poloidal wave number spectrum.
core of the plasma, propagating outward. Almost 40% coherence between the floating potential signals is observed in this frequency range in our case which is matching with the result, observed by G. S. Xu et al. [10] at HT-7 tokamak. Another peak is observed at the low frequency region, which is close to zero frequency and it quickly decayed. The similar zero-frequency peak in the potential fluctuations was also detected in HT-7 superconducting tokamak [21] and in a helical device [40]. The zero-frequency peak was considered to be associated with the zonal flows. For plasma shot 7799 (shown in Fig. 9), a broad band fluctuation, peaking at ∼35 kHz is observed above 15 kHz. G. S. Xu et al. [21] reported that such high frequency fluctuation have been generally associated with the drift-wave of the plasma. The zonal flows are believed to be a general feature of toroidal turbulence [41,42]. The existences of zonal flows can be obtained from the measurements of edge density and potential fluctuations. Phase contrast imaging measurements have observed a turbulent structure in the density field with a finite radial wavelength, and k ≈ 0, as predicted by theory and it indicating at the existence of zonal flows [43]. In order to support the identification of zonal flow, the poloidal wave number has been estimated, which have been shown in Fig. 10. The poloidal wave number is estimated using the following relation k (f ) =
xy (f )
(5)
Where xy is the phase difference between signal x and y and is the poloidal distance between x and y. It is seen that the poloidal wave number in the low frequency region is close to zero. It supports the possibility of presence of some low-frequency large-scale potential structures [21]. Such low frequency peak (∼0 Hz) in the potential fluctuations with k ≈ 0 is detected in different devices, which is considered to be associated with the zonal flows. Thus, the zero frequency peak is considered as zonal flow in our present work. Bispectral analysis is a powerful signal processing technique to study the nonlinear interactions among the fluctuating quantities. It has been applied to various plasma experiments to study the nonlinear interaction [44–47]. To study the nonlinear coupling, bispectral analysis of the edge floating potential fluctuation data is carried out in the present work. The bispectrum is the third order cumulant spectrum and is defined as Bˆ (f1 , f2 ) = Y (f1 ) Y (f2 ) Y ∗ (f3 )
(6)
Fig. 11. (Colour online) (a) 3-D plot and (b) 2-D plot of auto-bicoherence of edge floating potential fluctuation for shot no 7799.
where Y(f) is the Fourier component of the observed time series y(t), f is the frequency, and f3 = f1 ± f2 . The asterisk indicates the complex conjugate. Such bispectrum, composed of the Fourier components of the same time-series, is referred to as auto-bispectrum, whereas the bispectrum composed of different time series is referred to as cross-bispectrum. The cross-bispectrum is defined as Bˆ (f1 , f2 ) = X (f1 ) Y (f2 ) Z ∗ (f3 )
(7)
where X(f) and Z(f) are the Fourier components of the observed time-series x(t) and z(t), respectively. Qualitatively, the occurrence of three-wave interaction is investigated by measuring the squared bicoherence which is defined as bˆ 2 (f1 , f2 ) =
|?B (f1 , f2 ) | 2
2 2
|Y (f1 ) Y (f2 ) | |Y ∗ (f3 ) |
(8)
In the present work, the 3-D and 2-D plot of auto-bicoherence of floating potential fluctuation is shown in Fig. 11(a) and (b) . The time-domain window to be applied to each data segment is Hanning window. The used samples per segment are 1000 considering 50 points as overlapping points. It is seen from Fig. 11(a) and (b) that a strong nonlinear coupling among the floating potential fluctuations exists in the lowfrequency range about 0–15 kHz. But at higher frequency range, the nonlinear coupling among the fluctuating quantities is not significant. A detail studies on nonlinear coupling among the edge floating potential and density fluctuation using bispectral analysis are under progress which will be reported soon. The horizontal plasma displacement has been studied during these MHD activities. The horizontal plasma displacement for the entire discharge duration is shown in Fig. 12(a) for plasma shot 7799. The plasma column is normally required to be held at a stationary position for the above arguments to be valid. In-vessel flux loop and magnetic probes have been used to measure the horizontal plasma displacement during tokamak discharge. It is seen that initially plasma is produced almost at the centre and as the plasma
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
7
the different plasma turbulence mechanism. Some irregular fluctuations both in floating potential and ion saturation current have been observed during high MHD activity. During the high MHD activity, the standard deviation of the floating potential is found to be around 65% (for ion saturation ∼60%), which is much higher than the standard deviation of floating potential (∼10%) and ion saturation (5%) at low MHD region. Recent experimental observation shows that the electrostatic turbulence is modulated by Mirnov oscillations i.e. MHD activity at SST-1 tokamak. The high MHD activity synchronizes with the electrostatic fluctuation during SST-1 plasma discharge. It is found that the MHD activity modifies the radial electric field significantly. It is observed that the plasma turbulence is dominated by low-frequency and long-wavelength fluctuations. The cross power spectra show three distinct peaks around zero frequency which is associated with the zonal flow. The peak around 6 kHz is associated with the MHD mode and a broad band fluctuation above 15 kHz is associated with drift wave. Some large-scale coherent structures observed in the recent experiments, which indicate the long-distance cross correlation in the poloidal direction. These observations would serve as critical inputs towards the improvement of confinement characteristics of SST-1 plasma column. References
Fig. 12. (a) The horizontal plasma position during plasma discharge; (b) Enlarge view of horizontal plasma position during low and high MHD.
current increases, the plasma slowly moves toward the inboard side at SST-1 tokamak. While the plasma current shows almost a plateau nature, the horizontal plasma displacement is unchanged. For clear representation, the enlarged view of horizontal plasma displacement during low and high MHD is shown separately in Fig. 12(b). It is seen that the horizontal plasma position almost remains same during the MHD activity at SST-1 tokamak. Only ∼2.0 mm horizontal displacement during the MHD activity is observed at SST-1 tokamak discharge, which is within the experimental error bar. After the MHD activity, the plasma moves quickly towards the outboard side. Similar behaviour of horizontal plasma displacement have also been observed for shot no 7873. Thus, the above analyses have been carried out when the plasma column remains unchanged including its equilibrium characteristics. 4. Conclusions In the recent observations, some spontaneously generated MHD activities have been observed at SST-1 tokamak plasmas. The experimental results strongly validates the electrostatic fluctuation induced the plasma transport properties are associated with
[1] G.D. Conway, Plasma Phys. Control. Fusion 50 (2008) 124026. [2] W. Horton, Rev. Mod. Phys. 71 (1999) 735. [3] Z.O. Guimaraes-Filho, G.Z. dos Santos, I.L. Lima, R.L. Caldas, Nascimento I.C. Viana, Yu. K. Kuznetsov, J. Phys.: Conf. Series 246 (2010) 012014. [4] C. Hidalgo, M. A. Pedrosa, B. Goncalves, New J. Phys., (2002) 4 (51). 1–51.12. [5] S. Mazur, P. Nordlund, J.H. Brzozowski, J.R. Drake, K.D. Zastrow, Nucl. Fusion 34 (1994) 427. [6] P.R. Brunsell, Y. Maejima, Y. Vagi, Y. Hirano, T. Shimada, Phys. Plasmas 1 (1994) 2297. [7] B.J. Ding, G.L. Kuang, J.F. Shan, G.S. Xu, M. Song, B.N. Wan, Y.P. Zhao, J.G. Li, Plasma Phys. Control. Fusion 46 (2004) 1467–1478. [8] S. Coda, M. Porkolab, K.H. Burrell, Phys. Rev. Lett. 86 (2001) 4835. [9] D.F. Kong, et al., Nucl. Fusion 53 (2013) 123006. [10] G.S. Xu, B.N. Wan, M. Song, J. Li, Phys. Rev. Lett. 91 (19) (2003) 125001. [11] I.C. Nascimento, et al., Nucl. Fusion 47 (2007) 1570–1576. [12] F. Wagner, et al., Phys. Rev. Lett. 49 (1982) 1408. [13] I.C. Nascimento, et al., Nucl. Fusion 45 (2005) 796. [14] K.H. Finken, T.E. Evans, D. Reiter, K.H. Spatschek, W. Suttrop, Nucl. Fusion 48 (2008) 024001. [15] M.Z. Tokar, T.E. Evans, R. Singh, B. Unterberg, Phys. Plasmas 15 (2008) 072515. [16] M.J. Schaffer, J.E. Menard, M.P. Aldan, J.M. Bialek, T.E. Evans, R.A. Moyer, Nucl. Fusion 48 (2008) 024004. [17] B.A. Carreras, et al., Phys. Plasmas 7 (2000) 3278. [18] B.A. Carreras, et al., Phys. Plasmas 5 (1998) 3632. [19] B.A. Carreras, et al., Phys. Plasmas 6 (1999) 1885. [20] B.A. Carreras, et al., Phys. Rev. Lett. 80 (1998) 4438. [21] G.S. Xu, B.N. Wan, W. Zhang, Q.W. Yang, L. Wang, Y.Z. Wen, Phys. Plasmas 13 (2006) 102509. [22] P.H. Diamond, T.S. Hahm, Phys. Plasmas 2 (1995) 3640. [23] C.X. Yu, M. Gilmore, W.A. Peebles, T.L. Rhodes, Phys. Plasmas 10 (2003) 2772. [24] Y.C. Saxena, S.S.T.-1 Team, Nucl. Fusion 40 (6) (2000) 1069. [25] J. Dhongde, M. Bhandarkar, S. Pradhan, S. Kumar, S.S.T.-1 Team, Fusion Eng. Des. 108 (2016) 77–80. [26] P.C. Stangeby, Plasma Phys. Control. Fusion 37 (1995) 1031–1037. [27] R.A. Pitts, Plasma Phys. Control. Fusion 32 (1990) 1237–1248. [28] G.F. Matthews, Plasma Phys. Cotntrol. Fusion 36 (1994) 1595–1628. [29] M.V.A.P. Heller, R.M. Castro, Z.A. Brasılio, I.L. Caldas, R.P. Silva, Nucl. Fusion 35 (1995) 59. [30] P. Devynck, et al., Plasma Phys. Control. Fusion 47 (2005) 269. [31] M.V.A.P. Heller, I.L. Caldas, A.A. Ferreira, E.A.O. Saettone, A. Vannucci, J. Plas. Phys. 73 (2007) 295. [32] Z.O. Guimaraes-Filho, I.L. Caldas, R.L. Viana, M.V.A.P. Heller, I.C. Nascimento, Y.K. Kuznetsov, R.D. Bengtson, Phys. Plasmas 15 (2008) 062501. [33] J.S. Kim, D.H. Edgell, J.M. Greene, E.J. Strait, M.S. Chance, Plasma Phys. Control. Fusion 41 (1999) 1399–1420. [34] M. Dreval, C. Xiao, D. Trembach, A. Hirose, S. Elgriw, A. Pant, D. Rohraff, T. Niu, Plasma Phys. Control. Fusion 50 (2008) 095014. [35] V. Rozhansky E. Kaveeva and M. Tendler, 35th EPS Conf on Plasma Phys., Hersonissos, (9–13 2008) Vol. 32D, P-5.020. [36] L.G. Askinazi, V.E. Golant, V.A. Kornev, S.V. Lebedev, A.S. Tukachinsky, M.I. Vildjunas, N.A. Zhubr, Plasma Phys. Control. Fusion 48 (2006) A85–A91. [37] J.A. Krommes, M. Ottaviani, Phys. Plasmas 6 (1999) 3731. [38] V. Antoni, V. Carbone, R. Cavazzana, et al., Phys. Rev. Lett. 87 (2001) 045001.
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041
G Model FUSION-9007; No. of Pages 8
ARTICLE IN PRESS
8
B. Kakati et al. / Fusion Engineering and Design xxx (2017) xxx–xxx
[39] M. Vittoria, A.P. Heller, R.M. Castro, I.L. Caldas, Zoezer A. Brasilio, Ruy P. da Silva, T.B.R.-1 Team, Braz. J. Phys. 23 (3) (1993) 273. [40] A. Fujisawa, et al., Phys. Rev. Lett. 93 (2004) 165002. [41] S. Coda, M. Porkolab, K.H. Burrell, Phys. Rev. Lett. 86 (2001) 4835. [42] G.W. Hammett, et al., Plasma Phys. Controlled Fusion 35 (1993) 973. [43] G.R. McKee, R.J. Fonck, M. Jakubowski, K.H. Burrell, K. Hallatschek, R.A. Moyer, D.L. Rudakov, W. Nevins, G.D. Porter, P. Schoch, X. Xu, Phys. Plasmas 10 (2003) 1712.
[44] [45] [46] [47]
Y. Nagashima, et al., Plasma Phys. Control. Fusion 49 (2007) 1611–1625. Y. Nagashima, et al., Plasma Phys. Control. Fusion 48 (2006) A377–A386. G.S. Xu, B.N. Wan, M. Song, Phys. Plasmas 9 (1) (2002) 150. E.J. Powers, IEEE Trans. Plasma Sci. PS-7 (2) (1979) 120.
Please cite this article in press as: B. Kakati, et al., Edge transport and fluctuation induced turbulence characteristics in early SST-1 plasma, Fusion Eng. Des. (2017), http://dx.doi.org/10.1016/j.fusengdes.2016.12.041