- Email: [email protected]
Development of plasma control system for divertor configuration on QUEST
Fusion Engineering and Design 88 (2013) 1074–1077
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Development of plasma control system for divertor configuration on QUEST M. Hasegawa a,∗ , K. Nakamura a , H. Zushi a , K. Hanada a , A. Fujisawa a , K. Matsuoka a , O. Mitarai b , H. Idei a , Y. Nagashima a , K. Tokunaga a , S. Kawasaki a , H. Nakashima a , A. Higashijima a a b
Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka, Japan Tokai University, Toroku, Kumamoto, Japan
a r t i c l e
i n f o
Article history: Received 14 September 2012 Received in revised form 1 March 2013 Accepted 14 March 2013 Available online 10 April 2013 Keywords: Plasma shape identification Real-time control Divertor configuration Field-programmable gate array
a b s t r a c t A plasma control system to sustain divertor configurations is developed on QUEST (Q-shu university experiment with steady-state spherical tokamak). Magnetic fluxes are numerically integrated at 100 kHz using FPGA (Field-Programmable Gate Array) modules and transferred to a main calculation loop at 4 kHz. With these signals, plasma shapes are identified in real time at 2 kHz under the assumption that the plasma current can be represented as one filament current. This calculation is done in another calculation loop in parallel by taking advantage of a multi-core processor of the plasma control system. The inside and outside plasma edge positions are controlled to their target positions using PID (proportional-integralderivative) control loops. Whereas the outside edge position can not be controlled by the outer PF coil current, the inside edge position can be controlled by the inner PF coil current. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The establishment of steady-state operation is a key issue in nuclear fusion. The sustainment of a divertor plasma configuration detached from vacuum vessel walls is required in order to reduce the heat loads of limiters and the impurity contamination. In this sustainment, a plasma shape, namely the shape of the last closed flux surface (LCFS) should be identified in real time, and the edge positions of LCFS should be controlled by magnetic fields induced by poloidal field (PF) coils in real time. A number of methods to identify plasma shapes through magnetic measurements have been proposed [1–3]. In particular, the EFIT [4,5] which solves a force balance equation called the Grad-Shafranov equation has been implemented on a number of tokamaks and has been modified as the rtEFIT, which can calculate in real time. This rtEFIT is adopted for the plasma shape control in several tokamaks [6–8]. In this control, referred to as the isoflux control [7], several reference points of a poloidal cross section are chosen as control points, and PF coil currents are adjusted in order for control points to have the same magnetic flux each other.
∗ Corresponding author at: Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka, Japan. Tel.: +81 92 583 7988; fax: +81 92 573 6899. E-mail address: [email protected] (M. Hasegawa). 0920-3796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fusengdes.2013.03.035
On the other hand, in the QUEST (Q-shu university experiment with steady-state spherical tokamak) [9], a simple method is adopted to identify the plasma shape, assuming the plasma current to be one filament current in order to reduce the calculation amount and calculation time. This method can be realized with a scarce computational resource. The plasma edge positions found from the LCFS are controlled to the target edge positions by varying PF coil currents with PID (proportional-integral-derivative) control loops. This enables more intuitive operation compared to the isoflux control which refers to magnetic flux values of control points. The PF coils of QUEST are shown in Fig. 1. We introduce the hardware configuration of the plasma control workstation (WS) in Section 2, the plasma shape identification method in Section 3, and the plasma edge position control in Section 4. The results and discussions, and the conclusion are presented in Section 5 and 6, respectively. 2. Plasma control system for QUEST The WS is composed of PXI systems of the National Instruments Corporation, which contains a controller module (2.26 GHz Intel Core 2 Quad processor, 2 GBytes memory) based on a real-time operating system, one DIO module (16-channel digital inputs and outputs), and six FPGA (Field-Programmable Gate Array) modules (eight-channel analog inputs and outputs in each module). The WS controls seven power supplies for PF coils and toroidal field (TF) coils, two 8.2 GHz, 200 kW RF systems, one 2.45 GHz, 50 kW RF
M. Hasegawa et al. / Fusion Engineering and Design 88 (2013) 1074–1077
PF3-1
PF3-2
1600mm
HCU 1200
PF2 PF4-1
800
1075
magnetic fluxes through numerical integration of loop voltage signals with a sampling frequency of 100 kHz. Since subtle offset voltages that arise from the isolation amplifiers cause enormous drift errors in numerical integration, offset trimming routines are also installed on the FPGA boards (Fig. 2). This procedure measures a time-averaged offset voltage before the start of PF coil currents and subtracts this voltage from the raw voltage during numerical integration. In the WS, the several tasks can be performed in parallel because a multi-quad-core processor is used in the controller module. One task is the control of a DIO module and FPGA modules. Another task, referred to as a main loop, is the calculation of control signals by the acquired data. These two tasks are performed at 4 kHz.
PF1
400
3. Plasma shape identification
400
800
1200mm
0
PF4-2A,B PF7
-400
-800
PF4-3 PF6
-1200
A task that identifies the plasma shape generally requires a longer calculation time than the control loop period. Thus, on the WS, the plasma shape identification (PSI) loop task is separated from the main loop, and this loop can be performed in parallel with a freely settable frequency, taking advantage of the Core 2 Quad multi core technology. These two loops can transfer appropriate data to each other via buffer memory even if the frequencies of these loops are different. In order to identify the plasma shape, we first assume the plasma current to be one filament current. The plasma shape is then identified by the calculation of a magnetic flux profile. These processes are described below.
HCL -1600mm
PF5-1
PF5-2
Fig. 1. Poloidal cross section of QUEST and PF coil positions.
system, and four gas puff systems. The WS also acquires a plasma current signal, 22 loop voltage signals, and other signals, such as visible light from measurement devices. An FPGA is an integrated circuit that can be configured by the customer after manufacture. The advantage of using FPGA modules for analog input and output signals is high computational speed, which cannot be realized by the controller module. In this WS, in measuring the 22 loop voltage signals, the FPGA modules calculate
1. Find a coarse filament position using a least-mean square method referring to pre-calculated flux data tables. 2. Find a filament position (Rp , Zp ) making linear approximated flux functions around the coarse filament position. 3. Calculate a flux profile with coil currents, filament position (Rp , Zp ), and the plasma current. 4. Find the LCFS from the flux profile. 5. Calculate the plasma shape parameters. In processes 1 and 2, the filament position (Rp , Zp ) is determined considering the effects of eddy currents induced by PF coils [10] and are calculated in the main loop. The other processes are performed in the PSI loop. Since the magnetic flux profile can be calculated by PF coil currents, the plasma current, and its position, the PSI loop receives these data from the main loop.
Fig. 2. Basic concept of FPGA modules for 100 kHz numerical integration. The functions of offset trimming and numerical integration are configured in an FPGA module and are enabled, disabled, or initialized referring to the control signals from the controller module.
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M. Hasegawa et al. / Fusion Engineering and Design 88 (2013) 1074–1077
In order to calculate the magnetic flux profile in a short time, the flux data matrices of the grid-points induced by each coil and plasma current are preliminarily stored in the PSI loop. The grid area is set to 0.0 m < R < 1.5 m and −1.2 m < Z < 1.2 m, and the grid resolution is set to 50 and 80 in the horizontal and vertical directions, respectively. In contrast, the grid-point data is discrete with respect to position, and the plasma position calculated in the main loop is not discrete. In order to calculate the magnetic flux continuously induced by the plasma current, the data of three grid points near the plasma position are used considering their weights. The flux profile can be calculated as follows ˚ij =
k
ijk Ik +
3
wm ϕij˛ˇ Ip ,
(1)
m=1
where the subscripts i and j are the ith and the jth grid numbers of the R and Z directions, respectively, ij is the total flux, ijk is the flux induced by the kth PF coil, Ik is the kth PF coil current, Ip is plasma current, and ϕij˛ˇ is the flux induced by a filament current positioned at the ˛th grid point in the R direction and the ˇth grid point in the Z direction. The three grid points of (˛, ˇ) are selected as the nearest to the plasma position (Rp , Zp ), and wm is the weighting factor, where w1 + w2 + w3 = 1. Here, ϕij˛ˇ does not need to be calculated for all (i, j) and (˛, ˇ), but can be calculated as ϕij˛ , ˇ=1 because of its symmetric property, which reduces computer memory usage. The LCFS is searched with the flux profile calculated on the grid area. The grid point of the local minimum or the local maximum of a magnetic flux profile corresponds approximately to the calculated plasma position. Here, the local minimum case is assumed. The LCFS is searched by gradually broadening the closed flux surface area centered at this local minimum point. This resembles gradually dropping water into a hollow area. When the water touches the vacuum vessel, it means the limiter configuration, and the shape of LCFS is equal to the shape of a puddle. When the water spills out from a saddle point of the hollow area without touching the vacuum vessel, it means the divertor configuration, and the saddle point is a null point. Although this method might require more time to search an LCFS if the number of grid points is large, this method contributes to source code simplification because a unified approach can be used without considering the magnetic configuration. The plasma edge positions are calculated from the flux value of the LCFS using linear interpolation of grid-point data in order not to be discrete. Using these edge positions, shape parameters such as elongation, triangularity, and aspect ratio can be calculated. Since this calculation can be performed within 0.5 ms with a finer grid resolution compared to that of the rtEFIT, the frequency of the PSI loop is set to 2 kHz. The waveforms of plasma edges calculated in real time using this method are shown in Fig. 3. In this discharge, the magnetic configuration is changed from a limiter configuration to a divertor configuration between 2.0 s and 2.6 s with pre-programmed coil currents. During this period, the inside edge position is calculated to move outward and detach from the center stack of R = 200 mm. This indicates that the plasma configuration is changed from a limiter configuration to a divertor configuration. 4. Edge position control In the main loop, the applied voltage signals of PF coils are controlled by PID controllers referring to the actual coil currents in order to match the target coil currents. Normally, the target coil currents are set to preprogrammed values, but when the edge position controls are enabled, the target coil currents are calculated by PID controllers, referring to the actual plasma edge positions
Fig. 3. Waveforms of plasma shape calculated in real time. The magnetic configuration is changed from a limiter configuration to a divertor configuration between 2.0 s and 2.6 s with pre-programmed coil currents. (a) Plasma current, (b) radii of the outside edge position, the filament position, and the inside edge position. The inside edge position increases from 0.2 m to 0.3 m according to the change of the magnetic configuration. (c) Vertical positions of the topside edge position, the filament position, and the downside edge position. Contour plots of magnetic surfaces and mesh plots of LCFS in (d) a limiter configuration of 2.0 s and (e) a divertor configuration of 2.7 s.
calculated in the PSI loop in order to match the target plasma edge positions. Namely, for the control of one plasma edge position, two PID controllers are used. The PF4 coil and the PF17 coil are used to control the inside and outside edge positions, respectively. The PF4 coil is a seriesconnected coil of PF4-1, PF4-2A, PF4-2B, and PF4-3, and the PF17 coil is a series-connected coil of PF1 and PF7. These coil positions are close to the inside and outside edge positions. The inside edge position can be expected to move outward, when the PF4 coil current increases in the opposite direction to the plasma current. In addition, the outside edge position can be expected to move inward, when the PF17 coil current increases in the opposite direction to the plasma current.
M. Hasegawa et al. / Fusion Engineering and Design 88 (2013) 1074–1077
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Fig. 4. Time evolution of the inside edge position control ((a)–(d)) and the outside edge position control ((e)–(h)). (a) Plasma current, (b) target and actual inside edge positions, (c) PF4 coil current to control the inside edge position, and (d) other PF coil currents. (e) Plasma current, (f) target and actual outside edge positions, (g) PF17 coil current to control the outside edge position, and (h) other PF coil currents.
5. Results and discussion Fig. 4 shows the results for inside and outside edge position control. In Fig. 4(a)–(d), the inside edge position control starts from 2.0 s. The PF4 coil current increases from 2.0 s in order to detach plasma from the center stack. After that, the actual inside edge position is well controlled by changing the PF4 coil current slightly in accordance with the change of the target position. The case of the outside edge position control is shown in Fig. 4(e)–(h). Whereas the PF17 coil current increases by approximately 50 % between 2.5 s and 4.5 s in order to move the actual outside edge position inward, the actual edge position does not move inward and does not agree with the target value. When the plasma position (Rp , Zp ) and plasma current are kept constant, the outside plasma edge position is calculated to move inward according to the increase of the PF17 coil current in this calculation method. On the other hand, in Fig. 4(e), the plasma current increases slightly during the outside edge position control, whereas the plasma position (Rp , Zp ) is not changed. This increase inhibits the outside edge position control. One reason may be the loop voltage induced by the increase in the PF17 coil current. Since the increasing rates of vertical magnetic fields Bz at R = 0.8 m induced by PF4 and PF17 coils are 8 G/kA and 87 G/kA, respectively, the variations of Bz in the case of outside edge position control is larger than that in the case of inside edge position control. Alternatively, the number of higher energetic electrons that play a role in the plasma current drive may increase according to the change of the magnetic configuration or the increase of Bz . 6. Conclusion A plasma control system that can identify plasma shapes with scarce computational resource in real time was developed for divertor configurations on QUEST. In this system, FPGA modules are configured to perform offset trimming and 100 kHz numerical integration for magnetic fluxes and communicate with the controller module at 4 kHz. Taking advantage of the multi-core processor of the controller module, plasma shape identification can be achieved without burdening the main loop by preparing an additional
calculation loop. This PSI loop can identify plasma shape within 0.5 ms with fairly simple assumptions. However, this plasma shape identification method is clearly not suitable for non-circular plasma such as highly elongated plasma. In the future, the assumption that the plasma current is treated as one filament current should be verified by comparing the calculation results of equilibrium codes or the experimentally measured plasma edge positions. Whereas the inside edge position can be controlled with the PF4 coil by referring to these plasma edge positions, the outside edge position cannot be controlled with the PF17 coil. However, the outside edge position will be controllable if a control to keep the plasma current constant is adopted at the same time. If additional coil power supplies are installed on QUEST, the PF4-1, 2AB, 3 coils can be driven individually. Then, three controls, namely, the inside edge control, the outside edge control, and the plasma current control, can be adopted. Acknowledgement The present study was supported by and conducted as part of NIFS Collaboration Research Program (NIFS12KUTR076, NIFS11KUTR073). References [1] D.W. Swain, G.H. Neilson, Nuclear Fusion 22 (1982) 1015. [2] Y.S. Hwang, C.B. Forest, D.S. Darrow, G. Greene, M. Ono, Review of Scientific Instruments 63 (1992) 4747. [3] T. Yoshinaga, M. Uchida, H. Tanaka, T. Maekawa, Nuclear Fusion 47 (2007) 210. [4] L.L. Lao, H. St. John, R.D. Stambaugh, A.G. Kellman, W. Pfeiffer, Nuclear Fusion 25 (1985) 1611. [5] L.L. Lao, J.R. Ferron, R.J. Groebner, W. Howl, H. St. John, E.J. Strait, et al., Nuclear Fusion 30 (1990) 1035. [6] J.R. Ferron, M.L. Walker, L.L. Lao, H.E. St. John, D.A. Humphreys, J.A. Leuer, Nuclear Fusion 38 (1998) 1055. [7] D.A. Gates, J.R. Ferron, M. Bell, T. Gibney, R. Johnson, R.J. Marsala, et al., Nuclear Fusion 46 (2006) 17. [8] H. Wang, J. Luo, Q. Huang, Plasma Science and Technology 6 (2004) 2390. [9] K. Hanada, K. Sato, H. Zushi, K. Nakamura, M. Sakamoto, H. Idei, et al., Plasma and Fusion Research 5 (2010) S1007. [10] M. Hasegawa, K. Nakamura, K. Tokunaga, H. Zushi, K. Hanada, A. Fujisawa, et al., IEEJ 132 (2012) 477.
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Development of plasma control system for divertor configuration on QUEST M. Hasegawa a,∗ , K. Nakamura a , H. Zushi a , K. Hanada a , A. Fujisawa a , K. Matsuoka a , O. Mitarai b , H. Idei a , Y. Nagashima a , K. Tokunaga a , S. Kawasaki a , H. Nakashima a , A. Higashijima a a b
Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka, Japan Tokai University, Toroku, Kumamoto, Japan
a r t i c l e
i n f o
Article history: Received 14 September 2012 Received in revised form 1 March 2013 Accepted 14 March 2013 Available online 10 April 2013 Keywords: Plasma shape identification Real-time control Divertor configuration Field-programmable gate array
a b s t r a c t A plasma control system to sustain divertor configurations is developed on QUEST (Q-shu university experiment with steady-state spherical tokamak). Magnetic fluxes are numerically integrated at 100 kHz using FPGA (Field-Programmable Gate Array) modules and transferred to a main calculation loop at 4 kHz. With these signals, plasma shapes are identified in real time at 2 kHz under the assumption that the plasma current can be represented as one filament current. This calculation is done in another calculation loop in parallel by taking advantage of a multi-core processor of the plasma control system. The inside and outside plasma edge positions are controlled to their target positions using PID (proportional-integralderivative) control loops. Whereas the outside edge position can not be controlled by the outer PF coil current, the inside edge position can be controlled by the inner PF coil current. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The establishment of steady-state operation is a key issue in nuclear fusion. The sustainment of a divertor plasma configuration detached from vacuum vessel walls is required in order to reduce the heat loads of limiters and the impurity contamination. In this sustainment, a plasma shape, namely the shape of the last closed flux surface (LCFS) should be identified in real time, and the edge positions of LCFS should be controlled by magnetic fields induced by poloidal field (PF) coils in real time. A number of methods to identify plasma shapes through magnetic measurements have been proposed [1–3]. In particular, the EFIT [4,5] which solves a force balance equation called the Grad-Shafranov equation has been implemented on a number of tokamaks and has been modified as the rtEFIT, which can calculate in real time. This rtEFIT is adopted for the plasma shape control in several tokamaks [6–8]. In this control, referred to as the isoflux control [7], several reference points of a poloidal cross section are chosen as control points, and PF coil currents are adjusted in order for control points to have the same magnetic flux each other.
∗ Corresponding author at: Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka, Japan. Tel.: +81 92 583 7988; fax: +81 92 573 6899. E-mail address: [email protected] (M. Hasegawa). 0920-3796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fusengdes.2013.03.035
On the other hand, in the QUEST (Q-shu university experiment with steady-state spherical tokamak) [9], a simple method is adopted to identify the plasma shape, assuming the plasma current to be one filament current in order to reduce the calculation amount and calculation time. This method can be realized with a scarce computational resource. The plasma edge positions found from the LCFS are controlled to the target edge positions by varying PF coil currents with PID (proportional-integral-derivative) control loops. This enables more intuitive operation compared to the isoflux control which refers to magnetic flux values of control points. The PF coils of QUEST are shown in Fig. 1. We introduce the hardware configuration of the plasma control workstation (WS) in Section 2, the plasma shape identification method in Section 3, and the plasma edge position control in Section 4. The results and discussions, and the conclusion are presented in Section 5 and 6, respectively. 2. Plasma control system for QUEST The WS is composed of PXI systems of the National Instruments Corporation, which contains a controller module (2.26 GHz Intel Core 2 Quad processor, 2 GBytes memory) based on a real-time operating system, one DIO module (16-channel digital inputs and outputs), and six FPGA (Field-Programmable Gate Array) modules (eight-channel analog inputs and outputs in each module). The WS controls seven power supplies for PF coils and toroidal field (TF) coils, two 8.2 GHz, 200 kW RF systems, one 2.45 GHz, 50 kW RF
M. Hasegawa et al. / Fusion Engineering and Design 88 (2013) 1074–1077
PF3-1
PF3-2
1600mm
HCU 1200
PF2 PF4-1
800
1075
magnetic fluxes through numerical integration of loop voltage signals with a sampling frequency of 100 kHz. Since subtle offset voltages that arise from the isolation amplifiers cause enormous drift errors in numerical integration, offset trimming routines are also installed on the FPGA boards (Fig. 2). This procedure measures a time-averaged offset voltage before the start of PF coil currents and subtracts this voltage from the raw voltage during numerical integration. In the WS, the several tasks can be performed in parallel because a multi-quad-core processor is used in the controller module. One task is the control of a DIO module and FPGA modules. Another task, referred to as a main loop, is the calculation of control signals by the acquired data. These two tasks are performed at 4 kHz.
PF1
400
3. Plasma shape identification
400
800
1200mm
0
PF4-2A,B PF7
-400
-800
PF4-3 PF6
-1200
A task that identifies the plasma shape generally requires a longer calculation time than the control loop period. Thus, on the WS, the plasma shape identification (PSI) loop task is separated from the main loop, and this loop can be performed in parallel with a freely settable frequency, taking advantage of the Core 2 Quad multi core technology. These two loops can transfer appropriate data to each other via buffer memory even if the frequencies of these loops are different. In order to identify the plasma shape, we first assume the plasma current to be one filament current. The plasma shape is then identified by the calculation of a magnetic flux profile. These processes are described below.
HCL -1600mm
PF5-1
PF5-2
Fig. 1. Poloidal cross section of QUEST and PF coil positions.
system, and four gas puff systems. The WS also acquires a plasma current signal, 22 loop voltage signals, and other signals, such as visible light from measurement devices. An FPGA is an integrated circuit that can be configured by the customer after manufacture. The advantage of using FPGA modules for analog input and output signals is high computational speed, which cannot be realized by the controller module. In this WS, in measuring the 22 loop voltage signals, the FPGA modules calculate
1. Find a coarse filament position using a least-mean square method referring to pre-calculated flux data tables. 2. Find a filament position (Rp , Zp ) making linear approximated flux functions around the coarse filament position. 3. Calculate a flux profile with coil currents, filament position (Rp , Zp ), and the plasma current. 4. Find the LCFS from the flux profile. 5. Calculate the plasma shape parameters. In processes 1 and 2, the filament position (Rp , Zp ) is determined considering the effects of eddy currents induced by PF coils [10] and are calculated in the main loop. The other processes are performed in the PSI loop. Since the magnetic flux profile can be calculated by PF coil currents, the plasma current, and its position, the PSI loop receives these data from the main loop.
Fig. 2. Basic concept of FPGA modules for 100 kHz numerical integration. The functions of offset trimming and numerical integration are configured in an FPGA module and are enabled, disabled, or initialized referring to the control signals from the controller module.
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M. Hasegawa et al. / Fusion Engineering and Design 88 (2013) 1074–1077
In order to calculate the magnetic flux profile in a short time, the flux data matrices of the grid-points induced by each coil and plasma current are preliminarily stored in the PSI loop. The grid area is set to 0.0 m < R < 1.5 m and −1.2 m < Z < 1.2 m, and the grid resolution is set to 50 and 80 in the horizontal and vertical directions, respectively. In contrast, the grid-point data is discrete with respect to position, and the plasma position calculated in the main loop is not discrete. In order to calculate the magnetic flux continuously induced by the plasma current, the data of three grid points near the plasma position are used considering their weights. The flux profile can be calculated as follows ˚ij =
k
ijk Ik +
3
wm ϕij˛ˇ Ip ,
(1)
m=1
where the subscripts i and j are the ith and the jth grid numbers of the R and Z directions, respectively, ij is the total flux, ijk is the flux induced by the kth PF coil, Ik is the kth PF coil current, Ip is plasma current, and ϕij˛ˇ is the flux induced by a filament current positioned at the ˛th grid point in the R direction and the ˇth grid point in the Z direction. The three grid points of (˛, ˇ) are selected as the nearest to the plasma position (Rp , Zp ), and wm is the weighting factor, where w1 + w2 + w3 = 1. Here, ϕij˛ˇ does not need to be calculated for all (i, j) and (˛, ˇ), but can be calculated as ϕij˛ , ˇ=1 because of its symmetric property, which reduces computer memory usage. The LCFS is searched with the flux profile calculated on the grid area. The grid point of the local minimum or the local maximum of a magnetic flux profile corresponds approximately to the calculated plasma position. Here, the local minimum case is assumed. The LCFS is searched by gradually broadening the closed flux surface area centered at this local minimum point. This resembles gradually dropping water into a hollow area. When the water touches the vacuum vessel, it means the limiter configuration, and the shape of LCFS is equal to the shape of a puddle. When the water spills out from a saddle point of the hollow area without touching the vacuum vessel, it means the divertor configuration, and the saddle point is a null point. Although this method might require more time to search an LCFS if the number of grid points is large, this method contributes to source code simplification because a unified approach can be used without considering the magnetic configuration. The plasma edge positions are calculated from the flux value of the LCFS using linear interpolation of grid-point data in order not to be discrete. Using these edge positions, shape parameters such as elongation, triangularity, and aspect ratio can be calculated. Since this calculation can be performed within 0.5 ms with a finer grid resolution compared to that of the rtEFIT, the frequency of the PSI loop is set to 2 kHz. The waveforms of plasma edges calculated in real time using this method are shown in Fig. 3. In this discharge, the magnetic configuration is changed from a limiter configuration to a divertor configuration between 2.0 s and 2.6 s with pre-programmed coil currents. During this period, the inside edge position is calculated to move outward and detach from the center stack of R = 200 mm. This indicates that the plasma configuration is changed from a limiter configuration to a divertor configuration. 4. Edge position control In the main loop, the applied voltage signals of PF coils are controlled by PID controllers referring to the actual coil currents in order to match the target coil currents. Normally, the target coil currents are set to preprogrammed values, but when the edge position controls are enabled, the target coil currents are calculated by PID controllers, referring to the actual plasma edge positions
Fig. 3. Waveforms of plasma shape calculated in real time. The magnetic configuration is changed from a limiter configuration to a divertor configuration between 2.0 s and 2.6 s with pre-programmed coil currents. (a) Plasma current, (b) radii of the outside edge position, the filament position, and the inside edge position. The inside edge position increases from 0.2 m to 0.3 m according to the change of the magnetic configuration. (c) Vertical positions of the topside edge position, the filament position, and the downside edge position. Contour plots of magnetic surfaces and mesh plots of LCFS in (d) a limiter configuration of 2.0 s and (e) a divertor configuration of 2.7 s.
calculated in the PSI loop in order to match the target plasma edge positions. Namely, for the control of one plasma edge position, two PID controllers are used. The PF4 coil and the PF17 coil are used to control the inside and outside edge positions, respectively. The PF4 coil is a seriesconnected coil of PF4-1, PF4-2A, PF4-2B, and PF4-3, and the PF17 coil is a series-connected coil of PF1 and PF7. These coil positions are close to the inside and outside edge positions. The inside edge position can be expected to move outward, when the PF4 coil current increases in the opposite direction to the plasma current. In addition, the outside edge position can be expected to move inward, when the PF17 coil current increases in the opposite direction to the plasma current.
M. Hasegawa et al. / Fusion Engineering and Design 88 (2013) 1074–1077
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Fig. 4. Time evolution of the inside edge position control ((a)–(d)) and the outside edge position control ((e)–(h)). (a) Plasma current, (b) target and actual inside edge positions, (c) PF4 coil current to control the inside edge position, and (d) other PF coil currents. (e) Plasma current, (f) target and actual outside edge positions, (g) PF17 coil current to control the outside edge position, and (h) other PF coil currents.
5. Results and discussion Fig. 4 shows the results for inside and outside edge position control. In Fig. 4(a)–(d), the inside edge position control starts from 2.0 s. The PF4 coil current increases from 2.0 s in order to detach plasma from the center stack. After that, the actual inside edge position is well controlled by changing the PF4 coil current slightly in accordance with the change of the target position. The case of the outside edge position control is shown in Fig. 4(e)–(h). Whereas the PF17 coil current increases by approximately 50 % between 2.5 s and 4.5 s in order to move the actual outside edge position inward, the actual edge position does not move inward and does not agree with the target value. When the plasma position (Rp , Zp ) and plasma current are kept constant, the outside plasma edge position is calculated to move inward according to the increase of the PF17 coil current in this calculation method. On the other hand, in Fig. 4(e), the plasma current increases slightly during the outside edge position control, whereas the plasma position (Rp , Zp ) is not changed. This increase inhibits the outside edge position control. One reason may be the loop voltage induced by the increase in the PF17 coil current. Since the increasing rates of vertical magnetic fields Bz at R = 0.8 m induced by PF4 and PF17 coils are 8 G/kA and 87 G/kA, respectively, the variations of Bz in the case of outside edge position control is larger than that in the case of inside edge position control. Alternatively, the number of higher energetic electrons that play a role in the plasma current drive may increase according to the change of the magnetic configuration or the increase of Bz . 6. Conclusion A plasma control system that can identify plasma shapes with scarce computational resource in real time was developed for divertor configurations on QUEST. In this system, FPGA modules are configured to perform offset trimming and 100 kHz numerical integration for magnetic fluxes and communicate with the controller module at 4 kHz. Taking advantage of the multi-core processor of the controller module, plasma shape identification can be achieved without burdening the main loop by preparing an additional
calculation loop. This PSI loop can identify plasma shape within 0.5 ms with fairly simple assumptions. However, this plasma shape identification method is clearly not suitable for non-circular plasma such as highly elongated plasma. In the future, the assumption that the plasma current is treated as one filament current should be verified by comparing the calculation results of equilibrium codes or the experimentally measured plasma edge positions. Whereas the inside edge position can be controlled with the PF4 coil by referring to these plasma edge positions, the outside edge position cannot be controlled with the PF17 coil. However, the outside edge position will be controllable if a control to keep the plasma current constant is adopted at the same time. If additional coil power supplies are installed on QUEST, the PF4-1, 2AB, 3 coils can be driven individually. Then, three controls, namely, the inside edge control, the outside edge control, and the plasma current control, can be adopted. Acknowledgement The present study was supported by and conducted as part of NIFS Collaboration Research Program (NIFS12KUTR076, NIFS11KUTR073). References [1] D.W. Swain, G.H. Neilson, Nuclear Fusion 22 (1982) 1015. [2] Y.S. Hwang, C.B. Forest, D.S. Darrow, G. Greene, M. Ono, Review of Scientific Instruments 63 (1992) 4747. [3] T. Yoshinaga, M. Uchida, H. Tanaka, T. Maekawa, Nuclear Fusion 47 (2007) 210. [4] L.L. Lao, H. St. John, R.D. Stambaugh, A.G. Kellman, W. Pfeiffer, Nuclear Fusion 25 (1985) 1611. [5] L.L. Lao, J.R. Ferron, R.J. Groebner, W. Howl, H. St. John, E.J. Strait, et al., Nuclear Fusion 30 (1990) 1035. [6] J.R. Ferron, M.L. Walker, L.L. Lao, H.E. St. John, D.A. Humphreys, J.A. Leuer, Nuclear Fusion 38 (1998) 1055. [7] D.A. Gates, J.R. Ferron, M. Bell, T. Gibney, R. Johnson, R.J. Marsala, et al., Nuclear Fusion 46 (2006) 17. [8] H. Wang, J. Luo, Q. Huang, Plasma Science and Technology 6 (2004) 2390. [9] K. Hanada, K. Sato, H. Zushi, K. Nakamura, M. Sakamoto, H. Idei, et al., Plasma and Fusion Research 5 (2010) S1007. [10] M. Hasegawa, K. Nakamura, K. Tokunaga, H. Zushi, K. Hanada, A. Fujisawa, et al., IEEJ 132 (2012) 477.