velocity detection of plasma patterns from 2d bes data

Velocity Detection of Plasma Patternsfrom

2D BES Data

Young-chul Ghim(Kim)1,2, Anthony Field2, Sandor Zoletnik3

1 Rudolf Peierls Centre for Theoretical Physics, University of Oxford2 EURATOM/CCFE Fusion Association, Culham, U.K.

3KFKI RMKI, Association EURATOM/HAS

2, March, 2011

Prepared by Young-chul Ghim(Kim)

Quantity BES measures is Density Fluctuation.

2 /

Prepared by Young-chul Ghim(Kim)

Contents

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1. Brief description of zonal flows, sZFs, and GAMs

2. Density fluctuation from DIII-D data using CUDA

3. Meaning of measured velocity from 2D BES data

1. Detectable range of velocitya) How the study is performed.b) Mean flowc) Temporally fluctuation flow (i.e. GAMs)

2. Velocity measurements from DIII-D Data

3. Conclusion

Prepared by Young-chul Ghim(Kim)

ZFs are not divergence free in a tokamak.

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A Flux Surface (q=2 surface)

ϕ (toroidal)

θ (

polo

idal

)

0 (out-board)

π (in-board)

2π (out-board)

0 π 2π

B-field

Zonal Flow: VZF(θ)

Prepared by Young-chul Ghim(Kim)

So, consequences are generating sZF and/or GAMs.

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A Flux Surface (q=2 surface)

ϕ (toroidal)

θ (

polo

idal

)

0 (out-board)

π (in-board)

2π (out-board)

0 π 2π

B-field

Zonal Flow: VZF(θ)

sZF and/or GAMs

Prepared by Young-chul Ghim(Kim)

Structure of GAMs: (m, n) = (0, 0) and (1, 0)

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Both modes have the same temporal behavior:

Winsor et al. Phys. Fluids 11, 2448 (1968)

€

ωGAM2 =

CS2

q2R2 1+ 2q2( )

Spatial structure of GAMs

€

˜ φ GAMm =1 ~ ε ˜ φ GAM

m =0

where ε is the inverse aspect ratio.

€

˜ φ GAMm =1 ~ −sin θ( )

Prepared by Young-chul Ghim(Kim)

Density response to GAMs

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Due to m = 0 mode of GAM:

€

˜ φ GAMm =0 → Polarization Drift → Density fluctuation

→ ˜ n GAMm =0 ~ krρ i( )

2 ˜ φ GAMm =0

Due to m = 1 mode of GAM:

€

˜ φ GAMm =1 → e- Boltzmann Response → Density fluctuation

→ ˜ n GAMm =1 ~ ˜ φ GAM

m =1 ~ ε ˜ φ GAMm =0

Temporal behavior of density fluctuation:

€

ωGAM2 =

CS2

q2R2 1+ 2q2( )

Prepared by Young-chul Ghim(Kim)

Detecting ñGAM using 2D BES

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€

˜ n GAM = Am =0 exp iωGAM t( ) − Am =1 sin θ( )exp iωGAM t( )

• BES cannot detect m=1 mode of ñGAM because observation position is mid-plane.• How about m= 0 mode of ñGAM?

Krämer-Flecken et al. Phy. Rev. Lett. 97, 045006 (2006)

Prepared by Young-chul Ghim(Kim)

BES can detect GAMs from motions of ñ.

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To the perpendicular direction on a given flux surface:

€

˜ v ⊥GAMm =0 = −kr

˜ φ GAMm =0

( ) /B

˜ v ⊥GAMm =1 = −kr

˜ φ GAMm =1

( ) /BThese induce oscillating perpendicular motion of ñ.

To the radial direction:

These induce oscillating radial motion of ñ.But, their magnitudes may be small.

€

˜ v r GAMm =0 =

ωGAM

ωC Bkr

˜ φ GAMm =0

˜ v r GAMm =1 = −kθ

˜ φ GAMm =1

( ) /BΦ

Prepared by Young-chul Ghim(Kim)

Conclusion I

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As physicists, we want to know• how zonal flows are generated. • how they suppress turbulence.

First, we need to confirm existence of zonal flows.

Try to observe ñ associated with zonal flows. In general, not easy.

Try to observe ñ associated with GAMs. Hard with BES at the midplane

Try to observe GAM induced motions of ñ Possible with BES

Prepared by Young-chul Ghim(Kim)

Contents

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1. Brief description of zonal flows, sZFs, and GAMs

2. Density fluctuation from DIII-D data using CUDA

3. Meaning of measured velocity from 2D BES data

1. Detectable range of velocitya) How the study is performed.b) Mean flowc) Temporally fluctuation flow (i.e. GAMs)

2. Velocity measurements from DIII-D Data

3. Conclusion

Prepared by Young-chul Ghim(Kim)

Statistical analyses are performed on a GPU.

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Prepared by Young-chul Ghim(Kim)

DIII-D BES Data

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I have two sets of data which each consists of

• 7 poloidally separated channesl

• with 11 mm separation

• for about little bit more than ~ 2 seconds worth

• with 1MHz sampling frequency

Prepared by Young-chul Ghim(Kim)

Data Set #1: Density spectrogram (Ch.1)

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Some MHD modes?

IAW modes?

Prepared by Young-chul Ghim(Kim)

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Data Set #1: Density spectrogram (Ch.1 and 7)

Prepared by Young-chul Ghim(Kim)

Contents

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1. Brief description of zonal flows, sZFs, and GAMs

2. Density fluctuation from DIII-D data using CUDA

3. Meaning of measured velocity from 2D BES data

1. Detectable range of velocitya) How the study is performed.b) Mean flowc) Temporally fluctuation flow (i.e. GAMs)

2. Velocity measurements from DIII-D Data

3. Conclusion

Prepared by Young-chul Ghim(Kim)

17 /

Mean flows in a tokamak is mostly toroidal.

ϕ (toroidal)

θ (

polo

idal

) B-field line

v||

v (~vExB)

vplasma

vplasma = v|| + v

Prepared by Young-chul Ghim(Kim)

18 /

Mean flows in a tokamak is mostly toroidal.

ϕ (toroidal)

θ (

polo

idal

) B-field line

v||

v (~vExB)

vplasma

vplasma = v|| + v = vϕ + vθ

vϕ

vθ

Prepared by Young-chul Ghim(Kim)

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Poloidal motion: mostly ‘barber pole’ effect.

Prepared by Young-chul Ghim(Kim)

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Poloidal velocity from barber shop effect is close to ExB drift velocity.

ϕ (toroidal)

θ (

polo

idal

) B-field line

v||

v

vplasma

vplasma = v|| + v = vϕ + vθ

vϕ

vθ

vdetected

α

α

€

=v⊥

cos(α )~ v⊥

Prepared by Young-chul Ghim(Kim)

In addition, we have GAM induced velocity.

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ϕ (toroidal)

θ (

polo

idal

) B-field line

v||

v

vplasma

vϕ

vθ

vdetected

α

α

€

=v⊥

cos(α )~ v⊥

vGAM vGAMcos(α)

Prepared by Young-chul Ghim(Kim)

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Conclusion III

We have to be careful when we say ‘poloidal motion’ of a plasma in a tokamak measured by BES.

Poloidal motion of plasma small (on the order of diamagnetic flow)

Poloidal motion of patterns can be on the order of ExB flow (due to ‘barber pole’ effect)

Prepared by Young-chul Ghim(Kim)

Contents

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1. Brief description of zonal flows, sZFs, and GAMs

2. Density fluctuation from DIII-D data using CUDA

3. Meaning of measured velocity from 2D BES data

1. Detectable range of velocitya) How the study is performed.b) Mean flowc) Temporally fluctuation flow (i.e. GAMs)

2. Velocity measurements from DIII-D Data

3. Conclusion

Prepared by Young-chul Ghim(Kim)

24 /

Eddies generated by using GPU (CUDA programming)

€

˜ n R,z, t( ) = Ai exp −R − Ri( )

2

2λ R2 +

z + vz (R, t)(t − ti) − zi( )2

2λ z2 +

t − ti( )2

2τ life2

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟

⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥cos 2π

z + vz(R, t)(t − ti) − zi

λ z

⎡

⎣ ⎢

⎤

⎦ ⎥

i=1

N

∑

Equation to generate ‘eddies’

Assumed that eddies have Gaussian shapes in R, z, and t-directions plus wave structure in z-direction.

R

Zt vz(R,t)

Prepared by Young-chul Ghim(Kim)

vz(R,t) is set to have sheared and GAM induced flows.

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€

vz R, t( ) = ˜ v z R, t( ) * exp −t 2

τ GAM2

⎡

⎣ ⎢

⎤

⎦ ⎥sin 2πfGAM t( )

€

vmean R( ) = limT → ∞

1

Tvz R, t( )

0

T

∫ dt and vGAM R( ) = limT → ∞

1

Tdt vz R, t( ) − vmean R( )[ ]

2

0

T

∫

Prepared by Young-chul Ghim(Kim)

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Synthetic BES data are generated by using PSFs and generated eddies.

Prepared by Young-chul Ghim(Kim)

vz(t) is estimated using the CCTD method.

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Prepared by Young-chul Ghim(Kim)

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Data Set #1: Mean vz(t) of plasma patterns

Prepared by Young-chul Ghim(Kim)

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Back-of-envelope calculation of detectable range of mean velocity using CCTD method

Upper Limit Lower Limit

Using adjacent Channel

40 km/s 1.3 km/s

Using Farthest apart channels

120 km/s 4.0 km/s

Numerical Results ~ 80 km/s ~ 5 km/s

Sampling Frequency: 2 MHz 0.5 usecAdjacent channel distance: 2.0 cmFarthest apart channel distance: 6.0cmLife time of an eddy: 15 usec (This plays a role in lower limit. i.e.

before an eddy dies away, it needs to be seen by the next channel.)

Prepared by Young-chul Ghim(Kim)

Numerical results of detecting mean velocities.

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Upper limit

Lower limit

Prepared by Young-chul Ghim(Kim)

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Numerical results of detecting fluctuating velocities.

Prepared by Young-chul Ghim(Kim)

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Numerical results of detecting fluctuating velocities.

Prepared by Young-chul Ghim(Kim)

Conclusion IV

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We saw upper and lower limits of detectable mean flow velocity using BES with CCTD technique.

o Upper Limit is set by1) Sampling frequency2) Distance from a channel to next one

o Lower Limit is set by1) Life time of a structure2) Distance from a channel to next one

We saw thato The worse the NSR, the harder to detect GAMs o the faster the mean flow, the harder to detect

GAMs

Prepared by Young-chul Ghim(Kim)

Contents

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1. Brief description of zonal flows, sZFs, and GAMs

2. Density fluctuation from DIII-D data using CUDA

3. Meaning of measured velocity from 2D BES data

1. Detectable range of velocitya) How the study is performed.b) Mean flowc) Temporally fluctuation flow (i.e. GAMs)

2. Velocity measurements from DIII-D Data

3. Conclusion

Prepared by Young-chul Ghim(Kim)

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Data Set #1: Mean vz(t) of plasma patterns

Prepared by Young-chul Ghim(Kim)

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Data Set #1: Fluct. vz(t) of plasma patterns

Density is filtered 50.0 kHz < f < 100.0 kHz before vz(t) is calculated.

Prepared by Young-chul Ghim(Kim)

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Data Set #1: Fluct. vz(t) of plasma patterns

Density is filtered 0.0 kHz < f < 30.0 kHz before vz(t) is calculated.

Prepared by Young-chul Ghim(Kim)

Conclusion V

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As we just saw, detecting GAM features are not straight forward.

o It may be helpful to consider radial motions as well since we have radial motions of eddies due to

1) Polarization drift2) Finite poloidal wave-number associated with m=1 mode of GAM However, we do not know whether these radial motions are big

enough to be seen by the 2D BES.

Prepared by Young-chul Ghim(Kim)

Final Conclusions

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1. Discussed about ZFs, sZFs, and GAMS. Because of the observation positions of 2D BES, we use GAMs

to “confirm” the existence of zonal flows.

2. Discussed the meaning of poloidal velocities seen by the 2D BES. BES sees poloidal motions of ‘plasma patterns’ rather than bulk

plasmas.

3. Discussed detectable ranges of poloidal motions using the CCTD method.1. Mean vz: sampling freq., ch. separation dist., lifetime of eddies.2. Fluct. vz: NSR levels, vGAM/vmean.

4. DIII-D data showed that we have to be careful for detecting GAM-like features.

Velocity Detection of Plasma Patternsfrom

2D BES Data

Young-chul Ghim(Kim)1,2, Anthony Field2, Sandor Zoletnik3

1 Rudolf Peierls Centre for Theoretical Physics, University of Oxford2 Culham Centre for Fusion Energy, Culham, U.K.

3KFKI RMKI, Association EURATOM/HAS

28, February, 2011

Prepared by Young-chul Ghim(Kim)

Data Set #2: Density spectrogram (Ch.1)

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Prepared by Young-chul Ghim(Kim)

Data Set #2: Density spectrogram (Ch.1)

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Some MHD modes?

IAW modes?

Probably LH transition

Prepared by Young-chul Ghim(Kim)

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Data Set #2: Density spectrogram (Ch.1 and 7)

Prepared by Young-chul Ghim(Kim)

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Data Set #2: Mean vz(t) of plasma patterns

Prepared by Young-chul Ghim(Kim)

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Data Set #2: Fluct. vz(t) of plasma patterns

Density is filtered 50.0 kHz < f < 100.0 kHz before vz(t) is calculated.

Prepared by Young-chul Ghim(Kim)

46 /

Data Set #2: Fluct. vz(t) of plasma patterns

Density is filtered 0.0 kHz < f < 30.0 kHz before vz(t) is calculated.