Full-wave Simulations of Lower Hybrid Wave Propagation in the EAST Tokamak

Transcription

1 Full-wave Simulations of Lower Hybrid Wave Propagation in the EAST Tokamak P. T. BONOLI, J. P. LEE, S. SHIRAIWA, J. C. WRIGHT, MIT-PSFC, B. DING, C. YANG, CAS-IPP, Hefei 57 th Annual Meeting of the APS Division of Plasma Physics Savannah, GA November 18, 2015 Poster NP

2 Abstract Studies of lower hybrid (LH) wave propagation have been conducted in the EAST tokamak where electron Landau damping (ELD) of the wave is typically weak, resulting in multiple passes of the wave front prior to its being absorbed in the plasma core. Under these conditions it is interesting to investigate full-wave effects that can become important at the plasma cut-off where the wave is reflected at the edge, as well as full-wave effects such as caustic formation in the core. High fidelity LH full-wave simulations were performed for EAST using the TORLH field solver [1]. These simulations used suffcient poloidal mode resolution to resolve the perpendicular wavelengths associated with electron Landau damping of the LH wave at the plasma periphery, thus achieving fully converged electric field solutions at all radii of the plasma. Comparison of these results with ray tracing simulations [2, 3] will also be presented.

3 This work is the subject of the 2017 Theory and Performance Target Lower Hybrid current drive (LHCD) will be indispensable for driving off-axis current during long-pulse operation of future burning plasma experiments including ITER, since it offers important leverage for controlling damaging transients caused by magnetohydrodynamic instabilities. However, the experimentally demonstrated high efficiency of LHCD is incompletely understood [in weak damping regimes]. In FY 2017, massively parallel, high resolution simulations with 480 radial elements and 4095 poloidal modes will be performed using fullwave radiofrequency field solvers and particle Fokker-Planck codes to elucidate the roles of toroidicity and full-wave effects. The simulation predictions will be compared with experimental data from the superconducting EAST tokamak. This work spans the research interests of the CSWPI SciDAC Center, the MIT Theory Grant, the Alcator C-Mod Project and the EAST / KSTAR Scenario Extension and Control Collaboration.

4 LHCD in the EAST Tokamak LHCD experiments in EAST are in the weak damping regime where full-wave effects and interference effects can potentially be very important [4]: Ray tracing / Fokker Planck simulations show multi-pass nature of absorption: [2] C. Yang et al, PPCF (2014)

5 Simulation set-up Use experimental profiles and EFIT equilibrium reconstruction for discharge : Created Fourier MHD equilibrium representation for TorLH (equigs.dat) and kinetic profiles data file (equidt.data): B 0 = 2.31 T, I p = 373 ka, a = 0.42 m, R 0 = 1.85 m, T e (0) = 3.2 kev, n e (0) = m -3. RF parameters: P LH = 2 MW, f 0 = 4.6 GHz, n // = Status of TorLH / CQL3D executables ( ): NERSC: TorLH and CQL3D available. MIT Loki Cluster: TorLH and CQL3D avaliable. IPP Shenma Cluster: TorLH and CQL3D are available (PGI build).

6 Numerical implementation and mode resolution requirements for TorLH Semi-spectral ansatz is assumed for the electric field: im in E( x) Emn, ( ) e mn, Spectral decomposition in the poloidal (m) and toroidal (n) directions. E m,n () are represented by finite elements in the radial direction (cubic Hermite interpolating polynomials). Using the ansatz above, the wave equation can be put in a weak variational form (Galerkin method): Each toroidal mode (n) is solved separately assuming N m poloidal modes and N r radial elements. This results in a block tri-diagonal matrix to invert.

7 Matrix inversion is performed using a new 3D parallel solver [5] A D U L D U L D U L D U L D L, D, U are each dense block matrices of size (2 3 N m ) 2 Total of N r block rows Parallel decomposition of blocks is distributed over p 2 p 3 = pcblock processors. Solver distributes groups of rows over p 1 processors. Matrix inversion time scales like N r (N m ) 3 using p 1 p 2 p 3 cores.

8 Poloidal mode resolution requirements for TorLH to simulate LH wave propagation in EAST Must resolve the shortest perpendicular wavelength in the system, which is given by the LH dispersion relation: k k // pe For an EAST discharge at r/a ~ 0.5 with B 0 = 2.3 T, T e (0) ~ 1 kev, n e (0) ~ m -3, f 0 = 4.6 GHz, we have: m r k cm n m rk 1 17 (for // ~n //0 =2) 372 and N 2m1 745 m k cm n m rk 1 46 (for // ~n // ELD ~5.5) 1019 and N 2m May need N m ~ 4000 to resolve LH wave at edge ~ 45 cm. m

9 Convergence is only achieved on innermost flux surface (r/a 0.1) at N m = 255

10 Convergence still limited to flux surfaces at r/a < 0.3 as N m is increased from

11 Convergence is finally achieved out to r/a 0.3 as N m is increased to 1023

12 Convergence continues to improve on flux surfaces out to r/a 0.5 as N m is increased to 2047 Simulation performed using 2.5 hours of wall clock time on Hopper at NERSC using 7168 cores.

13 Find that convergence is achieved on all flux surfaces as N m is increased to 4095 Simulation required ~7.5 hours of wall clock time on Hopper platform at NERSC using 32,256 cores: 1.5 hours for matrix inversion and ~ 6 hours for power reconstruction.

14 LH power deposition profile is peaked on-axis at N m = 255, but starts to broaden as N m is increased to 511 Broadening of the LH power deposition profile is consistent with adding higher k // components to the spectral solution in TorLH that correspond to higher m.

15 Off-axis peak in LH power deposition profile appears as N m is increased from Broadening of the LH power deposition profile is consistent with adding higher k // components to the spectral solution in TorLH that correspond to higher m.

16 Parallel electric field of LH wave starts to exhibit features of multiple reflections and weak single pass absorption as N m is increased N m = 255 N m = 1023 N m = 2047

17 At N m = 4095 the full-wave absorption profile is clearly off-axis (for Maxwellian electron damping). N m = 4095

18 Dramatic reduction achieved in wall clock time for TorLH New 3D solver [5] implemented in power reconstruction subroutine of TorLH to recover E from solution: Results in a decrease in wall clock time for the 4095 mode simulation on Hopper from 7.5 hours to ~ 1 hour. Time for power reconstruction reduced from ~ 6.5 hours to ~ 500 sec. Necessary step for performing iterations between TorLH and CQL3D. May use vector extrapolation technique to improve convergence of iteration (see [1]), especially in weak damping regimes. Final step: Compare hard x-ray profiles and LH power deposition and current density profiles from TorLH / CQL3D and GENRAY / CQL3D.

19 Iteration Procedure for Simulation a) Execute TorLH in toric mode using Maxwellian electron Landau damping (ELD): i. Perform a resolution scan to determine how many poloidal modes are needed to resolve the LH wave in EAST. b) Re-run TorLH in qldce mode to compute the RF diffusion coefficients (D_ql) from the electric field solutions computed in Step (a): i. Remap D_ql from the TorLH (radial, velocity) space mesh to the CQL3D (radial / velocity) space mesh. c) Run CQL3D to obtain first iterate for the quasilinear electron distribution f e (v, v //, r): i. Create look-up table for Im{ zz } due to ELD. d) Repeat steps (a) (c) until f e (v, v //, r) and D_ql (f e ) are self-consistent.

20 References and Acknowledgements [1] J. C. Wright et al, Physics of Plasmas 16, (2009). [2] C. Yang et al, Plasma Physics and Controlled Fusion (2014). [3] S. Shiraiwa et al, 21st Topical Conference on Radio-frequency Power in Plasmas, April 2015, Lake ArrowHead, CA. [4] J. C. Wright et al, Plasma Physics and Controlled Fusion 56, (2014). [5] J. P. Lee and J. C. Wright, Computer Physics Communications 185, 2598 (2014). Work supported by the US DOE under Contract No. DE- SC and DE-FC02-01ER54648.