Light Impurity Transport Studiesin Alcator C-Mod*

I. O. Bespamyatnov,1 W. L. Rowan,1 C. L. Fiore,2

K. W. Gentle,1 R. S. Granetz,2 and P. E. Phillips1

1Fusion Research Center, The University of Texas at Austin

2MIT-PSFC

Poster Session PP6: Poster Session VIWednesday, November 19, 2008Marsalis A/B, 2:00pm - 5:00pm

50th Annual Meeting of the Division of Plasma PhysicsNovember 17–21, 2008; Dallas, Texas

*Supported by USDoE Awards DE-FG03-96ER54373 and DE-FC02-99-ER54512

Summary

• Local, CXRS measurements of light impurity density and temperature profiles were measured in L-mode, H-mode, and ITB discharges in Alcator C-Mod along with impurity flow measurements and radial electric field. The basic results are

– Light impurity densities peak in ITB discharges but the transport is not neoclassical.

– Hollow impurity density profiles are observed in H-mode discharges

• The computed ER profiles demonstrated the large difference between the H-mode and ITB discharges. Linear gyrokinetic stability analysis (GS2) demonstrated that shearing rate ω E×B prevails over the linear ITG growth rates γ max in the region where ITB forms

• These suggest new experiments

– Causes of impurity peaking and differences between light and heavy impurities

– Effect of turbulence on impurity transport

– These may lead to impurity control

• Some of these experiments would benefit from modulation of the impurity source and the possibilities on C-Mod are described.

• Impurity transport is a critical issue in burning plasmas due to fuel dilution and radiative cooling. The new experiments will provide information on the behavior of light impurities, on light impurity peaking, and may suggest means for impurity control.

Experiment

• L-mode, H-mode, and ITB are all shown in a single discharge.

• EDA H-mode is triggered by ICRF at 0.7 s.

• H-mode evolves to ITB

• ne profiles are shown at the indicated times in the t-series plots

• B5+ profiles, Te and Ti profiles are on the next page.

ne(x1014cm-3)

Boron n and T profiles

• Fully stripped boron ion, B5+ is the only boron ion present for R < 0.85 m. Impurity transport analysis using a fully stripped ion is much simpler that for other species.

• L-Mode. Relatively flat B5+ profile. Zeff = 1 - 1.1 and Ti < Te

• H-Mode. Hollow B5+ profile. Zeff = 1.3 - 1.4. Ti → Te

• ITB. Peaked B5+ profile. Ti ≈ Te

B5+ density B5+ temperature

Radial electric field ER

• Included for use in impurity transport analysis

• Inferred from momentum balance

• All terms are measured with CXRS

• Flow velocity terms usually dominate

• ER profile has similar shape for H-modes in LSN and USN

• ITB ER has an inner well and strong gradients

• Er behavior is similar to ITBs in JET and JT-60

• Reminiscent of the ERwell at the edge pedestal.

( ) ZZZZZ

ZR TnpBVBV

Zn

pE Ζ=−−

∇= ,ϕθθϕ

Poloidal and toroidal rotation

• Difference between measured and neoclassically calculated impurity poloidal rotation. (observed in other tokamaks: TFTR, DIII-D, JET)

• Possible effect of heating beams. J.Rice, Nuclear Fusion, Vol. 39, No. 9, (1999)

• C-Mod doesn’t employ heating beams and observes the same type of difference.

• Turbulence generally considered as a main source of the anomaly. K.H. Burrell, Plasma Phys. Control. Fusion 36,(1994)

• Strong co-current toroidal rotation is associated with H-mode phase.

Poloidal velocity

Toroidal velocity

Peaked Impurity Profile (ITB)

• Simulation of the peaked profiles yields an inward convection

• Neoclassical yields a much stronger inward convection

• Turbulence persists, is consistent with density peaking and may reduce impurity peaking.

Impurity Peaking Experiments

• Impurity transport is a critical issue in burning plasmas due to possible fuel dilution and radiative cooling

• Low collisionality experiments reveal peaking of heavy impurities and not light. Weisen, et al., Plasma Phys. Contr. Fusion 48, A457 (2006)

• Comparison to the particle profile may answer the question: Does the main ion gradient act through neoclassical pinch to drive impurity peaking?

• Comparison to heavy impurity profile. Peaking differs in some ITB results and in low collisionality experiments. Mass and charge dependence needs study. Examples Dux, et al., Nucl. Fusion 44, 260 (2004) in itb discharges; Weisen, et al., Plasma Phys. Contr. Fusion 48, A457 (2006) in low collisionality discharges; Takenaga, et al., Nucl. Fusion 43, 1235 (2003).

• Ware pinch is one source for inward convection. LHCD may offer the opportunity to eliminate it at least briefly.

Comparison with other machines

• Similar peaked and hollow impurity profiles are measured in other tokamaks: JET, DIII-D, JT-60

H. Chen., Nuclear Fusion, Vol. 41, No. 1 (2001)

JET

DIII-D Transition from L-mode to VH-mode.

R. Guirlet, Plasma Phys. Control. Fusion 48 (2006)

JT-60 RS ITB High-βp H-mode

H. Kishimoto, Nucl. Fusion 45 (2005)

Hollow Impurity Profile

• Analysis of the EDA H-mode profile with this flux ansatz

• In H-mode in C-Mod, vZ/DZ > 0 Convection is outward leading to a hollow profile

• Neoclassical theory predicts an outward convection due to the temperature gradient

• Hollow profile good for energy confinement: minimizes radiative loss

zzz

zz nvr

nD +

∂

∂−=Γ

∂

∂−

∂

∂⋅=

=

r

T

Tr

n

nDZv

ZBe

cTm

R

qD

Z

Z

i

i

PzZ

T

ZZZ

118.0

1

25.1222

25.1

Hollow Impurity ProfileTurbulent Impurity Transport?

ΓΓΓΓz ==== −−−−Dz

∂∂∂∂nz

∂∂∂∂r++++ vznz

pinch name dependence direction charge

dependence

mass

dependence

refs

curvature ∝

1

q

∂q

∂r

∂q

∂r> 0 inward

≠ f Z( ) ≠ f A( ) 1,2,3,4,5

thermodiffusion ∝

1

T

∂T

∂r TEMinward

ITGoutward

1

Z

≠ f A( ) 1,3,2,6

parallel

compression

TEMoutward

ITGinward

Z

A

Z

A

1,2,3

1 Guirlet, R., et al., 2006 PlasmaPhys. Control. Fusion 48 B63

2 Dubuit, N., et al., 2007 Phys. Plasmas 14 042301

3 Angioni C and Peeters A G 2006 Phys. Rev. Lett. 96 095003

4 Isichenko M B et al 1995 Phys. Rev. Lett. 74 4436

5 Baker D R and Rosenbluth M N 1998 Phys. Plasmas 5 2936

6 Coppi B and Spright C 1978 Phys. Rev. Lett. 41 551

Examples of impurity convection from turbulence theory

Hollow Impurity ProfileTurbulent Impurity Transport?

• Quasilinear impurity transport flux

• Quasilinear theory can be used to develop a description of impurity transport

which fits the ansatz

• Following Garbet, Phys. Plasmas 12, 082511 (2005), the impurity flux can be

written as

Γ = ˜ n z ˜ v E ,z

ΓΓΓΓz ==== −−−−Dz

∂∂∂∂nz

∂∂∂∂r++++ nzvz

++−=Γ

r

T

TC

RC

r

n

nDn z

zTcurv

z

zturbeqz

∂

∂

∂

∂ 121,

Ccurv = λs

λs = cos θ( )+ sθ sin θ( )θ ,φ

, s =r

q

∂q

∂r

v

D

curv

= −2λs

R

CT =1

Z

ω

ωDz

−ς

v

D

T

= −1

Z

ω

ωDz

−ζ1

Tz

∂Tz

∂r

θ <<1, λs ~ 1+ s−1

2

θ

2

Turbulent Impurity Transport (first results)

ohmic-mode H-mode

TD

v

r

n

n

z

z ∂

∂1

curvD

v

TD

v

r

n

n

z

z ∂

∂1

curvD

v

• Shot #1070718018 Ohmic-mode t = [0.48-0.50] H-mode t = [1.14 -1.16]

• The full details of the curvature pinch and the thermopinch are not included in the

calculation. In the case of the thermo pinch the details of the phase velocity are

omitted, only a sign has been included. In the case of the curvature pinch, the

spatial averaging over the angle is only estimated.

• Approximate evaluation of theory produces results similar to experiment

• Both curvature and thermodiffusion terms are negative and drive inward

convection

[ ]1−m

Shear stabilization

• Suppression of the turbulent eddies in the inhomogeneous plasma flow

• The maximum linear ITG growth rates were calculated by GS2 code for several time-phases of particular H-mode and ITB plasma discharges

• The distinctive feature of the ITB phase is the substantial increase in the E×Bshearing rate, due to the strong local ER gradients

Ψ=×

θθω

RB

E

d

dRB

q

r RBE maxγ - linear ITG growth rate

maxγω >×BE

Stabilization criterion

Comparison with other machines

• Suppression criterion: ωExB > γMAX

• DIII-D VH (improved confinement mode) is characterized by penetration of the H-mode edge transport barrier deeper into the plasma

• DIII-D ITB formation is preceded by the E×B shearing rate increase

• TFTR transition RS to ERS mode is preceded by changes in the ωExB, which proves that not only negative magnetic shear exhibit improved confinement

DIII-D VH-mode DIII-D ITB formation

TFTR

RS to ERS comparison

More Light Impurity Experiments

• Use turbulence to control the impurity profile shape?

– Example in C-Mod: Suppression due to ICRFOn-axis heaing produced an increase in TEM turbulence diffusivity due to a unfavorable temperature scaling of turbulent transport D. R. Ernst, et al., Phys. Plasmas 11, 2367 (2004).

– Heavy impurity peaking suppressed as wellRice J.E. et al Nucl. Fusion 42 510 (2002)

– What happens to the light impurities?

– Is suppression of impurity peaking due to a direct effect of turbulence or to the particle gradient acting through the neoclassical pinch term

• Additional options for experiments based on recent turbulence calculations which are displayed here.

Er in the ITB

• A local minimum in Er is observed in ITB discharges.

• There are hints of a similar feature in JET discharges as reported in K. Crombe et al. Phys. Rev. Lett. 95, 155003 (2005) and H. Shirai et al.Nuclear Fusion, Vol. 39 (1999)

• Suggests the same sort of E×B dynamics may be at work in the ITB as in the edge barrier.

C-Mod

JET

JT-60

Er in the ITB

• Future experiments will increase the number of observations withimproved sensitivity and spatial resolution to confirm this observation.

• The experiments will be expanded to Ohmic ITBs; that is, ITBstriggered by toroidal field ramps

• The poloidal and toroidal rotation measurements will benefit from improvements in spatial resolution and sensitivity.

Time DependentImpurity Transport Experiments

• Impurity transport can be described by

for both neoclassical transport and turbulent transport in the quasilinear limit

• The ratio v/D can be inferred from time independent measurements of the impurity profile.

• A time dependent measurement is required to separately infer both v and D

• Both D and v can be anomalous. The familiar tactic of taking v as neoclassical and the concentrating anomalous behavior in the diffusion coefficient is no longer the best approach to analysis since we are trying to understand peaking.

• There are two time-dependent methods

– CW: the impurity source is continuously varied

– Pulsed: the impurity source approximates a delta function.

ΓΓΓΓz ==== −−−−D∂∂∂∂nz

∂∂∂∂r++++ vznz

• In time-dependent measurements, the source in the impurity transport equation is modified in a controlled way and is time dependent

• CW Methods

– S is a repetitive waveform; square wave or sinusoidal, for example and accomplished by gas puffing

– Helium example: H. Takenaga, et al., Plasma Phys. Control. Fusion40, 183 (1998).

• Impurity Pulse

– S approximates a delta function, accomplished by laser ablation.

– Some examples: H. Chen, et al, Nucl. Fusion 41, 31 (2001); J. E. Rice, et al., Fusion Sci. Technol. 51, 357 (2007).

∂∂∂∂n jz

∂∂∂∂t++++ ∇∇∇∇ •••• ΓΓΓΓj

z ==== Sjz

Time DependentImpurity Transport Experiments

Summary

• Local, CXRS measurements of light impurity density and temperature profiles were measured in L-mode, H-mode, and ITB discharges in Alcator C-Mod along with impurity flow measurements and radial electric field. The basic results are

– Light impurity densities peak in ITB discharges but the transport is not neoclassical.

– Hollow impurity density profiles are observed in H-mode discharges

• The computed ER profiles demonstrated the large difference between the H-mode and ITB discharges. Linear gyrokinetic stability analysis (GS2) demonstrated that shearing rate ω E×B prevails over the linear ITG growth rates γ max in the region where ITB forms

• These suggest new experiments

– Causes of impurity peaking and differences between light and heavy impurities

– Effect of turbulence on impurity transport

– These may lead to impurity control

• Some of these experiments would benefit from modulation of the impurity source and the possibilities on C-Mod are described.

• Impurity transport is a critical issue in burning plasmas due to fuel dilution and radiative cooling. The new experiments will provide information on the behavior of light impurities, on light impurity peaking, and may suggest means for impurity control.