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research
Using the local gyrokinetic code, GS2, to investigate global ITG modes in tokamaks. (I) s-
α
{\alpha}
α
model with profile and flow shear effects
Authors
P. A. Abdoul
D. Dickinson
C. M. Roach
H. R. Wilson
Publication date
4 August 2014
Publisher
View
on
arXiv
Abstract
This paper combines results from a local gyrokinetic code with analytical theory to reconstruct the global eigenmode structure of the linearly unstable ion-temperature-gradient (ITG) mode with adiabatic electrons. The simulations presented here employ the s-
α
{\alpha}
α
tokamak equilibrium model. Local gyrokinetic calculations, using GS2 have been performed over a range of radial surfaces, x, and for ballooning phase angle, p, in the range -
Ï€
≤
p
≤
Ï€
{\pi} {\leq} p {\leq\pi}
Ï€
≤
p
≤
Ï€
, to map out the complex local mode frequency,
Ω
0
(
x
,
p
)
=
ω
0
(
x
,
p
)
+
i
γ
0
(
x
,
p
)
{\Omega_0(x, p) = \omega_0(x, p) + i\gamma_0(x, p)}
Ω
0
​
(
x
,
p
)
=
ω
0
​
(
x
,
p
)
+
i
γ
0
​
(
x
,
p
)
. Assuming a quadratic radial profile for the drive, namely
η
i
=
L
n
/
L
T
{\eta_i = L_n/L_T}
η
i
​
=
L
n
​
/
L
T
​
, (holding constant all other equilibrium profiles such as safety factor, magnetic shear etc.),
Ω
0
(
x
,
p
)
{\Omega_0(x, p)}
Ω
0
​
(
x
,
p
)
has a stationary point. The reconstructed global mode then sits on the outboard mid plane of the tokamak plasma, and is known as a conventional or isolated mode, with global growth rate,
γ
{\gamma}
γ
~ Max[
γ
0
(
x
,
p
)
{\gamma_0(x, p)}
γ
0
​
(
x
,
p
)
], where
γ
0
(
x
,
p
)
{\gamma_0(x, p)}
γ
0
​
(
x
,
p
)
is the local growth rate. Taking the radial variation in other equilibrium profiles (e.g safety factor q(x)) into account, removes the stationary point in
Ω
0
(
x
,
p
)
{\Omega_0(x, p)}
Ω
0
​
(
x
,
p
)
and results in a mode that peaks slightly away from the outboard mid-plane with a reduced global growth rate. Finally, the influence of flow shear has also been investigated through a Doppler shift,
ω
0
→
ω
0
+
n
Ω
′
x
{\omega_0 \rightarrow \omega_0 + n\Omega^{\prime}x}
ω
0
​
→
ω
0
​
+
n
Ω
′
x
, where n is the toroidal mode number and
Ω
′
{\Omega^{\prime}}
Ω
′
incorporates the effect of flow shear. The equilibrium profile variation introduces an asymmetry to the growth rate spectrum with respect to the sign of
Ω
′
{\Omega^{\prime}}
Ω
′
, consistent with recent global gyrokinetic calculations.Comment: 10 pages, 8 figures and 1 tabl
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Last time updated on 30/10/2017