Transcript Rotation speeds on DIII-D

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, Russia
ITPA
4th ITPA Meeting Apr 03 LRB
Overview
•
•
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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:
Er(r) = PC(r)
Zc e nC(r)
+ vfC Bq - vqC Bf
where Ti, vfC, vjC are
determined by CER
Since Er is the same for all species,
Measured
=
Pi(r)
+ vfi Bq - vqi Bf
Zi e ni(r)
Therefore,
vfi
•
•
=
vqi Bf Bq-1- Bq-1 ( Pi(r)
+ Er)
Zi e ni(r)
Neoclassical
NCLASS calculates relative parallel flow between species
(determined by the parallel friction from Coulomb collisions).
This allows neoclassical determination of vqi.
Largest difference in vfi will be in plasma with large Pi
4th ITPA Meeting Apr 03 LRB
Rotation Data Analyzed with
FORCEBAL and NCLASS codes
•
•
•
•
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(r)
Ti (r)
Vf (r)
Vq(r)
Pi(r) vfi (r)Er(r)
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
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•
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 vf, and poloidal vq, 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
sv (10-15 m3/s)
30
Ne X
20
Full Energy
C VI
10
Third
Energy
0
0
Half
Energy
20
He II
40
60
80
100
E (keV/amu)
•
•
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
CER Shifted Line Profile from
Energy Dependent Cross Section
1.2
Line Intensity (A.U.)
1
C5+ (n = 8  7)
Shifted Line
Ti = 15 keV
0.8
Full Energy
Component
0.6
0.4
0.2
Unshifted
Gaussian
(15 keV, 300 km/s)
Half Energy
Component
Third Energy
Component
0
-1250
-750
-250
250
750
1250
Line of Sight Velocity (km/s)
•
In this DIII-D QDB example for r=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.
4th ITPA Meeting Apr 03 LRB
Variation of Apparent Ti and Vt
As a Function of Real Ti
160
8
Vt_real - Vt_app (km/s)
Ti_real - Ti_app (keV)
9
He II
7
C VI
6
Ne X
5
RI mode
4
QDB
3
2
1
0
140
He II
120
C VI
100
Ne X
80
RI mode QDB
60
40
20
0
-20
0
5
10
15
20
25
30
0
Ti_real (keV)
•
•
5
10
15
20
25
Ti_real (keV)
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.
4th ITPA Meeting Apr 03 LRB
30
Example of Data from Simultaneous
C VI, Ne X, and He II Measurements with CER
DIII-D 106084
Analysis Time
Time (ms)
4th ITPA Meeting Apr 03 LRB
Experimental Plasma Conditions – RI-Mode Case
8·10
19
6
DIII-D 106084
1.450 s
5
Ti
Te
DIII-D 106084
1.450s
6·1019
T(keV)
n (m-3)
4
ne
4·1019
nD
3
2
2·1019
1
nC
0
0.0
•
•
0.2
0.4
r
0.6
0.8
1.0
0
0.0
0.2
0.4
r
0.6
0.8
1.0
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.
4th ITPA Meeting Apr 03 LRB
Experimental Plasma Conditions – RI-mode Case
2.0·1018
He4
C
Ne
DIII-D 106084
n (m-3)
1.5·1018
1.0·1018
5.0·1017
0
0.0
•
0.2
0.4
r
0.6
0.8
1.0
Impurity density profiles from the analyzed CER data for the RI-mode
case.
4th ITPA Meeting Apr 03 LRB
FORCEBAL Vtor Calculations for RI Mode Case
400
C
Ne
He4
D
DIII-D 106084
Vtor (km/s)
300
200
100
0
0.0
•
•
0.2
0.4
r
0.6
0.8
1.0
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.
4th ITPA Meeting Apr 03 LRB
Example of Data from Simultaneous
C VI and He II Measurements with CER in QDB Plasma
0
-5.0·10 5
Ip
Analysis
Time
-1.0·10 6
-1.5·10
6
6
-2.0·10
3.00
2.25
bN
1.50
0.75
0.00
13
3.5·10
2.5·10 13
ne
1.5·10 13
5.0·10 12
-5.0·10 12
3.5
2.5
PHD02UP
1.5
0.5
-0.5
3
2
GasE (He4)
He Puff
1
0
-1
1.5·10 7
1.0·10 7
PNBI
5.0·10 6
0
-5.0·10 6
0.0
•
1.0
2.0
3.0
4.0
Time (s)
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
DIII-D 105882
3.500s
n (m-3)
T(keV)
DIII-D 105882
3.500s
r
r
•
•
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.
4th ITPA Meeting Apr 03 LRB
Experimental Plasma Conditions – QDB Case
2.0·1018
DIII-D 105882
C
He4
n (m-3)
1.5·1018
1.0·1018
5.0·1017
0
0.0
•
0.2
0.4
r
0.6
0.8
1.0
Impurity density profiles from the analyzed CER data for the QDB
mode case.
4th ITPA Meeting Apr 03 LRB
CER Analyzed Profiles – QDB Case
15
500
C
He
C
He
Vtor (km/s)
400
Ti (keV)
10
300
200
100
5
0
DIII-D 105882
3.500s
0
0.0
0.2
•
•
0.4
-100
r
0.6
0.8
1.0
-200
0.0
DIII-D 105882
3.500s
0.2
0.4
r
0.6
0.8
1.0
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.
4th ITPA Meeting Apr 03 LRB
FORCEBAL Vtor Calculations for QDB Mode Case
FORCEBAL Run CH5
500
C
He
D
400
Vt (km/s)
300
200
100
0
DIII-D 105882
3.500s
-100
-200
0.0
•
•
0.2
0.4
r
0.6
0.8
1.0
Toroidal rotation velocities are shown for the QDB predictive run. Measured C Vtor 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.
4th ITPA Meeting Apr 03 LRB
Toroidal Mach Numbers
for QDB Mode Case
1.0
DIII-D 105882
3.5s
C
He4
D
Mtor
0.8
0.6
0.4
0.2
0.0
0.0
•
0.2
0.4
r
0.6
0.8
1.0
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 Run CH5
500
C
He
D
400
Vtor (km/s)
Vt (km/s)
200
100
0
•
•
300
200
100
0
DIII-D 105882
3.500s
-100
-200
0.0
C
He
400
300
-100
Experimental Data
500
0.2
0.4
r
0.6
0.8
1.0
-200
0.0
DIII-D 105882
3.500s
0.2
0.4
r
0.6
0.8
1.0
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.
4th ITPA Meeting Apr 03 LRB
CER Analyzed Profiles – QDB Case
Carbon and Neon Comparison
500
16
DIII-D 105887 3.5s
14
Ne X
C VI
Vtor (km/s)
12
10
Ti (keV)
C VI
Ne X
400
8
6
4
300
200
100
2
0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0
0.0
0.2
r
•
•
0.4
0.6
r
0.8
1.0
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.
4th ITPA Meeting Apr 03 LRB
1.2
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•
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
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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,
Plasmas, 8 (2001) 2153.
Phys.
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 crosssection 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 doublebarrier (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
1.5
C
Ne
DIII-D 106084
D
Mtor
1.0
0.5
0.0
0.0
•
0.2
0.4
r
0.6
0.8
1.0
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.
4th ITPA Meeting Apr 03 LRB
CER Analyzed Profiles – RI mode Case
6
400
C
He
Ne
5
C
He
Ne
Vtor (km/s)
300
Ti (keV)
4
3
200
2
100
1
0
0.0
0.2
•
•
0.4
r
0.6
0.8
1.0
0
0.0
0.2
0.4
r
0.6
0.8
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.
4th ITPA Meeting Apr 03 LRB
1.0
Analyzed He Density Profiles – QDB Case
CerFit: nz vs rho shot: 105882 time: 3500.0000
0.25
Helium - Vert Only
0.20
dimp105882.03500_Hel
* 1.00000
Vertical
Tangential
0.15
)
-3
m
19
0.10
nz(10
0.05
0.00
0.0
•
0.2
0.4
0.6
r
0.8
1.0
1.2
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 Run CHV
500
C
He
300
200
100
0
-100
•
•
300
200
100
0
DIII-D 105882
3.500s
-100
-200
0.0
C
He
400
Vtor (km/s)
Vtor (km/s)
400
Experimental Data
500
0.2
0.4
r
0.6
0.8
1.0
-200
0.0
DIII-D 105882
3.500s
0.2
0.4
r
0.6
0.8
1.0
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.
4th ITPA Meeting Apr 03 LRB