Comparisons of Measurements and Gyro-kinetic Simulations of Turbulence and Trans-port in Alcator C-Mod EDA H-Mode Discharges M. B. Sampsell, R. V. Bravenec Fusion Research Center, The University of Texas at Austin J. Candy General Atomics D. R. Ernst, Alcator C-Mod Team Plasma Science and Fusion Center, MIT W. M. Nevins Lawrence Livermore National Laboratory

Motivation Beam-emission spectroscopy (BES) has detected the “quasi-coher-ent mode” at the edge of enhanced D (EDA) H-mode plasmas. However, it has not detected any broadband fluctuations at the top of the H-mode pedestal. Why? No localized fluctuation measurements exist by any diagnostic. Approach: Calculate the turbulence from a nonlinear gyrokinetic code (GYRO*). Model the diagnostic and apply it to the computation results (“synthetic diagnostic”) * J. Candy, J. Comput. Phys. 186, 545 (2003).

EDA (enhanced D) H-mode discharge at start of ITB C-Mod EDA Profiles EDA (enhanced D) H-mode discharge at start of ITB Radius of interest: R  0.87 m, where density profile is very flat (if not inverted).

Spectrum above ~ 250 kHz entirely due to dark noise BES Spectra at R = 0.87 m during DNB after DNB dark noise Virtually identical spectra with or without DNB (represents background light) Spectrum above ~ 250 kHz entirely due to dark noise Expected S/N (power) for 1% fluctuations (f0 = f ~ 200 kHz): ~ 0.15

GYRO Simulation r0 = 0.825a = 0.192 m (ne0  2x1020 m-3, Te0  0.540 keV, BT = 5.5 T) 16 toroidal modes n = 0 – 120 (ks = 0 – 0.815) Kinetic electrons Periodic boundary conditions (no background EB shear) 115s x 115s simulation domain, 128 radial grid points One impurity: Boron Length of run: 867 a/cs  1.17 ms Other parameters:  = 0.825 R/a = 3.07 Ti/Te = 0.92 * = 0.0015 q = 3.95  = 1.40 Lni/a = 200 Zeff = 1.61 = 2.70  = 0.28 LTi/a = 0.23 ei = 1.2 s  = –0.12 LTe/a = 0.37

Agreement lends credibility to simulation. Energy Flux Total energy flux Qtot(W/cm2): GYRO TRANSP (Qe + Qi + Qz) 29.4 29.2 (Cannot distinguish electron and ion fluxes because Ti ~ Te) Agreement lends credibility to simulation.

Spatial Density Fluctuation Distribution Scale size  1 cm in nonlinear phase Average “downward” propagation (electron diamagnetic direction) This and subsequent analysis performed using GKV (W. M. Nevins, LLNL Rept. UCRL-TR-206016, August, 2004).

Calculated Density Fluctuations Densities (in units of 1019m-3) evaluated at (r,r0) = (19.2,0) cm: ne(t) ni(t) nz(t) ne and ni similar and in phase. nz fluctuations absent low frequencies.

Signal Fluctuations BES detects Doppler-shifted H emission from a neutral beam, which is a function of beam energy, impurity charge, and electron and ion densities.1,2 There are two diagnostic “filters”: The emissivity rate nev as a function of the densities. The diagnostic’s spatial sensitivity function which averages over any fine structure. 1 W. M. Mandl, et al., “Beam emission spectroscopy as a comprehensive plasma diagnostic tool,” Plasma Phys. Control. Fusion 35 1373 (1993). 2 I. H. Hutchinson,” Excited-state populations in neutral beam emission,” Plasma Phys. Control. Fusion 44 71 (2002).

Emissivity Fluctuations Emissivity rate e from Mandl et al. 40 keV/amu 20 13.3 3 6 Zeff 1 Eb Saturation with density  e ~ ne0.4 Emissivity decreases as Zeff increases (dilution).

Simulated Emissivity Fluctuations Time traces evaluated at (r,r0) = (19.2,0) cm: (ne0 = 1.96x1020 m-3, Zeff0 = 1.61, 0 = 3.07x105/s) ne(t)/ne0 Zeff(t)/Zeff0 (t)/0 Fluctuations in Zeff are small and somewhat out of phase with density. Emissivity fluctuation amplitude is about half that of density.

BES Spatial Sensitivity Function f(x,y) = f0 exp(-[(x-x0)/dx]px) exp(-[(y-y0)/dx]py) x0 = 19.2, y0 = 0, dx = 0.8, dy = 0.5, px = 4, py = 6

Simulated Signal Fluctuations Time traces evaluated at (r,r0) = (19.2,0) cm: (ne0 = 1.95x1020 m-3, 0 = 3.07x105/s) ne(t)/ne0 (t)/0 Signal High frequencies (high wave numbers) are lost.

Simulated Emissivity Spectra f (kHz) 0 24 48 72 96 120 Peak frequencies at ~ 8, 14 kHz Peak k  2 cm-1 Poloidal phase velocity  = /k  0.24, 0.44 km/s

Simulated Signal Spectra f (kHz) 0 24 48 72 96 120 Strong attenuation for f > 24 kHz Factor ~ 2 attenuation of low-f features

Summary GYRO simulation of top of EDA H-mode pedestal predicts correct total energy flux. H emissivity fluctuations from DNB are about half density fluctuations. Higher frequencies (> 25 kHz) in BES signal strongly attenuated by finite collection area, in apparent agreement with data.

Future Work Factor ~2 reduction of measured fluctuations from density fluctuations a given. Reduce BES collection area: two 1-mm optical fibers per channel instead of four Caveats: Will reduce signals by factor two. Ultimate radial spatial resolution (~ 0.9 cm) determined by optical aberrations and beam smearing. Decrease spacing between channels: Go to 6 x 6 densely packed fiber array rather than discrete four-fiber bundles separated by ~ 1 cm.