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Feasibility of Correlation ECE Diagnostic at C-Mod
12
Toroidal mode number (linear scale)
Electron temperature frequency response
120
(a)
ρ = 0.5
100
80
60
40
20
0
-1.5
-0.5
-1.0
0.0
0.5
1.5
1.0
(a/cs )ω
Growth Rate (a/c s ), most unstable mode at kθρ s = 0.5
4.0
6
22
0.
3.5
a/LTe
Electron
(b)
3
58
0.
16 0
1 .1
9
0.2
Ion
3.0
1.0
1.5
2.0
6
ρ = 0.5
0.22
9
0.193
1.5
12
0.
0.161
2.0
0.097
0.129
2.5
2.5
a/LTi
Figure 3. (Colour online) (a) The midplane electron temperature fluctuation
frequency spectrum from local GYRO simulation at ρ = 0.5. (b) The growth rate
(a/cs ) contours of the most unstable mode, evaluated at kθ ρs = 0.5, from the local
simulation at ρ = 0.5. The values of a/LT e and a/LT i that correspond to the simulation
results in (a) is shown by the yellow cross. The white shaded region indicates the
simulation ranges of gradient scale lengths.
4.2.1. Predicted fluctuation levels The predicted fluctuations are obtained from the
density and energy moments of the distribution function. A kinetic pressure relation
between density, temperature and pressure pe = Te ne is used to obtain the relation
between internal energy fluctuations and pressure fluctuations, ˜ = 3/2p̃e = 3/2(ne T̃e +
ñe Te ) [44]. We define the normalized electron temperature fluctuations, δTe = T̃e /Te as
T̃e /Te = (2/3)˜e /pe − ñe /ne .
(5)
The GYRO predicted fluctuation level at ρ = 0.5 is T̃e /Te = 1.52%, and is obtained
from a box-average of the local simulation result. Global simulation results (not shown)
are in agreement with this fluctuation level and also indicate that the fluctuation level
increases with radius.