- Email: [email protected]
Plasma start-up design and first plasma experiment in VEST
Fusion Engineering and Design 96–97 (2015) 274–280
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Plasma start-up design and first plasma experiment in VEST YoungHwa An, Jeongwon Lee, HyunYeong Lee, JongGab Jo, Bong-Ki Jung, Kyoung-Jae Chung, Young-Gi Kim, Jungmin Jo, Jeong-hun Yang, Yong-Su Na, T.S. Hahm, Y.S. Hwang ∗ Department of Nuclear Engineering, Seoul National University, Seoul, South Korea
h i g h l i g h t s • • • •
First plasma start-up experiment in VEST has been successfully carried out. A start-up design code is developed to generate start-up scenarios in predictive manner. Start-up scenarios are developed with the code and confirmed experimentally in VEST. Full tokamak equilibria (Ip = 70 kA, = 1.6 and qedge = 3.7) are achieved from the scenario.
a r t i c l e
i n f o
Article history: Received 6 October 2014 Received in revised form 24 April 2015 Accepted 7 May 2015 Available online 4 June 2015 Keywords: Spherical torus Start-up ECH pre-ionization
a b s t r a c t First plasma start-up experiment in Versatile Experiment Spherical Torus (VEST) has been successfully carried out with conventional start-up scheme using a central solenoid. A start-up design code has been developed for the development of start-up scenarios in VEST, which can predict evolutions of vacuum field structure and plasma current with given operation parameters from the PF coil power supply circuit considering the eddy currents. Start-up scenarios are successfully developed with the code, generating field null region in the inboard side at the onset of loop voltage in order to maximize the connection length, and then providing the required poloidal magnetic field for stable equilibrium as the plasma current evolves. Hydrogen is used as a working gas and the toroidal field of 0.1 T with 0.2 s flat-top is applied on magnetic axis during the discharge. With the assist of ECH (Electron Cyclotron Heating) preionization (6 kW, 2.45 GHz), a plasma current of ∼70 kA has been generated with the pulse duration of ∼10 ms. The elongation and edge safety factor are estimated to be 1.6 and 3.7 respectively. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The VEST (Versatile Experiment Spherical Torus) is the first Korean spherical torus, located at Seoul National University. The main device parameters are major radius of 0.4 m, aspect ratio of >1.3 and toroidal magnetic field of 0.1 T on axis. The main objective of VEST is to conduct basic research on a compact, high- spherical torus with an elongated chamber and novel partial ohmic solenoids. Partial solenoids will be utilized for the double plasma merging start-up, which was pioneered by UTST [1,2,3]. UTST has utilized outer PF coils to provide the loop voltage for double plasma merging start-up but partial solenoids of VEST are expected to provide
∗ Corresponding author. Tel.: +82 2 880 6276; fax: +82 2 889 2688. E-mail address: [email protected] (Y.S. Hwang). http://dx.doi.org/10.1016/j.fusengdes.2015.05.015 0920-3796/© 2015 Elsevier B.V. All rights reserved.
higher loop voltage with less stray field inside the vacuum vessel. Details of the device from key design concepts to commissioning results can be found in elsewhere [4–8]. After successful construction and commissioning of VEST, first plasma experiments have been conducted. ECH (Electron Cyclotron Heating) pre-ionization has been utilized for the reliable start-up with limited volt-second under severe eddy currents, and startup scenarios have been developed systematically by developing a start-up design code, which can predict the evolution of vacuum field structure with given operation parameters of the PF coil power supply circuits by considering eddy currents at the thick vacuum vessel wall. With the start-up code the start-up scenario of VEST has been improved so that plasma current, Ip of ∼70 kA with pulse duration of ∼10 ms has been achieved so far. Overall schematic drawing of VEST as well as the PF coil configuration is shown in Fig. 1.
Y. An et al. / Fusion Engineering and Design 96–97 (2015) 274–280
275
Following empirical formula is widely used to evaluate the condition for the reliable start-up with pre-ionization in practical use [9,10]; Et
Bt > 100 [V/m] Bp
(1)
where Et , Bt and Bp are the toroidal electric field, toroidal magnetic field and poloidal magnetic field, respectively. After successful current initiation with sufficient plasma breakdown, the equilibrium field should be provided for further Ip evolution; the vertical field proportional to Ip should be provided with decay index, n of 0–1.5 for the radial force balance with vertical stability as the plasma current develops [12–15]. Since it is not possible to provide high Et ·Bt /Bp for Ip initiation and stable equilibrium field for Ip ramp-up simultaneously, the plasma start-up generally starts with the formation of sufficient field null region followed by the stable equilibrium field. 2.2. Requirements for the start-up design For the development of start-up scenarios of VEST, the vacuum field structure inside the vacuum vessel and related parameters such as Et ·Bt /Bp and decay index should be calculated accurately in predictive manner with operation parameters of PF power supply. PF power supplies of VEST are based on the double swing circuit, in which the current waveform is determined by the capacitances, charging voltages and switching times. However, significant eddy currents are induced at the toroidally continuous vacuum vessel wall due to relatively thick wall for structural integrity and high electric field especially at the inside corner from the low aspect ratio [4], which results in the distortion of the vacuum field structure with reduced loop voltage. The PF current waveforms significantly affect and are affected by the current waveform of other PF coils and eddy currents via mutual inductance. Therefore, for the development the start-up scenarios, the power supply circuits coupled with each other and eddy currents at the wall should be modeled
Fig. 1. (a) Overall schematic drawing of VEST with dimension and (b) geometry of VEST PF coils (yellow), vacuum vessel wall (blue) and inboard limiter (red). (For interpretation of references to color in this figure legend, the reader is referred to the web version of this article.)
In this paper, detailed descriptions on the first plasma experiments of VEST are presented. In Section 2, start-up scenario development by using the start-up design code is described. In Section 3, results of the first plasma experiments are presented. Conclusions and future plans are followed in Section 4. 2. Start-up scenario development 2.1. Required conditions for the reliable start-up The plasma breakdown in tokamaks including spherical tori is generally described by Townsend avalanche theory [9–11].
Fig. 2. Calculated PF currents of the typical start-up scenario and the measured PF currents with identical operation parameters.
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simultaneously to predict the evolution of vacuum field structure accurately with given power supply parameters. In addition to the accurate estimation of the vacuum field, the initial guess of Ip evolution is required for the development of start-up scenarios since the vertical field proportional to Ip should be provided for equilibrium appropriately. 2.3. Development of the start-up design code
Fig. 3. Comparison of the estimated plasma current by the start-up design code and the actual plasma current measured during a discharge with identical operation parameters.
A start-up design code has been developed fulfilling the requirements explained above by integration of the circuit approximation model for eddy current estimation, the power supply circuit model for PF coil current estimation, and the plasma current estimation model required to determine the vertical field strength for equilibrium in self-consistent manner. The start-up design code is implemented based on the circuit approximation, which is widely used method for the estimation of eddy current in many devices [13–16]. The PF coils and vacuum vessel are discretized into multiple filaments with equivalent
Fig. 4. (a) A poloidal magnetic field strength contours [Gauss] at the current initiation phase (403 ms), (b) a Et ·Bt /Bp contour [V/m] at the current initiation phase (403 ms), (c) a poloidal magnetic field strength contour [Gauss] at the ramp-up phase (408 ms) and (d) a decay index contour at the ramp-up phase (408 ms).
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resistance and inductance. The current of each filament can be solved by a simple circuit equation as following: M
− → dI − → + R I = → V, dt
(2)
where M is the square matrix whose elements are the inductances between coils and vacuum vessel filaments, R is the diagonal matrix whose elements are the resistances of each filament, I is the vector of currents at each filament, and → V is the time transient voltage applied to each filament. The power supply circuit has been modeled by calculating the voltages applied to PF coils based on following equation: 1 Vn = − Cn
t
In ()d
(3)
t0
where Vn is the voltage of capacitor bank applied to each PF coil, Cn is the capacitance of each power supply and In is the current of each PF coil. This equation models the time transient voltage of the capacitor bank in each power supply, which is applied to each PF coil. The switching has been implemented by replacing the capacitance and the initial charging voltage at each switching time. In this manner, the PF current waveforms, eddy currents and voltage applied to PF coil by capacitor bank are calculated self-consistently. The wall geometry has been carefully developed for accurate calculation of eddy currents, and the resistance of cable between power supply and PF coil has been taken account for more accurate calculation. The estimated PF coil current by the code shows a good agreement with the measured PF coil current with identical operation parameters, as shown in Fig. 2. The actual vacuum field measured by magnetic probe and the estimated vacuum field by the code with given operational parameters have been compared as well, which shows a fairly good agreement with errors of less than 3%. In addition to the prediction of the vacuum field evolution, initial guess of Ip evolution is required for the estimation of the required vertical field for the equilibrium. By introducing CEjima ,
277
Ejima coefficient, for resistive consumption during ramp-up phase, Ip evolution can be expressed as following [13,14,17]: Vloop dIp = , Lp + 0 R0 CEjima dt
(4)
where Vloop is the loop voltage and Lp is the plasma inductance. CEjima ∼ 0.4 has been used for the estimation of Ip evolution in VEST, which is similar to values found in other devices such as NSTX and DIII-D [18,19]. As it is experimentally found in VEST that Ip initiation and subsequent ramp-up are possible only when the decay index is stable range with the direction of vertical field as equilibrium field, this condition has been used to determine the timing of Ip initiation. Relatively accurate estimation of Ip is possible as shown in Fig. 3, but the Ip evolution varies even with identical operational scenario, which is considered to be related with the wall condition and consequent change of resistive consumption of volt-seconds. Therefore, the vertical field has been adjusted based on the actually measured Ip during the discharge after an experiment is analyzed for the given start-up scenario. 2.4. Typical start-up scenario Start-up scenarios of VEST are developed in predictive manner by using the start-up design code. PF coil current waveforms of a typical discharge scenario are depicted in Fig. 2. While PF#1 (central solenoid) provides magnetic flux by double swing scheme, PF#10 generates field null configuration in accordance with PF#1. At the current initiation phase around 403 ms, large field null area where the poloidal magnetic field strength is below 10 Gauss is formed with Et ·Bt /Bp > 100 V/m [9] as shown in Fig. 4(a) and (b). After field null region is formed, PF#6 and PF#9 provide the vertical magnetic field for radial force balance and the radial field for vertical stability using the single swing scheme. At the Ip ramp-up phase, proper vertical and radial magnetic fields are provided for the force balance with vertical stability with 0 < n < 3/2 [12–15] as shown in Fig. 4(c) and (d).
Fig. 5. Typical discharge procedure of first plasma experiment in VEST.
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Fig. 6. Plasma current, loop voltage, H␣ and OI (777 nm) line emission during a typical plasma start-up in VEST. (Shot #10142).
Fig. 7. The plasma position and shape reconstructed by multi-filament approximation and fast camera image during a discharge. (Shot #10142).
Y. An et al. / Fusion Engineering and Design 96–97 (2015) 274–280
3. Ohmic start-up experiment in VEST 3.1. Typical discharge procedure and conditions Typical discharge procedure for the first plasma experiment in VEST is depicted in Fig. 5. At the onset of a discharge, the TF power supply is triggered and it takes about 200 ms for the TF coil current to reach the flat-top value of 8.3 kA (0.1 T at R0 = 0.4 m). Relatively long TF flat-top with the duration of 400 ms is generated with battery-powered TF coil. The TF power supply is turned off at 550 ms by sequentially turning off each battery module [4,7]. The PF#1 coil current is ramped up at 387 ms and starts to swing down at 400 ms providing loop voltage. Typically loop voltage of ∼3 V is provided but the loop voltage varies with time. Volt-seconds of up to ∼43 mV s can be provided by the PF#1 coil in the typical start-up scenario. Hydrogen is used as working gas and injected into vacuum vessel using piezoelectric valve at ∼340 ms. Typical operation pressure is 2–3 × 10−5 Torr with the base pressure of >5 × 10−7 Torr. The injected gas is pre-ionized by ECH at several tens of ms before the swing down of the PF#1 coil. Typically ECH power of 6 kW with the frequency of 2.45 GHz is injected for the pre-ionization. 3.2. Results of the first plasma experiment The Ip waveform during the typical discharge is shown in Fig. 6. The maximum Ip of ∼70 kA with the pulse duration of ∼10 ms has been obtained so far. Fig. 7 shows the time evolution of plasma boundary reconstructed by multi-filament method as well as fast camera images during the discharge. The fast camera image shows that the plasma column always starts to form at ∼403 ms in the inboard side where the toroidal electric field is highest, but soon it moves toward outboard side until sufficient vertical field is provided to push the plasma back toward inboard side. The formation of tokamak equilibrium with closed flux surfaces has been confirmed and the plasma elongation, has been calculated to be 1.6 with edge safety factor qa of 3.7. As shown in Fig. 6, Ip starts to kick-up at ∼403 ms when loop voltage exceeds ∼2 V and starts decreasing at ∼409 ms though sufficient loop voltage of ∼2 V is still provided. Both H␣ and OI line emission start increasing at this time, which indicates that oxygen or water vapor impurities from the inner vacuum vessel wall prevent further Ip increase and sustainment. The plasma boundary shown in Fig. 7 also tells that Ip starts to decrease when the plasma
279
touches the inboard tungsten limiter sheet indicating that impurities from the inboard side wall are critical in VEST. The fast camera image with H␣ filter also shows the bright emission at the inboard side when the plasma touches the inboard limiter. GDC (Glow Discharge Cleaning) has been conducted for wall conditioning in VEST using helium as working gas. The plasma current has been significantly increased with reduced OI line emission after wall conditioning by GDC as shown in Fig. 8. Further upgrade of the GDC system to increase ion fluence to the wall is under preparation. In addition, in-vacuum UV lamps will be installed for in situ UV irradiation to remove water on the inner surface of vacuum vessel [20]. The discharge scenario optimization to minimize the plasma wall interaction is under preparation as well. 4. Conclusions and future plans The start-up design code has been developed for the development of start-up scenarios in VEST, which can predict the vacuum field structure and the Ip evolution with given operation parameters considering the eddy currents at the wall and their influence on the PF coil current self-consistently. First plasma start-up experiments in VEST have been successfully carried out with the conventional start-up scheme using a central solenoid based on start-up scenarios developed by the start-up design code, and Ip of ∼70 kA with pulse duration of ∼10 ms has been achieved with the assist of 6 kW ECH pre-ionization. The evolution to full tokamak equilibrium is confirmed by the plasma boundary identification, and the elongation and edge safety factor are estimated to be 1.6 and 3.7, respectively. However, an early quench of Ip even with sufficient loop voltage is observed, which is considered to be resulted from the significant impurity influx by plasma wall interactions. Relatively accurate estimation of vacuum field evolution is possible even under severe eddy currents induced at the toroidally continuous wall by using rather simple circuit approximation method with careful adjustment of the wall model. The interaction between PF coils and eddy current has been estimated accurately by including simple model of power supply circuit as well. While rough estimation of the Ip is possible by a simple circuit model assuming proper Ejima coefficient, further investigation on the plasma model during the start-up is required for more accurate modeling of Ip evolution. A 0-D code that calculates the evolution of plasma parameters based on power balance and particle balance is under preparation for more accurate estimation of the resistive component of magnetic flux consumption and consequent change of Ip evolution. The plasma wall interaction model can be included for better estimation of the plasma resistivity as well. For further increase of Ip and pulse duration, improved GDC and in situ UV irradiation is under preparation for better wall condition. The improvement of discharge scenario is also in progress to minimize the plasma wall interaction. Since higher elongation can accommodate higher Ip as well as higher edge safety factor, the scenario optimization for higher elongation is on-going as well as the construction of the PF power-supply for the feedback control of plasma vertical position in the elongated plasma. In addition, investigation on the optimal condition for the ECH assisted start-up is on progress as well as various plasma start-up scenarios such as double null plasma merging scheme [1–3] using partial solenoid coils and various non-inductive start-up methods. As the target plasma is established, heating ad current drive experiments by using electron Bernstein wave and neutral beam injection will be attempted as well. Acknowledgments
Fig. 8. Plasma current and OI line emission before and after GDC.
This work was supported by National R&D Program through the National Research Foundation of Korea (NRF) funded
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by the Ministry of Science, ICT and Future Planning (No. 2014M1A7A1A03045367 and 2008-0061900) and also supported by the NRF (No. NRF-2012K2A2A6000505). References [1] T. Yamada, R. Imazawa, S. Kamio, R. Hihara, K. Abe, M. Sakumura, et al., Plasma Fusion Res. 5 (2010) S2100. [2] R. Imazawa, S. Kamio, R. Hihara, K. Abe, M. Sakamura, O. Cao, et al., Electric. Eng. Jpn. 179 (2012) 18. [3] M. Inomoto, T.G. Watanabe, K. Gi, K. Yamasaki, S. Kamio, R. Imazawa, et al., Nucl. Fusion 55 (2015) 033013. [4] K.J. Chung, Y.H. An, B.K. Jung, H.Y. Lee, C. Sung, Y.S. Na, et al., Plasma Sci. Technol. 15 (2013) 244. [5] K.J. Chung, Y.H. An, B.K. Jung, H.Y. Lee, J.J. Dang, J.W. Lee, et al., Fusion Eng. Des. 88 (2013) 787. [6] Y.H. An, K.J. Chung, D.H. Na, Y.S. Hwang, Fusion Eng. Des. 88 (2013) 1204. [7] B.K. Jung, K.J. Chung, Y.H. An, J.S. Kang, Y.S. Hwang, Fusion Eng. Des. 88 (2013) 1597. [8] J.W. Lee, K.J. Chung, Y.H. An, J.H. Yang, Y.G. Kim, B.K. Jung, et al., Fusion Eng. Des. 88 (2013) 1327.
[9] B. Lloyd, G.L. Jackson, T.S. Taylor, E.A. Lazarus, T.C. Luce, R. Prater, Nucl. Fusion 31 (1991) 2031. [10] ITER Physics Expert Group on Disruptions, Plasma Control, and MHD, ITER Physics Expert Group on Energetic Particles, Heating and Current Drive, ITER Physics Expert Group on Diagnostics, ITER Physics Basis Editors, Nuclear Fusion 39 (1999) 2577. [11] M.A. Lieberman, A.J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, Wiley-Interscience, 2005. [12] J. Wesson, Tokamaks, Clarendon Press, Oxford, New York, 2004. [13] J.A. Leuer, N.W. Eidietis, J.R. Ferron, D.A. Humphreys, A.W. Hyatt, G.L. Jackson, et al., IEEE Trans. Plasma Sci. 38 (2010) 333. [14] J.A. Leuer, B.J. Xiao, D.A. Humphreys, M.L. Walker, A.W. Hyatt, G.L. Jackson, et al., Fusion Sci. Technol. 57 (2010) 48. [15] J. Kim, W. Choe, M. Ono, Plasma Phys. Controlled Fusion 46 (2004) 1647. [16] R.D. Pillsbury, S.P. Hakkarainen, Proceedings of IEEE Thirteenth Symposium on Fusion Engineering, 1989, p. 642. [17] S. Ejima, R.W. Callis, J.L. Luxon, R.D. Stambaugh, T.S. Taylor, J.C. Wesley, Nucl. Fusion 22 (1982) 1313. [18] J.E. Menard, B.P. LeBlanc, S.A. Sabbagh, M.G. Bell, R.E. Bell, E.D. Fredrickson, et al., Nucl. Fusion 41 (2001) 1197. [19] G.L. Jackson, P.A. Politzer, D.A. Humphreys, T.A. Casper, A.W. Hyatt, J.A. Leuer, et al., Phys. Plasmas 17 (2010) 056116. [20] A. Berman, Vacuum 47 (1996) 327.
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Plasma start-up design and first plasma experiment in VEST YoungHwa An, Jeongwon Lee, HyunYeong Lee, JongGab Jo, Bong-Ki Jung, Kyoung-Jae Chung, Young-Gi Kim, Jungmin Jo, Jeong-hun Yang, Yong-Su Na, T.S. Hahm, Y.S. Hwang ∗ Department of Nuclear Engineering, Seoul National University, Seoul, South Korea
h i g h l i g h t s • • • •
First plasma start-up experiment in VEST has been successfully carried out. A start-up design code is developed to generate start-up scenarios in predictive manner. Start-up scenarios are developed with the code and confirmed experimentally in VEST. Full tokamak equilibria (Ip = 70 kA, = 1.6 and qedge = 3.7) are achieved from the scenario.
a r t i c l e
i n f o
Article history: Received 6 October 2014 Received in revised form 24 April 2015 Accepted 7 May 2015 Available online 4 June 2015 Keywords: Spherical torus Start-up ECH pre-ionization
a b s t r a c t First plasma start-up experiment in Versatile Experiment Spherical Torus (VEST) has been successfully carried out with conventional start-up scheme using a central solenoid. A start-up design code has been developed for the development of start-up scenarios in VEST, which can predict evolutions of vacuum field structure and plasma current with given operation parameters from the PF coil power supply circuit considering the eddy currents. Start-up scenarios are successfully developed with the code, generating field null region in the inboard side at the onset of loop voltage in order to maximize the connection length, and then providing the required poloidal magnetic field for stable equilibrium as the plasma current evolves. Hydrogen is used as a working gas and the toroidal field of 0.1 T with 0.2 s flat-top is applied on magnetic axis during the discharge. With the assist of ECH (Electron Cyclotron Heating) preionization (6 kW, 2.45 GHz), a plasma current of ∼70 kA has been generated with the pulse duration of ∼10 ms. The elongation and edge safety factor are estimated to be 1.6 and 3.7 respectively. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The VEST (Versatile Experiment Spherical Torus) is the first Korean spherical torus, located at Seoul National University. The main device parameters are major radius of 0.4 m, aspect ratio of >1.3 and toroidal magnetic field of 0.1 T on axis. The main objective of VEST is to conduct basic research on a compact, high- spherical torus with an elongated chamber and novel partial ohmic solenoids. Partial solenoids will be utilized for the double plasma merging start-up, which was pioneered by UTST [1,2,3]. UTST has utilized outer PF coils to provide the loop voltage for double plasma merging start-up but partial solenoids of VEST are expected to provide
∗ Corresponding author. Tel.: +82 2 880 6276; fax: +82 2 889 2688. E-mail address: [email protected] (Y.S. Hwang). http://dx.doi.org/10.1016/j.fusengdes.2015.05.015 0920-3796/© 2015 Elsevier B.V. All rights reserved.
higher loop voltage with less stray field inside the vacuum vessel. Details of the device from key design concepts to commissioning results can be found in elsewhere [4–8]. After successful construction and commissioning of VEST, first plasma experiments have been conducted. ECH (Electron Cyclotron Heating) pre-ionization has been utilized for the reliable start-up with limited volt-second under severe eddy currents, and startup scenarios have been developed systematically by developing a start-up design code, which can predict the evolution of vacuum field structure with given operation parameters of the PF coil power supply circuits by considering eddy currents at the thick vacuum vessel wall. With the start-up code the start-up scenario of VEST has been improved so that plasma current, Ip of ∼70 kA with pulse duration of ∼10 ms has been achieved so far. Overall schematic drawing of VEST as well as the PF coil configuration is shown in Fig. 1.
Y. An et al. / Fusion Engineering and Design 96–97 (2015) 274–280
275
Following empirical formula is widely used to evaluate the condition for the reliable start-up with pre-ionization in practical use [9,10]; Et
Bt > 100 [V/m] Bp
(1)
where Et , Bt and Bp are the toroidal electric field, toroidal magnetic field and poloidal magnetic field, respectively. After successful current initiation with sufficient plasma breakdown, the equilibrium field should be provided for further Ip evolution; the vertical field proportional to Ip should be provided with decay index, n of 0–1.5 for the radial force balance with vertical stability as the plasma current develops [12–15]. Since it is not possible to provide high Et ·Bt /Bp for Ip initiation and stable equilibrium field for Ip ramp-up simultaneously, the plasma start-up generally starts with the formation of sufficient field null region followed by the stable equilibrium field. 2.2. Requirements for the start-up design For the development of start-up scenarios of VEST, the vacuum field structure inside the vacuum vessel and related parameters such as Et ·Bt /Bp and decay index should be calculated accurately in predictive manner with operation parameters of PF power supply. PF power supplies of VEST are based on the double swing circuit, in which the current waveform is determined by the capacitances, charging voltages and switching times. However, significant eddy currents are induced at the toroidally continuous vacuum vessel wall due to relatively thick wall for structural integrity and high electric field especially at the inside corner from the low aspect ratio [4], which results in the distortion of the vacuum field structure with reduced loop voltage. The PF current waveforms significantly affect and are affected by the current waveform of other PF coils and eddy currents via mutual inductance. Therefore, for the development the start-up scenarios, the power supply circuits coupled with each other and eddy currents at the wall should be modeled
Fig. 1. (a) Overall schematic drawing of VEST with dimension and (b) geometry of VEST PF coils (yellow), vacuum vessel wall (blue) and inboard limiter (red). (For interpretation of references to color in this figure legend, the reader is referred to the web version of this article.)
In this paper, detailed descriptions on the first plasma experiments of VEST are presented. In Section 2, start-up scenario development by using the start-up design code is described. In Section 3, results of the first plasma experiments are presented. Conclusions and future plans are followed in Section 4. 2. Start-up scenario development 2.1. Required conditions for the reliable start-up The plasma breakdown in tokamaks including spherical tori is generally described by Townsend avalanche theory [9–11].
Fig. 2. Calculated PF currents of the typical start-up scenario and the measured PF currents with identical operation parameters.
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simultaneously to predict the evolution of vacuum field structure accurately with given power supply parameters. In addition to the accurate estimation of the vacuum field, the initial guess of Ip evolution is required for the development of start-up scenarios since the vertical field proportional to Ip should be provided for equilibrium appropriately. 2.3. Development of the start-up design code
Fig. 3. Comparison of the estimated plasma current by the start-up design code and the actual plasma current measured during a discharge with identical operation parameters.
A start-up design code has been developed fulfilling the requirements explained above by integration of the circuit approximation model for eddy current estimation, the power supply circuit model for PF coil current estimation, and the plasma current estimation model required to determine the vertical field strength for equilibrium in self-consistent manner. The start-up design code is implemented based on the circuit approximation, which is widely used method for the estimation of eddy current in many devices [13–16]. The PF coils and vacuum vessel are discretized into multiple filaments with equivalent
Fig. 4. (a) A poloidal magnetic field strength contours [Gauss] at the current initiation phase (403 ms), (b) a Et ·Bt /Bp contour [V/m] at the current initiation phase (403 ms), (c) a poloidal magnetic field strength contour [Gauss] at the ramp-up phase (408 ms) and (d) a decay index contour at the ramp-up phase (408 ms).
Y. An et al. / Fusion Engineering and Design 96–97 (2015) 274–280
resistance and inductance. The current of each filament can be solved by a simple circuit equation as following: M
− → dI − → + R I = → V, dt
(2)
where M is the square matrix whose elements are the inductances between coils and vacuum vessel filaments, R is the diagonal matrix whose elements are the resistances of each filament, I is the vector of currents at each filament, and → V is the time transient voltage applied to each filament. The power supply circuit has been modeled by calculating the voltages applied to PF coils based on following equation: 1 Vn = − Cn
t
In ()d
(3)
t0
where Vn is the voltage of capacitor bank applied to each PF coil, Cn is the capacitance of each power supply and In is the current of each PF coil. This equation models the time transient voltage of the capacitor bank in each power supply, which is applied to each PF coil. The switching has been implemented by replacing the capacitance and the initial charging voltage at each switching time. In this manner, the PF current waveforms, eddy currents and voltage applied to PF coil by capacitor bank are calculated self-consistently. The wall geometry has been carefully developed for accurate calculation of eddy currents, and the resistance of cable between power supply and PF coil has been taken account for more accurate calculation. The estimated PF coil current by the code shows a good agreement with the measured PF coil current with identical operation parameters, as shown in Fig. 2. The actual vacuum field measured by magnetic probe and the estimated vacuum field by the code with given operational parameters have been compared as well, which shows a fairly good agreement with errors of less than 3%. In addition to the prediction of the vacuum field evolution, initial guess of Ip evolution is required for the estimation of the required vertical field for the equilibrium. By introducing CEjima ,
277
Ejima coefficient, for resistive consumption during ramp-up phase, Ip evolution can be expressed as following [13,14,17]: Vloop dIp = , Lp + 0 R0 CEjima dt
(4)
where Vloop is the loop voltage and Lp is the plasma inductance. CEjima ∼ 0.4 has been used for the estimation of Ip evolution in VEST, which is similar to values found in other devices such as NSTX and DIII-D [18,19]. As it is experimentally found in VEST that Ip initiation and subsequent ramp-up are possible only when the decay index is stable range with the direction of vertical field as equilibrium field, this condition has been used to determine the timing of Ip initiation. Relatively accurate estimation of Ip is possible as shown in Fig. 3, but the Ip evolution varies even with identical operational scenario, which is considered to be related with the wall condition and consequent change of resistive consumption of volt-seconds. Therefore, the vertical field has been adjusted based on the actually measured Ip during the discharge after an experiment is analyzed for the given start-up scenario. 2.4. Typical start-up scenario Start-up scenarios of VEST are developed in predictive manner by using the start-up design code. PF coil current waveforms of a typical discharge scenario are depicted in Fig. 2. While PF#1 (central solenoid) provides magnetic flux by double swing scheme, PF#10 generates field null configuration in accordance with PF#1. At the current initiation phase around 403 ms, large field null area where the poloidal magnetic field strength is below 10 Gauss is formed with Et ·Bt /Bp > 100 V/m [9] as shown in Fig. 4(a) and (b). After field null region is formed, PF#6 and PF#9 provide the vertical magnetic field for radial force balance and the radial field for vertical stability using the single swing scheme. At the Ip ramp-up phase, proper vertical and radial magnetic fields are provided for the force balance with vertical stability with 0 < n < 3/2 [12–15] as shown in Fig. 4(c) and (d).
Fig. 5. Typical discharge procedure of first plasma experiment in VEST.
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Fig. 6. Plasma current, loop voltage, H␣ and OI (777 nm) line emission during a typical plasma start-up in VEST. (Shot #10142).
Fig. 7. The plasma position and shape reconstructed by multi-filament approximation and fast camera image during a discharge. (Shot #10142).
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3. Ohmic start-up experiment in VEST 3.1. Typical discharge procedure and conditions Typical discharge procedure for the first plasma experiment in VEST is depicted in Fig. 5. At the onset of a discharge, the TF power supply is triggered and it takes about 200 ms for the TF coil current to reach the flat-top value of 8.3 kA (0.1 T at R0 = 0.4 m). Relatively long TF flat-top with the duration of 400 ms is generated with battery-powered TF coil. The TF power supply is turned off at 550 ms by sequentially turning off each battery module [4,7]. The PF#1 coil current is ramped up at 387 ms and starts to swing down at 400 ms providing loop voltage. Typically loop voltage of ∼3 V is provided but the loop voltage varies with time. Volt-seconds of up to ∼43 mV s can be provided by the PF#1 coil in the typical start-up scenario. Hydrogen is used as working gas and injected into vacuum vessel using piezoelectric valve at ∼340 ms. Typical operation pressure is 2–3 × 10−5 Torr with the base pressure of >5 × 10−7 Torr. The injected gas is pre-ionized by ECH at several tens of ms before the swing down of the PF#1 coil. Typically ECH power of 6 kW with the frequency of 2.45 GHz is injected for the pre-ionization. 3.2. Results of the first plasma experiment The Ip waveform during the typical discharge is shown in Fig. 6. The maximum Ip of ∼70 kA with the pulse duration of ∼10 ms has been obtained so far. Fig. 7 shows the time evolution of plasma boundary reconstructed by multi-filament method as well as fast camera images during the discharge. The fast camera image shows that the plasma column always starts to form at ∼403 ms in the inboard side where the toroidal electric field is highest, but soon it moves toward outboard side until sufficient vertical field is provided to push the plasma back toward inboard side. The formation of tokamak equilibrium with closed flux surfaces has been confirmed and the plasma elongation, has been calculated to be 1.6 with edge safety factor qa of 3.7. As shown in Fig. 6, Ip starts to kick-up at ∼403 ms when loop voltage exceeds ∼2 V and starts decreasing at ∼409 ms though sufficient loop voltage of ∼2 V is still provided. Both H␣ and OI line emission start increasing at this time, which indicates that oxygen or water vapor impurities from the inner vacuum vessel wall prevent further Ip increase and sustainment. The plasma boundary shown in Fig. 7 also tells that Ip starts to decrease when the plasma
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touches the inboard tungsten limiter sheet indicating that impurities from the inboard side wall are critical in VEST. The fast camera image with H␣ filter also shows the bright emission at the inboard side when the plasma touches the inboard limiter. GDC (Glow Discharge Cleaning) has been conducted for wall conditioning in VEST using helium as working gas. The plasma current has been significantly increased with reduced OI line emission after wall conditioning by GDC as shown in Fig. 8. Further upgrade of the GDC system to increase ion fluence to the wall is under preparation. In addition, in-vacuum UV lamps will be installed for in situ UV irradiation to remove water on the inner surface of vacuum vessel [20]. The discharge scenario optimization to minimize the plasma wall interaction is under preparation as well. 4. Conclusions and future plans The start-up design code has been developed for the development of start-up scenarios in VEST, which can predict the vacuum field structure and the Ip evolution with given operation parameters considering the eddy currents at the wall and their influence on the PF coil current self-consistently. First plasma start-up experiments in VEST have been successfully carried out with the conventional start-up scheme using a central solenoid based on start-up scenarios developed by the start-up design code, and Ip of ∼70 kA with pulse duration of ∼10 ms has been achieved with the assist of 6 kW ECH pre-ionization. The evolution to full tokamak equilibrium is confirmed by the plasma boundary identification, and the elongation and edge safety factor are estimated to be 1.6 and 3.7, respectively. However, an early quench of Ip even with sufficient loop voltage is observed, which is considered to be resulted from the significant impurity influx by plasma wall interactions. Relatively accurate estimation of vacuum field evolution is possible even under severe eddy currents induced at the toroidally continuous wall by using rather simple circuit approximation method with careful adjustment of the wall model. The interaction between PF coils and eddy current has been estimated accurately by including simple model of power supply circuit as well. While rough estimation of the Ip is possible by a simple circuit model assuming proper Ejima coefficient, further investigation on the plasma model during the start-up is required for more accurate modeling of Ip evolution. A 0-D code that calculates the evolution of plasma parameters based on power balance and particle balance is under preparation for more accurate estimation of the resistive component of magnetic flux consumption and consequent change of Ip evolution. The plasma wall interaction model can be included for better estimation of the plasma resistivity as well. For further increase of Ip and pulse duration, improved GDC and in situ UV irradiation is under preparation for better wall condition. The improvement of discharge scenario is also in progress to minimize the plasma wall interaction. Since higher elongation can accommodate higher Ip as well as higher edge safety factor, the scenario optimization for higher elongation is on-going as well as the construction of the PF power-supply for the feedback control of plasma vertical position in the elongated plasma. In addition, investigation on the optimal condition for the ECH assisted start-up is on progress as well as various plasma start-up scenarios such as double null plasma merging scheme [1–3] using partial solenoid coils and various non-inductive start-up methods. As the target plasma is established, heating ad current drive experiments by using electron Bernstein wave and neutral beam injection will be attempted as well. Acknowledgments
Fig. 8. Plasma current and OI line emission before and after GDC.
This work was supported by National R&D Program through the National Research Foundation of Korea (NRF) funded
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