Identification of TEM turbulence through direct comparison of nonlinear gyrokinetic simulations with phase contrast imaging density fluctuation measurements

Abstract

Nonlinear gyrokinetic simulations of Trapped Electron Mode (TEM) turbulence have repro-duced measured particle fluxes and thermal energy fluxes, within experimental uncertainty, in Alcator C-Mod [1, 2]. This has provided a model for internal transport barrier control with on-axis ICRH in Alcator C-Mod, without adjustable model parameters. The onset of TEM turbulent transport limits the density gradient, preventing radiative collapse. Here we move beyond comparisons of simulated and measured fluxes to a more fundamental and direct comparison with density fluctuation spectra. Using a new synthetic diagnostic, excellent agreement is obtained between wavelength spectra from nonlinear GS2 simulations, and spectra measured by Phase Contrast Imaging. The density fluctuations are associ-ated with the steep density gradient in the C-Mod ITB, which provides spatial localization for the chordal PCI measurement. Gyrokinetic stability analysis shows that Trapped Electron Modes are strongly desta-bilized inside the ITB foot by the addition of on-axis ICRH. Nonlinear GS2 simulations reproduce the relative increase in fluctuation level when on-axis heating is applied. Further, we have extended the GS2 Lorentz collision operator to include classical diffusion associated with the ion finite Larmor radius, and have implemented collisional energy diffusion, together with particle, momentum, and energy conserva-tion terms. Classical diffusion is shown to strongly stabilize trapped electron modes with k θ ρ i > 2 for realistic C-Mod collisionalities. A series of detailed nonlinear gyrokinetic simulations show the nonlin-ear upshift [1, 2] in the TEM critical density gradient increases favorably with collisionality.

Full text

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Plasma Science and Fusion Center
Massachusetts Institute of Technology
Cambridge MA 02139 USA






1Physics Department, Univ. of Maryland, College Park, MD, USA
2Physics Departmetnt, Cornell University, Ithaca, NY, USA



This work was supported by the U.S. Department of Energy, Grant DE-FC02-
99ER54512. Reproduction, translation, publication, use and disposal, in whole or in part,
by or for the United States government is permitted.

Submitted for publication to Nuclear Fusion.

PSFC/JA-06-34

Identification of TEM Turbulence through Direct
Comparison of Nonlinear Gyrokinetic Simulations
with Phase Contrast Imaging Density Fluctuation
Measurements


D.R. Ernst, N. Basse, W. Dorland1, C.L. Fiore, L. Lin, A. Long2,
M. Porkolab, K. Zeller, K. Zhurovich


June 2006

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Identification of TEM Turbulence through Direct Comparison of
Nonlinear Gyrokinetic Simulations with Phase Contrast Imaging Density
Fluctuation Measurements
D. R. Ernst 1), N. Basse 1), W. Dorland 2), C. L. Fiore 1), L. Lin 1), A. Long 3), M. Porkolab 1),
K. Zeller 1), and K. Zhurovich 1)
1) Plasma Science and Fusion Center, Mass. Inst. of Technology, Cambridge, MA, USA
2) Physics Department, Univ. of Maryland, College Park, MD, USA
3) Physics Department, Cornell University, Ithaca, NY, USA
e-mail contact of main author: dernst@psfc.mit.edu
Abstract. Nonlinear gyrokinetic simulations of Trapped Electron Mode (TEM) turbulence have repro-
duced measured particle fluxes and thermal energy fluxes, within experimental uncertainty, in Alcator
C-Mod [1, 2]. This has provided a model for internal transport barrier control with on-axis ICRH in
Alcator C-Mod, without adjustable model parameters. The onset of TEM turbulent transport limits the
density gradient, preventing radiative collapse. Here we move beyond comparisons of simulated and
measured fluxes to a more fundamental and direct comparison with density fluctuation spectra. Using
a new synthetic diagnostic, excellent agreement is obtained between wavelength spectra from nonlinear
GS2 simulations, and spectra measured by Phase Contrast Imaging. The density fluctuations are associ-
ated with the steep density gradient in the C-Mod ITB, which provides spatial localization for the chordal
PCI measurement. Gyrokinetic stability analysis shows that Trapped Electron Modes are strongly desta-
bilized inside the ITB foot by the addition of on-axis ICRH. Nonlinear GS2 simulations reproduce the
relative increase in fluctuation level when on-axis heating is applied. Further, we have extended the GS2
Lorentz collision operator to include classical diffusion associated with the ion finite Larmor radius, and
have implemented collisional energy diffusion, together with particle, momentum, and energy conserva-
tion terms. Classical diffusion is shown to strongly stabilize trapped electron modes with kθρi> 2 for
realistic C-Mod collisionalities. A series of detailed nonlinear gyrokinetic simulations show the nonlin-
ear upshift [1, 2] in the TEM critical density gradient increases favorably with collisionality.
1. Introduction
0
0.0
4
10
2
6
8
Thomson Scattering, 0.827(s)
Electron Density (1020m−3)
on + off−axis
ICRH
off−axis
ICRH
(20 ms intervals)
ICRH [x10 W/cm ]
3
0.80 − 1.28 s
0.20.40.60.81.0
FIG. 1. Density profile evolution in the C-Mod
ITB, from CCD based visible Bremsstrahlung.
Trapped electron mode turbulence is relevant
to particle and electron thermal energy trans-
port. Several types of TEM exist, driven
by either the electron density gradient, or
by the electron temperature gradient. The
most significant modes are associated with
non-resonant “bad curvature” drive as well
as toroidal precession drift resonance. TEM
turbulence is most relevant when toroidal
ITG modes are either stable or weakly un-
stable. This scenario arises in a variety of
contexts, such as internal transport barriers,
cases with strong density peaking, cases with
Te> Ti, and low density regimes in which
confinement scales favorably with density.
Understanding of the mechanisms underly-
ing particle and electron thermal energy transport could impact future devices such as ITER,
1

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where core fueling is greatly reduced, and electrons are heated directly by α-particles. In the
AlcatorC-Modcasesstudied, TEMturbulenceproducesstrongparticleandelectronthermalen-
ergy transport as the density gradient, and the electron temperature, increase. This mechanism
provides a model for the observed control [3, 4, 5, 6] of the density profile in the C-Mod ITB
using on-axis ICRH. In earlier efforts, radial and poloidal wavelength spectra from gyrokinetic
particle simulations of ITG turbulence, with adiabatic electrons [7], were observed to resem-
ble density fluctuations in TFTR [8], as measured by localized Beam Emission Spectroscopy.
Recent gyrokinetic simulations of ITG turbulence have attained sufficient realism to reproduce
experimental heat fluxes [9], but comparisons with between nonlinear simulations and fluctu-
ation measurements have not been forthcoming. Similarly, nonlinear gyrokinetic simulations
of pure TEM turbulence have just begun, for the density gradient driven [1, 2] and temperature
gradient driven [10, 11] cases.
2. Experimental Scenario
1.0
1.4
keV
0.4)
e
T (
A. U.
1
2
3
4
PCI
GS2
˜
0.81.0 1.11.2 1.3
Time (s)
0.9
4
6
8
neZ1/2
eff
x 1020m−3
off−axis
on−axis
PRF
3.0
1.5
0.0
MW
kR(cm )
−1
Wavenumber
−5
+5
Phase Contrast Imaging
+1
0
−1
[A.U.]
+2
−2
1.025
1.220
FIG. 2. Injected power, Tein ITB, PCI fluctu-
ation power from chord 12 with GS2 nonlin-
ear simulations before/during on-axis ICRH
(normalized at 1.22 s), maximum electron
density, and log of PCI autopower spectrum
(20-80 kHz) vs. kRand time.
The C-Mod ITB provides a unique opportu-
nity in two respects. First, the strong fluctu-
ations in the ITB, driven by the strong den-
sity gradient, allow spatial localization of the
chordal phase contrast imaging density fluctu-
ation measurement. Second, without core par-
ticle fueling, ITER like densities, and ∼1 mm
between density spatial channels, the C-Mod
experiments provide an excellent test bed for
particle transport studies. This study focuses
on a case in which the full available ICRH
source power (∼4 MW) was injected both off-
axis, near the half-radius (2.3 MW), and on-
axis (1.6 MW), to maintain the C-Mod ITB.
Off-axis heating is used to first establish EDA
H-Mode, an ELM-free, quiescent regime with
steady pedestal density, which is regulated by
the Quasi Coherent (QC) mode in the pedestal
[12]. The ITB forms during 25-30 energy con-
finement times as a result of the Ware pinch
[13], with ITG turbulence suppressed by off-
axis heating, which broadens the temperature
profile. The electron density profiles at 20 ms
intervals are shown in Fig. 1, as a function of
ρ∼r/a, the normalized square root of toroidal
flux. The CCD based visible Bremsstrahlung
emission profiles are acquired with sub-ms
sampling and ∼1 mm channel spacing [14].
Thomson scattering data for the early EDA
H-Mode phase is also shown. The profile of
neZ1/2
file, attains a quasi-steady value shortly after
on-axis ICRH is applied at 1.10 seconds, as
shown in Fig. 2. The on-axis ICRH produces
eff, hereafter referred to as the density pro-
2

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˜
˜˜
˜
10
5
0
5
10
10
50
5
10
Z [cm]
65.8o
145o
Region of flux
tube included
in GS2 integral
k = 1.19
d = 0.06
r = 0.38
Integration over parts of
flux tube viewed by PCI
(Poloidal Projection)
PCI Viewing Geometry
(a)
(b)
PCI laser chords
0
R − R [cm]
FIG.3. (a)32PCIlaserchords, and(b)integration
domain for synthetic PCI in GS2.
−5
Wavenumber k [cm ]
Autopower spectrum
from PCI at 1.22 sec., show-
ing quasi-coherent mode is well-
separated from the low fre-
quency turbulence of interest.
05
−1
QC
mode
Log(autopower) [A.U.] 1.22 s
R
50
100
150
200
250
Frequency [kHz]
FIG. 4.
a 30% increase in electron temperature in the ITB, as shown in Fig. 2. The PCI wavenumber
spectrum, integrated over the frequency range 20-80 kHz, is also shown as a function of time in
Fig. 2. Strong density fluctuations appear in the range 1 < kR< 5 cm−1during on-axis heating.
The 32 vertical PCI [15] laser chords are shown in Fig. 3(a). The laser beams pass through a
phase plate and interfere with a reference beam on a detector array. The radius of a laser spot
on the detector is proportional to the scattering wavenumber, and its azimuthal location is per-
pendicular to the magnetic field, for field-aligned fluctuations. The spectrum as a function of
wavenumber in the major radius direction is obtained using the 32 channels. A wider freqency
range is shown in Fig. 4 at 1.22 seconds, during on-axis heating. The edge quasi-coherent mode,
above 80 kHz, is separated from the low freqency turbulence of interest. In wavelength spectra
to follow, we have removed the QC mode frequencies using a notch filter, followed by an ex-
ponential fit in frequency. The wavelength spectra resulting from integration over 20-80 kHz,
10-80 kHz, or the entire frequency range (filtering the QC mode), are nearly identical. For this
2004 discharge, the PCI system had 13 cm coverage in major radius, 10 MHz sampling, and a
wavenumber range extending to ±8.3 cm−1, using a 25 W CO2laser with 10.6 µm wavelength.
Recent upgrades have increased the laser power to 60 W, the wavelength range to ±40 cm−1, a
new phase plate mask has differentiated top and bottom QC mode spectra, and a new absolute
calibration system has been developed.
3. Gyrokinetic Turbulence Simulations and Comparison with Fluctuation Data
To explore the origin of the strong density fluctuations observed during on-axis heating, we
consider two times for analysis, before on-axis heating (1.025 s) and during on-axis heating
(1.220 s). We first carry out linear gyrokinetic stability analysis using the GS2 code [16, 17],
in conjunction with automated data preparation and analysis tools [18]. We have recently de-
veloped a graphical profile fitting tool fiTS for C-Mod temperature and density profile data
(sample profiles are shown in Fig. 1 and Fig. 5(c)). TRANSP analysis provides the consis-
tent magnetic equilibrium and profile data for GS2. At each radius, kθρiis scanned over the
range 0 to 2 to determine the maximum linear growth rate. Classical diffusion, described in
Sec. 4., is included for all points, effectively limiting the unstable range of wavelengths. Prior
to on-axis heating, toroidal ITG modes are dominant inside the ITB, and TEMs are stable, as
shown in Fig. 5(a). Here all positive growth rates are ITG modes unless otherwise indicated. In
3

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Fig. 5(d), the main effect of the on-axis ICRH is to increase the temperature by ∼30% inside
the ITB foot. At the same time, the region over which the driving factor for the TEM, the
inverse density gradient scale length, is large,
expands. This combination of factors strongly
destabilizes TEMs inside the ITB, indicated
by the shaded region in Fig. 5(a).The
Zeffgradient scale length is the most signifi-
cant source of uncertainty in this calculation
[1]. In principle, the Zeffprofile can be ob-
tained from the square of the ratio of visi-
ble Bremsstrahlung and Thomson scattering
data, but with ±50% statistical error.Fur-
ther, with effectively three channels inside the
ITB foot, Thomson scattering, which is cal-
ibrated to ECE cutoff at lower densities, does
notyieldreliableITBdensitygradientsforthis
case. Here we have assumed a flat Zeffpro-
file, and taken the density gradient scale length
from the visible Bremsstrahlung array. Sta-
bility analysis using Thomson scattering den-
sityprofilesandinferredZeffprofilesyieldsthe
same qualitative result – that TEMs are driven
unstable inside the ITB during on-axis ICRH,
with a very similar growth rate profile.

0.0
0.2
0.3
0.1
0.4
Mrad/s
Max. Growth Rate (GS2)
TEM
1.025 s
1.220 s
0.0 0.20.40.60.8 1.0
0
2
4
6
8
0.5
1.0
1.5
0
2
4
1040323033 3679
x 10 m
20
−3
keV
MW
(a)
(b)
(c)
(d)
(TORIC 32 modes)
r
(Thomson Scattering)
(Vis. Bremsstrahlung)
FIG. 5. (a) Growth rate profiles before and
during on-axis ICRH, (b) Electron density
profiles, (c) Electron temperature profiles,
and (d) volume integrated ICRH power ab-
sorbed from TRANSP (TORIC).
Density fluctuations from a sample nonlinear
GS2 simulation at 1.22 seconds, ρ = 0.4, are
shown in Fig. 6. The simulation shown re-
quired over 24 hours on 2640 processors on an
IBM SP Power 3 system (NERSC). Another
simulation was carried out for the same radius
at time 1.025 seconds. An initial comparison
with PCI chordal fluctuation data, without the synthetic diagnostic, is shown in Fig. 2(c). The
nonlinear simulations appear to reproduce the measured relative increase in density fluctuation
level, with the application of on-axis ICRH.
1.20.00.20.40.60.81.0
Time (ms)
Density fluctuations
0.0
0.2
0.4
0.6
0.8
1.0
1.2
GS2
1.22 sec in ITB
11 poloidal modes
39 radial modes
FIG. 6.
from nonlinear GS2 simulation
at1.22s, duringon-axis heating.
To provide a direct comparison with PCI fluctuation data,
wedevelopedasyntheticPCIdiagnostic forGS2[19]. The
GS2 simulation domain is a field line following flux tube
extending several toroidal transits, with a cross-section
typically 60-100 ion gyro-radii in size (multiple radial cor-
relation lengths) at the outboard midplane. The simula-
tion domain deforms with magnetic shear. Clebsch coor-
dinates (ψ,α,θ) are used, where ψ labels flux surfaces,
α = ζ−qθ labels field lines, and θ is the poloidal projec-
tion of the coordinate parallel to the magnetic field. The
synthetic diagnostic involves transforming from the flux-
tube simulation’s Clebsch coordinates to Cartesian coor-
dinates, and integrating the density fluctuations over por-
4