- Email: [email protected]
Blob birth and propagation characteristics on the HL-2A tokamak
Journal of Nuclear Materials 415 (2011) S475–S478
Contents lists available at ScienceDirect
Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Blob birth and propagation characteristics on the HL-2A tokamak L.W. Yan 1,⇑, J. Cheng, W.Y. Hong, K.J. Zhao, J. Qian, Q.W. Yang, J.Q. Dong, X.R. Duan, Y. Liu Southwestern Institute of Physics, Chengdu, PR China
a r t i c l e
i n f o
Article history: Available online 29 October 2010
a b s t r a c t Blob birth and propagation characteristics have been investigated on the HL-2A tokamak using the novel probe combination of a radial eight-probe array and a poloidal ten-probe array toroidally separated by 210 cm. Outside of the separatrix, close zero parallel wave number along a magnetic field line was found. Inside the separatrix 4–8 mm, density gradient has a maximum and the skewness is close to zero. Blob poloidal velocity changes its direction across the separatrix, which is consistent with E B driven mechanism. Based on the significant correlation along a magnetic line, blob propagation across the separatrix in poloidal–radial plane is clearly observed with condition average. At the far SOL, blob radial velocity is 0.5–0.6 km/s, which dominates the particle loss in the SOL. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The fast radial transport in the scrape-off layer (SOL) of tokamak plasma is intermittent and convective. One of possible mechanisms for convective transport is associated with the radial movement of plasma blobs, which locate in poloidal and radial plane and extend along a magnetic field line. The convective transport can increase particle recycling, reduce divertor efficiency and lead to the high erosion of the first wall. Theoretically, it has been predicted that blobs move towards the first wall at the low field side due to E B drift, where charge separation inside blobs is driven by the gradient and curvature of magnetic field [1–3]. The blobs were observed in many experiments using Langmuir probes and fast cameras. These experiments are focused on their statistical characteristics. On the TCV tokamak, there is good agreement between the blob characteristics measured with reciprocating Langmuir probes and simulation results of 2D interchange turbulence [4]. Blob frequency reduction during L-H transition was observed with gas puff imaging in NSTX [5]. The blobs are also observed in linear and helical devices [6]. In the large plasma device (LAPD), the link between the holes inside plasma column and the blobs in the limiter shadow was observed [7]. The experiment in the linear device VINETA implied the blobs originating from quasi-coherent drift wave [8]. In the versatile toroidal facility (VTF), the dependence of blob radial velocity on the neutral particle density is reported [9]. The suppression of turbulent blob transport by a resonant magnetic perturbation is studied in TEXTOR [10]. Different
⇑ Corresponding author. Address: Southwestern Institute of Physics, Division 102, P.O. Box 432, No.3, South Section 3, Ring Road 2, Chengdu, Sichuan 610041, PR China. Tel.: +86 28 82850310; fax: +86 28 82850300. E-mail address: [email protected] (L.W. Yan). 1 Presenting author. 0022-3115/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnucmat.2010.10.032
contribution to the cross-field transport from turbulent instabilities and blobs is also analyzed in TORPEX [11]. The blob birth zone and propagation characteristics are important for understanding its dynamics. Until now, there is no report about the study with probe arrays, especially the dependence of the significant coherence along a magnetic field line, which is focused on this paper. Plasma blobs are observed to be formed just inside the separatrix, where the density gradient has a maximum and the corresponding skewness is close to zero. Based on the long-range correlation, blob propagation in poloidal–radial plane (2D) is clearly observed with condition average method. The remained parts of the paper are organized as follows. The experimental setup is described in Section 2. The experimental results are given in Section 3. The last section is for the conclusions.
2. Experimental setup The blob experiments were performed in ohmically heated deuterium discharges on HL-2A with R = 1.65 m and a = 0.4 m [12]. Main experimental parameters are Ip = 165 kA, Bt = 1.8 T, and line-averaged density ne = 1.9 1019 m3. A novel combination of a poloidal probe array with a radial one is used to study blobs. Their experimental setup is shown in Fig. 1. The first is a poloidal probe array with ten-tips localized at the position A, in which the first-tip is 2.1 cm below midplane. The second is a radial probe array with eight-tips localized at the position B, where each tip is 5.2 cm above midplane. The separation between adjacent probes is 4.0 mm. Each tip is 2.0 mm in length and 1.5 mm in diameter. The toroidal separation between array A and B is about 210 cm. There is another four-tip array at the position B besides the radial eight-tip array. Both are installed on a reciprocating probe system with inward velocity 1.0 m/s [13]. The four-tip array is used to measure local electron temperature and density. Other probes
L.W. Yan et al. / Journal of Nuclear Materials 415 (2011) S475–S478
(Is-)/σ (Is-)/σ
S476
4 2 0 -2 -4 4 2 0 -2 -4 400
Δ r=-8 mm
(a)
Δ r=-4 mm
(b)
405
-1
415
420
(c)
10
PDF
410
t (ms)
(d)
-2
10
-3
10
-4
-2
0
2
(I s -)/ σ
4 -4 -2
0
2
(I s -)/ σ
4
Fig. 2. Time evolutions of Is fluctuations normalized by its standard deviation, (Is)/r, in (a) and (b) and the corresponding semi-logarithmic PDF in (c) and (d). The radial measured positions are Dr = 8, 4 mm. The dotted line in (c) and (d) is the best gaussian fit to each PDF curve.
Fig. 1. Schematic of the Langmuir probe arrangement in HL-2A. Poloidal ten-tip array and radial eight-tip array are localized at position A and B, respectively. Their toroidal separation is 210 cm.
are for floating potential or ion saturation current with the negative based voltage of Vb 160 V. Such probe arrangement provides enough flexibility for observing blob statistical and 2D propagation characteristics based on the significant toroidal correlation. Experimental data are acquired with a frequency fs = 1 MHz and the accuracy of 12 bits. 3. Experimental results 3.1. The comparison of spectral characteristics across the separatrix Usually, the power spectrum inside the separatrix is different from that outside it. The former is routinely dominated by zonal flows, which had been widely investigated in HL-2A with Langmuir probe arrays [14–17]. Recently, the statistical characteristics of blob turbulence across separatrix were also investigated using five-tip probe array [18]. However, the long-range correlation along a magnetic field has not been investigated. The separatrix is identified by the EFIT code with an error of 5 mm. According to two-point correlation method [19], the parallel wave number inside the separatrix 8 mm in 10–150 kHz is estimated to be 6.4 104 cm1, which is so close to zero. The average wave number and its full width at half magnitude outside the separatrix 8 mm are estimated to be 8.4 104 cm1 and 4.6 103 cm1, respectively. Parallel correlation length and propagation velocity are 4.4 m and 2.2 105 m/s, respectively. The latter is higher than local ion sound speed Cs 3.8 104 m/s.
100 ms are used to estimate their PDFs. The former signal is dominated by negative burst events, named density holes, the corresponding PDF deviates to a negative value, as shown in Fig. 2c. Simulation [20] indicates that the inward propagation of density holes may be a mechanism for impurity transport. The latter has the positive burst events and their PDF becomes slightly asymmetric with a tail towards positive values, as seen in Fig. 2d. Due to the separatrix with an error of 5 mm, it is difficult to exactly determine the radial position with symmetric PDF, but our observation implies that there is a symmetric PDF position between Dr = 8 mm and Dr = 4 mm. The deviation degree from the gaussian distribution can be characterized by the skewness, which is zero for a gaussian distribution. The radial profile of the skewness for each PDF is estimated at eight radial probe positions, as shown in Fig. 3a. Each point is averaged with 100 ms data. From Dr = 8 mm to Dr = 4 mm, the skewness changes sign from negative to positive. It is an important observation that the skewness is close to zero inside the separatrix, marked by the shaded area in Fig. 3a. After the temperature fluctuation is neglected, the inverse radial scale length of density gradient is calculated with L1 n ¼ rne =ne , as shown in Fig. 3b, which has a maximum when the skewness
3.2. The blob birth zone The radial eight-tip array is used to investigate the statistical characteristics of turbulence. The probability distribution function (PDF) of ion saturation current is used to characterize the deviation from gaussian distribution. Fig. 2a and b show ion saturation current (Is) evolutions normalized by standard deviation (Is)/r at Dr = 8 mm and Dr = 4 mm, respectively. The time series with
Fig. 3. Radial profile of the skewness of a PDF (a) and the inverse radial density gradient scale length L1 ne ¼ rIs =Is (b). In the shaded region, the skewness changes its sign.
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L.W. Yan et al. / Journal of Nuclear Materials 415 (2011) S475–S478
is close to zero. This result indicates that the blob birth zone is consistent with maximum density gradient.
Fix
(b)
0
(c)
1
(d)
0
θ
d (cm)
-1
-1 -40 -20
0 20 40 -40 -20 0 20 40
Δτ (μs)
Δτ (μs)
Fig. 4. Spatiotemporal correlation functions of floating potentials at four radial positions, Dr = 5 mm (a), 5 mm (b), 15 mm (c) and 25 mm (d). The poloidal movement of blobs changes its direction across the separatrix.
Move Fit
1.0 0.8 0.6 0
1
2
3
4
5
6
Δ r (cm) Fig. 5. Radial profile of blob radial velocity estimated with the fixed and movable reference signals, denoted with squares and circles, respectively.
radial velocities have the same trend to decrease with radius. In the far SOL, the radial velocity reduces to 0.6 km/s, which is about 1%–2% of local ion sound speed.
3.4. Long-range correlation of the blob In this section, our focus is put on the maximum correlation along a field line in the SOL, though the interchange mode was detected inside the separatrix. The array A localizes at a radial position Dr 4 mm, where Dr denotes the distance between the separatrix and any tip in array A. Fig. 6 shows 2D representation of conditional average of potentials measured with radial eightprobe and poloidal ten-probe arrays. Based on the significant correlation along a field line with the toroidal separation of 210 cm, the blob 2D images are obtained for the first time with the two probe array signals through condition average. We can effectively discriminate coherent structures from incoherent turbulence dependent on preset condition, such as several times standard deviation (2.5r). Time interval of two adjacent figures is 5 ls. Two blobs appear in observation region. The first has poloidal size about 10 mm, as shown in Fig. 6a, and then it propagates with pronounced poloidal movement, as shown in Fig. 6b. Meantime, another blob appears below the first blob. In Fig. 6c, the first blob becomes weaker and the second blob enters into the observation zone. The first blob completely disappears and the second one continues to move, suggesting that the lifetime of blobs is over 15 ls, as shown in Fig. 6d. Blob propagation velocity can be estimated to be V = Dl/Dt, where Dl is the movement distance within the delay time Dt. Blob poloidal velocity is estimated as 2.0–2.8 km/s, while the radial velocity is given in Fig. 5. These results are consistent with those measured by reciprocating five-tip array [18].
Δdθ (mm)
(a)
1
θ
d (cm)
Turbulence theory predicts that density blobs propagate in the poloidal and radial directions [1]. The blob poloidal movement characteristics can be extracted from spatiotemporal correlation function with poloidal ten-tip array for homogeneous fluctuations. Used the spatiotemporal correlation function, the lifetime and spatial size of fluctuation correlation structures (blobs) are estimated with e-folding length of a peak. The slope in poloidal–temporal correlation function is relevant to poloidal velocity. Therefore, main blob parameters can be determined from the correlation function. Fig. 4 shows spatiotemporal correlation functions of floating potentials at four different radial positions. At the position Dr = 5 mm (a), the poloidal size and lifetime are estimated as 3.0 cm and 20 ls, respectively. The poloidal velocity is 1.5 km/s, which is in electron diamagnetic drift direction. At the Dr = 5 mm (b), the poloidal speed is 1.8 km/s, and propagates in ion diamagnetic drift direction. At the Dr = 15 mm (c), the spatial size and poloidal velocity decrease to about 1.0 cm and 0.6 km/s. At the Dr = 25 mm (d), the spatial size is only about 0.5 cm. In addition, ion saturation currents are measured with the same probe array. The results are similar with those of floating potentials. They indicate that the poloidal movement of blobs changes its direction across the separatrix, and then poloidal velocity gradually decreases from near SOL to far SOL, which is consistent with the previous observation of blob poloidal movement being driven by E B drift [18]. Blob radial velocity is a key parameter for understanding crossfield transport. The spatiotemporal correlation function is not suitable for estimating it because the assumption of homogeneous fluctuations is invalid in radial direction. Therefore, blob radial characteristics are extracted by cross-condition average [21]. In this experiment, the blob radial velocity is measured with the reciprocating four-probes with inward velocity of 1.0 m/s, implying radial movement of 2 mm in 2.0 ms, which is comparable with probe spatial resolution of 2 mm. Therefore, the probe distance within 2 mm can be neglected. Each time window in 2 ms is overlapped with 50% and within the window the blob radial velocities are simultaneously estimated with two different reference signals. One reference signal is from a movable probe in array B; the other is from a fixed probe in array A toroidally separated by 210 cm. The former is denoted by circles, the latter is given by triangles in Fig. 5. A peak of cross-conditional average at Ds = 0 responds to blob radial velocity. Fig. 5 shows the radial profiles of blob radial velocities in one discharge with the two reference signals. It is clear that two
Δdθ(cm)
3.3. The blob propagation characteristics
Vr (km/s)
1.2
30
(a)
(b)
(c)
(d)
20 10 30 20 10 0
-10
0
10 -10
Δ r (mm)
0
10
Δ r (mm)
Fig. 6. The 2D images of floating potential at four different delay times chosen by condition average. The time interval is 5 ls. The initial blob is inclined in 2D plane with poloidal movement.
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4. Conclusions Blob birth and propagation characteristics have been investigated in the HL-2A tokamak using a novel combination of two probe arrays toroidally separated by 210 cm. Outside the separatrix, parallel wave number along a magnetic field line is close to zero, consistent with the theoretical prediction of interchange instability. The initial blobs are formed just inside the separatrix, where the density gradient has a maximum and the skewness is close to zero. Blob poloidal velocity changes its direction across the separatrix, and blob radial velocity is comparable using movable and fixed probe reference signals, which tends to decrease with the distance away from the separatrix. Based on the significant correlation along a magnetic field line, blob propagation image in poloidal and radial plane is obtained with the condition average for the first time. Two blobs appear in the observation region and then pass the separatrix. These observations give clear images of blob propagation characteristics at the boundary plasma in HL2A. The long-range correlation characteristics of blob turbulence have also been verified. Acknowledgments The authors would like to thank Prof. B. S. Yuan for identifying the position of the separatrix and the HL-2A team for good cooper-
ation. This work is partially supported by the National Science Foundation of China under Grant No. 10775044, the Chinese National Magnetic Confinement Fusion Science Program under Grant No. 2009GB106006 and by the JSPS-CAS Core-University Program in the field of Plasma and Nuclear Fusion.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
S.I. Krasheninnikov et al., Phys. Lett. A 283 (2001) 368. D.A. DIppolito et al., Phys. Plasmas 9 (2002) 222. N. Bisai et al., Phys. Plasmas 12 (2005) 102515. O.E. Garcia et al., Plasma Phys. Control Fusion 48 (2006) L1. M. Agostini et al., Phys. Plasmas 14 (2007) 102305. J.M. Dewhurst et al., Plasma Phys. Control Fusion 50 (2008) 095013. T.A. Carter, Phys. Plasmas 13 (2006) 010701. T. Windisch et al., Phys. Plasmas 13 (2006) 122303. N. Katz et al., Phys. Rev. Lett. 101 (2008) 015003. Y. Xu et al., Nucl. Fusion 49 (2009) 035005. M. Podesta et al., Phys. Rev. Lett. 101 (2008) 045001. X.R. Duan et al., Nucl. Fusion 49 (2009) 104012. L.W. Yan et al., Rev. Sci. Instrum. 76 (2005) 093506. K.J. Zhao et al., Phys. Rev. Lett. 96 (2006) 255004. L.W. Yan et al., Nucl. Fusion 47 (2007) 1673. J. Cheng et al., Nucl. Fusion 49 (2009) 085030. A.D. Liu et al., Phys. Rev. Lett. 103 (2009) 095002. J. Cheng et al., Plasma Phys. Control Fusion 52 (2010) 055003. J.M. Beall et al., J. Appl. Phys. 53 (1982) 3933. D.A. Russell et al., Phys. Rev. Lett. 93 (2004) 265001. H.L. Pecseli, J. Trulsen, Phys. Fluids B1 (1989) 1616.
Contents lists available at ScienceDirect
Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Blob birth and propagation characteristics on the HL-2A tokamak L.W. Yan 1,⇑, J. Cheng, W.Y. Hong, K.J. Zhao, J. Qian, Q.W. Yang, J.Q. Dong, X.R. Duan, Y. Liu Southwestern Institute of Physics, Chengdu, PR China
a r t i c l e
i n f o
Article history: Available online 29 October 2010
a b s t r a c t Blob birth and propagation characteristics have been investigated on the HL-2A tokamak using the novel probe combination of a radial eight-probe array and a poloidal ten-probe array toroidally separated by 210 cm. Outside of the separatrix, close zero parallel wave number along a magnetic field line was found. Inside the separatrix 4–8 mm, density gradient has a maximum and the skewness is close to zero. Blob poloidal velocity changes its direction across the separatrix, which is consistent with E B driven mechanism. Based on the significant correlation along a magnetic line, blob propagation across the separatrix in poloidal–radial plane is clearly observed with condition average. At the far SOL, blob radial velocity is 0.5–0.6 km/s, which dominates the particle loss in the SOL. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The fast radial transport in the scrape-off layer (SOL) of tokamak plasma is intermittent and convective. One of possible mechanisms for convective transport is associated with the radial movement of plasma blobs, which locate in poloidal and radial plane and extend along a magnetic field line. The convective transport can increase particle recycling, reduce divertor efficiency and lead to the high erosion of the first wall. Theoretically, it has been predicted that blobs move towards the first wall at the low field side due to E B drift, where charge separation inside blobs is driven by the gradient and curvature of magnetic field [1–3]. The blobs were observed in many experiments using Langmuir probes and fast cameras. These experiments are focused on their statistical characteristics. On the TCV tokamak, there is good agreement between the blob characteristics measured with reciprocating Langmuir probes and simulation results of 2D interchange turbulence [4]. Blob frequency reduction during L-H transition was observed with gas puff imaging in NSTX [5]. The blobs are also observed in linear and helical devices [6]. In the large plasma device (LAPD), the link between the holes inside plasma column and the blobs in the limiter shadow was observed [7]. The experiment in the linear device VINETA implied the blobs originating from quasi-coherent drift wave [8]. In the versatile toroidal facility (VTF), the dependence of blob radial velocity on the neutral particle density is reported [9]. The suppression of turbulent blob transport by a resonant magnetic perturbation is studied in TEXTOR [10]. Different
⇑ Corresponding author. Address: Southwestern Institute of Physics, Division 102, P.O. Box 432, No.3, South Section 3, Ring Road 2, Chengdu, Sichuan 610041, PR China. Tel.: +86 28 82850310; fax: +86 28 82850300. E-mail address: [email protected] (L.W. Yan). 1 Presenting author. 0022-3115/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnucmat.2010.10.032
contribution to the cross-field transport from turbulent instabilities and blobs is also analyzed in TORPEX [11]. The blob birth zone and propagation characteristics are important for understanding its dynamics. Until now, there is no report about the study with probe arrays, especially the dependence of the significant coherence along a magnetic field line, which is focused on this paper. Plasma blobs are observed to be formed just inside the separatrix, where the density gradient has a maximum and the corresponding skewness is close to zero. Based on the long-range correlation, blob propagation in poloidal–radial plane (2D) is clearly observed with condition average method. The remained parts of the paper are organized as follows. The experimental setup is described in Section 2. The experimental results are given in Section 3. The last section is for the conclusions.
2. Experimental setup The blob experiments were performed in ohmically heated deuterium discharges on HL-2A with R = 1.65 m and a = 0.4 m [12]. Main experimental parameters are Ip = 165 kA, Bt = 1.8 T, and line-averaged density ne = 1.9 1019 m3. A novel combination of a poloidal probe array with a radial one is used to study blobs. Their experimental setup is shown in Fig. 1. The first is a poloidal probe array with ten-tips localized at the position A, in which the first-tip is 2.1 cm below midplane. The second is a radial probe array with eight-tips localized at the position B, where each tip is 5.2 cm above midplane. The separation between adjacent probes is 4.0 mm. Each tip is 2.0 mm in length and 1.5 mm in diameter. The toroidal separation between array A and B is about 210 cm. There is another four-tip array at the position B besides the radial eight-tip array. Both are installed on a reciprocating probe system with inward velocity 1.0 m/s [13]. The four-tip array is used to measure local electron temperature and density. Other probes
L.W. Yan et al. / Journal of Nuclear Materials 415 (2011) S475–S478
(Is-
S476
4 2 0 -2 -4 4 2 0 -2 -4 400
Δ r=-8 mm
(a)
Δ r=-4 mm
(b)
405
-1
415
420
(c)
10
410
t (ms)
(d)
-2
10
-3
10
-4
-2
0
2
(I s -)/ σ
4 -4 -2
0
2
(I s -)/ σ
4
Fig. 2. Time evolutions of Is fluctuations normalized by its standard deviation, (Is
Fig. 1. Schematic of the Langmuir probe arrangement in HL-2A. Poloidal ten-tip array and radial eight-tip array are localized at position A and B, respectively. Their toroidal separation is 210 cm.
are for floating potential or ion saturation current with the negative based voltage of Vb 160 V. Such probe arrangement provides enough flexibility for observing blob statistical and 2D propagation characteristics based on the significant toroidal correlation. Experimental data are acquired with a frequency fs = 1 MHz and the accuracy of 12 bits. 3. Experimental results 3.1. The comparison of spectral characteristics across the separatrix Usually, the power spectrum inside the separatrix is different from that outside it. The former is routinely dominated by zonal flows, which had been widely investigated in HL-2A with Langmuir probe arrays [14–17]. Recently, the statistical characteristics of blob turbulence across separatrix were also investigated using five-tip probe array [18]. However, the long-range correlation along a magnetic field has not been investigated. The separatrix is identified by the EFIT code with an error of 5 mm. According to two-point correlation method [19], the parallel wave number inside the separatrix 8 mm in 10–150 kHz is estimated to be 6.4 104 cm1, which is so close to zero. The average wave number and its full width at half magnitude outside the separatrix 8 mm are estimated to be 8.4 104 cm1 and 4.6 103 cm1, respectively. Parallel correlation length and propagation velocity are 4.4 m and 2.2 105 m/s, respectively. The latter is higher than local ion sound speed Cs 3.8 104 m/s.
100 ms are used to estimate their PDFs. The former signal is dominated by negative burst events, named density holes, the corresponding PDF deviates to a negative value, as shown in Fig. 2c. Simulation [20] indicates that the inward propagation of density holes may be a mechanism for impurity transport. The latter has the positive burst events and their PDF becomes slightly asymmetric with a tail towards positive values, as seen in Fig. 2d. Due to the separatrix with an error of 5 mm, it is difficult to exactly determine the radial position with symmetric PDF, but our observation implies that there is a symmetric PDF position between Dr = 8 mm and Dr = 4 mm. The deviation degree from the gaussian distribution can be characterized by the skewness, which is zero for a gaussian distribution. The radial profile of the skewness for each PDF is estimated at eight radial probe positions, as shown in Fig. 3a. Each point is averaged with 100 ms data. From Dr = 8 mm to Dr = 4 mm, the skewness changes sign from negative to positive. It is an important observation that the skewness is close to zero inside the separatrix, marked by the shaded area in Fig. 3a. After the temperature fluctuation is neglected, the inverse radial scale length of density gradient is calculated with L1 n ¼ rne =ne , as shown in Fig. 3b, which has a maximum when the skewness
3.2. The blob birth zone The radial eight-tip array is used to investigate the statistical characteristics of turbulence. The probability distribution function (PDF) of ion saturation current is used to characterize the deviation from gaussian distribution. Fig. 2a and b show ion saturation current (Is) evolutions normalized by standard deviation (Is
Fig. 3. Radial profile of the skewness of a PDF (a) and the inverse radial density gradient scale length L1 ne ¼ rIs =Is (b). In the shaded region, the skewness changes its sign.
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L.W. Yan et al. / Journal of Nuclear Materials 415 (2011) S475–S478
is close to zero. This result indicates that the blob birth zone is consistent with maximum density gradient.
Fix
(b)
0
(c)
1
(d)
0
θ
d (cm)
-1
-1 -40 -20
0 20 40 -40 -20 0 20 40
Δτ (μs)
Δτ (μs)
Fig. 4. Spatiotemporal correlation functions of floating potentials at four radial positions, Dr = 5 mm (a), 5 mm (b), 15 mm (c) and 25 mm (d). The poloidal movement of blobs changes its direction across the separatrix.
Move Fit
1.0 0.8 0.6 0
1
2
3
4
5
6
Δ r (cm) Fig. 5. Radial profile of blob radial velocity estimated with the fixed and movable reference signals, denoted with squares and circles, respectively.
radial velocities have the same trend to decrease with radius. In the far SOL, the radial velocity reduces to 0.6 km/s, which is about 1%–2% of local ion sound speed.
3.4. Long-range correlation of the blob In this section, our focus is put on the maximum correlation along a field line in the SOL, though the interchange mode was detected inside the separatrix. The array A localizes at a radial position Dr 4 mm, where Dr denotes the distance between the separatrix and any tip in array A. Fig. 6 shows 2D representation of conditional average of potentials measured with radial eightprobe and poloidal ten-probe arrays. Based on the significant correlation along a field line with the toroidal separation of 210 cm, the blob 2D images are obtained for the first time with the two probe array signals through condition average. We can effectively discriminate coherent structures from incoherent turbulence dependent on preset condition, such as several times standard deviation (2.5r). Time interval of two adjacent figures is 5 ls. Two blobs appear in observation region. The first has poloidal size about 10 mm, as shown in Fig. 6a, and then it propagates with pronounced poloidal movement, as shown in Fig. 6b. Meantime, another blob appears below the first blob. In Fig. 6c, the first blob becomes weaker and the second blob enters into the observation zone. The first blob completely disappears and the second one continues to move, suggesting that the lifetime of blobs is over 15 ls, as shown in Fig. 6d. Blob propagation velocity can be estimated to be V = Dl/Dt, where Dl is the movement distance within the delay time Dt. Blob poloidal velocity is estimated as 2.0–2.8 km/s, while the radial velocity is given in Fig. 5. These results are consistent with those measured by reciprocating five-tip array [18].
Δdθ (mm)
(a)
1
θ
d (cm)
Turbulence theory predicts that density blobs propagate in the poloidal and radial directions [1]. The blob poloidal movement characteristics can be extracted from spatiotemporal correlation function with poloidal ten-tip array for homogeneous fluctuations. Used the spatiotemporal correlation function, the lifetime and spatial size of fluctuation correlation structures (blobs) are estimated with e-folding length of a peak. The slope in poloidal–temporal correlation function is relevant to poloidal velocity. Therefore, main blob parameters can be determined from the correlation function. Fig. 4 shows spatiotemporal correlation functions of floating potentials at four different radial positions. At the position Dr = 5 mm (a), the poloidal size and lifetime are estimated as 3.0 cm and 20 ls, respectively. The poloidal velocity is 1.5 km/s, which is in electron diamagnetic drift direction. At the Dr = 5 mm (b), the poloidal speed is 1.8 km/s, and propagates in ion diamagnetic drift direction. At the Dr = 15 mm (c), the spatial size and poloidal velocity decrease to about 1.0 cm and 0.6 km/s. At the Dr = 25 mm (d), the spatial size is only about 0.5 cm. In addition, ion saturation currents are measured with the same probe array. The results are similar with those of floating potentials. They indicate that the poloidal movement of blobs changes its direction across the separatrix, and then poloidal velocity gradually decreases from near SOL to far SOL, which is consistent with the previous observation of blob poloidal movement being driven by E B drift [18]. Blob radial velocity is a key parameter for understanding crossfield transport. The spatiotemporal correlation function is not suitable for estimating it because the assumption of homogeneous fluctuations is invalid in radial direction. Therefore, blob radial characteristics are extracted by cross-condition average [21]. In this experiment, the blob radial velocity is measured with the reciprocating four-probes with inward velocity of 1.0 m/s, implying radial movement of 2 mm in 2.0 ms, which is comparable with probe spatial resolution of 2 mm. Therefore, the probe distance within 2 mm can be neglected. Each time window in 2 ms is overlapped with 50% and within the window the blob radial velocities are simultaneously estimated with two different reference signals. One reference signal is from a movable probe in array B; the other is from a fixed probe in array A toroidally separated by 210 cm. The former is denoted by circles, the latter is given by triangles in Fig. 5. A peak of cross-conditional average at Ds = 0 responds to blob radial velocity. Fig. 5 shows the radial profiles of blob radial velocities in one discharge with the two reference signals. It is clear that two
Δdθ(cm)
3.3. The blob propagation characteristics
Vr (km/s)
1.2
30
(a)
(b)
(c)
(d)
20 10 30 20 10 0
-10
0
10 -10
Δ r (mm)
0
10
Δ r (mm)
Fig. 6. The 2D images of floating potential at four different delay times chosen by condition average. The time interval is 5 ls. The initial blob is inclined in 2D plane with poloidal movement.
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4. Conclusions Blob birth and propagation characteristics have been investigated in the HL-2A tokamak using a novel combination of two probe arrays toroidally separated by 210 cm. Outside the separatrix, parallel wave number along a magnetic field line is close to zero, consistent with the theoretical prediction of interchange instability. The initial blobs are formed just inside the separatrix, where the density gradient has a maximum and the skewness is close to zero. Blob poloidal velocity changes its direction across the separatrix, and blob radial velocity is comparable using movable and fixed probe reference signals, which tends to decrease with the distance away from the separatrix. Based on the significant correlation along a magnetic field line, blob propagation image in poloidal and radial plane is obtained with the condition average for the first time. Two blobs appear in the observation region and then pass the separatrix. These observations give clear images of blob propagation characteristics at the boundary plasma in HL2A. The long-range correlation characteristics of blob turbulence have also been verified. Acknowledgments The authors would like to thank Prof. B. S. Yuan for identifying the position of the separatrix and the HL-2A team for good cooper-
ation. This work is partially supported by the National Science Foundation of China under Grant No. 10775044, the Chinese National Magnetic Confinement Fusion Science Program under Grant No. 2009GB106006 and by the JSPS-CAS Core-University Program in the field of Plasma and Nuclear Fusion.
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