- Email: [email protected]
Study of MHD activity in the HT-7 superconducting tokamak
Physics Letters A 342 (2005) 175–180 www.elsevier.com/locate/pla
Study of MHD activity in the HT-7 superconducting tokamak M. Asif ∗ , X. Gao, J.G. Li, B.N. Wan, the HT-7 Team Institute of Plasma Physics, Chinese Academy of Sciences, P.O. Box 1126, Hefei, Anhui 230031, PR China Received 17 May 2005; accepted 20 May 2005 Available online 31 May 2005 Communicated by F. Porcelli
Abstract An attempt is made to explain the behavior of the magneto-hydrodynamic (MHD) instabilities observed at values of the edge safety factor 3 < q(a) < 4, on the HT-7 superconducting tokamak. For the poloidal-magnetic-field fluctuations observed at the Mirnov coils, Mirnov-coil analysis shows that the MHD activity consists predominantly of m = 2 mode. Estimates are given for the characteristic growth time of the m = 2 mode, τg , and the related rate of island growth, dW/dt. The experimental value of τg is found to be smaller than the linear theoretical one, and thus satisfy the condition τA < τg < τS (where ideal timescale is τA , and the resistive timescale is τS ). However, the experimental and theoretical calculation of dW/dt are found to be in reasonable agreement with each other. 2005 Elsevier B.V. All rights reserved. PACS: 52.55.Fa; 52.35.Py; 52.35.Mw; 52.70.Ds Keywords: Magneto-hydrodynamic; Mirnov coil; Disruptions; Characteristic time
1. Introduction The most advanced approach towards the achievement of the relevant fusion reactor parameters is the confinement of plasma within a magnetic field in a socalled tokamak. Tokamaks are one of the leading candidates for magnetically confined fusion owing to their good particle and energy confinement. The stability of * Corresponding author.
E-mail address: [email protected] (M. Asif). 0375-9601/$ – see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2005.05.032
plasmas in magnetic fields is one of the primary research subjects in the area of controlled thermonuclear fusion and both theoretical and experimental investigations have been actively pursued. Tokamak plasmas are susceptible to major disruptions when the plasma density or current exceeds critical values. It is generally believed that these tokamak major disruptions are caused by the non-linear growth of tearing mode perturbations. The tearing mode instability and the associated magnetic islands can lead to a degradation of tokamak plasma performance and eventually to a disruption.
176
M. Asif et al. / Physics Letters A 342 (2005) 175–180
This Letter reports on detailed investigations into the confinement properties of tokamak discharges at values of the edge safety factor 3 < q(a) < 4, and on the magnetohydrodynamic (MHD) characteristics of these discharges. Here, the usual definition of q(a) is employed, i.e., q(a) = (a/R)(Bϕ /Bp ), where Bp = µ0 Ip /(2πa). Tearing modes are known to play an important role in confinement degradation and disruptions in tokamaks [1,2]. They are resistive instabilities driven by the free energy contained in the poloidal magnetic field. Due to their resonant character, they are localized around flux surfaces and change the topology of the magnetic-flux distribution through the formation of magnetic islands. At present, there exist several distinct MHD models of tokamak disruptions [3–6]. Understanding in detail the various mechanisms that can lead to disruption is important for achieving tokamak confinement, and especially so with a view to suppressing disruptions [7]. It has been observed that the presence of the m = 2/n = 1 mode often leads to a major disruption in the HT-7. The purpose of this study is to investigate the major disruptions occurring at values of the edge safety factor 3 < q(a) < 4, in the HT-7 superconducting tokamak, and to compare the theoretical and experimental results for the rate of island growth. Previous experimental evidence has shown that disruptions are connected with MHD activity and that the timescale involved is intermediate between the resistive and the ideal MHD timescales [8]. The motivation for this study on disruption control in the HT-7 superconducting tokamak is to clarify which of the different disruption scenarios applies in this particular tokamak, which factors leading to disruption modes needs particular study, and how the growth time depends on the detailed experimental conditions. Since all of these aspects need to be understood in our attempt to access model of disruption control, this subject has been considered both experimentally and theoretically.
2. Experimental set-up HT-7 is a medium sized tokamak [9–11], in circular cross section with superconducting toroidal coils and the main purpose is to explore high performance plasma operation under steady-state condition. It has a major radius of R = 1.22 m, a minor radius of
a = 0.27 m defined by one poloidal water-cooling limiter, one toroidal water-cooling belt limiter at high field side and a new set of actively cooled toroidal doublering graphite limiters at bottom and top of the vacuum vessel was developed recently for long pulse operation, and up to 240 s of long plasma has been achieved with new graphite limiters in the HT-7 in 2004 [9, 11]. There are two layers of thick copper shells, and between them are located 24 superconducting coils, which can create and maintain a toroidal magnetic field (BT ) of up to 2.5 T. The HT-7 ohmic heating transformer has an iron core and it can offer a magnetic flux of 1.7 V s at its maximum. The HT-7 tokamak is normally operated with IP = 100–250 kA, BT = 1–2.5 T, line-averaged density 1–6 × 1019 m−3 . The HT-7 tokamak is equipped with more than 30 diagnostics. The main diagnostics for present experiments are as follows: the electron density profile measured by a vertical 5-channel far-infrared (FIR) hydrogen cyanide (HCN) laser interferometer, a multichannel soft X-ray array, an electron–cyclotron emission diagnostic, Soft X-ray pulse-height-analysis (SXPHA) diagnostic, a 16-channel XUV bolometer array to measure plasma radiation losses, a multichannel Hα (Dα ) radiation array, 4-channel visible bremsstrahlung emission, 10-channels CIII line emission, an impurity optical spectrum measurement system and an electromagnetic measurement system. The magnetic fluctuations are observed with two arrays of magnetic probes, which are set up on the inside of the vacuum vessel wall at different positions in the toroidal direction. Each array has 12 probes around the plasma in a circle section. From the outer-middle plane, every probe is installed at 30◦ with respect to the nearest neighboring probes. The frequency response of the probe is more than 100 kHz. The affective winding area is 1430 cm2 . Of particular importance is the detection of specific modes from the Mirnov-coil signals. Upon time-integrating a Mirnov signal B˙ θ , we find the perturbed poloidal field, from which a given mode can be singled out by means of Mirnov-coil analysis. The spatial structure and temporal evolution of coherent MHD modes observed in the HT-7 superconducting tokamak have been inferred from the experimental signals by using spectral techniques. Using multichannel fluctuation data analysis by the singular value decomposition method (SVD) [12,13], the poloidal number m is obtained. Frequently, large m = 2 magnetic per-
M. Asif et al. / Physics Letters A 342 (2005) 175–180
177
Fig. 1. Operational region of the HT-7 tokamak. Dotted areas represent conditions with large MHD activity.
turbations were observed before a major disruption. Toroidal mode numbers n can be obtained in a similar way by extending the analysis to Mirnov coils located at different toroidal angles. Discharge conditions were chosen at values of the edge safety factor 3 < q(a) < 4. Fig. 1 shows this operating region with large MHD activity, which frequently leads to disruptions at values of the edge safety factor 3 < q(a) < 4.
3. Results and discussion Fig. 2 shows a typical shot with plasma current of 130 kA, BT = 1.7 T and the line-averaged density about 4.5 × 1019 m−3 . Magnetic analysis by singular value decomposition method (SVD) [12,13], for the discharge in Fig. 2 shows that the MHD activity consists predominantly of m = 2 modes with a rotation frequency of about 8.8 kHz, started at 361 ms, increasing, then the major disruption was triggered at 364.5 ms (see Fig. 3). An abrupt outward shift of the plasma column was observed (Fig. 2(f)). The plasma energy was reduced quickly by 38% (see Fig. 4) just before the major disruption. In HT-7, the most dangerous MHD instability is the m/n = 2/1 resistive tearing mode, which is driven by the plasma current density gradient. In this experiment, at q(a) = 3.8, no mode locking is observed, the observed MHD activity can be associated with tearing mode, a non-linear instability with low m/n modes. The observed Mirnov signals can equally well be explained as tearing modes induced by current channel
Fig. 2. Typical HT-7 discharge with MHD disruption. (a) Plasma current, (b) loop voltage, (c) central chord soft X-ray emission SXV0, (d) Mirnov-coil signal MAT0, (e) central line-averaged density, (f) horizontal displacement signal (cm).
changes. The physical mechanism, however, which finally triggers the MHD disruption in high q(a) > 3 deuterium plasmas is essentially the same [1]. The poloidally asymmetric increase of the plasma resistivity due to MARFE (multifaceted asymmetric radiation from the edge) cooling leads to a global contraction of the current channel, as has been shown theoretically by Lackner [14]. Qualitatively, because of the equilibrium constraint, the ohmic resistance of cold MARFE (a few eV) appears in series with the hot plasma resistance (several tens of eV) on each flux surface, resulting in a substantial increase of the average edge resistivity. As a consequence of the current contraction, the gradient of j (r) is step, leading to a higher value of the instability parameter ∆ . This results in the formation of quasi-stationary, rotating islands, located near the rational surface, for m/n = 2/1 mode the q = 2 surface. After knowing the current density profile, J ∼ (1 − X 2 )α , where X = r/a, the q-profile can be calculated by using the formula q(r) = q(a)
X2 . 1 − (1 − X 2 )α+1
(1)
178
M. Asif et al. / Physics Letters A 342 (2005) 175–180
Fig. 3. The result of the SVD analysis. (a) The first order temporal eigenvector of the mode, (b) the spacial eigenvector corresponding to the temporal eigenvector in Fig. 3(a). It shows the main mode number is m = 2.
Fig. 4. Time evaluation of plasma energy for discharge No. 66361.
Fig. 5. Calculated q(r) profile for discharge No. 66361.
With q(a) = 3.8, and α = 3 (shot No. 66361), the calculated q(r) profile is shown in Fig. 5. In the range of the MHD activity, m = 2 modes, the resonant layer of q is located at 0.7a as shown in Fig. 5. Fig. 6 shows that the characteristic time τg for the final growth of the m = 2 mode is about 2000 µs. The timescale for linear MHD-mode growth is generally bounded from below by the ideal timescale τA , and from above by the resistive timescale τS : τA < τg < τS .
(2)
Here, τA ≡ a/VA , with VA the Alfvén velocity, is the poloidal Alfvén time and the resistive timescale is given by [2] τS ∼ = τR0.6 × τA0.4 ,
(3)
Fig. 6. Poloidal-magnetic-field fluctuation for shot No. 66361, on the expanded timescale 362–365 ms.
M. Asif et al. / Physics Letters A 342 (2005) 175–180
where τR ≡ µ0 a 2 /η(0), with η(0) the resistivity at the plasma center, is the resistive skin time. In the HT-7 superconducting tokamak, the Alfvén velocity is about 3.2×106 m s−1 and η(0) ∼ = 5×10−8 m, which value follows for Te = 600 eV and Zeff = 1.25 from the classical Spitzer parallel resistivity [15] 1.56 η ≡ 36.04 × 10−5 × Zeff 1 + 1.08 + Zeff −3/2
× Te
(eV).
where rs is the radius of the mode rational surface, rc the radius of the detecting Mirnov coil, m the poloidal mode number, δBθ (t) the amplitude of a given mode signal B˜ θ (t), and Bθ the unperturbed poloidal field. With rs = 18.9 cm, rc = 36.3 cm, δBθ /Bθ = 0.002 and m = 2, we find from Eq. (5) W ∼ = 3.2 cm. Dividing this by τg = 2000 µs, the rate of island growth is found to be (6)
It is instructive to compare this with the prediction of Rutherford non-linear theory [1]: dw ∆ × η(0) ≡ , dt 2µ0
(7)
where ∆ is the jump in the logarithmic derivative of the perturbed helical flux function ψ across the resonant surface [16]. We assume that ∆ is of the order of 0.9 cm−1 [17] and again take η(0) ≈ 5 × 10−8 m. If we make the further assumption that ∆ does not change significantly during the rapid growth phase, then Eq. (7) predicts dw ≈ 0.02 × 104 cm s−1 , dt
which is only a factor 5 smaller than the experimental estimate Eq. (6). In view of the considerable uncertainties involved in the calculation of the two values Eqs. (6) and (8), this can be considered as a good agreement. The corresponding island grow so rapidly (at rates roughly consistent with Rutherford non-linear tearing-mode theory) that they reach estimated sizes sufficient to cause disruption.
(4)
With these values we calculate τA = 0.08 µs and τR = 1830 ms, hence by using Eq. (3), we find for the resistive timescale τS = 2100 µs. On the other hand, the growth time for the explosive growth of the precursor MHD activity shown in Fig. 6 has been found to be about 2000 µs. This value is smaller than τS , and it satisfies the condition of Eq. (2). The magnetic-island width can be estimated by means of the formula 2 rc m δBθ w =2 , (5) rs m rs Bθ
dw ∼ w ∼ = 0.1 × 104 cm s−1 . = dt τg
179
(8)
4. Conclusions In this work we have described detailed measurements of disrupting deuterium plasmas in the ohmicheating regime. The major disruption studied here consist of behavior of the magneto-hydrodynamic instabilities (m = 2), observed at values of the edge safety factor 3 < q(a) < 4, and growth of the m = 2 magnetic island. The rate of island growth is observed to be 0.1 × 104 cm s−1 , corresponding to a characteristic growth time τg = 2000 µs. The experimental value of τg is found to be smaller than the linear theoretical one, and thus satisfy the condition τA < τg < τS . The experimental and theoretical estimates of dW/dt are found to be reasonable agreement with each other. Since all of these aspects need to be understood in our attempt to access model of disruption control. This model will be used for the disruption control system in the future on HT-7 tokamak.
Acknowledgements The authors wish to thank the HT-7 team for helps during these experiments. This work has been supported by the National Natural Science Foundation of China (contract No. 10005010).
References [1] J.A. Wesson, et al., Nucl. Fusion 29 (1989) 641. [2] F.C. Schuller, Plasma Phys. Controlled Fusion 37 (1995) A135. [3] A. Sykes, J.A. Wesson, Phys. Rev. Lett. 44 (1980) 1215. [4] H.R. Hicks, et al., Nucl. Fusion 22 (1982) 117. [5] M.F. Turner, J.A. Wesson, Nucl. Fusion 22 (1982) 1069. [6] R.B. White, et al., Phys. Rev. Lett. 39 (1977) 1618. [7] A. Vannucci, et al., Nucl. Fusion 31 (1991) 1127.
180
[8] [9] [10] [11] [12]
M. Asif et al. / Physics Letters A 342 (2005) 175–180
G.L. Jahns, et al., Nucl. Fusion 28 (1988) 881. X. Gao, et al., J. Nucl. Mater. 337–339 (2005) 835. M. Asif, et al., Phys. Lett. A 336 (2005) 61. M. Asif, et al., Phys. Plasmas (2005), in press. C. Nardone, et al., Plasma Phys. Controlled Fusion 34 (1992) 1447.
[13] [14] [15] [16] [17]
T. Dudok de Wit, et al., Phys. Plasmas 1 (1994) 3288. K. Lackner, IPP Garching, 1991, personal communication. M. Ghoranneviss, et al., Nucl. Fusion 43 (2003) 210. P.H. Rutherford, Phys. Fluids 16 (1973) 1903. J. Chen, et al., Nucl. Fusion 30 (1990) 2271.
Study of MHD activity in the HT-7 superconducting tokamak M. Asif ∗ , X. Gao, J.G. Li, B.N. Wan, the HT-7 Team Institute of Plasma Physics, Chinese Academy of Sciences, P.O. Box 1126, Hefei, Anhui 230031, PR China Received 17 May 2005; accepted 20 May 2005 Available online 31 May 2005 Communicated by F. Porcelli
Abstract An attempt is made to explain the behavior of the magneto-hydrodynamic (MHD) instabilities observed at values of the edge safety factor 3 < q(a) < 4, on the HT-7 superconducting tokamak. For the poloidal-magnetic-field fluctuations observed at the Mirnov coils, Mirnov-coil analysis shows that the MHD activity consists predominantly of m = 2 mode. Estimates are given for the characteristic growth time of the m = 2 mode, τg , and the related rate of island growth, dW/dt. The experimental value of τg is found to be smaller than the linear theoretical one, and thus satisfy the condition τA < τg < τS (where ideal timescale is τA , and the resistive timescale is τS ). However, the experimental and theoretical calculation of dW/dt are found to be in reasonable agreement with each other. 2005 Elsevier B.V. All rights reserved. PACS: 52.55.Fa; 52.35.Py; 52.35.Mw; 52.70.Ds Keywords: Magneto-hydrodynamic; Mirnov coil; Disruptions; Characteristic time
1. Introduction The most advanced approach towards the achievement of the relevant fusion reactor parameters is the confinement of plasma within a magnetic field in a socalled tokamak. Tokamaks are one of the leading candidates for magnetically confined fusion owing to their good particle and energy confinement. The stability of * Corresponding author.
E-mail address: [email protected] (M. Asif). 0375-9601/$ – see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2005.05.032
plasmas in magnetic fields is one of the primary research subjects in the area of controlled thermonuclear fusion and both theoretical and experimental investigations have been actively pursued. Tokamak plasmas are susceptible to major disruptions when the plasma density or current exceeds critical values. It is generally believed that these tokamak major disruptions are caused by the non-linear growth of tearing mode perturbations. The tearing mode instability and the associated magnetic islands can lead to a degradation of tokamak plasma performance and eventually to a disruption.
176
M. Asif et al. / Physics Letters A 342 (2005) 175–180
This Letter reports on detailed investigations into the confinement properties of tokamak discharges at values of the edge safety factor 3 < q(a) < 4, and on the magnetohydrodynamic (MHD) characteristics of these discharges. Here, the usual definition of q(a) is employed, i.e., q(a) = (a/R)(Bϕ /Bp ), where Bp = µ0 Ip /(2πa). Tearing modes are known to play an important role in confinement degradation and disruptions in tokamaks [1,2]. They are resistive instabilities driven by the free energy contained in the poloidal magnetic field. Due to their resonant character, they are localized around flux surfaces and change the topology of the magnetic-flux distribution through the formation of magnetic islands. At present, there exist several distinct MHD models of tokamak disruptions [3–6]. Understanding in detail the various mechanisms that can lead to disruption is important for achieving tokamak confinement, and especially so with a view to suppressing disruptions [7]. It has been observed that the presence of the m = 2/n = 1 mode often leads to a major disruption in the HT-7. The purpose of this study is to investigate the major disruptions occurring at values of the edge safety factor 3 < q(a) < 4, in the HT-7 superconducting tokamak, and to compare the theoretical and experimental results for the rate of island growth. Previous experimental evidence has shown that disruptions are connected with MHD activity and that the timescale involved is intermediate between the resistive and the ideal MHD timescales [8]. The motivation for this study on disruption control in the HT-7 superconducting tokamak is to clarify which of the different disruption scenarios applies in this particular tokamak, which factors leading to disruption modes needs particular study, and how the growth time depends on the detailed experimental conditions. Since all of these aspects need to be understood in our attempt to access model of disruption control, this subject has been considered both experimentally and theoretically.
2. Experimental set-up HT-7 is a medium sized tokamak [9–11], in circular cross section with superconducting toroidal coils and the main purpose is to explore high performance plasma operation under steady-state condition. It has a major radius of R = 1.22 m, a minor radius of
a = 0.27 m defined by one poloidal water-cooling limiter, one toroidal water-cooling belt limiter at high field side and a new set of actively cooled toroidal doublering graphite limiters at bottom and top of the vacuum vessel was developed recently for long pulse operation, and up to 240 s of long plasma has been achieved with new graphite limiters in the HT-7 in 2004 [9, 11]. There are two layers of thick copper shells, and between them are located 24 superconducting coils, which can create and maintain a toroidal magnetic field (BT ) of up to 2.5 T. The HT-7 ohmic heating transformer has an iron core and it can offer a magnetic flux of 1.7 V s at its maximum. The HT-7 tokamak is normally operated with IP = 100–250 kA, BT = 1–2.5 T, line-averaged density 1–6 × 1019 m−3 . The HT-7 tokamak is equipped with more than 30 diagnostics. The main diagnostics for present experiments are as follows: the electron density profile measured by a vertical 5-channel far-infrared (FIR) hydrogen cyanide (HCN) laser interferometer, a multichannel soft X-ray array, an electron–cyclotron emission diagnostic, Soft X-ray pulse-height-analysis (SXPHA) diagnostic, a 16-channel XUV bolometer array to measure plasma radiation losses, a multichannel Hα (Dα ) radiation array, 4-channel visible bremsstrahlung emission, 10-channels CIII line emission, an impurity optical spectrum measurement system and an electromagnetic measurement system. The magnetic fluctuations are observed with two arrays of magnetic probes, which are set up on the inside of the vacuum vessel wall at different positions in the toroidal direction. Each array has 12 probes around the plasma in a circle section. From the outer-middle plane, every probe is installed at 30◦ with respect to the nearest neighboring probes. The frequency response of the probe is more than 100 kHz. The affective winding area is 1430 cm2 . Of particular importance is the detection of specific modes from the Mirnov-coil signals. Upon time-integrating a Mirnov signal B˙ θ , we find the perturbed poloidal field, from which a given mode can be singled out by means of Mirnov-coil analysis. The spatial structure and temporal evolution of coherent MHD modes observed in the HT-7 superconducting tokamak have been inferred from the experimental signals by using spectral techniques. Using multichannel fluctuation data analysis by the singular value decomposition method (SVD) [12,13], the poloidal number m is obtained. Frequently, large m = 2 magnetic per-
M. Asif et al. / Physics Letters A 342 (2005) 175–180
177
Fig. 1. Operational region of the HT-7 tokamak. Dotted areas represent conditions with large MHD activity.
turbations were observed before a major disruption. Toroidal mode numbers n can be obtained in a similar way by extending the analysis to Mirnov coils located at different toroidal angles. Discharge conditions were chosen at values of the edge safety factor 3 < q(a) < 4. Fig. 1 shows this operating region with large MHD activity, which frequently leads to disruptions at values of the edge safety factor 3 < q(a) < 4.
3. Results and discussion Fig. 2 shows a typical shot with plasma current of 130 kA, BT = 1.7 T and the line-averaged density about 4.5 × 1019 m−3 . Magnetic analysis by singular value decomposition method (SVD) [12,13], for the discharge in Fig. 2 shows that the MHD activity consists predominantly of m = 2 modes with a rotation frequency of about 8.8 kHz, started at 361 ms, increasing, then the major disruption was triggered at 364.5 ms (see Fig. 3). An abrupt outward shift of the plasma column was observed (Fig. 2(f)). The plasma energy was reduced quickly by 38% (see Fig. 4) just before the major disruption. In HT-7, the most dangerous MHD instability is the m/n = 2/1 resistive tearing mode, which is driven by the plasma current density gradient. In this experiment, at q(a) = 3.8, no mode locking is observed, the observed MHD activity can be associated with tearing mode, a non-linear instability with low m/n modes. The observed Mirnov signals can equally well be explained as tearing modes induced by current channel
Fig. 2. Typical HT-7 discharge with MHD disruption. (a) Plasma current, (b) loop voltage, (c) central chord soft X-ray emission SXV0, (d) Mirnov-coil signal MAT0, (e) central line-averaged density, (f) horizontal displacement signal (cm).
changes. The physical mechanism, however, which finally triggers the MHD disruption in high q(a) > 3 deuterium plasmas is essentially the same [1]. The poloidally asymmetric increase of the plasma resistivity due to MARFE (multifaceted asymmetric radiation from the edge) cooling leads to a global contraction of the current channel, as has been shown theoretically by Lackner [14]. Qualitatively, because of the equilibrium constraint, the ohmic resistance of cold MARFE (a few eV) appears in series with the hot plasma resistance (several tens of eV) on each flux surface, resulting in a substantial increase of the average edge resistivity. As a consequence of the current contraction, the gradient of j (r) is step, leading to a higher value of the instability parameter ∆ . This results in the formation of quasi-stationary, rotating islands, located near the rational surface, for m/n = 2/1 mode the q = 2 surface. After knowing the current density profile, J ∼ (1 − X 2 )α , where X = r/a, the q-profile can be calculated by using the formula q(r) = q(a)
X2 . 1 − (1 − X 2 )α+1
(1)
178
M. Asif et al. / Physics Letters A 342 (2005) 175–180
Fig. 3. The result of the SVD analysis. (a) The first order temporal eigenvector of the mode, (b) the spacial eigenvector corresponding to the temporal eigenvector in Fig. 3(a). It shows the main mode number is m = 2.
Fig. 4. Time evaluation of plasma energy for discharge No. 66361.
Fig. 5. Calculated q(r) profile for discharge No. 66361.
With q(a) = 3.8, and α = 3 (shot No. 66361), the calculated q(r) profile is shown in Fig. 5. In the range of the MHD activity, m = 2 modes, the resonant layer of q is located at 0.7a as shown in Fig. 5. Fig. 6 shows that the characteristic time τg for the final growth of the m = 2 mode is about 2000 µs. The timescale for linear MHD-mode growth is generally bounded from below by the ideal timescale τA , and from above by the resistive timescale τS : τA < τg < τS .
(2)
Here, τA ≡ a/VA , with VA the Alfvén velocity, is the poloidal Alfvén time and the resistive timescale is given by [2] τS ∼ = τR0.6 × τA0.4 ,
(3)
Fig. 6. Poloidal-magnetic-field fluctuation for shot No. 66361, on the expanded timescale 362–365 ms.
M. Asif et al. / Physics Letters A 342 (2005) 175–180
where τR ≡ µ0 a 2 /η(0), with η(0) the resistivity at the plasma center, is the resistive skin time. In the HT-7 superconducting tokamak, the Alfvén velocity is about 3.2×106 m s−1 and η(0) ∼ = 5×10−8 m, which value follows for Te = 600 eV and Zeff = 1.25 from the classical Spitzer parallel resistivity [15] 1.56 η ≡ 36.04 × 10−5 × Zeff 1 + 1.08 + Zeff −3/2
× Te
(eV).
where rs is the radius of the mode rational surface, rc the radius of the detecting Mirnov coil, m the poloidal mode number, δBθ (t) the amplitude of a given mode signal B˜ θ (t), and Bθ the unperturbed poloidal field. With rs = 18.9 cm, rc = 36.3 cm, δBθ /Bθ = 0.002 and m = 2, we find from Eq. (5) W ∼ = 3.2 cm. Dividing this by τg = 2000 µs, the rate of island growth is found to be (6)
It is instructive to compare this with the prediction of Rutherford non-linear theory [1]: dw ∆ × η(0) ≡ , dt 2µ0
(7)
where ∆ is the jump in the logarithmic derivative of the perturbed helical flux function ψ across the resonant surface [16]. We assume that ∆ is of the order of 0.9 cm−1 [17] and again take η(0) ≈ 5 × 10−8 m. If we make the further assumption that ∆ does not change significantly during the rapid growth phase, then Eq. (7) predicts dw ≈ 0.02 × 104 cm s−1 , dt
which is only a factor 5 smaller than the experimental estimate Eq. (6). In view of the considerable uncertainties involved in the calculation of the two values Eqs. (6) and (8), this can be considered as a good agreement. The corresponding island grow so rapidly (at rates roughly consistent with Rutherford non-linear tearing-mode theory) that they reach estimated sizes sufficient to cause disruption.
(4)
With these values we calculate τA = 0.08 µs and τR = 1830 ms, hence by using Eq. (3), we find for the resistive timescale τS = 2100 µs. On the other hand, the growth time for the explosive growth of the precursor MHD activity shown in Fig. 6 has been found to be about 2000 µs. This value is smaller than τS , and it satisfies the condition of Eq. (2). The magnetic-island width can be estimated by means of the formula 2 rc m δBθ w =2 , (5) rs m rs Bθ
dw ∼ w ∼ = 0.1 × 104 cm s−1 . = dt τg
179
(8)
4. Conclusions In this work we have described detailed measurements of disrupting deuterium plasmas in the ohmicheating regime. The major disruption studied here consist of behavior of the magneto-hydrodynamic instabilities (m = 2), observed at values of the edge safety factor 3 < q(a) < 4, and growth of the m = 2 magnetic island. The rate of island growth is observed to be 0.1 × 104 cm s−1 , corresponding to a characteristic growth time τg = 2000 µs. The experimental value of τg is found to be smaller than the linear theoretical one, and thus satisfy the condition τA < τg < τS . The experimental and theoretical estimates of dW/dt are found to be reasonable agreement with each other. Since all of these aspects need to be understood in our attempt to access model of disruption control. This model will be used for the disruption control system in the future on HT-7 tokamak.
Acknowledgements The authors wish to thank the HT-7 team for helps during these experiments. This work has been supported by the National Natural Science Foundation of China (contract No. 10005010).
References [1] J.A. Wesson, et al., Nucl. Fusion 29 (1989) 641. [2] F.C. Schuller, Plasma Phys. Controlled Fusion 37 (1995) A135. [3] A. Sykes, J.A. Wesson, Phys. Rev. Lett. 44 (1980) 1215. [4] H.R. Hicks, et al., Nucl. Fusion 22 (1982) 117. [5] M.F. Turner, J.A. Wesson, Nucl. Fusion 22 (1982) 1069. [6] R.B. White, et al., Phys. Rev. Lett. 39 (1977) 1618. [7] A. Vannucci, et al., Nucl. Fusion 31 (1991) 1127.
180
[8] [9] [10] [11] [12]
M. Asif et al. / Physics Letters A 342 (2005) 175–180
G.L. Jahns, et al., Nucl. Fusion 28 (1988) 881. X. Gao, et al., J. Nucl. Mater. 337–339 (2005) 835. M. Asif, et al., Phys. Lett. A 336 (2005) 61. M. Asif, et al., Phys. Plasmas (2005), in press. C. Nardone, et al., Plasma Phys. Controlled Fusion 34 (1992) 1447.
[13] [14] [15] [16] [17]
T. Dudok de Wit, et al., Phys. Plasmas 1 (1994) 3288. K. Lackner, IPP Garching, 1991, personal communication. M. Ghoranneviss, et al., Nucl. Fusion 43 (2003) 210. P.H. Rutherford, Phys. Fluids 16 (1973) 1903. J. Chen, et al., Nucl. Fusion 30 (1990) 2271.