4 th 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.

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


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.


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


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()


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


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.


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.


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


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


Example of Data from Simultaneous C VI, Ne X, and He II Measurements with CER

Time (ms)

DIII-D 106084

Analysis Time


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


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


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


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.


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


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


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


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


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.


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


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

)


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.


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.


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.


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.


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


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

)


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.


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

4 th 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.

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