Study of Current Decay Time during Disruption in JT-60U Tokamak

Transcription

1 1 EX/7-Rc Study of Current Decay Time during Disrution in JT-60U Tokamak M.Okamoto 1), K.Y.Watanabe ), Y.Shibata 3), N.Ohno 3), T.Nakano 4), Y.Kawano 4), A.Isayama 4), N.Oyama 4), G.Matsunaga 4), K.Kurihara 4), M.Goto ), S.Sakakibara ), M.Sugihara 5) and Y.Kamada 4) and JT-60 team 4) 1) Ishikawa National College of Technology, Ishikawa , Jaan ) National Institute for Fusion Science, Toki , Jaan 3) Graduate School of Engineering, Nagoya University, Nagoya , Jaan 4) Jaan Atomic Energy Agency, Ibaraki , Jaan 5) ITER Organization, Cadarache, France contact of main author: okamoto@ishikawa-nct.ac.j Abstract. The lasma current decay time during initial hase of the radiation induced disrution in JT-60U tokamak is studied based on the lasma inductance and resistance estimated by exerimental data. The features of this study are as follows; (i) the electron temerature rofile during the current quench is estimated by the electron cyclotron emission (ECE) diagnostic systems and the measurement of He I line emission intensity ratios, and the lasma inductance is estimated by the CCS (Cauchy-Condition Surface) method with the magnetics [1]. (ii) in the radiation induced disrution lasmas, it is found that the time change rate of the lasma inductance during current quench is an imortant arameter as well as the lasma resistance to redict the current decay time. 1. Introduction Disrution is one of the most crucial issues for the tokamak fusion reactors. Intense eddy currents and large halo currents generated during the current quench of the disrution induce large electromagnetic forces on the vacuum vessel and in-vessel comonents. The forces could be large enough to mechanically break the in-vessel comonents []. In order to estimate the force induced by eddy currents, recise rediction of lasma current decay time is imortant. The database for ITER (International Thermonuclear Exerimental Reactor) [3] is established by using the current decay time τ normalized by the lasma cross-sectional area S. The area-normalized τ is induced by the L/R model based on a simle series circuit of the lasma resistance R and inductance L, where τ can be described by L /R. In this model, τ/s can be reresented by (L /πr 0 )/η, it is little deendence on the device size and is strongly deendence on the electron temerature T e and effective charge Z eff, where R 0 and η are the lasma major radius and resistivity, resectively. In the database, the lower bound on areanormalized τ, which is taken as 1.7 ms/m [4], is used as the criterion value for design of ITER. In order to exerimentally evaluate the validity of the L/R model, very low T e and Z eff during current quench must be measured by the diagnostic system with high time resolution. D. G. Whyte and D.A.Humhrevs had estimated the T e and Z eff during current quench using measurement of helium recombination radiation and reorted the relation between the current decay time and classical resistivity [5,6]. However, the systematic analysis of the current decay time and electron temerature during current quench has not reorted yet. In this aer, the T e rofile during current quench is estimated by ECE diagnostic systems and measurement of He I emission intensity ratios. We verify the validity of L/R model using the initial hase of current quench of radiation induced disrutive lasma with τ/s = 5 ~ 40 ms/m. The measurement of T e using ECE diagnostic systems in lasma core region is

2 EX/7-Rc ossible during initial hase of slow current decay disrution in JT-60U Tokamak. In the edge region, T e can be estimated by He I emission intensity ratio. The fundamental validity of the T e measurement based on He I emission line intensity ratio was confirmed by comaring with T e measurement by Langmuir robes in JT-60U [7] and NAGDIS-II [8], etc. According to ref. 7, T e estimated by He I line intensity ratio is almost same with T e by the robe within the factor of and the former is systematically smaller than the latter. We analyze 9 disrutive lasma shots with massive neon gas uffing. The safety factor, toroidal magnetic strength and NBI ower just before current quench is not same among the shots. In addition, the time evolution of lasma inductance during current quench is focused, and relation between current decay time and lasma inductance is evaluated. The equilibrium calculation of MHD, which is calculated by the CCS method, is used to estimate the lasma inductance.. Model of Current Decay Time If tokamak lasma is assumed to be reresented by a simle series circuit consisting of R and L, the energy conservation equation is exressed as 1 t t 1 L I + R 0 I dt = V 0 exi dt + L 0I 0, (1) where I and V ex is the lasma current and the externally alied voltage, L 0 and I 0 is lasma inductance and current just before current quench, resectively. When Eq. 1 is transformed, it becomes the following circuit equation: 1 L & I + LI& + R I = Vex. () In the small tokamaks, the right-hand side of Eq. cannot be neglect because the absolute value of the left-hand side of Eq. is the same order of magnitude as the absolute value of V ex [9]. On the other hand, the absolute value of V ex is usually smaller than the left-hand side of Eq. in the large tokamaks. This characteristic becomes more remarkable when device size becomes large. If R and L are constant in time, and V ex can be neglect, the temoral evolution of I can be exressed by the following equation, I = I 0 ex( t / τ L / R ), (3) where τ L/R = L /R is the time constant of I decay. Equation 3 is valid when the current decay time is very short and lasma resistance is sufficiently large. When the current decay time can be aroximated by τ L/R = L /R, the area-normalized current decay time τ /S can be exressed as τ L L R / πr / 0 =, (4) S η where R 0 is the lasma major radius, η is the lasma resistivity, and η = R S/πR 0. τ L/R /S has little deendence on the device size, because L is aroximately roortional to R 0, and has a strong deendence on η, which is rimarily determined by T e and Z eff in the classical Sitzer formula [10]. Thus, the database for ITER rediction is established in terms of the area-normalized current decay time τ /S [3]. However, when R and L greatly change in time, Eq. 4 cannot be valid. Therefore, to verify the L/R model, it is necessary to measure L and R in time during current quench exerimentally. 3. Exerimental Result 3.1. Relation Between Area-normalized Current Decay Time and Plasma Resistivity

3 3 EX/7-Rc In this aer, we study the current decay time in the radiation induced disrution by the massive neon gas uffing. The tyical waveform of lasma current I, line integrated electron density n e, lasma stored energy W and gas ressure of neon at disrution are shown in Fig. 1. After neon gas uffing, line integrated n e is gradually increased and W is decreased, and then the current quench and raid increase of line integrated n e are observed. We focus on the current decay during the initial hase of the current quench shown by the region enclosed by dotted line in Fig. (a), where I dros by 10%, because the T e rofile can be estimated by ECE diagnostic systems exerimentally. The exerimental current decay time during initial hase of current quench is defined by the following equation, τ % = I 0 ( I / t), (5) where I 0 is the lasma current at the current quench start time. In this discharge, thermal quench is haened around at sec and current quench is started about at 1.09 sec. From Fig. (c), it is found that T e rofile becomes flat at thermal quench and then returns to a eaked rofile in the initial hase. In this hase, T e in the core region is about 400 ev. Roughly seaking, because the otical thickness is small at T e < 100 ev, the sensitivity of ECE diagnostic systems becomes low and T e at normalized minor radius ρ > 0.4 cannot be estimated by ECE diagnostic systems. Here we use the He I emission intensity ratio method in (a) (b) t I FIG. 1. The tyical waveform of radiation induced disrution in JT-60U. (c) (d) (e) FIG. 3. Poloidal cross-section view of JT-60U lasma. Blue line means the line of sight for HeI sectroscoy. FIG.. The evaluation of (a) lasma current I and (b) electron temerature T e measured by ECE diagnostic system, (c) major radial rofile of T e., (d) He I emission intensity and (e) electron temerature by using HeI emission Intensity ratios method.

4 4 EX/7-Rc the case that the estimated T e by ECE is less than 100 ev. In order to measure the electron temerature, it is necessary to to measure three He I lines at the same time of ( 1 P 3 1 D), ( 3 P 3 3 S) and 78.1 nm ( 1 P 3 1 S) resectively. A sectrometer equied with three band ass interference filters makes it ossible to measure the time evolution of T e with a sufficient time resolution. Figure 3 shows the line of sight for measurement of ECE (crosses) and He I emission intensity (solid line). The He I emission intensity is measured from the outer diverter region though the edge region of ρ > 0.7. Figure (d) and (e) shows the measurement result of He I emission intensity and the estimated electron temerature. From Fig. (d), it is found that He I emission intensity increase raidly about at t = sec, which is the thermal quench start time. Before the thermal quench, the He I emission mainly comes from the diverter region because He neutrals only exist in this region. On the other hand, after the thermal quench, the He I emission comes from the edge region also because T e raidly decreases in the whole region due to the thermal quench. Since the measurement value of He I emission intensity is the integration value on line of sight and the measurement osition of T e estimated by He I emission intensity ratio cannot secify, it s osition is assumed ρ = 0.7. FIG. 4. Profile of electron temerature measured by ECE systems and He I sectroscoy at t = sec. Figure 4 shows the assumed T e rofile using measurement values of ECE diagnostic systems and He I emission intensity ratios method at t = sec. In this figure, oened circles and cross mean T e estimated by ECE systems and He I sectroscoy, resectively. The T e of ρ = and is assumed by a linear function. Unfortunately, we cannot obtain the accurate rofile of the lasma resistivity because the lasma effective charge Z eff cannot be measured in the initial hase of current quench. In order to seculate Z eff, we use the ionic fraction data of neon calculated by Arnaud and Rohtenflug [11]. If the mixing ratios of deuterium and neon gas are 9 : 1, 7 : 3 and 1 : 1 and these ratios are uniform in sace, the calculation results of Z eff and η are shown in Fig. 5. The η is calculated by Sitzer formula and assumed Z eff. In Fig. 5, the uer and lower values of error bar are values calculated using assumtions of D : Ne = 1 : 1 and 9 : 1, resectively. The values of Z eff in the core and edge region are about 7 and, resectively. In order to investigate the relation between area-normalized τ and lasma resistivity, we FIG. 5. Profile of lasma effective charge and resistivity at t = sec. The effective charge is calculated using the assumtion of D : Ne = 9 : 1, 7 : 3 and 1 : 1. FIG. 6. The area-normalized current decay time as a function the area-averaged T e -3/

5 5 EX/7-Rc use area-averaged T e -3/ calculated by T 3/ = ( / 3/ e S S T e ), (6) where S is the lasma cross-section area. This value is roortional to the area-averaged lasma resisitivity η with Z eff = 1. The area-averaged η can be estimated by η rofile in Fig.5 and following equation, η = S ( S / η ). (7) The relation between area-normalized τ and area-averaged T -3/ e is shown in Fig. 6. In Fig. 6, the T is calculated by Eq. 6 and the rofile of time averaged T -3/ e during the initial 3/ e hase of current quench. In the similar way, τ L/R /S is calculated by Eq. 4, 7 and the rofile of time averaged η. The uer and lower values of error bar of τ L/R /S are values calculated using assumtions of D : Ne = 9 : 1 and 1 : 1, resectively. It is found that the exerimental areanormalized τ is indeendent of the area-averaged T e -3/ and the rediction area-normalized decay time τ L/R /S calculated from L/R model is much longer than the exerimental value, esecially in the case of small exerimental values. It seems that this result means the L/R model does not verify and L is not constant and greatly changes in time during initial hase of current quench. 3.. Time Evolution of Plasma Inductance using CCS Method We use the CCS method using magnetic sensor signals due to evaluate the temoral evolution of lasma inductance and lasma shae. This method can obtain the exact analytical solution based on the boundary element method using a static Maxwell equation with a Green function in a toroidal axisymmetric region [1]. In a case of several magnetic sensors, we can obtain the aroximate solution of the magnetic field and flux according to the accuracy and the number of sensors. It was confirmed that the error of Shafranov lambda value calculated by this method is less than 0.1 in JT-60U measurement systems, which have 1 magnetic coils and 15 magnetic flux loos. Figures 7 show the results calculated by using a Cauchy condition (both Dirichlet and Neumann conditions) on a hyothetical surface. From Fig. 7(d), because R 0 is almost constant and S changes a little, lasma column hardly moves in the initial hase of current quench. In Fig. 7(b), since the lasma internal inductance l i is decrease raidly around at t = sec, the current density rofile becomes flat at thermal quench. This result is consistent of the measurement of T e using ECE systems as Fig. 1(c). After the flatting of current density rofile, it is found that l i much (a) (b) (c) (d) FIG. 7. The evolution of (a) lasma current, (b) lasma internal and inductance,(c) lasma internal and external inductance and (d) lasma cross-section and major radius evaluated by CCS method.

6 6 EX/7-Rc increases in time. This result is also consistent of ECE measurement results because T e rofile changes eaked rofile in Fig.1 (c). In Fig. 7(c), the lasma internal and external inductance is calculated by following equations, L i = µ 0R0li /, (8) L e = µ 0R0 ( ln8r0 / a ), (9) where a is the lasma minor radius. It is found that time change rate of L i is much larger than that of L e and time change rate of L is mainly determined by that of L i. Figure 8 shows the comarison of absolute value of R, L and time change rate of L in the initial hase of current quench. The R and L are calculated by R = πr 0 η /S and L = L i + L e, resectively and these values are time averaged values during initial hase of current quench. It is found that the absolute value of time change rate of L is the same order of magnitude as that of R or much larger than R in the short current decay time region. In addition, the exerimental current decay time is deendent on the time change rate of L. Therefore, it is necessary that the time change rate of L is taken into account in the circuit equation in order to accurately redict the current decay time in the initial hase of current quench Current Decay Model during Initial Phase of Current Quench From Eq. with V ex = 0, we obtain the following equation: I & L& / + R =. (10) I L To simlify the equation, if L & = L / t, R and L is constant in time, the rediction current decay time τ model can be reresented by τ L model = L / t + R. (11) Figure 9 shows the comarison of rediction times, which are calculated by L/R model and Eq. 11, and exerimental time. As FIG. 8. The lasma resistance R, the lasma inductance L and the time change rate of the lasma inductance as a function of current decay time. FIG.9. The comarison of the exerimental value and the model rediction value of current decay time in initial hase of current quench. shown in Fig.8, although is τ L/R much larger than the exerimental decay time in the short decay time region, τ model is same order of magnitude as exerimental decay time in some disrutive discharges and exerimental decay time increases with τ model. The time evolution of lasma inductance is almost determined by the change rate of lasma internal inductance. The above result indicates that the change rate of the lasma internal inductance associated with current rofile lays a key role to redict the recise current decay time during initial hase of current quench in JT-60U radiation induced disrutive lasmas. Here it should be noted the absolute value of τ model is not quite same as that of the exerimental decay time in Fig. 9. This result is mainly from an estimation error of lasma inductance because the

7 7 EX/7-Rc deendency of exerimental decay time on T e would be smaller than that on time change rate of L. As the candidate of the estimation error of inductance, the neglect of the eddy current during current quench in the CCS method should be considered in near future. 4. Summary We have investigated the current decay time using the initial hase of JT-60U radiation induced disrutive discharges exerimentally. The lasma resistance is estimated by ECE diagnostic systems and He I emission intensity ratios and the lasma inductance is calculated by CCS method using magnetic sensor signals. It is exerimentally confirmed that the areanormalized decay time in initial hase of current quench is indeendent of the electron temerature and decay time calculated from L/R model is larger than the exerimental decay time. This result indicates that the lasma inductance greatly changes in time. The time change rate of lasma inductance estimated by CCS method is the same order of magnitude as lasma resistance or much larger than lasma resistance. So, we consider a new model of the current decay time, which is taking the time evolution of the lasma inductance into account in the circuit equation. The rediction of the current decay time redicted by the new model is strongly deendent on the exerimental time and these absolute values are almost same. Therefore, the change rate of the lasma internal inductance lays a key role to redict the recise current decay time during initial hase of current quench in JT-60U tokamak. Here, it should be noted the new rediction value is not quite same as the exerimental value. As the reason of this result, the neglect of the eddy current during current quench in the CCS method is considered. As the future works, we should imrove the CCS method by taking the eddy current effect into account and make sure the validity of the CCS method through the direct measurement of the current rofile like the MSE. In this aer, we have just investigated the validity of L/R model. As a next ste, we should investigate what dominate the time change rate of the lasma inductance. This is one of our future subjects. References [1] Kurihara K., Fusion Eng. Des., 51-5 (000) [] Masaki K., Ando T., Kodama K., Arai T. et al., J. Nucl. Mater. 0- (1995) 390. [3] Progress in the ITER Physical Basis, Nuclear Fusion 47 (007) S171. [4] Wesley J.C., Hyatt A.W., Strait E. J. and Schissel D. P. et al., Proceedings of 1st IAEA Fusion Energy Conference, Chengdu, 16-1 Oct. (006) IT/P1-1. [5] Whyte D.G., Humhrevs D.A. and Taylor P. L., Phys. Plasma 19 (000) 405. [6] Humhrevs D.A. and Whyte D.G., Phys. Plasma 19 (000) [7] Kubo H., Goto M. and Takenaga H. et al., J. Plasma and Fusion Res., 75 (1999) 945. [8] Kajita S., Ohno N. and Takamura S. et al., Physics of Plasmas, 13 (006) [9] Okamoto M., Ohno N. and Takamura S., J. Plasma and Fusion Res., 3 (008) [10] Sitzer L. and Härm R., Physical Review 89 (1953) 977. [11] Arnaud M., Rohtenflug R., Astron. Astrohys. Sul. Ser. 60 (1985) 45.