Theory Work in Support of C-Mod

Transcription

1 Theory Work in Support of C-Mod 2/23/04 C-Mod PAC Presentation Peter J. Catto for the PSFC theory group MC & LH studies ITB investigations Neutrals & rotation BOUT improvements

2 TORIC ICRF Mode Conversion Simulations Show Interaction of FW, ICW and IBW (Wright, Bonoli APS 03) D- 3 He Melby et al. PRL 2003 PCI line-integrated density measures waves to right of MC layer in C-Mod, with a peak spacing indicative of ICW wavelength As poloidal magnetic field increases ICW propagates and IBW damping length decreases, and up-down asymmetry due to upand down-shifts in wave vector increases (Perkins 1977)

3 Off-axis ICRF Mode Conversion in C-Mod Y. Lin et al, 15 Top. Conf. On RF Power in Plasmas, 2003 f rf = 80 MHz, 22.5%H, 77.5% D B t = 5.27 T, I p = 1 MA, n e = m -3, T e = 1.8 kev t = sec, E antenna Large H minority fraction allows MC electron heating to dominate over minority heating: D-H hybrid layer at r/a = 0.35 (HFS) Good agreement of TORIC with experimental power density absorbed per power in and MC efficiency: Experiment: 20% TORIC: 18%

4 LHRF: TORIC Simulates "Ring" of Reflecting FWs and Slow LHWs (Wright, Bonoli) m=0 SW FW _ Process: FW coupled at plasma edge, propagates inward, and converts to slow LHW Slow LHW propagates out to edge cut-off, reflects inward, and converts back to FW Process repeats itself until wave power is fully damped

5 Region of Reflecting Fast and Slow LH Waves Extends Poloidally Around Cross-section LH full-wave field pattern reminiscent of ray tracing results (ray tracing absorption closer to axis than full wave)

6 Advanced Tokamak (AT) and Steady State (SS) Operating Regimes Require Off-Axis Current Profile Control Lower Hybrid waves damp efficiently at high v // 2.5v te : Minimizes parasitic absorption of LH waves on fusion alphaparticles (relevant to ITER) Minimizes effects of particle trapping High current drive efficiency at accessible densities: r/a 0.6 AT and SS experiments planned for Alcator C-Mod and ITER will utilize off-axis LHCD: Worthwhile to compare predictions of different simulation models for LHCD Use test cases from C-Mod and ITER-FEAT

7 Summary of Fokker Planck Model Comparisons (Bonoli, Harvey) Lower Hybrid Models Compared: CQL3D: exact numerical 2-D (p^, p // ) solution of Fokker-Planck equation ACCOME: combines adjoint solution of FPE with a 1-D (p // ) damping model 1-D damping includes an approximate analytic model for 2-D pitch angle scattering effects: Works well for the broad quasi-linear plateaus characteristic of many LHCD experiments Results of Comparison: Exact 2-D solver CQL3D consistently predicts 35-50% more current drive than adjoint method (38% more efficient for ITER) Reason for Failure of the Adjoint Method: Analytic model for including pitch angle scattering in 1-D wave damping fails as the quasilinear plateau narrows: [f(1d) f(2d)] A situation typical of Alcator C-Mod and ITER

8 CQL3D Predicts 50% More LH Current & Penetration than ACCOME for LHCD in C-Mod P LH = 2.4 MW (P counter = MW), f = 4.6 GHz ACCOME CQL3D I LH = 0.21 MA I LH = 0.32 MA

9 Z eff m 3 Role of Trapped Electron Modes in ITB Control with on-axis ICRH ne x 10 5 rad/s Ohmic off-axis + on-axis ICRH, Double Barrier steep density gradient drives TEM ITG TEM GS2 2 MW off-axis MW on-axis ICRH, Double Barrier off-axis ICRH, Double Barrier off-axis ICRH T=0 ITB off-axis ICRH adiabatic electrons γ max ω/ ρ foot r a Flat Density 10 MW/m 3 D. R. Ernst, P. T. Bonoli et al., APS (2003) Invited Talk Off-axis ICRH produces EDA H-Mode, followed by ITB formation (density peaking). Initially little outward particle transport due to marg. stable ITG Ware pinch forms ITB where ITG modes suppressed (no turbulent pinch) Density steepens to turn on pure TEM & turn off ITG TEM outward particle flux increases to balance Ware pinch in stable equilibrium

10 x 10 5 rad/s m -1 kev ITB formation phase ends at each radius with TEM onset in ITB (ρ=0.4) TEM onset 1/ Lne Temperature Max. Linear Growth Rate ExB Shear Rate in barrier (ρ=0.4) add 0.6 MW on-axis ICRH In late phase of discharge, when V TOR ~0, ExB shear unimportant Density gradient scale length L ne stops getting shorter with TEM onset (~ 1.0 sec) On-axis ICRH increases temperature starting 1.25 sec D eff [m 2 /s] foot of barrier 0.08 ρ ITB 0.02 Formation Time (s) Ware-Corrected Particle Diffusivity D TEM e T 3/2 (gyrobohm scaling) n/ t increases to reduce & arrest density rise n t + ( nv Ware D eff n D. R. Ernst, P. T. Bonoli et al. APS 03 Invited Talk ) = 0

11 Gradients in ITB Follow ITG Stability Boundary Before Barrier Formation Several hundred linear GS2 runs trace out stability boundaries Initially, ITB marginally stable to toroidal ITG modes (L H s) As L n shortens (up to ~ 1 sec), "Trapped-Electron-ITG" modes weakly grow When pure TEM stability boundary is crossed, trajectory stagnates near a/l n ~ 2.2 D. R. Ernst et al., to be published a/ln weak dependence on LT TEM DOMINANT STABLE Trajectory of ITB (ρ=0.4) increasing γ 0.70 Time (s) = ITG/TEM increasing γ ITG a/l T

12 Gyrokinetic Turbulence Simulations in C-Mod ITB Reproduce Measured Particle/Heat Transport m 2 / s x10 20 m -2 s -1 x 10 5 rad/s Max. Growth Rate Real Frequency/10 PARTICLE FLUX Γe T EM Γ WARE e PARTICLE DIFFUSIVITY D T EM e D eff e turbulence simulation transport analysis Nonlinear GS2 simulations at 1.20 sec, preceding on-axis ICRH New nonlinear upshift in TEM critical density gradient due to zonal flows Error bars on density gradient primarily from uncertainty in Z eff gradient m 2 / s EFF. THERMAL DIFFUSIVITY χ T EM eff χ T RANSP eff VB measures n e Z 1/2 eff with R~1 mm: Also need direct core n e meas. with R~ cm. NL UPSHIFT a/l ne D. R. Ernst, P. T. Bonoli et al., APS (2003) Invited Talk

13 "Spontaneous" Rotation of C-Mod Helander, Fulop, Catto: PoP 10, 4396 (2003), PRL 89, (2002) C-Mod rotates without a momentum source Possible mechanism: Magnetic field - breaks symmetry by allowing a directed ion heat flow (with toroidal and parallel components) if dt/dr 0 CX coupling to neutrals results in ion heat flow terms in neutral viscosity - "heat viscosity": V r fiv r +2q r /5p Heat viscosity allows radial momentum transport to wall in a stationary plasma resulting in a transient plasma push Result: The steady state solution satisfying no radial flux of toroidal angular momentum is rotating

14 Neutral Control of Rotation MAST, Helander, Fulop, Catto Toroidal ion flow is not a flux function It matters where the neutrals are located poloidally! In L mode want to fuel so that the outboard flow is large and generates flow shear in regions of strong ballooning MAST observation: much easier access to H mode for inboard fueling Theory prediction: larger outboard counter current E r & toroidal flow for inboard fueling in MAST & C-Mod MAST observation: outboard impurity flow difference between inboard and outboard fueling cases is counter current and about magnitude predicted (a few cm inside separatrix) - Field, Carolan, Conway,... IAEA/NF

15 MAST Measurements HELIOS diagnostic measures outboard rotation of He + Inboard puff Outboard puff At least qualitative agreement: *counter-current rotation a few cm inside separatrix in L-mode *stronger with inboard than with outboard refuelling Doppler shift of impurity line radiation used to measure outboard rotation for different neutral fueling

16 C-Mod Neutral Fueling Experiment (Terry) A neutral fueling experiment similar to MAST planned Repeat MAST neutral fueling & impurity (He) injection using localized inboard and outboard gas puffs in L mode * puffs rate varying from ~10 19 to few x atoms/sec * inboard puff of D 2 seeded with He, observe outboard He+ rotation velocity * outboard puff of D 2 seeded with He, observe outboard He+ rotation velocity * observe edge turbulence with Gas Puff Imaging diagnostic and observe core rotation Can poloidally localized fueling control toroidal flow and electric field on outboard ballooning side of C-Mod?

17 BOUT Modeling of C-Mod Edge Simakov, Catto: PoP 10, 4744 (2003) & Catto, Simakov: PoP 11, 90 (2004) Working to improve BOUT 3D edge modeling BOUT: collisional 2 fluid code needs improvements 1. It only approximately preserves conservation properties 2. It retains incomplete pressure anisotropy and gyroviscosity - heat flow corrections ignored Derived an improved description for BOUT 1. evolve density, temperatures, ion parallel flow, vorticity (or potential) + Ampere's & parallel Ohm's 2. locally conserves number and total energy, ensures divergence-free current and magnetic field 3. recovers Pfirsch-Schlüter heat flows, current, and parallel ion flow of Hazeltine BOUT electric field model still needs improvement

18 Summary of Recent C-Mod Related PSFC Theory Work TORIC spectral code studies of C-Mod: MC of FW to ICW & IBW as in PCI Off-axis MC for large minority in agreement with i) power density absorbed/power input ii) MC efficiency Off-axis LHCD in C-Mod and ITER: CQL3D in 2D predicts more CD than 1D Accome

19 Roles of TEM & ITG modes in C-Mod ITB: GS2 and TRANSP agree within uncertainties Ware balanced by TEM flux in barrier Rotation in C-Mod & MAST: Need B, neutral heat viscosity & wall L mode outboard rotation depends on fuel location BOUT modeling of C-Mod edge: Equations are being improved