Upload
marjory-woods
View
215
Download
3
Embed Size (px)
Citation preview
4th ITPA Meeting Apr 03 LRB
Rotation of Impurity Species in the DIII-D Tokamak and Comparison with
Neoclassical Theory
L.R. Baylor, K.H. Burrell*, R.J. Groebner*, W.A. Houlberg, M. Murakami, D.R. Ernst#,
and The DIII-D Team
Oak Ridge National Laboratory
*General Atomics,#MIT
at the
4th ITPA Meeting
April 8-11, 2003
St. Petersburg, RussiaITPA
4th ITPA Meeting Apr 03 LRB
Overview
• Experiments have been performed on DIII-D to examine the relationship of the toroidal rotation velocity between different impurity ion species in the same plasma shot.
• Data has been taken for C VI, He II, and Ne X lines in QDB, PEP, and RI-mode ITB plasmas.
• Initial analysis of data from an RI-mode ITB plasma and a QDB mode plasma have been done and indicate trends that are consistent with neoclassical theory.
4th ITPA Meeting Apr 03 LRB
Rotation of Impurity Species
• Er derived from radial force balance:
Since Er is the same for all species,
Er(r) = + vC B - vC BPC(r)c e nC(r)
Pi(r)i e ni(r)
+ vi B - vi B =
where Ti, vC, vC aredetermined by CER
vi = vi BB–B
Pi(r) + Er)i e ni(r)
• NCLASS calculates relative parallel flow between species (determined by the parallel friction from Coulomb collisions).
This allows neoclassical determination of vi.
• Largest difference in vi will be in plasma with large Pi
Therefore, Neoclassical
Measured
4th ITPA Meeting Apr 03 LRB
Rotation Data Analyzed with FORCEBAL and NCLASS codes
Er()Pi() vi ()
• Raw input data is processed and then fit to profiles with the 4D fitting codes.
• Profile data is then input with an EFIT equilibrium to the FORCEBAL code, which computes radial force balance.
• NCLASS library [Houlberg] is called by FORCEBAL to obtain neoclassical poloidal rotation flux function.
• Local toroidal and poloidal rotation velocities of any species are reconstructed.
ni()Ti ()V ()V()
4th ITPA Meeting Apr 03 LRB
CER is the Key Diagnostic for these Measurements CER Layout on DIII-D - Plan View
• For further details of the DIII-D CER diagnostic see the web site:
http://fusion.gat.com/diag/cer
4th ITPA Meeting Apr 03 LRB
Detailed Analysis of CER Data is Needed to Take into Account the Energy Dependent Cross Section
• The charge exchange recombination (CER) diagnostic uses a spectrometer to measure the spectra of charge exchange lines. [Isler]
• The layout of this diagnostic on DIII-D is shown on the following page. [Gohil]
• The Doppler broadened and Doppler shifted visible emission from the relevant ion species (C, He, Ne) is used to determine the ion temperature, Ti, and toroidal v, and poloidal v, rotation velocities. [Groebner - Poster RP1.035]
• Comparisons of rotation of main ions and impurity ions were made in the edge [Kim, 1994] where the low temperature makes the effect of the energy dependent cross-section quite small.
4th ITPA Meeting Apr 03 LRB
Energy Dependent Cross Sections
0 100400
30
20
10
E (keV/amu)
v (
10-1
5 m
3/s
)
Ne X
C VI
He II
60 8020
Full Energy
HalfEnergy
Third Energy
• The three beam energy components sample an energy dependent cross section.
• An analytical approximation of the cross section [von Hellermann] is used.
4th ITPA Meeting Apr 03 LRB
0
0.2
0.4
0.6
0.8
1
1.2
-1250 -750 -250 250 750 1250
Line of Sight Velocity (km/s)
Lin
e In
ten
sity
(A
.U.)
CER Shifted Line Profile from Energy Dependent Cross Section
• In this DIII-D QDB example for =0.3, a line shift of ~100 km/s occurs due to the CX cross section. (CXRS code [Groebner], cross section
approximation [von Hellermann])
• The shifted line results from the three energy components is very nearly Gaussian in shape.
Unshifted Gaussian (15 keV, 300 km/s)Full Energy
Component
Half EnergyComponent
Third EnergyComponent
Shifted LineC5+ (n = 8 7)Ti = 15 keV
4th ITPA Meeting Apr 03 LRB
Variation of Apparent Ti and Vt As a Function of Real Ti
• The apparent Ti and Vtor are calculated with CXRS code [Groebner] for a real range of Ti and Vtor of 0 km/s at a 45 degree viewing angle. The difference between the real Ti and Vtor and the apparent value are found by fitting a Gaussian to the resulting calculated spectrum. Three beam energy values are used.
• The Ti variation is 1-2 keV and Vtor is ~ 80 km/s for the range of interest in the QDB plasma case.
9
0 5 10 15 20 25 30
Ti_real (keV)
Ti_
rea
l -
Ti_
app
(ke
V)
0
1
2
3
4
5
6
7
8 He II
C VI
Ne X
-20
0
20
40
60
80
100
120
140
160
Vt_
rea
l -
Vt_
app
(km
/s) He II
C VI
Ne X
0 5 10 15 20 25 30
Ti_real (keV)
QDBRI modeQDBRI mode
4th ITPA Meeting Apr 03 LRB
Example of Data from Simultaneous C VI, Ne X, and He II Measurements with CER
Time (ms)
DIII-D 106084
Analysis Time
4th ITPA Meeting Apr 03 LRB
Experimental Plasma Conditions – RI-Mode Case
• RI-mode mode plasmas offer conditions to observe the difference in toroidal rotation profiles with neon and helium as well as naturally occurring carbon impurities.
• These plasmas are characterized with a peaked density profile and peaked ion temperature profile.
n (m
-3)
T(k
eV)
DIII-D 106084 1.450s
DIII-D 106084 1.450 s
ne
nD
nC
0.0 0.2 0.4 0.6 0.8 1.00
1
2
3
4
5
6Ti Te
0.0 0.2 0.4 0.6 0.8 1.00
2·1019
4·1019
6·1019
8·1019
4th ITPA Meeting Apr 03 LRB
Experimental Plasma Conditions – RI-mode Case
• Impurity density profiles from the analyzed CER data for the RI-mode case.
n (m
-3)
DIII-D 106084
0.0 0.2 0.4 0.6 0.8 1.00
5.0·1017
1.0·1018
1.5·1018
2.0·1018He4 CNe
4th ITPA Meeting Apr 03 LRB
FORCEBAL Vtor Calculations for RI Mode Case
• Toroidal rotation velocities are shown for the RI mode case using the measured C rotation as input.
• C, Ne, and He4 have similar Vtor, while D is predicted to rotate faster than the impurity species.
DIII-D 106084
Vto
r (k
m/s
)
0.0 0.2 0.4 0.6 0.8 1.00
100
200
300
400C Ne He4 D
4th ITPA Meeting Apr 03 LRB
Example of Data from Simultaneous C VI and He II Measurements with CER in QDB Plasma
Time (s)
-2 .0·10 6
-1.5·10 6
-1.0·10 6
-5.0·10 5
0
0 .00
0.75
1.50
2.25
3.00
-5 .0·10 12
5.0·10 12
1.5·10 13
2.5·10 13
3.5·10 13
-0 .5
0.5
1.5
2.5
3.5
-1
0
1
2
3
-5.0·10 60
5.0·10 6
1.0·10 71.5·10 7
0.0 1.0 2.0 3.0 4.0
Ip
N
ne
PHD02UP
GasE (He4)
PNBI
He Puff
Analysis Time
• Time evolution for the QDB case. A He puff occurs at 3.2s and the analysis shown is for 3.5s. Note the negative Ip indicates counter NBI injection.
4th ITPA Meeting Apr 03 LRB
Experimental Plasma Conditions – QDB Case
• Quiescent double barrier (QDB) mode plasmas [Burrell] offer the best conditions to observe the difference in toroidal rotation profiles due to the high pressure gradient and low level of anomalous transport.
• These plasmas are characterized with a peaked density profile and broad ITB in the ion channel.
n (m
-3)
DIII-D 105882 3.500s
T(k
eV)
DIII-D 105882 3.500s
4th ITPA Meeting Apr 03 LRB
Experimental Plasma Conditions – QDB Case
• Impurity density profiles from the analyzed CER data for the QDB mode case.
0.0 0.2 0.4 0.6 0.8 1.00
5.0·1017
1.0·1018
1.5·1018
2.0·1018C He4
n (m
-3)
DIII-D 105882
4th ITPA Meeting Apr 03 LRB
CER Analyzed Profiles – QDB Case
• Ti profiles from C VI and He II lines compare very well across most of the plasma minor radius as expected.
• Measured toroidal velocity shows some distinct lower velocity for the He species across most of the profile.
0.0 0.2 0.4 0.6 0.8 1.0
Ti (
keV
)
0
5
10
15
C He
0.0 0.2 0.4 0.6 0.8 1.0
Vto
r (k
m/s
)
-200
-100
0
100
200
300
400
500
C He
DIII-D 105882 3.500s
DIII-D 105882 3.500s
4th ITPA Meeting Apr 03 LRB
FORCEBAL Vtor Calculations for QDB Mode Case
• Toroidal rotation velocities are shown for the QDB predictive run. Measured C V tor is
used in the calculation as are density profiles for C and He.
• The He rotation is predicted to be slower than for C. D is predicted to rotate much slower than the impurity species in this counter injection case. Ne is predicted to be virtually identical to C.
0.0 0.2 0.4 0.6 0.8 1.0
Vt (
km/s
)
-200
-100
0
100
200
300
400
500
C He D
DIII-D 105882 3.500s
FORCEBAL Run CH5
4th ITPA Meeting Apr 03 LRB
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0C He4 D
Toroidal Mach Numbers for QDB Mode Case
DIII-D 105882 3.5s
Mto
r
• Toroidal Mach numbers are shown for the QDB predictive run. For C and lighter species the Mach number is < 1 for most of the profile as is necessary for the neoclassical formalism.
4th ITPA Meeting Apr 03 LRB
Analyzed Rotation Profiles – QDB Case
• Forcebal calculated He and D toroidal rotation profiles for monotonic He density profile. Agreement with He data shown in data plot is quite good.
• Measured toroidal velocity shows distinct lower velocity for the He species across most of the profile as expected from the calculation.
0.0
Vto
r (k
m/s
)
-200
-100
0
100
200
300
400
500
0.2 0.4 0.6 0.8 1.0
C He
DIII-D 105882 3.500s
0.0 0.2 0.4 0.6 0.8 1.0
Vt (
km/s
)
-200
-100
0
100
200
300
400
500
C He D
DIII-D 105882 3.500s
FORCEBAL Run CH5 Experimental Data
4th ITPA Meeting Apr 03 LRB
CER Analyzed Profiles – QDB Case Carbon and Neon Comparison
• Ti profiles from C VI and Ne X lines compare very well across most of the plasma minor radius as expected.
• Measured toroidal velocity shows no distinct difference in velocity for the Ne species across the profile.
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
100
200
300
400
500
C VINe X
Vto
r (k
m/s
)
DIII-D 105887 3.5s
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0
2
4
6
8
10
12
14
16
Ne XC VI
Ti (
keV
)
4th ITPA Meeting Apr 03 LRB
Initial Conclusions
• Good data sets were obtained in a dedicated experiment in Neon seeded ITB (RI-mode), QDB, and PEP mode plasmas.
• Proper comparison with theory requires analyzing CER data for effects of an energy-dependent charge exchange cross section. Results from the extended CERFIT program are used in this work (Groebner, APS 2002 Poster RP1.035).
• Neoclassical poloidal rotation is assumed in all cases. Toroidal Mach numbers are in general less than unity thus minimizing centrifugal force effects on the impurities.
• Initial analysis results from the RI-mode case indicate minimal differences in the Vtor profiles. The neoclassical prediction for this case has very little Vtor difference between the C, He, and Ne.
• Initial analysis from the QDB plasma with He and C measurements show a lower Vtor for He across the whole profile on the order of that predicted from the neoclassical theory. C and Ne have the same velocity as expected.
4th ITPA Meeting Apr 03 LRB
Summary
• Experiments have been performed on DIII-D to examine the relationship of the toroidal rotation velocity between different impurity ion species in the same plasma shot.
• Data has been taken for C VI, He II, and Ne X lines in QDB, PEP, and RI-mode ITB plasmas.
• Initial analysis of data from an RI-mode ITB plasma and a QDB mode plasma have been done and indicate trends that are consistent with neoclassical theory.
• Further detailed analysis of other cases needs to be completed before a definitive conclusion on the rotation behavior can be made.
4th ITPA Meeting Apr 03 LRB
References
• Von Hellerman, M., Plasma Phys. Control. Fusion 37 (1995) 71.
• Burrell, K.H., Excitation rate integral derivation, Unpublished 1998.
• Houlberg, W.A., et al., NCLASS, Phys. Plasmas, 4 (1997) 3230.
• Burrell, K. – Quiescent Double Barrier Mode Paper, Phys.
Plasmas, 8 (2001) 2153.
• Isler, R.C., CER review paper, Plasma Phys. Control. Fusion, 36 (1994) 171.
• Groebner, R. , CXRS code development, Poster RP1.035, to be published.
• Gohil, P., et al., The CER Diagnostic System on the DIII-D Tokamak, Proceedings of 14th Symposium, IEEE (1991) 1199.
• Bell, R.E., et al., TTF 1999.
• Kim, J., et al., Phys. Rev. Lett. 72, (1994) 2199.
4th ITPA Meeting Apr 03 LRB
Abstract
Toroidal rotation velocity profiles of carbon, helium, and neon have been measured on the DIII-D tokamak with the charge exchange recombination (CER) spectroscopy diagnostic. Neoclassical theory predicts a Z dependent relation between the toroidal rotation speeds of the different impurities. In order to make an accurate comparison with theory, the CER data analysis requires taking into account the energy dependent charge-exchange cross sections for the different species. Upgrades in the CER analysis code to take this cross-section effect into account have been made and checked with transitions that have different energy dependence. The toroidal rotation speed of these impurities was measured in quiescent double-barrier (QDB) mode, RI-mode, and pellet enhanced performance (PEP) mode discharges. Differences in the toroidal rotation speeds of the impurities in the same discharge are compared with neoclassical theory using the FORCEBAL/NCLASS code. Results of the comparison with neoclassical theory are presented and implications for transport barrier formation are discussed.
4th ITPA Meeting Apr 03 LRB
Predicted Toroidal Mach Numbers for RI Mode Case
DIII-D 106084
Mto
r
• Toroidal Mach numbers are shown for the Ri mode case. For C and lighter species the Mach number is < 1 for most of the profile as required for the neoclassical formalism.
0.0 0.2 0.4 0.6 0.8 1.00.0
0.5
1.0
1.5C Ne
D
4th ITPA Meeting Apr 03 LRB
CER Analyzed Profiles – RI mode Case
• Ti profiles from C VI, He II, and Ne X lines compare very well across most of the plasma minor radius as expected.
• Line of sight velocities (nearly tangential) are shown for C, He and Ne. C and Ne agree well where the Mach number is <1. He agreement with the C is not so good in Ti or Vtor.
0.0 0.2 0.4 0.6 0.8 1.0
Vto
r (k
m/s
)
0
100
200
300
400
CHe
Ne
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
5
6
C HeNe
Ti (
keV
)
4th ITPA Meeting Apr 03 LRB
CerFit: nz vs rho shot: 105882 time: 3500.0000
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.00
0.05
0.10
0.15
0.20
0.25Helium - Vert Only dimp105882.03500_Hel
* 1.00000n z
(10
19 m
-3)
Analyzed He Density Profiles – QDB Case
Vertical Tangential
• Helium density profile fit from vertical CER data overlayed with earlier fit to tangential only data.
4th ITPA Meeting Apr 03 LRB
Analyzed Rotation Profiles – QDB Case
• Forcebal calculated He toroidal rotation profile (dashed red curve) for Vertical CER He density profile. Agreement with He data (solid red curve) shown in data plot is quite good.
• Measured toroidal velocity shows distinct lower velocity for the He species across most of the profile as expected from the calculation.
0.0
Vto
r (k
m/s
)
-200
-100
0
100
200
300
400
500
0.2 0.4 0.6 0.8 1.0
C He
DIII-D 105882 3.500s
0.0 0.2 0.4 0.6 0.8 1.0
Vto
r (k
m/s
)
-200
-100
0
100
200
300
400
500
C He
DIII-D 105882 3.500s
FORCEBAL Run CHV Experimental Data