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Monte Carlo Simulation Study of Neoclassical Transport and Plasma Heating in LHD

Monte Carlo Simulation Study of Neoclassical Transport and Plasma Heating in LHD. S. Murakami Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan Collaboration:

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Monte Carlo Simulation Study of Neoclassical Transport and Plasma Heating in LHD

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  1. Monte Carlo Simulation Study of Neoclassical Transport and Plasma Heating in LHD S. Murakami Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan Collaboration: A. Wakasa, H. Yamada, H. Inagaki, K. Tanaka, K. Narihara, S. Kubo, T. Shimozuma, H. Funaba, J.Miyazawa, S. Morita, K. Ida, K.Y. Watanabe, M. Yokoyama, H. Maassberg, C.D. Beidler, A. Fukuyama, T. Akutsu1), N. Nakajima2), V. Chan3), M. Choi3), S.C. Chiu4), L. Lao3), V. Kasilov5),T. Mutoh1), R. Kumazawa1), T. Seki1), K. Saito1), T. Watari1), M. Isobe1), T. Saida6), M. Osakabe1), M. Sasao6) and LHD Experimental Group

  2. Monte Carlo Simulations in LHD • DCOM/NNWDirect orbit following MC and NNW databaseNeoclassical Transport Analysis • GNET5D Drift Kinetic EquationEnergetic particle distribution (2nd ICH)

  3. Flexibility of LHD Configuration • 3D configuration of helical system=> Complex motions of trapped particles • Energetic particle confinement • Neoclassical transport • In LHD the experiments have been performed in the inward shifted config. Ideal MHD unstable configuration (Rax<3.6m) • No degradation of the plasma confinement has been observed in the Rax=3.6m experiments and, furthermore, the energy confinement is found to be better than that of theRax=3.75m case. It is reasonable to consider the experiment shifting Rax further inwardly, where NC transport and EP confinement would be improved. Inward shift

  4. Neoclassical Transport Optimized Configuration Neoclassical transport analysis (by DCOM) S. Murakami, et al., Nucl. Fusion 42 (2002) L19. A. Wakasa, et al., J. Plasma Fusion Res. SERIES, Vol. 4, (2001) 408. Rax=3.75m Rax=3.6m Rax=3.53m Tokamak plateau p • We evaluate the neoclassical transport in inward shifted configurations by DCOM. • The optimum configuration at the 1/n regime => Rax=3.53m.(eeff < 2% inside r/a=0.8) • A strong inward shift of Rax can diminish the NT to a level typical of so-called ''advanced stellarators''.

  5. Trapped Particle Orbit Rax=3.75m Rax=3.6m Rax=3.53m Toroidal projection Classical s-optimized E=3.4MeVp=0.47p r0=0.5a0=p0=0.0 NC optimized • Inward shift of Rax improves the trapped particle orbit.

  6. Experiment for The Neoclassical Transport Study s53130 • The plasma confinement in the long-mean-free-path regime of LHDis investigated to make clear the role of neoclassical transport. • The transport coefficients are compared between the three configurations: Rax=3.45m, 3.53m and 3.6m, 3.75m, 3.9m. • We set the magnetic field strength (~1.5T) to become a similar heating deposition profile (r/a~0.2). ECH (off axis heating) 0 r/a 1.0

  7. Configuration Dependency on E in LMFP Plasma The global confinement in the LMFP plasma also show clear eff dependency.

  8. Rax dependence on  (r/a=0.5) Rax=3.53m Rax=3.60m Rax=3.75m r/a=0.5 Rax=3.75m Rax=3.90m

  9. Rax dependence on  (r/a~0.75) Rax=3.53m Rax=3.60m Rax=3.75m Rax=3.90m

  10. Calculation method of Diffusion coefficients We evaluated a mono-energetic diffusion coefficient, D11, using Monte Carlo technique MHD equilibrium MHD equilibrium obtained by VMEC +NEWBOZ ORBIT calculation Motions of particles are calculated based on Equations of Motionsin the Boozer coordinates. (using 50 of magnetic Fourier models) COLLISION The pitch angle scattering are given in term of l, Comparison of the DKES and DCOM results shows good agreement from P-S regime through 1/n regime s;+1 or –1 with equal probabilities n ; the collision frequency

  11. There are some interpolation techniques. 1) direct linear interpolation the diffusion coefficients has strong nonlinear. this technique is also time-consuming and is not accurate. 2) use the common analytical relations depending on each collisionality regime, with their matching conditions. neural network The particle flux k = e, i. The energy flux j = 1 ; The particle transport coefficient.（ De11） j = 3 ; The thermal conductivity. ( ce ) - neural network fitting - DCOM (Introduction 2) To calculation of the transport coefficient for the given distribution function, e.g. Maxwellian, it is necessary to interpolate the monoenergetic results. energy integral

  12. x1 w1 hidden layer z y x2 S s wn output xn input layer input output layer inputs ; x1, x2, …xn weighted sum using a non-liner activation function sigmoid( ) output ; y THE BASIC ACTION of NEURAL NETWORK multilayer perceptron neural network The example of the sigmoid function

  13. ω is renewed in order to make error function, a minimum. THE ALGORITHM OF THE NETWORK CONSTRUCTION. Neural network the calculation result of DCOM (n, G, r, , Rax, D) By using the value which was Normalized, the generality of the database is raised[13]. input (n*, Er*, rRax ) output ( D* ) wj wi n* D* training data (n*, G, r, Rax, D*) G n*, G, r, Rax D’ r D’ is output, when n*, G, r and Rax is substituted for the input in the network. Rax This time, D’ is as a function of weight w.  On all training data, the learning is repeated in order to make E a minimum. Finally, it becomes E<Ec, and the network is completed.

  14. CONSTRUCTION RESULTS OF THE NETWORK 1 Rax = 3.75 [m] r/a=0.5 Open signs; DCOM results used training data Solid lines; NNW results Comparison of the DCOM results and outputs from the NNW shows good agreement good interpolation of G DCOM results not used as the training data DCOM/NNW: D* can be evaluated with arbitrary n, Er, r and Rax.

  15. CONSTRUCTION RESULTS OF THE NETWORK 2 D*(*, r/a) D*(*, Rax)

  16. Neoclassical Heat Flux (r/a=0.5) DCOM PECH Rax=3.53m Rax=3.60m Te [KeV] Rax=3.75m r/a=0.5 Rax=3.75m Rax=3.90m

  17. Neoclassical Heat Flux (r/a~0.75) PECH Rax=3.53m Rax=3.60m Rax=3.75m Rax=3.90m

  18. Conclusions (NC Analysis by DCOM/NNW) • We have experimentally studied the electron heat transportin the low collisionality ECH plasma (ne<1.0x1019m-3) changing magnetic configurations (Rax=3.45m, 3.53m and 3.6m, 3.75m, 3.9m) in LHD. • The global energy confinement has shown a higher confinement in the NC optimized configuration and a clear eff dependency on the energy confinement has been observed. • A higher electron temperature anda lower heat transport have been observed in the core plasma of NC optimized configuration (Rax=3.53m). • The comparisons of heat transport with the NC transport theory (DCOM) have shown that the NC transport plays a significant role in the energy confinement in the low collisionality plasma. • These results suggest that the optimization process is effective for energy confinement improvement in the low-collisioality plasma of helical systems.

  19. Monte Carlo Simulations in LHD • DCOM/NNWDirect orbit following MC and NNW databaseNeoclassical Transport Analysis • GNET5D Drift Kinetic EquationEnergetic particle distribution (2nd ICH)

  20. Fast wave is excited at outer higher magnetic field. ICRF Heating Experiment in LHD • ICRF heating experiments have been successfully done and have shown significant performance (steady state experiments) of this heating method in LHD.(Fundamental harmonic minority heating) • Up to 1.5MeV of energetic tail ions have been observed by NDD-NPA. s13151 ICRF resonance surface

  21. NBI#1 NBI#2 NBI#3 Perpendicular NBI and 2nd Harmonic ICRF Heating • Higher harmonic heating is efficient for the energetic particle generation. (Acceleration, vperp, is proportional to Jn) • The perpendicular injection NBI has been installed in LHD (2005). NBI#4P < 3MW (<6MW), E= 40keV • The perp. NBI beam ions would enhance the 2nd-harmonics ICRF heating (high init. E). • We investigate the combined heating of perp. NBI and 2nd-harmonics ICRF. HFREYA NBI#4 100keV 1MeV kperp

  22. A B C Pellet Shot61213 ki 2nd Harmonics ICH Experiments ki=0.7 (E=40keV,B=Bres) ・Tail temperature was same. ・Population increased by by a factor of three. H+/(H++He2+)=0.5

  23. mod-B on flux surface (r/a=0.6) p Trapped particle poloidal angle p 0 0 p toroidal angle ICRF Heating in Helical Systems • ICRF heating generates highly energetic tail ions, which drift around the torus for a long time (typically on a collisional time scale). • Thus, the behavior of these energetic ions is strongly affected by the characteristics of the drift motions, that depend on the magnetic field configuration. • In particular, in a 3-D magnetic configuration, complicated drift motions of trapped particles would play an important role in the confinement of the energetic ions and the ICRF heating process. • Global simulation is necessary! Orbit in the real coordinates. Orbit in Boozer coordinates.

  24. ICH+NBI Simulation Model by GNET • We solve the drift kinetic equation as a (time-dependent) initial value problem in 5D phase space based on the Monte Carlo technique. C(f): linear Clulomb Collision OperatorQICRF: ICRF heating termwave-particle interaction modelSbeam: beam particle source => by NBI beam ions(HFREYA code)Lparticle: particle sink (loss) => Charge exchange loss => Orbit loss (outermost flux surface) • The energetic beam ion distribution fbeam is evaluated through a convolution of Sbeam with a characteristictime dependent Green function, G.

  25. Monte Carlo Simulation for G • Complicated particle motionEq. of motion in the Boozer coordinates (c)3D MHD equilibrium (VMEC+NEWBOZ) • Coulomb collisionsLiner Monte Carlo collision operator [Boozer and Kuo-Petravic]Energy and pitch angle scattering • The QICRF term is modeled by the Monte Carlo method. When the test particle pass through the resonance layer the perpendicular velocity of this particle is changed by the following amount

  26. RF Electric Field by TASK/WM Pabs Pabs Simplified RF wave model RF electric field: Erf=Erf0 tanh((1-r/a)/l)(1+cos, Erfo=0.5~1.5kV/m kperp=62.8m-1, k//=0 is assumed. Wave frequency: fRF=38.47MHz, On-axis Off-axis

  27. Beam Ion Distribution of Perp. NBI w/o ICH (v-space) Teo=Tio=3.0keV, ne0=2.0x1019m-3, Eb=40keV Perp. NBI beam ion distribution Rax=3.60m • Higher distribution regions can be seen near the beam sources (E0, E1/2, E1/3). (left: lower level, right: higher level and cutting at r/a=0.8) • The beam ion distribution shows slowing down and pitch angle diffusion in velocity space. E0 E1/2 E1/3

  28. Distribution Function ICRF+NBI#4(perp. injection) Erf=0.5kV/m Erf=0.0kV/m Erf=1.2kV/m Erf=0.8kV/m

  29. NBI heating Beam Ion Distribution with 2nd Harmonics ICH 2nd-harmonic heating 1200 • We can see a large enhancement of the energetic tail formation by 2nd-harmonics ICH. • It is also found that the tail formation occurs near r/a~0.5.(resonance surface and stable orbit) 1000 800 600 Energy [keV] 400 200  0.0 r/a  Pitch angle 1.0 

  30. Beam Ion Pressure Profile with 2nd Harmonics ICH Erf0=1.0kV/m Erf0=2.5kV/m Erf0=0.0kV/m Teo=Tio=1.6keV, ne0=1.0x1019m-3 B=2.75T@R=3.6m, fRF=76.94MHz, k//=5m-1, kperp=62.8m-1

  31. Simulation Results (GNET) LHD (Rax=3.6m) Contour plot of fbeam(r, v//, vperp) 10 vperp/vth0 5 0 15 0.2 10 Sink of f by radial trnspt. of trapped ptcl. 0.4 5 slowing down 0.6 vc v///vth0 r/a 0 0.8 -5 1.0 GNET

  32. Distribution Function with 2nd ICH ICRF+NBI#1(tang. injection) Erf=1.5kV/m Erf=0.5kV/m Beam energy Beam energy

  33. NB#1 Ctr.-NB SD-NPA CNPA (PCX) NB#2 Co.-NB SiFNAArray@5.5L SiFNA@6I NDD NB#3 Ctr.-NB NB#4 perp.-NB SiFNA@6Operp. E//B-NPA NDD Optimization Effect on Energetic Particle Confinement • To clarify the magnetic field optimization effect on the energetic particle confinement the NBI heating experiment has been performed shifting the magnetic axis position, Rax;Rax =3.75m, 3.6m and 3.53mfixing Bax=2.5T • We study the NBI beam ion distributionby neutral particle analyzers.

  34. Simulation of NPA (2nd ICRF+NBI) • We have simulated the NPA using the GNET simulation results. • The tail ion energy is enhanced up to 200keV and a larger tail formation can be seen.

  35. Conclusions (ICH Analysis by GNET) • We have been developing an ICRF heating simulation code in toroidal plasmas using two global simulation codes: TASK/WM(a full wave field solver in 3D) and GNET(a DKE solver in 5D). • The GNET (+TASK/WM) code has been applied to the analysis of ICRF heating in the LHD(2nd-harmonic heating with perp. NBI). • A steady state distributionof energetic tail ions has been obtained and the characteristics of distributions in the real and phase space are clarified. • The GNET simulation results of the combined heating of the perp. NBI and 2nd-harmonic ICRF have shown effective energetic particle generation in LHD. • FNA count number has been evaluated using GNET simulation results and a relatively good agreement has been obtained.

  36. Full Wave Analysis: TASK/WM

  37. Rax dependence of eff (r/a=0.5) Rax=3.60m Rax=3.53m Rax=3.75m Rax=3.90m

  38. Rax dependence of eff (r/a~07.5) Rax=3.53m Rax=3.60m Rax=3.90m Rax=3.75m

  39. Heating Efficiency of Perp. NBI • In low density case the heating efficiencies are similar in the Rax=3.53 and 3.6m cases while the efficiency is very low in the Rax=3.75m case. • In higher density the efficiency of Rax=3.6m case is decreased.

  40. Trapped Particle Oribt in LHD Rax=3.60m,=0.6% Rax=3.50m,=0.6% Rax=3.75m,=0.6% Rax=3.50m,=1.2% Rax=3.75m,=1.2% Rax=3.60m,=1.2%

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