Strike Point Control on EAST Using an Isoflux Control Method

Plasma Science and Technology, Vol.17, No.9, Sep. 2015 Strike Point Control on EAST Using an Isoflux Control Method XING Zhe ( ) 1, XIAO Bingjia ( ) 1,2, LUO Zhengping ( ) 1, M. L. WALKER 3, D. A. HUMPHREYS 3 1 Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China 2 School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China 3 General Atomics, General Atomics Ct., San Diego, CA 92186, USA Abstract For the advanced tokamak, the particle deposition and thermal load on the divertor is a big challenge. By moving the strike points on divertor target plates, the position of particle deposition and thermal load can be shifted. We could adjust the Poloidal Field (PF) coil current to achieve the strike point position feedback control. Using isoflux control method, the strike point position can be controlled by controlling the X point position. On the basis of experimental data, we establish relational expressions between X point position and strike point position. Benchmark experiments are carried out to validate the correctness and robustness of the control methods. The strike point position is successfully controlled following our command in the EAST operation. Keywords: EAST, plasma control system, strike point control PACS: 52.55.Dy, 52.55.Fa DOI: 10.1088/1009-0630/17/9/09 (Some figures may appear in colour only in the online journal) 1 Introduction In the advanced tokamak, the plasma is confined by a magnetic field [1] with elongated cross-section [2]. The plasma is directed to the divertor region, which is designed to absorb the heat of the energetic byproduct particles, and then impacts on special plates at an appropriate distance far from the hot plasma core [3]. These plates are referred to as the divertor target plates. Fig. 1 illustrates the EAST geometry and one typical plasma shape. To better adjust the particle deposition and thermal load, the magnetic field should be varied in order to change the strike point position on the divertor target plates. For advanced tokamak operation, a reliable control of the strike point position is necessary for the study of plasma facing materials on the divertor target plates. Furthermore, the strike point control should be integrated into the plasma control system as a part of the plasma shape feedback controller [4]. Moving the strike point position to reduce the local average thermal loading has been demonstrated on JET [5], NSTX [6], and DIII-D [7]. Considering that the Plasma Control System (PCS) on EAST is adopted from DIII-D [8,9], we apply a similar realtime strike point control algorithm using rtefit-isoflux method [10]. At first, we establish relational expressions between X point position and strike point position for the strike point control based on historical experimental data. Benchmark experiments were then carried out to validate the correctness and robustness of the control methods. Finally, the strike point position was successfully controlled following our command in the EAST operation. Our results are discussed in the summary. Fig.1 The plasma shape (black line), the vacuum vessel (green line), the four divertor target plates (blue line) on the first wall (magenta line), the control segments (gray line), and the region for searching X points (gray grids) in rtefit supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2012GB105000 and 2014GB103000) 774

XING Zhe et al.: Strike Point Control on EAST Using an Isoflux Control Method 2 rtefit-isoflux algorithm on EAST To achieve shape control in a tokamak, we need to gather information about the plasma shape during discharge. The plasma shape parameters cannot be measured directly. We may reconstruct the plasma boundary, X point locations and some other parameters from the available diagnostic data, such as external magnetic measurements. By now, many efficient methods and numerical codes for equilibrium reconstruction have been developed. In EAST, the real time equilibrium reconstruction code (rtefit) [10] is applied to obtain plasma shape parameters. The rtefit is the real time version of the equilibrium reconstruction code EFIT [11]. EFIT code provides the approximate equilibrium solution to the Grad-Shafranov equation which best fits the external diagnostic data. The rtefit algorithm is integrated into the isoflux shape control algorithms for PCS [8,12]. In the isoflux control scheme [13,14], we set a series of the control segments (the gray bars in Fig. 1) which intersect the plasma last closed flux surface at the control points. These control points define the top and bottom of the plasma shape, and also the outer and inner gap. Particularly, in the case of divertor shape discharges, the control points include the X points. In the shape controller, one of the control points is chosen as the reference point. For the divertor discharge, the X point is typically used as the reference point. If the X point is not unique, such as double null shape, then the reference point is the one with the higher poloidal flux. The poloidal flux differences between the reference point and each of the other control points are used as error signals to control the plasma boundary. The X point position differences between the computed and the desired location are used as error signals to control the X points. These error signals will be translated to the control command for current adjustments in the poloidal field coils. In the isoflux control method, a preliminary method for achieving strike point control has been included [14]. Taking the inner strike point control method as an example, the desired position on the inner divertor plate and the radial position of X point are selected as control points. The strike point position error is generated as an control error signal, which is used to control the vertical position of X point instead of the X point vertical position error. Consequently, we can control the strike point by controlling the X point position. To achieve the strike point control, we need to fit the relational expressions between the X point position and the strike point position by using statistical tools based on historical experimental data. 3 Strike point position control using isoflux control method There are three kinds of strike point control mode during discharge [14] : 775 (I) Inner strike point control; (II) Outer strike point control; and, (III) Both inner and outer strike point control. Considering the three strike point control modes, we need to fit three groups of expressions to determine the X point locations with the desired strike point positions: (I) Programming the inner strike point positions and the radial position of the X point to compute vertical position of the X point: zxtop = zxtop (rxtop, z strike in, r strike in); zxbot = zxbot (rxbot, z strike in, r strike in). (II) Programming the outer strike point positions and the vertical position of the X point to compute radial position of the X point: rxtop = rxtop (zxtop, z strike out, rxbot = rxbot (zxbot, z strike out, r strike out). (III) Programming both inner strike point and outer strike point positions to compute the X point positions: rxtop = rxtop (z strike in, r strike in, z strike out, zxtop = zxtop (z strike in, r strike in, z strike out, rxbot = rxbot (z strike in, r strike in, z strike out, zxbot = zxbot (z strike in, r strike in, z strike out, where the top X point depends on the upper strike points, and the bottom X point depends on the lower strike points. As noted above, the plasma shape parameters, except for the strike point position, can be evaluated by rtefit. To fit the relational expressions between the X point position and the strike point position, we need to determine the strike point position based on the equilibrium data provided by rtefit. We can then collect a large enough sample from the historical experimental data. 3.1 Determination of strike point position based on rtefit data We retrieve necessary data, such as the poloidal flux at the plasma boundary, the poloidal flux on the rectangular grid points (33 33 rectangular grids shown in Fig. 2), and the corresponding X point positions. Based on the flux values of the 33 33 rectangular grid points, we adopt an interpolation technique to compute the flux values on the divertor target plates (the area of target plate is divided to 500 500 rectangular grids). The grid point on the divertor target plate with the flux value approximately equal to the plasma boundary flux is considered as the strike point. For this work, we choose cubic spline interpolation for the two-dimensional interpolation. Spline interpolation uses low-degree polynomials in each of the intervals, and chooses the polynomial pieces such that they fit smoothly together. Like polynomial interpolation, spline interpolation incurs a smaller error than linear interpolation, and the interpolation function is

Plasma Science and Technology, Vol.17, No.9, Sep. 2015 smoother. To test the algorithm, we take the results of shot 33750 at 4.3715 s as an example. The estimated result of the strike point positions is plotted (the red hexagrams in Fig. 3) with the poloidal flux contour of the plasma boundary as a reference. The details of the four strike points are shown in Fig. 4. Fig.3 The estimated results of the strike points (four red hexagrams on the divertor target plates). The solid line is the poloidal flux contour of the plasma boundary Fig.2 The plasma shape (black line), the vacuum vessel (green line), the four divertor target plates (black line) on the first wall (blue line). The 33 33 grids (gray line) are the equilibrium reconstruction area of rtefit 3.2 Fitting function We collect 450 sets of (strike point positions, X point positions) as the sample data to fit the relational expressions between X point position and strike point position. The sample distribution is shown in Fig. 5. (a) Upper strike point on inner plate (b) Upper strike point on inner plate (c) Lower strike point on inner plate (d) Lower strike point on outer plate Fig.4 The details of the four strike points (red hexagram). The distance between the grid point (red circle) of the inner divertor target plate is 0.56 mm, while the outer one is 0.49 mm 776

XING Zhe et al.: Strike Point Control on EAST Using an Isoflux Control Method +d [(R strike out R strike in ) 2 +(Z strike out Z strike in ) 2 ], (5) Z x = a + b (Z strike out + Z strike in ) + c (R strike out R strike in ) 2 + (Z strike out Z strike in ) 2 +d [(R strike out R strike in ) 2 +(Z strike out Z strike in ) 2 ]. (6) Taking the expression form Eq. (1) as an example, if we choose z strike in, (rxbot-r strike in) and SQUARE (rxbot-r strike in) as three independent variables, we can do multiple linear fitting instead of nonlinear fitting. Based on the 450 sets of sample data, the coefficients of relational expressions for the three strike point control modes are obtained (shown in Table 1). (a) Sample data in the upper divertor region Table 1. The parameters of the fitting functions for the three strike point control modes Control a b c d mode I Zx top 0.3631 1.134 1.587 4.439 Zx bottom 0.4081 1.142 1.883 4.977 II Rx top 0.05417 0.8790 0.4392 1.270 Rx bottom 0.1337 0.8398 0.3918 1.197 III Rx top 21.47 0.1730 81.77 86.51 Zx top 6.675 0.5780 29.68 31.15 Rx bottom 17.46 0.1599 64.48 67.70 Zx bottom 4.657 0.5750 20.84 21.49 (b) Sample data in the lower divertor region Fig.5 The distribution of sample data for fitting For the strike point control mode (I) as noted above: Z xtop = a + b Z strike + c (R xtop R strike ) +d (R xtop R strike ) 2, (1) Z xbot = a + b Z strike + c (R xbot R strike ) +d (R xbot R strike ) 2. (2) For the strike point control mode (II) as noted above: R xtop = a + b R strike + c (Z strike Z xtop ) +d (Z strike Z xtop ) 2, (3) R xbot = a + b R strike + c (Z strike Z xbot ) +d (Z strike Z xbot ) 2. (4) For the strike point control mode (III) as noted above: R x = a + b (R strike out + R strike in ) + c (R strike out R strike in ) 2 + (Z strike out Z strike in ) 2 3.3 Benchmark test To benchmark the relational expressions, we selected ten time slices from the experimental data at random, and calculated the relative errors of X point positions between the rtefit results and the estimated results by using the relational expressions. As shown in Fig. 6, the relative errors are less than 1%. We connect the strike point and the estimated X point with a straight line, which is easy for us to examine whether or not the calculation result fits with the poloidal flux contour of the plasma boundary (as shown in Fig. 7). The results of the benchmark proved the validity of the relational expressions for the three strike point control modes. We then implemented the strike point control experiments based on these relational expressions using an isoflux control method. 4 Strike point control experiments We modified the strike point control module in the isoflux control algorithm on EAST. The flexibility of the strike point control was proven in the EAST experiment operation. Our experimental results are analyzed below. 777

Plasma Science and Technology, Vol.17, No.9, Sep. 2015 (a) Top X point (b) Bottom X point Fig.6 The relative error between the rtefit results and the calculation results using fitting function of top (a) and bottom (b) X points position Fig.7 The estimated results of the X points (red star) by using fitting expressions in three strike point control mode: (a) Mode I, (b) Mode II, (c) Mode III. The red hexagrams on the target plates are strike points. The plasma last closed flux surface is illustrated in blue solid line 4.1 Reference experiment With the constant target value of the X point position, we can estimate the desired strike point position. From the experimental results shown in Fig. 9, we found that the strike points had oscillated around the desired value, and the margin of difference was 1%5%. At first, we took shot 36744 without controlling the strike point position as the reference experiment. In the reference shot, we turned on the X point control in the discharge process. The control effect of X point is shown in Fig. 8. Fig.8 The experimental X point position (black line) and the target value (red dashed line) during discharge process of shot 36744 Fig.9 The strike point position (black line) and the desired value (red dashed line) during discharge process of shot 36744 (without strike point control) 778

XING Zhe et al.: Strike Point Control on EAST Using an Isoflux Control Method 4.2 Inner strike point control experiment In shot 36768, we tested control mode I as the representation, controlling both upper and lower inner strike points. With the same discharge setting of shot 36744, we turned on the strike point control since 3.2 s (target Z of the inner lower strike point is 94 cm and target Z of the inner upper strike point is 93 cm). Referring to the experimental results of shot 36768 (shown in Fig. 10), we observed that both upper and lower strike points had been controlled to oscillate around the target position. Furthermore, in comparison to the reference experiment, the oscillation amplitude of shot 36768 is less than that of shot 36744. Consequently, the inner strike point control works well by using the modified algorithm. We achieved the purpose of controlling the strike points to stay around our target position on EAST. referring to the sample space shown in Fig. 5. On the other hand, we carry out the strike point control by controlling X point positions using the isoflux control method. The control precision of the strike points depends on the control effect of the X points. To find the cause of this problem, we analyzed the control effect of X points (shown in Fig. 12). In control mode I, the active control variables are the radial positions of X point and inner strike point positions. The desired vertical positions of X point are estimated as the red dashed line in Fig. 12. Fig.11 The strike point position (black line) and the target value (red dashed line) during discharge process of shot 36770 (with inner strike point control) Fig.10 The strike point position (black line) and the target value (red dashed line) during discharge process of shot 36768 (with inner strike point control) Considering the primary aim of strike point control, we should control the strike points to move over an appropriate area of the divertor target plates during discharge. In shot 36769 and shot 36770, we set timevarying target positions of inner strike points in the discharge process. Taking shot 36770 as an example, the target strike control points varied from 3.2 s to 4.5 s, with Z of the lower inner strike control point shifting from 94 cm to 89 cm and Z of the upper inner strike control point shifting from 93 cm to 88 cm. The experimental results of shot 36770 are shown in Fig. 11. From 3.2 s to 4.5 s, the inner strike points shifted on the divertor target plate when the target value had changed. After 4.5 s, the strike points oscillated slightly around a constant position, the amplitude was less than 1%. We also noticed that there was an obvious gap between the actual strike point position and the target position. The active control failed to move the strike point to the target position accurately after 4.5 s. On one hand, the relational expressions between X point position and strike point position are valid in this shot Fig.12 The experimental X point position (black line) and the desired value (red dashed line) during discharge process of shot 36770 (with inner strike point control) From 3.2 s to 4.5 s, the target R of X points remains constant (shown in Fig. 12) while the inner strike points are expected to shift on the divertor target plates. However, before 3.2 s, the actual R of X point was far from the target value. During 3.2 s to 4.5 s, it was controlled to approach the target position instead of staying around the target position as expected. Even when the target position had been reached after 4 s, the oscillation of actual R of X point was a little big. This 779

explains why the strike points could not reach the target position till 4.5 s, even though they were successfully controlled to shift in the right direction. As a result, the actual Z of X point could not agree with the desired value very well while the strike points shift. Similar inaccurate control effect of X points was also found in the reference shot (shown in Fig. 8). We need to improve the control effect of X point position by adjusting control parameters in the future. While the strike points move as programmed, we should control the X points to reach the target position. 5 Summary A reliable control of the strike point position is very important for advanced tokamak operation. We applied the strike point control algorithm using rtefit-isoflux control method on EAST. We fitted the relational expressions for the strike point control by a statistical technique that was based on historical experimental data, and then incorporated them into the plasma control system as a part of the plasma shape controller. Benchmark experiments on EAST were carried out to validate the correctness and robustness of the control methods. We achieved the aim of moving the strike points on the divertor target plates under control. The control precision of the strike point positions was limited to the control effect of the X point position. We will adjust the control parameters to improve the control effect of X point position in the future. Furthermore, we can in this way implement the study of plasma facing materials on divertor target plates more effectively. It is of great importance to better adjust the particle deposition and thermal load for future experiments on EAST. Plasma Science and Technology, Vol.17, No.9, Sep. 2015 References 1 Wesson J. 1997, Tokamaks. Oxford University Press, Oxford, UK 2 Pironti A and Walker M. 2005, IEEE Control Systems Magazine, 25: 30 3 Beghi A and Cenedese A. 2005, IEEE Control Systems Magazine, 25: 44 4 Mirnov S, Wesley J, Fujisawa N, et al. 1999, Nuclear Fusion, 39: 2577 5 Ariola M and Pironti A. 2005, IEEE Control Systems Magazine, 25: 65 6 Kolemen E, Gates D A, Rowley C W, et al. 2010, Nuclear Fusion, 50: 105010 7 Petrie T W, Fenstermacher M E, Lasnier C J. 2001, Fusion Technology, 39: 916 8 Ferron J R, Penaflor B, Walker M L, et al. 1996, Fusion Engineering, 2: 870 9 Xiao Bingjia, Humphreys D A, Walker M L, et al. 2008, Fusion Engineering and Design, 83: 181 10 Ferron J R, Walker M L, Lao L L, et al. 1998, Nuclear Fusion, 38: 1055 11 Lao L L, John H St, Stambaugh R D, et al. 1985, Nuclear Fusion, 25: 1611 12 Penaflor B G, Ferron J R, Walker M L, et al. 2008, Fusion Engineering and Design, 83: 176 13 Walker M L, Humphreys D A, Ferron J R. 1997, Proceedings of the 36th IEEE Conference, 4: 37 14 Ferron J R, Walker M L, Penaflor B, et al. 2003, Application Programmer s Guide to the Plasma Control System, DIII-D Documents. General Atomics, Gneral Atomics Ct., San Diego (Manuscript received 16 October 2014) (Manuscript accepted 26 December 2014) E-mail address of XING Zhe: xzpb@ipp.ac.cn 780