Development of LH wave fullwave simulation based on FEM

Transcription

1 Development of LH wave fullwave simulation based on FEM S. Shiraiwa and O. Meneghini on behalf of LHCD group of Alacator C-Mod PSFC, MIT 2010/03/10 San-Diego, CA Special acknowledgements : R. Parker, P. Bonoli, and J. Wright

2 Motivation C-Mod LH experiments 2D LH full wave simulation LHEAF simulation model Maxwellian plasma Scalability (ITER scale plasma) Work in progress Coupling with Fokker-Planck codes Comparison with C-Mod experiments Summary

3 Motivation C-Mod LH experiments 2D LH full wave simulation LHEAF simulation model Maxwellian plasma Scalability (ITER scale plasma) Work in progress Coupling with Fokker-Planck codes Comparison with C-Mod experiments Summary

4 Alcator C-Mod

5 LHCD on Alcator C-Mod Langmuir probes Source Limiter Grill antenna on the C port (till 2008) 4.6GHz 3MW (12 klystrons, will be increased to 16) Grill antenna Stainless steel grill (2006) 4 rows, 88 columns Variable phase ( ) Up to 1.2 MW was successfully coupled

6 Current profile control has been demonstrated n = 1.56 LH ON Off axis (10,11,12) MHD activity central Shift of central current (r/a < 0.4) to peripheral region was confirmed by MSE constrained EFIT. Further analysis using kinetic + magnetic EFIT suggested that very good LHCD discharges may have had reversed shear. Need more experiment to eliminate an ambiguity of MSE pitch angle measurement caused by thermal birefringence

7 Emerging hypothesis to explain density limit emphasize the importance of including SOL in wave modeling As density increases, the hard X-ray emission count rate reduces much more significantly than the codes prediction Other experimental observation, such as large SOL current at high density, also suggests something is going on in edge region Inclusion of collisional power loss in GENRAY/CQL3D simulation shows better agreement with experiment (G. Wallace, APS2009 and Thesis)

8 New LHCD launcher based on four way splitter concept (O. Meneghini, RF conf, Gent, (2009) To couple more power Preserve n// flexibility Power splitting in the poloidal direction

9 Motivation C-Mod LH experiments 2D LH full wave simulation LHEAF simulation model Maxwellian plasma Scalability (ITER scale plasma) Work in progress Coupling with Fokker-Planck codes Comparison with C-Mod experiments Summary

10 Core simulations has been done by ray-tracing Standard method of LH wave simulation has been the ray tracing WKB is questionable near the cutoff/caustic Ambiguity in the launched spectrum Fullwave approach (TORIC-LH) is based on spectral representation of field (Spectral solvers) Direct evaluation of the electric field is necessary for comparison with the experiment Wave Physics in k-space easier to implement Computationally heavy / handling of SOL/antenna is difficult FEM Can handle complicated geometry Tends to make numerically sparse matrix Widely used in engineering applications Non-local wave physics is difficult to implement by courtesy of G. Wallace

11 Lower Hybrid wave Analysis based on Fem (LHEAF) 2D FEM simulation on the poloidal cross section Based on single mode analysis SOL/launcher can be included seamlessly COMSOL + MATLAB COMSOL : Solve Maxwell equation MATLAB : (gray : work in progress) Hot plasma effect Fokker-Planck calculation (1D/2D) Off-site calculation

12 LHEAF wave model : cold plasma + collisions + ELD

13 ELD was implemented via iterative method ε ε

14 In 5-7 iteration steps, convergence was obtained Effective damping ( (Ν)Leff) and power absorption profile shows that solution converges in 5-7 steps Alcator-C 5keV case Effective damping Initial guess Step 2 Step 4 Step 7

15 Temperature dependence of wave field Parallel electric field (Pin = 1kW) 30 min per step on desktop computer 2 quad core 3GHz 16 GB As temperature increases, wave penetration becomes shorter Between 2.5 kev and 3keV, propagation becomes multi-pass The reflection from the plasma is ~4%.

16 Comparison with other codes Solid: LHEAF, Dashed: Ray Solid: LHEAF, Dashed: TORIC-LH * TORIC-LH solution was scaled to match total absorbed power (by courtesy of J. Wright) Three codes all uses different approaches shows good agreement LHEAF(FEM), Ray-Tracing, and TORIC-LH (spectral) Disagreement remains at 2.5 kev, which is in the multi-pass regimes.

17 Scalability of sparse matrix solvers In the case of 2D LHEAF simulation 1st order vector elements Complex, non-symmetric matrix Assembly (matrix filling) and solution time with pre-ordering (eg. AMD) Linearly scales with degree of freedom (DoF) Quadratically scales with the poloidal cross sectional area

18 Full wave simulation on ITER scale plasma Take advantage of spatial localization of LH wave Ray trajectory of used to determine meshed region

19 Motivation C-Mod LH experiments 2D LH full wave simulation LHEAF simulation model Maxwellian plasma Scalability (ITER scale plasma) Work in progress Coupling with Fokker-Planck codes Comparison with C-Mod experiments Summary

20 1D Fokker-Planck was integrated Stationary solution for 1D FP equation is used Collisional diffusion and drag coefficient of a thermal (maxwellian) background plasma is used Quasilinear diffusion coefficient is evaluated using the parallel spectrum of the wave electric field c v v dv f e v = exp 2 Dc v D ql v 2 vt 1 e collisional diffusion drag quasilinear diffusion Parallel distribution function is evaluated at each step of the ELD iteration (k) (and correspondingly Λ Leff ) is modified Hermitian part of the dielectric tensor is unchanged (the wave propagation is described by the cold plasma dispersion)

21 Fast electron effects appears on the power deposition Maxwellian 1D FP tends to make the deposition profile broader Comparison with other codes is under way

22 LHEAF must be validated using experimental data log E// +1 Te = 4 kev ne = m-3 n// = 1.9

23 Dql is evaluated from real space E// to couple with 2D FP Evaluating parallel diffusion from transit time acceleration Parallel diffusion is plug into 2D FP through coordinate transformation

24 Hard X-ray synthetic diagnostics is under preparation Count rate Channel

25 Summary FEM has a couple of advantage such as... Seamless handling from the vacuum to the core plasma Efficient (allows fast solution or solving large problems) Accelerate the development of antenna design and wave simulation Lower Hybrid Wave Analysis based on Fem (LHEAF) Toroidal geometry. Single mode analysis by Floquet/Bloch like boundary conditions Iterative procedure to handle Electron Landau damping Fokker Planck Comparison with other codes show good agreement (in the single pass regime) ray tracing TORIC-LH Possibility of ITER scale plasma simulation is shown Application to C-mod, SOL, 2D FP, inclusion of multiple toroidal modes are under way