1. 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

2. 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).

3. 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).

4. 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

5. GYRO Simulation
r0 = 0.825a = m (ne0  2x1020 m-3, Te0  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:
 = R/a = 3.07 Ti/Te = 0.92 * =
q =  = Lni/a = 200 Zeff = 1.61
=  = LTi/a = 0.23 ei = 1.2 s
 = –0.12 LTe/a = 0.37

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

7. 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 , August, 2004).

8. 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.

9. 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 (1993).
2 I. H. Hutchinson,” Excited-state populations in neutral beam emission,” Plasma Phys. Control. Fusion (2002).

10. 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).

11. 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.

12. 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

13. 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.

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

15. Simulated Signal Spectra
f (kHz)
Strong attenuation for f > 24 kHz
Factor ~ 2 attenuation of low-f features

16. 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.

17. 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.