Transport analysis of the LHD plasma using the integrated code TASK3D

1. w3 w3 output w2 w2 w0 w0 w1 output weighted sum weighted sum weighted sum y w2 wn x1 y = f (z) y = f (z) x2 ・ ・ ・ xn N 2tN Transport analysis of the LHD plasma using the integrated code TASK3D Action of a neuron. synapse neuron A. Wakasa, A. Fukuyama, S. Murakami, a) C.D. Beidler, a) H. Maassberg, b) M. Yokoyama, b) M. Sato Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan a) Max-Planck-Institute fürPlasmaphysik, EURATOM Ass., Greifswald, Germany b)National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, Japan axon input electric signal cell body dendrite Engineering model of a neuron. This work is supported by Grant-in-Aid for Scientific Research (S) (20226017) from JSPS, Japan. inputs weight w1 x1 neuron Introduction Construction of the neoclassical transport database using Neural network in LHD: DCOM+GSRAKE/NNW for LHD, DGN/LHD Monte Carlo calculation of diffusion coefficient x2 w1 y = f (z) y = f (z) In helical devices, the neoclassical transport is important issue. ・ ・ ・ DCOM code evaluate the monoenergeticlocal diffusion coefficient. y = f (z) = tanh(z) xn Neoclassical transport inhelical device N mono-energetic particles are released. The drift velocity of the guiding center The helical trapped particles increase the neoclassical diffusion in the low collision frequency regime. ● initial radial positionr0 Neural network (NNW) is a technique that imitates the cranial nerve of the living body. Because NNW can have a strong nonlinear feature, the NNW is applicable to fitting of arbitrary, nonlinear function. The diffusion coefficient D The particle orbits are directly traced. initial poloidal position are set uniformly. anomalous transport initial toroidal position ● radial electric field 1/nregime ●collision frequency v||: the velocity parallel to magnetic field. ・・・ nregime P-S regime : the velocity perpendicular to magnetic field. The diffusion coefficient is obtained by calculating the dispersion as this expression, banana regime B: the magnetic field E: the electric field q: charge of the particle m: the particle mass As the temperature of plasma is raised in helical device, the neoclassical transport increases up to the anomalous transport or more. plateau regime bias bias classical transport Collision The pitch angle scattering rj r0 Lorentz collision operator high temperature The collision frequency n r0: initila position of particles accurate examination of the neoclassical transport is necessary in helical device. rj: the position of jth particle after t sec. An arbitrary I/O relation can be given to NNW byadjusting the weight to an appropriate value. We adjust the weight values of NNW using the results of DCOMand GSRAKE. 1960 DCOM results and 200 GSRAKE results are precomputed for training data in each Raxis. nd: the deflection collision frequency Therefore, We have developed a Monte Carlo simulation code, the Diffusion Coefficient Calculator by the Monte Carlo Method, DCOM. N : the number of particles t : time l = cosh Connection of the results of DCOM and GSRAKE Training data In the LMFP regime, a necessary computing time of DCOM code increases in inverse proportion to collision frequency. (e.g. at n*=1×10-8, 500 hours are required.) DCOM can calculate the mono-energetic diffusion coefficient without convergence problemeven if in LMFP regime ofthefinite beta plasma where a large number of Fourier modes of the magnetic field must be considered. DCOM DCOM results andGKASE results 1960 + 200 = 2160 ・Raxis = 3.75m: ( n*, G, r/a, D*, b0) Consequently, the DCOM results are insufficient in extremely low collision frequency regime. ・Raxis = 3.60m: ( n*, G, r/a, D*, b0 ) ▼the problems of the computing time. The necessary CPU time increases rapidly in the LMFP regime because we have to trace particle orbits for long time. neural network inputs In extremely low collision frequency regime, we combine the results of GSRAKEcode with the results of DCOM to construct the neoclassical transport database. The values which should output (DCOM and GSRAKE results). Therefore, We apply the results of GSRAKE code to the neoclassical transport database in the extremely low collision regime. n*1, G1, r/a1,b0,1 outputs ・・・ n*2, G2, r/a2, b0,2 GSRAKE code is a general solution of the ripple-averaged kinetic equation. D1, NNW D*1 It is necessary to interpolate DCOM results when we take the convolutions of the mono-energetic diffusion coefficient because DCOM and GSRAKE results are discrete data. ・・・ GSRAKE can estimate the diffusion coefficients with less computation time but not as detailed as in DCOM. D2, NNW D*2 n*N, GN, r/aN, b0,N ・・・ ・・・ We apply the Neural Network technique to the fitting of DCOM results. DN, NNW D*N Normalized collision frequency Raxis=3.60m A neoclassical transport data base, DCOM+GSRAKE/NNW for LHD (DGN/LHD) has been constructed. b0=0.0% GSRAKE Normalized radial electric field First, weight values are given randomly, so, NNW outputs wrong diffusion coefficient. We modify weight values appropriately by minimizing the root mean square error between the training data and NNW results. we newly apply DGN/LHD as a neoclassical transport analysis module to TASK/3D, which is the integrated simulation code in helical plasmas, and study the role of the neoclassical transport in several typical LHD plasmas. Normalized diffusion coefficient, D* Normalized diffusion coefficient DCOM The adjustable parameters of the NNW model are determined by a modified quasi-Newton method, the BFGS method. Normalized collision frequency, n*

2. Module structure of TASK3D The outputs of each database: DCOM/NNW and DGN/LHD Comparison of anomalous transport model Raxis=3.60 m b0=0.0 % r/a=0.5 Rax=3.60[m] B=2.75 [T] b0=1.00[%] 8×10-4 DGN/LHD DCOM/NNW At the plasma of standard profile of temperature and of density, the outputs of DCOM/NNW are accurate enough. 6×10-4 density profile is fixed. We incorporated neoclassical transport database DGN/LHD into TASK3D. 4×10-4 Use neoclassical transport module, DGN/LHD 2×10-4 DGN/LHD 0.0 particle pinch velocity = 0. thermal pinch velocity : proportional to Bohm (i) In extremely low collision frequency regime, because the computational results of DCOM don't exist, the outputs of the DCOM/NNW are inaccurate. Because the neoclassical transport database, DGN/LHD, contains the result of GSRAKE, the outputs of DGN/LHD are appropriate even in the extremely low collision frequency regime. (ii) : current diffusive interchange mode [1] The results of Neoclassical transport analysis In non-axisymmetric systems, the radial electric field Erare determined from ambipolar condition, Test analysis(1): Low-collisional plasma (high T and low n) where G are neoclassical particle fluxes. (i) Bohm model (ii) CDIM model Raxis=3.60 m b0=0.0% Here, D1, D2, and D3 are calculated by using DGN/LHD. Using this ambipolar radial electric field, TR module solves particle and heat transport equations. r/a=0.5 Test simulation of LHD plasma by using TASK3D Comparison of single helisity model and DGN/LHD n* in the 5vth≈ 2×10-7 D* we must consider energy convolution to extremely low collision regime. Rax=3.75[m] B=1.5 [T] b0=0.04[%] Summary Only neoclassical transport are assumed. We have been constructed the neoclassical transport database for LHD plasmas by using neural network technique. Ambipolar radial electric field Thermal conductivity of electron particle pinch velocity The GSRAKE results in the extremely low collision regime have been included in Neural network database, DGN/LHD. = 0. thermal pinch velocity We incorporated neoclassical transport database DGN/LHDinto TASK3D. 2 types of neoclassical modules ・single helisity model (Shaing model) The transport simulation with pinch velocities and more factual model of c has to be done. ・neoclassical transport module, DGN/LHD Future work ・ Neural network technique will be applied to the database of calculated results of TASK. Radial electric field: almost the same Thermal conductivity: By using DGN/LHD, ion root：increases by a factor of about 2. electron root：increases by a factor of about 1.5. [1] Itoh K., Itoh S.-I. and Fukuyama A. 1992 Phys. Rev.Lett. 69 1050 By using new neoclassical transport database, DGN/LHD, an accurate evaluation of the neoclassical transport in low-collisional plasma become possible.