Short wavelength ion temperature gradient driven instability in toroidal plasmas
-
Upload
kristian-vidar -
Category
Documents
-
view
38 -
download
4
description
Transcript of Short wavelength ion temperature gradient driven instability in toroidal plasmas
Short wavelength ion temperature gradient driven instability in
toroidal plasmas
Zhe Gao,a) H. Sanuki,b) K. Itohb) and J. Q. Dongc)
a) Department of Engineering Physics, Tsinghua University, Beijing 100084, Chinab) National Institute for Fusion Science, Toki, Gifu 509-5292, Japan
c) Southwestern Institute of Physics, Chengdu 610041, ChinaElectronic mail: [email protected]
1st Plasma Theory and Simulation (PTS) WorkshopChengdu Sep. 13-15 2004
OUTLINE
Background Model Local slab limit Parameter dependences Critical temperature gradient Conclusions
Background (I)
microinstabilitiesmicro-turbulenceanomalous transport
ion transport - reduced to NC level; electron transport - still anomalous / ETB Experimental observations: Turbulent diagnostics anomalous electron transport is
possibly attributable to short wavelength modes
Profile stiffness a threshold in temperature gradient Two kinds of well-known microinstabilities: ETG modes e.g. F. Jenko et al, PoP 8, 4096 (2000),J. Q. Dong et al, NF 43, 1 (2003)
TE modes e.g. J. Weiland et al NF 29, 1810 (1989)
Background (II)
comparisons with experimental results e.g F Ryter et al, PPCF 43, A323 (2001)
some on ETG: s/q dependence in Tore Supra
some on TEM: modulated Te evolution in ASDEX-U
other remarkable experiment results
Not all tokamaks observed “stiffness” in Te; e.g. JC DeBoo EPS conf. 2002
Clear link between long and short wavelength fluctuation;
e.g. GD Conway PRL 84,1463 (2002)
Measured high k fluctuation in the ion diamagnetic direction;
e.g. KL Wong PLA 236, 339 (1997)
electron transport might be controlled by multi-source instabilities simultaneously, or by different instability depending on different discharge condition.
Background (III)
Short wavelength ITG modes ( , ) Local mode in a shearless slab AI Smolyakov et al, PRL 89, 125005 (2002).
A new TG driven short wavelength mode or “ double-humped behavior” in Pu et al, PF 28,1722 (1985) ?
Nonlocal mode in a toroidal geometry A. Hirose et al, PoP 9, 1659 (2002).
“electron transit effect driving”, “ essentially a slab mode” , “shear is destabilizing”
0r 1iyk
Model
Gyro-kinetic equation ( ballooning representation in s-a equlibrium )
Poisson’s Equ. & Ampere’s law
Both ions and electrons are nonadiabatic: the transit effect, the finite Larmor radius effects and the curvature and magnetic gradient drift
Local slab limit:
The local short wavelength mode is attributable to the Landau damping stabilization/destabilization mechanism and the nonmonotonic behaviors of the real frequency with wavelength variation.
Some explanations in Smolyakov et al are not correct
ctirti vkvk //max// ~
Local slab limit : influences of electron kinetics and k//Ln
2.0// nLk
Toroidal modes : analytical discussion
ˆˆ 20
////
*i
Di
Ti
i
Mii
i
Miii J
vkT
Fq
T
Fqf
////* vkDii
)exp()(
12ˆˆ~0
*0 ii
ii
i
i
i
ii bbI
T
qn
T
qn
)exp()(121 0* iiii
effi
effi bbIZ
Z
2* intii bLv iii bbbI 21)exp()(0 ib
inDi *~
ion response
and it integral
(under the condition )
If electron is adiabatic
Noted: , as
Local slab limit: Landau mechanism
Toroidal: magnetic drift resonance
cvkvk //////// ~
cDiDi ~
Toroidal modes : wave spectrums
Parameters: , , , , , The SWITG mode still exists even with adiabatic electrons
assumption.
0 1 2 3 40.00
0.05
0.10
0.15
0.20
0.25
k
s/*e
ks
(a)
0 1 2 3 4
-0.6
-0.4
-0.2
0.0 l=0 mode l=1 mode l=2 mode with adiabatic electrons
rk s/
*e
ks
(b)
5.2e 5.2i 1 effi ZM8.0ˆ s 5.1q1.0n
Toroidal modes: toroidicity
more easily stabilized by toroidicity than the conventional ITG mode
condition broken
0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.200.00
0.02
0.04
0.06
0.08
0.10
/*e
n(=L
n/R)
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
-0.45
-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10
r/*e
n(=L
n/R)
l=0 l=1 l=2
////* vkDii
Toroidal modes : eigenfunctions
-40 -20 0 20 40-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
real part imaginary part
(a)
-40 -30 -20 -10 0 10 20 30 40-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
(b)
-40 -20 0 20 40
-1.0
-0.5
0.0
0.5
1.0
1.5
(c)
-4 -3 -2 -1 0 1 2 3 4
0.0
0.4
0.8
1.2
(d)
-4 -3 -2 -1 0 1 2 3 41.2
0.8
0.4
0.0
-0.4
-0.8
-1.2
(e)
-4 -3 -2 -1 0 1 2 3 4-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
q
(f)
Broaden structures along the magnetic field line and have oscillatory tailswhen nonadiabatic electron response are considered
Toroidal modes : temperature gradients dependence
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.60.00
0.02
0.04
0.06
0.08
0.10
/*e
i
l=0 l=1 l=2
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.60.00
0.02
0.04
0.06
0.08
0.10
/*e
e
l=0 l=1 l=2
Each of the three modes has a eta_i threshold and the threshold of the fundamental mode is lower that those of higher order modes.
The fundamental SWITG mode is unstable when both eta_i and eta_e exceed thresholds. But the higher order modes persist unstable even eta_e decreases to zero
Toroidal modes: Te/Ti dependence
2ik
The SWITG mode can be stabilized by hot ions (small Te/Ti) ITG driven modes
0 1 2 3 4 50.0
0.1
0.2
0.3
(a)
-/ *i
Zeff
Te/T
i
0 1 2 3 4 5
-0.35
-0.30
-0.25
-0.20
-0.15
l=0 mode at Zeff
=1
l=1 mode at Zeff
=1
l=2 mode at Zeff
=1
l=0 mode at Te/T
i=1
l=1 mode at Te/T
i=1
l=2 mode at Te/T
i=1
(b)
Zeff
Te/T
i
-r/
*i
Toroidal modes : isotope effects
The normalized growth rate and frequency is insensitive to isotope mass
1 2 3 40.02
0.04
0.06
0.08
0.10
0.12
/*e
mi/1836m
e
l=0 mode l=1 mode l=2 mode
(a)
1 2 3 4
-0.30
-0.25
r/*e
mi/1836m
e
(b)
0.2ik Maximum growth rate
2/1.~ imconstk
Toroidal modes : magnetic shear
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.00.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
/*e
s
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0-0.31
-0.30
-0.29
-0.28
-0.27
-0.26
-0.25
-0.24
-0.23
-0.22
-0.21
-0.20
-0.19
-0.18
-0.17
-0.16
-0.15
l=0 l=1 l=2
r/*e
s
The stabilizing effect of shear is confirmed although the shear needed to stabilize the fundamental mode is rather strong
The grow rate of the fundamental mode at negative shear is almost same as that at positive shear, while obvious low growth rate exists at negative shear for higher order modes
The high order mode may grows faster than the fundamental mode in the weak shear regime
Toroidal modes : beta effect
0.000 0.002 0.004 0.006 0.008 0.0100.00
0.04
0.08
0.12
/*e
e
(a)
0.000 0.002 0.004 0.006 0.008 0.010
-0.30
-0.25
-0.20
-0.15 l=0 mode l=1 mode l=2 mode ES model with
r/*e
e
(b)
The fundamental mode is easily stabilized by finite beta, mainly due to the coupling effect to shear Alfven waves (SAWs), not the ballooning parameter
The higher order modes are more hardly stabilized, which might be explained
by the fact that the higher order modes have lower frequencies.
Critical temperature gradient vs. Ln/R
0.10 0.15 0.20 0.25 0.30 0.35
2
4
6
8
10
12
14
16
18
20
22
24
(R/L
ti) c
n
i=3
i=1
i=0.75
0.10 0.12 0.14 0.16 0.18 0.20
10
15
20
25
30
35
40
45
50
n
(R/L
Te) c
Unstable
Stable
R/LTi: saturation in the large enough εn region
R/LTe : cannot cross the εn barrier
Critical temperature gradient Vs. Te/Ti
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.07
8
9
10
11
12
13
14
15
16
17
18
19
20
21
(R/L
ti) c
Te/T
i
n=0.2
0 1 2 3 4 5 6
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
max
/[*e
(i-
ic)]
Te/T
i
R/LTi deceases as Te/Ti increase
Critical temperature gradient Vs. kθ
“sub-steady-state” region for ITG critical electron temperature gradient varies with wavelength
0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0
-2
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
k
(R/L
te) c
i=3,
n=0.2
i=1,
n=0.1
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
4
6
8
10
12
14
16
18
(R/L
ti) c
k
i=3,
n=0.2
i=1,
n=0.1
Coupling between l=0 and l=2 modes
0.0 0.5 1.0 1.5 2.0 2.5
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
e
1 2
k=1.4
0.0 0.5 1.0 1.5 2.0 2.5
-0.56
-0.54
-0.52
-0.50
-0.48
-0.46
-0.44
-0.42
r
e
1 2
-0.5 0.0 0.5 1.0 1.5 2.0 2.50.00
0.04
0.08
0.12
0.16
e
1 2
k=1.2
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
e
1 2
k=1.6
-0.5 0.0 0.5 1.0 1.5 2.0 2.5
-0.44
-0.42
-0.40
-0.38
r
e
1 2
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6-0.64
-0.60
-0.56
-0.52
-0.48
r
e
1 2
Critical temperature gradient for the l=1 mode
0.10 0.15 0.20 0.25 0.3010
11
12
13
14
15
16
17
(R/L
Ti) c
n
i=1
i=3
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.05
10
15
20
(R/L
Ti) c
i
0 1 2 3 4 50.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
/[ *e
(i-
ic)]
i
ηi- ηe diagram for l=0 and l=1 modes
electron kinetics strongly influences the l=0 mode but only slightly influences the l=1 mode
in the region where ηe is relative smaller, the l=1 mode is dominant
1 2 3 4 5
-1
0
1
2
3
4
1=
2
e
i
1=0
2=0
=3, n=0.2
0 1 2 3 4 50
1
2
3
4
5
6
1=0
0=0
e
i
A
B
C
D
E
0=
1
=1,n=0.1
Conclusions
The SWITG instability occurs due to the toroidal drift resonance mechanism in the short wavelength region and exist even if adiabatic electrons are assumed
Parameter dependences of the SWITG mode is similar as those of the conventional ITG mode
Nonadiabatic electron response can influence the fundamental SWITG mode.
The SWITG instability has a medium wavelength, so might be more difficult to be suppressed by the E*B flow shear than the ITG instability while could induce higher transport than the ETG mode.
The SWITG mode may be attributed to electron transport, however, it seems the ion kinetic is necessary and basic.
ACKNOWLEDGMENTS
Most of this work is performed during Z.G.’s visiting at the National Institute for Fusion Science, Japan.