- Email: [email protected]
Development of real-time plasma current profile reconstruction with POINT diagnostic for EAST plasma control
Fusion Engineering and Design 120 (2017) 1–8
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Research Paper
Development of real-time plasma current profile reconstruction with POINT diagnostic for EAST plasma control Y. Huang a , B.J. Xiao a,b , Z.P. Luo a,∗ , J.P. Qian a , S. Li a , Y. Chen a , H.Q. Liu a , L.Q. Xu a , Y. Yuan a , Q.P. Yuan a a b
Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China School of Nuclear Science & Technology, University of Science & Technology of China, China
h i g h l i g h t s • • • • •
Plasma current profile reconstruction algorithms using POINT are implemented with GPU parallel computation in P-EFIT code. P-EFIT using experimental magnetic plus POINT data could provide reasonable plasma current density and q profile results. A real-time POINT DAQ system and data interface between PCS and P-EFIT’s GPU server are built. This system could satisfy time feasibility requirements for real-time plasma control. This work is essential for advanced tokamak real-time plasma current profile control to maximize performances.
a r t i c l e
i n f o
Article history: Received 6 November 2016 Received in revised form 28 April 2017 Accepted 2 May 2017 Keywords: Equilibrium reconstruction Plasma current profile Real-time GPU parallel computation EAST
a b s t r a c t This paper describes the plasma current profile reconstruction algorithms using POlarimeterINTerferometer(POINT) measurements in GPU parallel equilibrium reconstruction code P-EFIT for EAST plasma control. Real-time POINT diagnostic data acquisition system is designed to satisfy the requirement for real-time reconstruction. The static time-slice and experimental simulation benchmark calculations using experimental magnetic plus POINT data of EAST discharge are conducted, which show that P-EFIT could provide reasonable plasma current and q profile in 0.7 ms in real-time with 65 × 65 spatial grid resolution. These results show that P-EFIT with POINT diagnostic could provide equilibrium reconstruction results for real-time plasma current and q profile control which will be applied in the near future. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Plasma current profile is one of the most important factors determining the MHD stability and confinement in Tokamaks. For this reason, plasma current profile control is essential to optimize plasma performance for advanced tokamak operation. Real-time current profile reconstruction is necessary to provide information for plasma current profile control. For EAST long pulse high performance operation, current density profile reconstruction and control are highly desirable. Experimental equilibrium reconstruction provides information such as plasma boundary, current density and safety factor profiles for tokamak operation and research. EFIT reconstructs equilibrium by finding the Grad-Shafranov solution that is the least squares
∗ Corresponding author. E-mail address: [email protected] (Z.P. Luo). http://dx.doi.org/10.1016/j.fusengdes.2017.05.005 0920-3796/© 2017 Elsevier B.V. All rights reserved.
best fit to the experimental measurements. It efficiently combines equilibrium and fitting iterations to search for an optimum solution [1–4] and has been widely used in many tokamaks worldwide. However, the full algorithms of EFIT is computation intensive to be used in real-time control particularly for the high spatial grid resolution [5]. In [6,7], a real-time version-EFIT (RT-EFIT) and an efficient numerical solver for the Grad-Shafranov equation based on OpenMP parallel computation have been developed. Additionally in [8,9], a parallelized version EFIT code based on GPU for magnetic reconstructions, P-EFIT has been developed which significantly accelerate the whole computation process. P-EFIT efficiently takes advantage of massively parallel GPU cores and significantly accelerates the EFIT reconstruction algorithms and it has been successfully implemented for plasma control in EAST. For equilibrium reconstruction with external magnetic diagnostics only, only global parameters such as plasma boundary, ˇP , li, and Ip can be determined [1,2]. To reconstruct the q profile, internal profile measurements such as MSE must be used in con-
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junction with the external magnetic data. To fully reconstruct the equilibrium including the q and pressure profiles and the associated magnetic geometry self-consistently, kinetic profiles must be used in conjunction with the MSE and external magnetic data [4]. Real-time equilibrium reconstruction with MSE diagnostic is critical to provide q profile for plasma current profile control [10], when it comes to EAST, EAST do not equip MSE diagnostic until now. Fortunately, a new POINT diagnostic in EAST [11,12] can provide important internal profile information, which can be used as internal current profile constraints for equilibrium reconstruction. The diagnostic of POlarimeter-INTerferometer(POINT), well known as Faraday rotation, allows measuring the density times the magnetic field component parallel to the laser beam propagation direction. The Faraday rotation measurements can capture fast evolution of current profile information, provides off midplane magnetic field information which can be used to improve the accuracy of internal plasma surface elongation. The method of using Faraday rotation for the current density profile reconstruction was first mentioned in the later 1980s [13], applied in JET [14] together with other constraints and suggested for ITER [15] to improve the accuracy of the equilibrium reconstruction. An algorithm to determine the current density profile by resolving the equilibrium equation was developed in [16]. It was shown that POINT measurements could be used as the internal information in the current profile reconstruction. Moreover, the equilibrium reconstruction of EAST current profile based on POINT diagnostic is demonstrated using the EFIT equilibrium reconstruction code in [17]. These achievements make the implementation of real-time equilibrium reconstruction with POINT diagnostic possible. In this paper, design of real-time GPU parallel equilibrium reconstruction with POINT diagnostic for plasma control in EAST is presented. In section 2, the basic plasma equilibrium reconstruction and its implementation on GPU parallel computing are described briefly, then the detailed extension of P-EFIT algorithms on POINT diagnostic constraints is presented. In section 3, equilibrium reconstruction results of single timeslice and experimental whole discharge simulation test with magnetic plus POINT diagnostics, structure of real-time POINT data acquisition(DAQ) system are presented. Both equilibrium reconstruction and timing results are presented to prove that P-EFIT can provide equilibrium reconstruction with internal current profile information and satisfy time feasibility requirements for real-time plasma control. The built system would be applied for plasma current density and q profile control on EAST in the near future.
2.1. Introduction on GPU parallel equilibrium reconstruction algorithm P-EFIT takes the algorithm of EFIT [1–3] as its basic framework. Its principle is to compute the poloidal flux distribution in the R, Z plane, then obtain the toroidal current density distribution in this plane, which should satisfy a least-square best fit to the diagnostic data under the model given by the Grad-Shafranov equation. = −0 RJ ,
J = RP ( ) +
0 FF ( ) 42 R
P
FF
np −1
np −1
=
˛n
n N
−ı
n=0 nF −1
=
n=0
nF N
˛n
n=0 nF −1
ˇn
n N
−␦
nF N
(2) n
n=0
The value of linear parameters ␣n , ˇn and Jϕ are fitted from available measurements and constraints. P and FF are set to be zero at the boundary when ı = 1 at ohmic or L-mode discharge, and set to be finite value at boundary when ı = 0 at H-mode discharge. The unknown parameters ␣n and ˇn can be combined into unknown parameter vector ˛ ¯ directly to the measurements and constraints ¯ through the response matrix R as vector M R˛ = M.
(3)
Here, response matrix R contains relationship between parameters ␣n , ˇn with measurements and constraints [4]. P-EFIT is based on the EFIT framework but takes advantage of massively parallel GPU cores to significantly accelerate the computation. The equilibrium reconstruction algorithm is consist of several middle-scale matrix computation sequentially which need to be iterated, parallelizing these algorithms requires many computational cores and large amount of communication between cores. There are standard linear algebra routines in CUDA library, but the size of matrix in equilibrium reconstruction algorithms is too small to achieve good performance by directly using them. When developing modules in P-EFIT, we need to design customized parallel algorithm. Efficiently distributing hundreds of GPU cores and minimizing the communication between them are basic principle. For this reason, each parallel algorithms in P-EFIT are carefully designed through combining the needs of numerical algorithms and the GPU capacity. Some optimization for middle-scale matrix multiplication and an algorithm which could solve block tri-diagonal block linear system in parallel on GPU is described in [8,9]. 2.2. GPU parallel plasma current profile reconstruction algorithm using POINT measurements P-EFIT follows the algorithms and physical approach which have been discussed detailedly in [16,17]. In EAST, POINT diagnostic can provide 11 channels of line-integrated plasma density and Faraday rotation angle measurements. The Faraday rotation angle and the phase shift ϕ caused by the electron density are given by
2. Algorithms of parallel equilibrium reconstruction with POINT diagnostic
∗
represented as a linear combination of a number NP and NF of basis functions [4].
(1)
Here, is the poloidal magnetic flux per radian of the toroidal angle ϕ enclosed by a magnetic surface, F = 2RBϕ /0 is the poloidal current function, Bϕ is the toroidal magnetic field, and and ∗ = R2 ∇ ·(∇ /R2 ). The equilibrium solution of poloidal flux toroidal current density of plasma Jϕ are obtained on a rectangular grid which covers the entire area of the vacuum vessel. In EFIT, Jϕ is
=
ϕR -ϕL = 2.62 × 10−13 2 2
ϕ=
ϕR + ϕL = 2.82 × 10−15 2
ne B// dl
(4)
ne dl
(5)
where ϕR and ϕL are the phase shift for the R- and L- wave, B// is the component of the magnetic field along propagation of the laser beam, ne is the electron density, and is the wavelength of the beam. To incorporate the Faraday rotation data in equilibrium reconstruction, firstly, an equilibrium reconstruction is performed using external magnetic data only to provide initial flux mapping. Taking the magnetic flux surfaces from this magnetic only reconstruction as an initial guess, a reconstruction iteration with POINT and external magnetic data is then performed. The electron density profile is determined by fitting the line-integrated density data Eq. (5). Then fitting to Faraday rotation angles for multiple chords and
Y. Huang et al. / Fusion Engineering and Design 120 (2017) 1–8
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external magnetic data are carried out by inverting the response matrix that now includes the response from the Faraday rotation measurements based on Eq. (4). Then, new equilibrium flux surfaces are reconstructed and the reconstruction iteration with POINT and external magnetic data is repeated to get final solutions. Assuming that the electron density is a function of normalized flux, electron density is equal on a same flux surface, the density profile ne can be described as a polynomial plus a hyperbolic tangent representation [18], this representation allows electron density to have an edge pedestal and a finite value at boundary. ne
N
=
m
i
i−1 N
+ m+1 tanh(
N)
(6)
i=1
Here, N is the normalized flux, the unknown parameter i can be related to the measurements through Eq. (6) in a matrix form as AX = B, where A is the density response matrix, X is the unknown vector of i , and B is the experimental line integrated density vector. By fitting the electron density measurements line-integrated data, i and ne N can be determined. Although line-integrated density measurements do not contain the necessary spatial resolution for the determination the edge density pedestal, the Tanh term is included to allow a more accurate description of the density profile when more refined density measurements from Thomson Scattering or reflectometry are available. Then, combining ne N and line-integrated Faraday rotation angle measurements data by Eq. (5), additional constraints are appended into response matrix R in Eq. (3). Previous P-EFIT version is limited to reconstruction with magnetic diagnostics only and plasma current representation is fixed to polynomial representation as Eq. (2) with NP = 2, NF = 1, ı = 1. This settled plasma current representation and limited diagnostics reduce the difficulty of designing parallel algorithms when P-EFIT was initially developed. When extending the capacity to allow more diagnostics, the most challenging problem is to allow parallel algorithms to adjust automatically with variable matrices’ size due to different plasma current representations and diagnostics. Framework and algorithms are redesigned to allow flexible polynomial plasma current representations. For example, to obtain the response matrix R, multiplication of two large matrices, whose size are changed based on plasma current representation, is needed. By dividing the matrices into small pieces, the cost of matrix element multiplications is reduced [8]. Newly designed preprocessing algorithm is applied to divide a matrix into small 2D pieces and assign each piece an index in the 3rd dimension based on settled optimizing strategy. As shown in Fig. 1, matrix is divided into Blocks which are organized in Grid, each Block has Threads to calculate each matrix element multiplications. When adding POINT constraints into response matrix R, to guarantee good computational performance, unique GPU parallel algorithms are designed for plasma current profile reconstruction algorithm using POINT measurements. The POINT diagnostic responses are separately computed and organized into the response matrix R. When determining the electron density profile by fitting the POINT line-integrated density data, 11 Blocks which contain 65 threads are distributed to calculate matrix A formed by Eq. (5&6). Each Block calculates one channel of line-integrated i−1 plasma density response, each thread calculates N and tanh( N ) on grid, solving AX = B to get the unknown vector of i is similar to the method in [8,9]. Then forming the POINT response matrix by Eq. (4) into R, 11 Blocks which contain 65 threads are distributed, each Block calculates one channel of Faraday rotation angle mea-
Fig. 1. Description of threads distribution algorithm. After dividing the matrices into small 2d pieces which are distributed to Threads (blue parts) in Blocks (yellow parts), the algorithm assign each Block (yellow parts) an index in the 3rd dimension (grid, green part). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
surements response, each thread calculates 2.62 × 10−13 2 ne B// on grid, the method of relating B// to plasma current parameters ␣n , ˇn is similar to magnetic diagnostics’s green table function in [8,9].
3. Implementation and benchmark tests 3.1. Structure of real-time plasma current profile reconstruction system 3.1.1. Real-time GPU parallel equilibrium reconstruction system P-EFIT is running in a GPU server which is a Linux workstation with one Intel(R) Xeon(R) CPU E31230 @ 3.20 GHz and one NVIDIA Tesla K20c GPU card. Since GPU server is an independent system to PCS, a ReFlective Memory(RFM) network between them was built to share the real-time data [9]. For each time-slice in real-time, PEFIT performs new equilibrium reconstruction iteration using the most recent diagnostic data with equilibrium result of last timeslice as the initial input and provide equilibrium results to PCS. P-EFIT reads 75 single-precision numbers consisted of one time and 74 magnetic diagnostic data from PCS through RFM. PCS reads about 25 single-precision numbers, which depends on the number of control segments, consisted of control errors on control segments and x-points from P-EFIT through RFM. Totally about 400 bytes data is transferred through RFM in about 50us between PCS and P-EFIT’s GPU server in real-time. Real-time POINT diagnostic data is needed when P-EFIT reconstructs equilibrium and plasma current profile.
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3.1.2. Structure of real-time POINT diagnostic data acquisition(DAQ) system In EAST, POINT diagnostic can provide 11 channels of line-integrated plasma density and Faraday rotation angle measurements with high time resolution (up to ∼1 us). An independent real-time POINT diagnostic data acquisition system is built as Fig. 2 shows. The main hardware structure of real-time POINT DAQ system contains controller(NI PXIe-8135 with LabVIEW Real-time) [19], DAQ card(NI PXIe-6358) [20] and RFM card(GE PCI-5565PIOC). The original POINT diagnostic electrical signal is acquired and then transformed into valid physical signal which is transferred to P-EFIT GPU server through RFM network. The sample rate of POINT diagnostic data is 20 kHz, and the whole POINT diagnostic signal path consumes about 60us which both satisfy the requirements for realtime reconstruction and plasma control. In this paper, some timing results are showed, all these results are tested on the hardware environment discussed in this section. 3.2. Off-line static time-slice equilibrium reconstruction with POINT diagnostic Before the implementation of real-time current density profile reconstruction, off-line static time-slice benchmark tests are needed to demonstrate the correctness of the POINT diagnostic constraints which improve the current density profile reconstruction in P-EFIT. In this section, P-EFIT executes in off-line equilibrium reconstruction mode which is similar to EFIT in [17] and reconstructs single time-slice equilibrium with multiple iterations until convergence. The magnetic and POINT diagnostics data from an EAST divertor discharge 62573 at 4.0 s is used. In this case, JT plasma current representation [4], a particularly useful parametrization and boundary condition for use with external magnetic reconstruction in both L-and H-mode discharges, is used no matter whether POINT diagnostics is used. In JT plasma current representation, NP = 2, NF = 3, ı = 0 in polynomial representation for P and FF in Eq. (2) are chosen with adding two more constraints as shown in Eq. (7). P( FF (
N)
= ˛0 + ˛1 ×
N ) = ˇ0 + ˇ1 ×
N N
+ ˇ2 ×
2 N
0.1 × ˛0 + 0.1 × ˛1 = 0
(7)
0.1 × ˇ0 + 0.1 × ˇ1 + 0.1 × ˇ2 = 0 Jϕ = RP (
N) +
0 FF ( N ) 42 R
In Fig. 3, reconstructed magnetic flux surface, plasma boundary and q profile along the horizontal mid-plane (Z = 0) are compared between results from using magnetic diagnostics only and magnetic plus POINT diagnostics. The plasma boundary reconstructed using magnetic plus POINT data match that using external magnetic data, whereas, the internal flux surfaces exist differences. As expected, there is an obvious difference on q profiles. When it comes to plasma current and q profile, POINT diagnostic provide effective constraints. The axial safety factor q0 from the magnetically reconstructed case is 1.66, while the value from the case using POINT data is about 0.88. However, the q value near the plasma
Fig. 2. hardware structure of real-time POINT diagnostic data acquisition system.
boundary (q95 ) matches between two cases. It is necessary to mention that the sawtooth activity is observed by soft x-ray diagnostic at this time, which means the qmin should be less than 1.0. The radius of q = 1 rational surface can be approximated by the inversion radius of sawtooth [21,22]. The quality of the current profile reconstruction is verified by the locations of q = 1 rational surface which derived from the sawtooth oscillation. From vertical soft x-ray diagnostic channels in EAST, the q = 1 surface where sawtooth activity occurs locates at R = 1.83 m (high field side) and 1.967 m (low field side) in mid-plane (Z = 0). There is a good agreement between soft x-ray diagnostic with q profile reconstructed by using magnetic plus POINT data. The Fig. 4 shows the results that measured Faraday rotation angle and line-integrated Ne density are compared with the results calculated from P-EFIT when reconstructing with magnetic plus POINT data. To check the sensitivity of the fitting parameters of P and FF , we vary the NF from 1 to 3 in magnetic reconstruction and 3–4 in magnetic plus POINT reconstruction. In EAST, NF from 1 to 3 is usually sufficient for magnetic reconstruction and when NF is larger than 3, it is hard to get convergent magnetic equilibrium reconstruction results in P-EFIT. NF from 3 to 4 can provide enough degree of freedom for plasma current profile reconstruction when using magnetic plus POINT data. In Table 1, comparisons of global parameters of using the external magnetic data against those results reconstructed using magnetic plus POINT data are given. As expected, with or without the POINT constraints, there is no big difference on the global parameters such as plasma current (Ip), poloidal beta (p ), stored energy (Wmhd) and internal inductance (li) as NF is increased. As discussed in section 2.2 and showed in Fig. 4(a), Ne profile is directly fitted from 11 channels of line-integrated plasma density measurement with a polynomial plus a hyperbolic tangent representation as shown in Fig. 5. Combining Ne profile and 11 channels of Faraday rotation angle measurements data, POINT can provide additional constraints with magnetic diagnostics in reconstruction. It is seen that the calculated Faraday rotation angle and line-integrated Ne density profile from P-EFIT match those POINT measurements.
Table 1 Comparisons of global parameters of using the external magnetic data against those results reconstructed using magnetic plus POINT data with varying NF from 1 to 3. Shot: [email protected]
Ip (100kA)
p
Wmhd (100 kJ)
li
qmin
q95
Mag only (NP = 2, NF = 1) Mag only (NP = 2, NF = 2) Mag only (NP = 2, NF = 3) Mag + POINT (NP = 2, NF = 3) Mag + POINT (NP = 2, NF = 4)
5.60 5.60 5.60 5.60 5.60
0.54 0.55 0.53 0.48 0.47
1.24 1.29 1.22 1.10 1.10
0.99 0.99 1.01 1.12 1.14
1.74 1.67 1.66 0.89 0.88
4.59 4.58 4.59 4.63 4.61
Y. Huang et al. / Fusion Engineering and Design 120 (2017) 1–8
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Fig. 3. (a) magnetic flux surface, plasma boundary comparison between results using external magnetic data (blue lines) with magnetic plus POINT data (red lines). (b) comparison of reconstructed q profile between results using external magnetic data (blue lines) with magnetic plus POINT data (red lines) and the location of q = 1 surface from soft x-ray diagnostic (green crosses) (c) comparison of reconstructed plasma current density profile between results using external magnetic data (blue lines) with magnetic plus POINT data (red lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3.3. Experimental simulation benchmark test Through reference [17] and the off-line static time-slice test in section 3.2, it is proved that EFIT and P-EFIT could obtain an equilibrium result with magnetic plus POINT diagnostics which match other diagnostics. For real-time equilibrium reconstruction in plasma control, P-EFIT adopted a similar strategy in RT-EFIT [6], each time-slice calculation conducts only one iteration by using the equilibrium result from last time-slice and most recent diagnostics data as the input [9]. When POINT diagnostic data is used addi-
tionally, to verify the correctness of this approach, an experimental environment simulation benchmark is carried out to test real-time algorithms. For EAST PCS, there is a running mode called hardware test, in which all the hardware instruments are used and diagnostic data are read from history experimental shot. In this test, magnetic and POINT diagnostics data from 4.0 s to 6.0 s of EAST divertor discharge 62573 is used. As showed in Fig. 6, the reconstructed qmin using external magnetic diagnostics only are compared against those reconstructed using magnetic plus POINT data. It is found experimentally that the
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Y. Huang et al. / Fusion Engineering and Design 120 (2017) 1–8
Fig. 4. (a) comparison between measured line-integrated Ne density (red dots) with results calculated from P-EFIT when reconstructing with magnetic plus POINT data (blue line). (b) comparison between measured Faraday rotation angle (red dots) with results calculated from P-EFIT when reconstructing with magnetic plus POINT data (blue line). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. density profile reconstruction from POINT’s 11 channels of line-integrated plasma density measurement.
Fig. 6. time evolution of qmin for an EAST diverter discharge, shot 62573 from 4.0 s to 6.0s.
sawtooth activity is observed by SXR during the time from 4.0 s to 6.0 s in this discharge. From this observation, it can be concluded that the qmin should be less than 1.0 when the sawtooth oscillation. The qmin results reconstructed by using magnetic plus POINT data stay below 1.0 during the whole sawtooth period when those results from magnetic reconstruction are nearby 1.70. At the same time, the comparison between real-time one iteration qmin results with off-line multiple iteration qmin results from P-EFIT is showed to demonstrate the validity of the real-time calculation. The Fig. 7 shows the time evolution of the actual line-integrated density measurements and Faraday rotation measurements are compared with the results computed from P-EFIT (magnetic plus POINT reconstruction) for 11 channels. At each chord location, The synthetic densities and Faraday rotation angles computed from P-EFIT agree well with the measurements of line average density and the Faraday angle from 4.0 s to 6.0 s in this discharge.
plasma control in EAST, it can provide magnetic reconstruction results in 0.35 ms, about 0.3 ms for equilibrium calculation, 0.03 ms for control error calculation and 0.02 ms for exchanging data [9]. The main advantage of P-EFIT is the acceleration of computation, we focus on the cost time of per iteration for plasma control, this time means the control frequency P-EFIT can provide for plasma control system. As Fig. 8 shows, When using magnetic plus POINT data, compared with magnetic reconstruction, P-EFIT costs about 0.65 ms per iteration, the additional 0.3 ms is mainly consumed by response matrix of POINT diagnostic calculation, Ne density profile fitting and other POINT diagnostic related calculations in section 2.2. Considering all the calculation and data transfer, 65 × 65 spatial grids P-EFIT can provide results in less than 0.7 ms when using magnetic plus POINT data, it still can satisfy time feasibility requirements in real-time reconstruction for plasma discharge control.
3.4. Computational performance
4. Conclusion and future developments
The static time-slice and experimental simulation benchmark test have proved that P-EFIT can provide reasonable equilibrium results with magnetic plus POINT diagnostics and real-time one iteration approach is valid with additional POINT diagnostic. 65 × 65 spatial grids P-EFIT has been successfully implemented for
In this paper, development of real-time plasma current profile reconstruction with POINT diagnostic for EAST plasma control is described. P-EFIT using experimental magnetic plus POINT data could provide reasonable equilibrium reconstruction results of plasma current density and q profile in real-time. Based on data
Y. Huang et al. / Fusion Engineering and Design 120 (2017) 1–8
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Fig. 7. comparison of synthetic density and Faraday rotation angle against those POINT measurements. (left), line-integrated density by POINT measurement (blue lines) and inverse integrated analysis from P-EFIT’s magnetic plus POINT reconstruction (red lines), (right) Faraday rotation angle by POINT measurement (blue lines) and inverse analysis from P-EFIT’s magnetic plus POINT reconstruction (red lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Execution time evolution of P-EFIT’s one iteration in whole discharge.
interface between plasma control system(PCS) and P-EFIT’s GPU server [9], a real-time POINT diagnostic data acquisition(DAQ) system is built to satisfy time feasibility requirements for real-time plasma control. This work provides plasma current and q profile information which is essential for advanced tokamak plasma current profile control in real-time to maximize performances. It is also important for understanding and interpretation of confinement and stabilities in tokamak physics [23]. The built system would be applied for plasma current density and q profile control on EAST in the near future.
Acknowledgments This work is supported by the National Magnetic Confinement Fusion Research Program of China (No.2014GB103000, No.
2015GB102004), the National Natural Science Foundation of China (No.11575245, No.11375237, No. 11405205)
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[8] X.N. Yue, et al., Fast equilibrium reconstruction for tokamak discharge control based on GPU, Plasma Phys. Controlled Fusion 55.8 (2013) 085016. [9] Y. Huang, et al., Implementation of GPU parallel equilibrium reconstruction for plasma control in EAST, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/ j.fusengdes.2016.02.048. [10] P. Gohil, et al., Control of plasma profiles in DIII-D discharges, Plasma Phys. Controlled Fusion 48.5A (2006) A45 (). [11] H.Q. Liu, et al., Internal magnetic field measurements by laser-based POlarimeter-INTerferometer (POINT) system on EAST, J. Instrum. 11.01 (2016) C01049. [12] H.Q. Liu, et al., Faraday-effect polarimeter-interferometer system for current density measurement on EAST, Rev. Sci. Instrum. 85.11 (2014) 11D405. [13] Hofmann Ferdinand, Gilbert Tonett, Tokamak equilibrium reconstruction using Faraday rotation measurements, Nucl. Fusion 28.10 (1988) 1871. [14] M. Brix, et al., Accuracy of EFIT equilibrium reconstruction with internal diagnostic information at JET, Rev. Sci. Instrum. 79.10 (2008) 10F325. [15] R. Imazawa, Y. Kawano, Y. Kusama, A new approach of equilibrium reconstruction for ITER, Nucl. Fusion 51.11 (2011) 113022.
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Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Research Paper
Development of real-time plasma current profile reconstruction with POINT diagnostic for EAST plasma control Y. Huang a , B.J. Xiao a,b , Z.P. Luo a,∗ , J.P. Qian a , S. Li a , Y. Chen a , H.Q. Liu a , L.Q. Xu a , Y. Yuan a , Q.P. Yuan a a b
Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China School of Nuclear Science & Technology, University of Science & Technology of China, China
h i g h l i g h t s • • • • •
Plasma current profile reconstruction algorithms using POINT are implemented with GPU parallel computation in P-EFIT code. P-EFIT using experimental magnetic plus POINT data could provide reasonable plasma current density and q profile results. A real-time POINT DAQ system and data interface between PCS and P-EFIT’s GPU server are built. This system could satisfy time feasibility requirements for real-time plasma control. This work is essential for advanced tokamak real-time plasma current profile control to maximize performances.
a r t i c l e
i n f o
Article history: Received 6 November 2016 Received in revised form 28 April 2017 Accepted 2 May 2017 Keywords: Equilibrium reconstruction Plasma current profile Real-time GPU parallel computation EAST
a b s t r a c t This paper describes the plasma current profile reconstruction algorithms using POlarimeterINTerferometer(POINT) measurements in GPU parallel equilibrium reconstruction code P-EFIT for EAST plasma control. Real-time POINT diagnostic data acquisition system is designed to satisfy the requirement for real-time reconstruction. The static time-slice and experimental simulation benchmark calculations using experimental magnetic plus POINT data of EAST discharge are conducted, which show that P-EFIT could provide reasonable plasma current and q profile in 0.7 ms in real-time with 65 × 65 spatial grid resolution. These results show that P-EFIT with POINT diagnostic could provide equilibrium reconstruction results for real-time plasma current and q profile control which will be applied in the near future. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Plasma current profile is one of the most important factors determining the MHD stability and confinement in Tokamaks. For this reason, plasma current profile control is essential to optimize plasma performance for advanced tokamak operation. Real-time current profile reconstruction is necessary to provide information for plasma current profile control. For EAST long pulse high performance operation, current density profile reconstruction and control are highly desirable. Experimental equilibrium reconstruction provides information such as plasma boundary, current density and safety factor profiles for tokamak operation and research. EFIT reconstructs equilibrium by finding the Grad-Shafranov solution that is the least squares
∗ Corresponding author. E-mail address: [email protected] (Z.P. Luo). http://dx.doi.org/10.1016/j.fusengdes.2017.05.005 0920-3796/© 2017 Elsevier B.V. All rights reserved.
best fit to the experimental measurements. It efficiently combines equilibrium and fitting iterations to search for an optimum solution [1–4] and has been widely used in many tokamaks worldwide. However, the full algorithms of EFIT is computation intensive to be used in real-time control particularly for the high spatial grid resolution [5]. In [6,7], a real-time version-EFIT (RT-EFIT) and an efficient numerical solver for the Grad-Shafranov equation based on OpenMP parallel computation have been developed. Additionally in [8,9], a parallelized version EFIT code based on GPU for magnetic reconstructions, P-EFIT has been developed which significantly accelerate the whole computation process. P-EFIT efficiently takes advantage of massively parallel GPU cores and significantly accelerates the EFIT reconstruction algorithms and it has been successfully implemented for plasma control in EAST. For equilibrium reconstruction with external magnetic diagnostics only, only global parameters such as plasma boundary, ˇP , li, and Ip can be determined [1,2]. To reconstruct the q profile, internal profile measurements such as MSE must be used in con-
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junction with the external magnetic data. To fully reconstruct the equilibrium including the q and pressure profiles and the associated magnetic geometry self-consistently, kinetic profiles must be used in conjunction with the MSE and external magnetic data [4]. Real-time equilibrium reconstruction with MSE diagnostic is critical to provide q profile for plasma current profile control [10], when it comes to EAST, EAST do not equip MSE diagnostic until now. Fortunately, a new POINT diagnostic in EAST [11,12] can provide important internal profile information, which can be used as internal current profile constraints for equilibrium reconstruction. The diagnostic of POlarimeter-INTerferometer(POINT), well known as Faraday rotation, allows measuring the density times the magnetic field component parallel to the laser beam propagation direction. The Faraday rotation measurements can capture fast evolution of current profile information, provides off midplane magnetic field information which can be used to improve the accuracy of internal plasma surface elongation. The method of using Faraday rotation for the current density profile reconstruction was first mentioned in the later 1980s [13], applied in JET [14] together with other constraints and suggested for ITER [15] to improve the accuracy of the equilibrium reconstruction. An algorithm to determine the current density profile by resolving the equilibrium equation was developed in [16]. It was shown that POINT measurements could be used as the internal information in the current profile reconstruction. Moreover, the equilibrium reconstruction of EAST current profile based on POINT diagnostic is demonstrated using the EFIT equilibrium reconstruction code in [17]. These achievements make the implementation of real-time equilibrium reconstruction with POINT diagnostic possible. In this paper, design of real-time GPU parallel equilibrium reconstruction with POINT diagnostic for plasma control in EAST is presented. In section 2, the basic plasma equilibrium reconstruction and its implementation on GPU parallel computing are described briefly, then the detailed extension of P-EFIT algorithms on POINT diagnostic constraints is presented. In section 3, equilibrium reconstruction results of single timeslice and experimental whole discharge simulation test with magnetic plus POINT diagnostics, structure of real-time POINT data acquisition(DAQ) system are presented. Both equilibrium reconstruction and timing results are presented to prove that P-EFIT can provide equilibrium reconstruction with internal current profile information and satisfy time feasibility requirements for real-time plasma control. The built system would be applied for plasma current density and q profile control on EAST in the near future.
2.1. Introduction on GPU parallel equilibrium reconstruction algorithm P-EFIT takes the algorithm of EFIT [1–3] as its basic framework. Its principle is to compute the poloidal flux distribution in the R, Z plane, then obtain the toroidal current density distribution in this plane, which should satisfy a least-square best fit to the diagnostic data under the model given by the Grad-Shafranov equation. = −0 RJ ,
J = RP ( ) +
0 FF ( ) 42 R
P
FF
np −1
np −1
=
˛n
n N
−ı
n=0 nF −1
=
n=0
nF N
˛n
n=0 nF −1
ˇn
n N
−␦
nF N
(2) n
n=0
The value of linear parameters ␣n , ˇn and Jϕ are fitted from available measurements and constraints. P and FF are set to be zero at the boundary when ı = 1 at ohmic or L-mode discharge, and set to be finite value at boundary when ı = 0 at H-mode discharge. The unknown parameters ␣n and ˇn can be combined into unknown parameter vector ˛ ¯ directly to the measurements and constraints ¯ through the response matrix R as vector M R˛ = M.
(3)
Here, response matrix R contains relationship between parameters ␣n , ˇn with measurements and constraints [4]. P-EFIT is based on the EFIT framework but takes advantage of massively parallel GPU cores to significantly accelerate the computation. The equilibrium reconstruction algorithm is consist of several middle-scale matrix computation sequentially which need to be iterated, parallelizing these algorithms requires many computational cores and large amount of communication between cores. There are standard linear algebra routines in CUDA library, but the size of matrix in equilibrium reconstruction algorithms is too small to achieve good performance by directly using them. When developing modules in P-EFIT, we need to design customized parallel algorithm. Efficiently distributing hundreds of GPU cores and minimizing the communication between them are basic principle. For this reason, each parallel algorithms in P-EFIT are carefully designed through combining the needs of numerical algorithms and the GPU capacity. Some optimization for middle-scale matrix multiplication and an algorithm which could solve block tri-diagonal block linear system in parallel on GPU is described in [8,9]. 2.2. GPU parallel plasma current profile reconstruction algorithm using POINT measurements P-EFIT follows the algorithms and physical approach which have been discussed detailedly in [16,17]. In EAST, POINT diagnostic can provide 11 channels of line-integrated plasma density and Faraday rotation angle measurements. The Faraday rotation angle and the phase shift ϕ caused by the electron density are given by
2. Algorithms of parallel equilibrium reconstruction with POINT diagnostic
∗
represented as a linear combination of a number NP and NF of basis functions [4].
(1)
Here, is the poloidal magnetic flux per radian of the toroidal angle ϕ enclosed by a magnetic surface, F = 2RBϕ /0 is the poloidal current function, Bϕ is the toroidal magnetic field, and and ∗ = R2 ∇ ·(∇ /R2 ). The equilibrium solution of poloidal flux toroidal current density of plasma Jϕ are obtained on a rectangular grid which covers the entire area of the vacuum vessel. In EFIT, Jϕ is
=
ϕR -ϕL = 2.62 × 10−13 2 2
ϕ=
ϕR + ϕL = 2.82 × 10−15 2
ne B// dl
(4)
ne dl
(5)
where ϕR and ϕL are the phase shift for the R- and L- wave, B// is the component of the magnetic field along propagation of the laser beam, ne is the electron density, and is the wavelength of the beam. To incorporate the Faraday rotation data in equilibrium reconstruction, firstly, an equilibrium reconstruction is performed using external magnetic data only to provide initial flux mapping. Taking the magnetic flux surfaces from this magnetic only reconstruction as an initial guess, a reconstruction iteration with POINT and external magnetic data is then performed. The electron density profile is determined by fitting the line-integrated density data Eq. (5). Then fitting to Faraday rotation angles for multiple chords and
Y. Huang et al. / Fusion Engineering and Design 120 (2017) 1–8
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external magnetic data are carried out by inverting the response matrix that now includes the response from the Faraday rotation measurements based on Eq. (4). Then, new equilibrium flux surfaces are reconstructed and the reconstruction iteration with POINT and external magnetic data is repeated to get final solutions. Assuming that the electron density is a function of normalized flux, electron density is equal on a same flux surface, the density profile ne can be described as a polynomial plus a hyperbolic tangent representation [18], this representation allows electron density to have an edge pedestal and a finite value at boundary. ne
N
=
m
i
i−1 N
+ m+1 tanh(
N)
(6)
i=1
Here, N is the normalized flux, the unknown parameter i can be related to the measurements through Eq. (6) in a matrix form as AX = B, where A is the density response matrix, X is the unknown vector of i , and B is the experimental line integrated density vector. By fitting the electron density measurements line-integrated data, i and ne N can be determined. Although line-integrated density measurements do not contain the necessary spatial resolution for the determination the edge density pedestal, the Tanh term is included to allow a more accurate description of the density profile when more refined density measurements from Thomson Scattering or reflectometry are available. Then, combining ne N and line-integrated Faraday rotation angle measurements data by Eq. (5), additional constraints are appended into response matrix R in Eq. (3). Previous P-EFIT version is limited to reconstruction with magnetic diagnostics only and plasma current representation is fixed to polynomial representation as Eq. (2) with NP = 2, NF = 1, ı = 1. This settled plasma current representation and limited diagnostics reduce the difficulty of designing parallel algorithms when P-EFIT was initially developed. When extending the capacity to allow more diagnostics, the most challenging problem is to allow parallel algorithms to adjust automatically with variable matrices’ size due to different plasma current representations and diagnostics. Framework and algorithms are redesigned to allow flexible polynomial plasma current representations. For example, to obtain the response matrix R, multiplication of two large matrices, whose size are changed based on plasma current representation, is needed. By dividing the matrices into small pieces, the cost of matrix element multiplications is reduced [8]. Newly designed preprocessing algorithm is applied to divide a matrix into small 2D pieces and assign each piece an index in the 3rd dimension based on settled optimizing strategy. As shown in Fig. 1, matrix is divided into Blocks which are organized in Grid, each Block has Threads to calculate each matrix element multiplications. When adding POINT constraints into response matrix R, to guarantee good computational performance, unique GPU parallel algorithms are designed for plasma current profile reconstruction algorithm using POINT measurements. The POINT diagnostic responses are separately computed and organized into the response matrix R. When determining the electron density profile by fitting the POINT line-integrated density data, 11 Blocks which contain 65 threads are distributed to calculate matrix A formed by Eq. (5&6). Each Block calculates one channel of line-integrated i−1 plasma density response, each thread calculates N and tanh( N ) on grid, solving AX = B to get the unknown vector of i is similar to the method in [8,9]. Then forming the POINT response matrix by Eq. (4) into R, 11 Blocks which contain 65 threads are distributed, each Block calculates one channel of Faraday rotation angle mea-
Fig. 1. Description of threads distribution algorithm. After dividing the matrices into small 2d pieces which are distributed to Threads (blue parts) in Blocks (yellow parts), the algorithm assign each Block (yellow parts) an index in the 3rd dimension (grid, green part). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
surements response, each thread calculates 2.62 × 10−13 2 ne B// on grid, the method of relating B// to plasma current parameters ␣n , ˇn is similar to magnetic diagnostics’s green table function in [8,9].
3. Implementation and benchmark tests 3.1. Structure of real-time plasma current profile reconstruction system 3.1.1. Real-time GPU parallel equilibrium reconstruction system P-EFIT is running in a GPU server which is a Linux workstation with one Intel(R) Xeon(R) CPU E31230 @ 3.20 GHz and one NVIDIA Tesla K20c GPU card. Since GPU server is an independent system to PCS, a ReFlective Memory(RFM) network between them was built to share the real-time data [9]. For each time-slice in real-time, PEFIT performs new equilibrium reconstruction iteration using the most recent diagnostic data with equilibrium result of last timeslice as the initial input and provide equilibrium results to PCS. P-EFIT reads 75 single-precision numbers consisted of one time and 74 magnetic diagnostic data from PCS through RFM. PCS reads about 25 single-precision numbers, which depends on the number of control segments, consisted of control errors on control segments and x-points from P-EFIT through RFM. Totally about 400 bytes data is transferred through RFM in about 50us between PCS and P-EFIT’s GPU server in real-time. Real-time POINT diagnostic data is needed when P-EFIT reconstructs equilibrium and plasma current profile.
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3.1.2. Structure of real-time POINT diagnostic data acquisition(DAQ) system In EAST, POINT diagnostic can provide 11 channels of line-integrated plasma density and Faraday rotation angle measurements with high time resolution (up to ∼1 us). An independent real-time POINT diagnostic data acquisition system is built as Fig. 2 shows. The main hardware structure of real-time POINT DAQ system contains controller(NI PXIe-8135 with LabVIEW Real-time) [19], DAQ card(NI PXIe-6358) [20] and RFM card(GE PCI-5565PIOC). The original POINT diagnostic electrical signal is acquired and then transformed into valid physical signal which is transferred to P-EFIT GPU server through RFM network. The sample rate of POINT diagnostic data is 20 kHz, and the whole POINT diagnostic signal path consumes about 60us which both satisfy the requirements for realtime reconstruction and plasma control. In this paper, some timing results are showed, all these results are tested on the hardware environment discussed in this section. 3.2. Off-line static time-slice equilibrium reconstruction with POINT diagnostic Before the implementation of real-time current density profile reconstruction, off-line static time-slice benchmark tests are needed to demonstrate the correctness of the POINT diagnostic constraints which improve the current density profile reconstruction in P-EFIT. In this section, P-EFIT executes in off-line equilibrium reconstruction mode which is similar to EFIT in [17] and reconstructs single time-slice equilibrium with multiple iterations until convergence. The magnetic and POINT diagnostics data from an EAST divertor discharge 62573 at 4.0 s is used. In this case, JT plasma current representation [4], a particularly useful parametrization and boundary condition for use with external magnetic reconstruction in both L-and H-mode discharges, is used no matter whether POINT diagnostics is used. In JT plasma current representation, NP = 2, NF = 3, ı = 0 in polynomial representation for P and FF in Eq. (2) are chosen with adding two more constraints as shown in Eq. (7). P( FF (
N)
= ˛0 + ˛1 ×
N ) = ˇ0 + ˇ1 ×
N N
+ ˇ2 ×
2 N
0.1 × ˛0 + 0.1 × ˛1 = 0
(7)
0.1 × ˇ0 + 0.1 × ˇ1 + 0.1 × ˇ2 = 0 Jϕ = RP (
N) +
0 FF ( N ) 42 R
In Fig. 3, reconstructed magnetic flux surface, plasma boundary and q profile along the horizontal mid-plane (Z = 0) are compared between results from using magnetic diagnostics only and magnetic plus POINT diagnostics. The plasma boundary reconstructed using magnetic plus POINT data match that using external magnetic data, whereas, the internal flux surfaces exist differences. As expected, there is an obvious difference on q profiles. When it comes to plasma current and q profile, POINT diagnostic provide effective constraints. The axial safety factor q0 from the magnetically reconstructed case is 1.66, while the value from the case using POINT data is about 0.88. However, the q value near the plasma
Fig. 2. hardware structure of real-time POINT diagnostic data acquisition system.
boundary (q95 ) matches between two cases. It is necessary to mention that the sawtooth activity is observed by soft x-ray diagnostic at this time, which means the qmin should be less than 1.0. The radius of q = 1 rational surface can be approximated by the inversion radius of sawtooth [21,22]. The quality of the current profile reconstruction is verified by the locations of q = 1 rational surface which derived from the sawtooth oscillation. From vertical soft x-ray diagnostic channels in EAST, the q = 1 surface where sawtooth activity occurs locates at R = 1.83 m (high field side) and 1.967 m (low field side) in mid-plane (Z = 0). There is a good agreement between soft x-ray diagnostic with q profile reconstructed by using magnetic plus POINT data. The Fig. 4 shows the results that measured Faraday rotation angle and line-integrated Ne density are compared with the results calculated from P-EFIT when reconstructing with magnetic plus POINT data. To check the sensitivity of the fitting parameters of P and FF , we vary the NF from 1 to 3 in magnetic reconstruction and 3–4 in magnetic plus POINT reconstruction. In EAST, NF from 1 to 3 is usually sufficient for magnetic reconstruction and when NF is larger than 3, it is hard to get convergent magnetic equilibrium reconstruction results in P-EFIT. NF from 3 to 4 can provide enough degree of freedom for plasma current profile reconstruction when using magnetic plus POINT data. In Table 1, comparisons of global parameters of using the external magnetic data against those results reconstructed using magnetic plus POINT data are given. As expected, with or without the POINT constraints, there is no big difference on the global parameters such as plasma current (Ip), poloidal beta (p ), stored energy (Wmhd) and internal inductance (li) as NF is increased. As discussed in section 2.2 and showed in Fig. 4(a), Ne profile is directly fitted from 11 channels of line-integrated plasma density measurement with a polynomial plus a hyperbolic tangent representation as shown in Fig. 5. Combining Ne profile and 11 channels of Faraday rotation angle measurements data, POINT can provide additional constraints with magnetic diagnostics in reconstruction. It is seen that the calculated Faraday rotation angle and line-integrated Ne density profile from P-EFIT match those POINT measurements.
Table 1 Comparisons of global parameters of using the external magnetic data against those results reconstructed using magnetic plus POINT data with varying NF from 1 to 3. Shot: [email protected]
Ip (100kA)
p
Wmhd (100 kJ)
li
qmin
q95
Mag only (NP = 2, NF = 1) Mag only (NP = 2, NF = 2) Mag only (NP = 2, NF = 3) Mag + POINT (NP = 2, NF = 3) Mag + POINT (NP = 2, NF = 4)
5.60 5.60 5.60 5.60 5.60
0.54 0.55 0.53 0.48 0.47
1.24 1.29 1.22 1.10 1.10
0.99 0.99 1.01 1.12 1.14
1.74 1.67 1.66 0.89 0.88
4.59 4.58 4.59 4.63 4.61
Y. Huang et al. / Fusion Engineering and Design 120 (2017) 1–8
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Fig. 3. (a) magnetic flux surface, plasma boundary comparison between results using external magnetic data (blue lines) with magnetic plus POINT data (red lines). (b) comparison of reconstructed q profile between results using external magnetic data (blue lines) with magnetic plus POINT data (red lines) and the location of q = 1 surface from soft x-ray diagnostic (green crosses) (c) comparison of reconstructed plasma current density profile between results using external magnetic data (blue lines) with magnetic plus POINT data (red lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3.3. Experimental simulation benchmark test Through reference [17] and the off-line static time-slice test in section 3.2, it is proved that EFIT and P-EFIT could obtain an equilibrium result with magnetic plus POINT diagnostics which match other diagnostics. For real-time equilibrium reconstruction in plasma control, P-EFIT adopted a similar strategy in RT-EFIT [6], each time-slice calculation conducts only one iteration by using the equilibrium result from last time-slice and most recent diagnostics data as the input [9]. When POINT diagnostic data is used addi-
tionally, to verify the correctness of this approach, an experimental environment simulation benchmark is carried out to test real-time algorithms. For EAST PCS, there is a running mode called hardware test, in which all the hardware instruments are used and diagnostic data are read from history experimental shot. In this test, magnetic and POINT diagnostics data from 4.0 s to 6.0 s of EAST divertor discharge 62573 is used. As showed in Fig. 6, the reconstructed qmin using external magnetic diagnostics only are compared against those reconstructed using magnetic plus POINT data. It is found experimentally that the
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Fig. 4. (a) comparison between measured line-integrated Ne density (red dots) with results calculated from P-EFIT when reconstructing with magnetic plus POINT data (blue line). (b) comparison between measured Faraday rotation angle (red dots) with results calculated from P-EFIT when reconstructing with magnetic plus POINT data (blue line). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. density profile reconstruction from POINT’s 11 channels of line-integrated plasma density measurement.
Fig. 6. time evolution of qmin for an EAST diverter discharge, shot 62573 from 4.0 s to 6.0s.
sawtooth activity is observed by SXR during the time from 4.0 s to 6.0 s in this discharge. From this observation, it can be concluded that the qmin should be less than 1.0 when the sawtooth oscillation. The qmin results reconstructed by using magnetic plus POINT data stay below 1.0 during the whole sawtooth period when those results from magnetic reconstruction are nearby 1.70. At the same time, the comparison between real-time one iteration qmin results with off-line multiple iteration qmin results from P-EFIT is showed to demonstrate the validity of the real-time calculation. The Fig. 7 shows the time evolution of the actual line-integrated density measurements and Faraday rotation measurements are compared with the results computed from P-EFIT (magnetic plus POINT reconstruction) for 11 channels. At each chord location, The synthetic densities and Faraday rotation angles computed from P-EFIT agree well with the measurements of line average density and the Faraday angle from 4.0 s to 6.0 s in this discharge.
plasma control in EAST, it can provide magnetic reconstruction results in 0.35 ms, about 0.3 ms for equilibrium calculation, 0.03 ms for control error calculation and 0.02 ms for exchanging data [9]. The main advantage of P-EFIT is the acceleration of computation, we focus on the cost time of per iteration for plasma control, this time means the control frequency P-EFIT can provide for plasma control system. As Fig. 8 shows, When using magnetic plus POINT data, compared with magnetic reconstruction, P-EFIT costs about 0.65 ms per iteration, the additional 0.3 ms is mainly consumed by response matrix of POINT diagnostic calculation, Ne density profile fitting and other POINT diagnostic related calculations in section 2.2. Considering all the calculation and data transfer, 65 × 65 spatial grids P-EFIT can provide results in less than 0.7 ms when using magnetic plus POINT data, it still can satisfy time feasibility requirements in real-time reconstruction for plasma discharge control.
3.4. Computational performance
4. Conclusion and future developments
The static time-slice and experimental simulation benchmark test have proved that P-EFIT can provide reasonable equilibrium results with magnetic plus POINT diagnostics and real-time one iteration approach is valid with additional POINT diagnostic. 65 × 65 spatial grids P-EFIT has been successfully implemented for
In this paper, development of real-time plasma current profile reconstruction with POINT diagnostic for EAST plasma control is described. P-EFIT using experimental magnetic plus POINT data could provide reasonable equilibrium reconstruction results of plasma current density and q profile in real-time. Based on data
Y. Huang et al. / Fusion Engineering and Design 120 (2017) 1–8
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Fig. 7. comparison of synthetic density and Faraday rotation angle against those POINT measurements. (left), line-integrated density by POINT measurement (blue lines) and inverse integrated analysis from P-EFIT’s magnetic plus POINT reconstruction (red lines), (right) Faraday rotation angle by POINT measurement (blue lines) and inverse analysis from P-EFIT’s magnetic plus POINT reconstruction (red lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Execution time evolution of P-EFIT’s one iteration in whole discharge.
interface between plasma control system(PCS) and P-EFIT’s GPU server [9], a real-time POINT diagnostic data acquisition(DAQ) system is built to satisfy time feasibility requirements for real-time plasma control. This work provides plasma current and q profile information which is essential for advanced tokamak plasma current profile control in real-time to maximize performances. It is also important for understanding and interpretation of confinement and stabilities in tokamak physics [23]. The built system would be applied for plasma current density and q profile control on EAST in the near future.
Acknowledgments This work is supported by the National Magnetic Confinement Fusion Research Program of China (No.2014GB103000, No.
2015GB102004), the National Natural Science Foundation of China (No.11575245, No.11375237, No. 11405205)
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