Theoretical Studies of Toroidal Rotation Induced by Lower Hybrid Wave Fields

Transcription

1 Theoretical Studies of Toroidal Rotation Induced by Lower Hybrid Wave Fields RF SciDAC meeting 2010(PPPL) Jungpyo(J.P.) Lee -MIT John Wright MIT Peter Catto MIT Paul Bonoli MIT Felix Parra Oxford Christ Church

2 Outline Background Motivation for rotation studies C-Mod experimental results Momentum source and stress tensor Wave part TORIC-LH Full wave solution Self-consistent dist.func.: Iterations with CQL3D Tor. Ang. Mom. Source computation Issues and Future Plans Transport Part Phenomenological Analysis: Diffusion, Pinch, Residual terms Low flow gyrokinetics by Felix Parra GS2 modification Issues and Future Plans 2

3 Background: Advanced Tokamak Scenarios rely on current profile control which can be done using LH waves Lower Hybrid Wave Off-axis Current Drive (Magnetic Shear) Toroidal Rotation Supplement bootstrap current ITB optimal Control MHD [tearing, Sawtooth] stabilization (A.Ince-Cushman et al, C-Mod) 3

4 C-Mod Experimental HiReX toroidal rotation result Toroidal rotation radial profile in C-Mod (Top: LH wave on, Bottom:LH wave off) To explain this rotation profiles, it may need - Off-axis LH wave momentum source - Inward Momentum convective terms - Counter-current dir. core toroidal rotation - Viscosity flow(diffusive term) - Co-current dir. core toroidal rotation - Outward Momentum convective terms (Ron Parker, 2009 APS Poster) Cmod shot Measured by Yuri Podpaly, John Rice, and Matt Reinke 4

5 Tor. Mom. Source and Viscosity Tensor Lower Hybrid Wave (n_par=-1.9) induces an ion counter-current toroidal rotation by an unkown mechanism Easy Interpretation by summation of electron and ion equations and the use of quasi-neutrality =0 Transport Analysis Wave Analysis Where,, and LH momentum input to electrons compete with off diagonal element of ion stress tensor 5

6 I. WAVE PART 6

7 Full wave solution with Non-Maxwellian Dist. Func. Maxwell Equations of TORIC-LH Assume one fixed toroidal mode(n), and small electron Larmor radius. Quasilinear diffusion coefficient for non-maxwellian dis.function. Define the relativistic Fokker-Plank Eqn, in terms of the outer-midplane distribution function, F, and,,, 7

8 Momentum input calculation in TORIC-LH Bounce averaging power absorption by two methods Power absorption can be defined with bounce time, (1) (2) where,, and. Similarly for the toroidal angular momentum input calculation 8

9 Iterations between TORIC-LH and CQL3D Self-consistent velocity distribution Velocity Distribution Fn. f CQL3D (Harvey 1992 (IAEA Bounce averaged Fokker-Planck code that solves for f(v) u /v te Qusilinear Diffusion Coeff. v TORIC-LH (Wright 2004CPC,2009PoP) Calculates the rf fields and the bounce avg. quasilinear flux(d ql df/dv) by f(v) u /v te 9

10 Iteration Convergence in terms of Power absorption profiles Iteration by python until Step 8 profiles almost agree E field F u/u_norm The dist. Func. at r/a=0.7 in Cql3D of the step8 Poloidal mode number The poloidal spectrum in TORIC of the step8 10

11 Electric field of Lower Hybrid Wave in TORIC-LH 3D E field Reconstruntion with 20 n-mode 2D E field with n_par=-1.9 Radial power absorption profile by 3D reconstuction 11

12 Computation of Tor.Ang.Mom. Source of LH wave Calculation of in Step 8 of TORIC-LH Comparison with experimental data of toroidal momentum increase rate when lower hybrid turns on 12

13 Issues and Future Plan for Wave Part Numerical Iteration Convergence More careful control of the iterations between TORIC-LH and CQL3D Increased velocity space resolution or absolute velocity grid in TORIC-LH Increased poloidal mode resolution in TORIC-LH (New Solver Required) 3-D reconstruction with more toroidal modes (New Solver Required) Theoretical Verification Validation of the quasi linear diffusion coefficient in the toroidal geometry in terms of non-linear mode coupling Experimental Data Time resolution problem of HiReX Reliability of the HiReX rotation data (Low emissivity in plasma periphery) Verification of current drive by Lower Hybrid wave using MSE-EFIT 13

14 II. TRANSPORT PART 14

15 Tor.Ang.Mom.Transport The toroidal angular momentum transport eqn. Radial Flux of Tor.Ang.Mom definitions (1) Phenomenological Analysis-(Hahm,Peeters, Diamond, Gurcan ) (2) Off-axis Stress Analysis-(Parra, Catto ) (3) Separate particle and momentum transport 15

16 Phenomenological Analysis (a) Turbulent Equipartiption diffusion and pinch by [Hahm,POP2008;GurcanPRL2008] Define the divergence free variable. Then, the perturbed values by turbulence makes 16

17 Phenomenological Analysis (b) Coriolis effect on diffusion and pinch[peeters,pop2009] The rotation frequency, the normalized rotation velocity,and velocity shear Coriolis terms in drift and diamagnetic frequency in G.K.E In the radial flux, the relation exists, (c) Residual Stress(Reynolds Stress) by [Gurcan POP2007] The centroid shift of the potential. from the resonance surface, by velocity shear induce the symmetry breaking on It results in the reynolds stress 17

18 Analysis for Low Flow Gyrokinetics by Parra(1) Order of Radial Flux of Tor.Ang.Mom GyroBohm Diffusion, Low toroidal rotation(w/o NB) The order of f needed to find the radial E field (Extended quasineutrality from until to until by Felix even for turbulent plasma) Tokamak genmetry 18

19 Analysis for Low Flow Gyrokinetics by Parra(2) Ion distribution function and potential orders -Axis symmetric long wavelength N.C. Part -Asymmetric short wavelength Turbulence part -Long wavelength part due to the beating of two short wavelength of (i.e. makes a part of ) <A diagram to find the radial E field: Number means the equation index in Parra, PPCF2010> 19

20 Analysis for Low Flow Gyrokinetics by Parra(3) Radial flux of Tor.Ang.Mom for low flow order Off-diagonal stress and quasineutralilty Moment method with full ion Fokker-Plank Eqn. Transport averaging 20

21 Radial Flux of Tor. Ang. Mom with LH wave Transient Effect Diffusion Reynolds Stress Inward Pinch Collision LH wave effects 21

22 GS2 Implementation 1 st δ-order Gyrokinetic Equation Generalized potential ; Non-linearity of solutions(potential and δ-order dist.func.) Curvature and Grad-B drift frequency Drift frequency Flux tube simulation Balloning Theory on the perturbation ITG, TEM, ETG, Zonal flow... Possible modification for low flow gyrokinetics by Parra Replacement of F0 due to the neoclassical contribution, Confirmation of the order of the reynolds stress term, in the radial flux of tor.ang.mom 22

23 Possible Issues of low flow analysis Inward momentum pinch? Quasineutrality until 4 th order in delta? Order analysis reality (GyroBohm, low flow) LH wave effect on ions (C_ii C_ii+C_ie) Transform of f in terms of coordinate Long time gyrokinetics requires a full f code with vorticity equations Up-down symmetry assumption Numerical analysis accuracy and sensitivity Extension to other rotation mechanisms (intrinsic rotation, IBW,ECCD..) 23

24 -END- Thank You! 감사합니다! 24