Guttenfelder, APS-DPP 2014, New Orleans LA

Investigating electromagnetic effects on core transport in Alcator C-Mod H-mode discharges

W. Guttenfelder1, N.T. Howard2, J. Irby3, F.M. Poli1,

A.E. White3, W.F. Bergerson4, D.L. Brower4, J. Candy5, W.X. Ding4, C.E. Kessel1, C. Sung3, S.M. Wolfe3, P. Xu

1 Princeton Plasma Physics Laboratory2 ORISE3 Massachusetts Institute of Technology4 University of California – Los Angeles5 General Atomics

APS-DPP, New OrleansOct. 27-31, 2014

Guttenfelder, APS-DPP 2014, New Orleans LA

Overview & Summary

• Beginning validation of gyrokinetic simulations for high- ITER-like H-mode plasmas in Alcator C-Mod– N=1.3-2.1 H-modes unstable to ITG (r/a~0.5-0.8), sub-dominant microtearing

modes (MTM) also predicted– Baseline nonlinear simulations are dominated by ITG, but ion/electron heat fluxes

do not match experiment– Varying Te & Ti gradients to match fluxes changes balance of ITG vs. MTM,

challenges nonlinear simulations (requires large numerical resolution)

• Characterizing expected importance of electromagnetic effects– Finite reduces predicted ion heat fluxes from ITG by 50%– EM flutter transport contributions are small (1% for heat, 15% for particle flux)

• Using synthetic diagnostic, predict sensitivity of polarimeter diagnostic to ne, Br using synthetic diagnostic– |B/B0| ~ 1% |n/n0|, negligible influence of B on Faraday rotation– Will likely change if predicted character of turbulence changes (ITGMTM) with

gradient variations

2

Guttenfelder, APS-DPP 2014, New Orleans LA

EXPERIMENTAL DETAILS

3

Guttenfelder, APS-DPP 2014, New Orleans LA

Analysis based on ITER-like H-mode discharges with N=1.3-2.1

• ITER-like discharges with 2.5-5 MW ICRH heating (Kessel, NF 2013)

• Using reduced BT=2.6 T to achieve high N and fGW (higher * compared to ITER)

• Dominant electron heating, Te~Ti, no torque (expect low rotation, but no measurement)

• Following transport analysis and gyrokinetic scoping studies around 1.3 s

0

0.2

0.4

0.6

I p (M

A)

0

2

4

n (1

020 m

−3 )

0

2

4

6

PR

F (

MW

)

0

1

2

β N

0

0.5

1

f GW

0 0.5 1 1.50

0.5

1

H98

t (s)

1120717006

1120719005

1120719014

4

Guttenfelder, APS-DPP 2014, New Orleans LA

0 0.2 0.4 0.6 0.8 10

10

20

30

40

ne (1019 m−3)

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

(−) te, (−−) ti (keV)

0 0.2 0.4 0.6 0.8 1

0

1

2

3

4

a/Ln

0 0.2 0.4 0.6 0.8 10

2

4

6

8

a/LT

0 0.2 0.4 0.6 0.8 110

−2

10−1

100

101

(−) νei

(cs/a)

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

(−) βe (%)

0 0.2 0.4 0.6 0.8 11.55

1.6

1.65

1.7

1.75

Zeff

r/a0 0.2 0.4 0.6 0.8 1

0

1

2

3

4(−) q, (−−) s

r/a

1120717006

1120719005

1120719014

TRANSP runs & profiles

• 1120717006 (1300 ms) TRANSP ID 87637

• 1120719005 (1300 ms) TRANSP ID 87632

• 1120719014 (1300 ms) TRANSP ID 87634

• Measured Ti profiles unavailable - scaled i,NCto match neutron rate

– New experiment planned to get Ti, v, and MSE-constrained q profile

• Flat Zeff assumed

• For GYRO sims, keeping D & B (sometimes Mo)

(-) ne, (--) nD

5

Guttenfelder, APS-DPP 2014, New Orleans LA

Fluctuation data available from polarimeter, PCI, TCI and reflectometer for validation with simulations

Guttenfelder, APS-DPP 2014, New Orleans LA

LINEAR GYROKINETICS

7

Guttenfelder, APS-DPP 2014, New Orleans LA

0 0.2 0.4 0.6 0.8 1−1.5

−1

−0.5

0

0.5

1

kθρ

s

ωr (c

s/a)

CMOD 1120719014, 1300 ms

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

kθρ

s

γ (cs/a)

r/a=0.5

0.6

0.7

0.8

Initial linear GYRO stability simulations show that ITG dominates r/a=0.6-0.8

• Microtearing modes (MTM) exist for ks<0.4 at r/a=0.5, 0.6– Distinguishable from eigenfunctions/spatial structure (not shown)– Tracking MTM when subdominant using eigenvalue solver (dashed line)

• Clearly distinct dispersion in real frequencies• Similar results for other two shots

8

Linear runs using GYRO

4 kinetic species, D,B,Mo,e(Zeff~1.6)

Electromagnetic(A|| only, e~0.24-0.85%)

Collisions

MTM

ITG

Real frequencies Growth rates

Guttenfelder, APS-DPP 2014, New Orleans LA

Linear ITG weakly stabilized by finite beta (r/a=0.6)

• MTM has threshold at e~0.3% ~ 1/2e,exp, predicts much larger EM fluctuations, |BMTM/B0| ~ 20% of |nMTM/n0|

• Fits for 1120719014 (N=2.1) give a/LTi ~ 1.4a/LTe (r/a=0.6)– a/LTi ~ a/LTe in the other two shots (no ion measurements)

• Let’s investigate sensitivity to gradients

9

0 0.2 0.4 0.6 0.8 1−0.4

−0.2

0

0.2

0.4

0.6

ωr (c

s/a)

βe (%)

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

γ (cs/a)

βe (%)

MTM k

θρ

s=0.2

ITG k

θρ

s=0.3

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

0.25

|δBr|/|δφ|

βe (%)

11207190051120719014

Real frequencies Growth rates

Guttenfelder, APS-DPP 2014, New Orleans LA

ITG stiff with ion temperature gradient (a/LTi),MTM stiff with electron temperature gradient (a/LTe)

• ITG independent of a/LTe

• MTM independent of a/LTi

• MTM much stronger when increasing a/LTe to better match a/LTi~2.7

0 1 2 3−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

a/LTe

ωr (c

s/a)

CMOD 112071914, 1300 ms

0 1 2 30

0.02

0.04

0.06

0.08

0.1

a/LTe

γ (cs/a)

ITG kθρ

s=0.4

MT kθρ

s=0.2

a/LTi

0 1 2 3−0.5

0

0.5

a/LTi

ωr (c

s/a)

CMOD 112071914, 1300 ms

0 1 2 30

0.02

0.04

0.06

0.08

0.1

a/LTi

γ (cs/a)

ITG kθρ

s=0.4

MT kθρ

s=0.2

a/LTe

10

Real frequencies Growth rates

Guttenfelder, APS-DPP 2014, New Orleans LA

Microtearing present over broad radial region, but always subdominant to ITG

• MTM getting stronger further out in radius, but so is ITG

0.4 0.5 0.6 0.7 0.8−0.5

0

0.5

1

r/a

ωr (c

s/a)

CMOD 112071914, 1300 ms

kθρ

s=0.2

0.4 0.5 0.6 0.7 0.80

0.05

0.1

0.15

0.2

0.25

0.3

r/a

γ (cs/a)

ITG kθρ

s=0.4

MT kθρ

s=0.2

11

Real frequencies Growth rates

Guttenfelder, APS-DPP 2014, New Orleans LA

MTM shows non-monotonic dependence with collisionality, as predicted in core of NSTX & AUG

• Same dependence predicted in core of NSTX [Guttenfelder, 2012] and ASDEX-UG [Doerk, 2012]

• Perhaps expected to be less relevant at lower collisionality(ITER r/a~0.6, e ~ 10-2 cs/a)

0 1 2 3−0.5

0

0.5

νe (c

s/a)

ωr (c

s/a)

CMOD 112071914, 1300 ms

0 1 2 30

0.05

0.1

0.15

0.2

νe (c

s/a)

γ (cs/a)

ITG kθρ

s=0.4

MT kθρ

s=0.2

12

Real frequencies Growth rates

Guttenfelder, APS-DPP 2014, New Orleans LA

NONLINEAR GYROKINETICS

13

Guttenfelder, APS-DPP 2014, New Orleans LA

Initial nonlinear run for 1120719014, 1300 ms, r/a=0.6

• For base case, fluxes dominated by ES contributions (Qi=4.8 MW, Qe=1.9 MW)• Inconsistent with TRANSP analysis (Qi,exp=0.6 MW, Qe,exp=4.4 MW)• Only ~1% EM contribution (~Br) to Qe

14

Nonlinear runs using GYRO3 kinetic species, D,B,e (Zeff~1.6)Electromagnetic (A||, e~0.6%)Collisions

Resolution parametersLx Ly = 125 127 snx ny = 25624 (n=5)ks [min, max] = [0.049, 1.14]krs [min, max] = [0.050, 3.21][n||,n,ne]=[14,8,8]2

0 500 1000−50

0

50

100

150

200

Γe (1019 m−2s−1)

t (a/cs)

0 500 1000

0

2

4

6

8

10

12

Qi (MW)

t (a/cs)

0 500 1000−1

0

1

2

3

4

5

6

Qe (MW)

t (a/cs)

ES

EM

tot

Guttenfelder, APS-DPP 2014, New Orleans LA

Ion heat flux (Qi) decreases ~50% with finite e

• Qe shows weaker dependence, e increases– Heat flux dependence similar to previous studies (e.g. Pueschel, PoP 2008)

• Biggest EM flutter contribution is to particle flux (~15% inward)

15

0 0.2 0.4 0.6 0.8

0

2

4

6

8

Qi (

MW

)

βe (%)

0 0.2 0.4 0.6 0.8−1

0

1

2

3

4

5

Qe (

MW

)

βe (%)

1120719014, 1300 msr/a=0.6

0 0.2 0.4 0.6 0.8−10

0

10

20

30

Γe (

1020

#/s

)

βe (%)

tot

ES

EM

exp

Ion heat flux Electron heat flux Electron particle flux

Guttenfelder, APS-DPP 2014, New Orleans LA

Try to match fluxes by adjusting gradients – 1.2-1.4a/LTegives larger Qe approaching experiment

• But also increases Qi (further from experiment)• Will probably need a corresponding decrease in a/LTi

16

0 1 2 3

0

2

4

6

8

Qi (

MW

)

a/LTe

0 1 2 3−1

0

1

2

3

4

5

Qe (

MW

)

a/LTe

1120719014, 1300 msr/a=0.6

0 1 2 3−10

0

10

20

30

Γe (

1020

#/s

)

a/LTe

tot

ES

EM

exp

Ion heat flux Electron heat flux Electron particle flux

Guttenfelder, APS-DPP 2014, New Orleans LA

0.8a/LTi (for 1.2a/LTe) reduces Qi and e much closer to experiment

• Also brings down Qe significantly (further from experiment)• BUT there are serious numerical resolution problems…

17

0 1 2 3

0

2

4

6

8

Qi (

MW

)

a/LTe

0 1 2 3−1

0

1

2

3

4

5

Qe (

MW

)

a/LTe

1120719014, 1300 msr/a=0.6

0 1 2 3−10

0

10

20

30

Γe (

1020

#/s

)

a/LTe

1.0×a/LTi

0.8×a/LTi

exp

Ion heat flux Electron heat flux Electron particle flux

Guttenfelder, APS-DPP 2014, New Orleans LA

Insufficient resolution for reduced a/LTi simulations

• Pathological peaking at highest ks modes in electron heat flux spectra

18

10−1

100

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

kθρ

s

Δ(Γ

e/ΓG

B)

/ Δ(k

θρ

s)

10−1

100

10−2

10−1

100

101

102

kθρ

s

Δ(Q

i/QG

B)

/ Δ(k

θρ

s)

10−1

100

100

kθρ

s

Δ(Q

e/QG

B)

/ Δ(k

θρ

s)

1.9092.2912.291

Particle flux spectra Ion heat flux spectra Electron heat flux spectra

Base1.2a/LTe1.2a/LTe, 0.8a/LTi

Guttenfelder, APS-DPP 2014, New Orleans LA

Linear tests for n=90 (ks=0.88) using nonlinear numerical resolution setup show insufficient resolution

• Artificial growth (n=90, ks=0.88) with insufficient resolution, need nx~500 to recover flux-tube results (i.e. ~0, stable mode)

• Seems that it’s necessary to resolve rational surfaces associated with highest ks modes, x/s1/(4sks)~0.25 (nx500)

– rrat/s = 1/sks = 1 (for ks=0.88, q=1.17, s=1.13)– Working on nonlinear simulations

0 50 100 150 200 250

−0.4

−0.2

0

0.2

0.4

0.6

(−−) ωr (−) γ

t

nx=128

256

400

500

19

Guttenfelder, APS-DPP 2014, New Orleans LA

Relative EM amplitude increases linearly with e

• Br/B0 ~ few % of e/Tene/ne0

• Even if turbulence doesn’t change character, expect B to get bigger is polarimeter expected to be sensitive to B fluctutions?

20

0 0.2 0.4 0.6 0.80

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

|δA|||/|δφ|

βe (%)

Σn>0

Σn≥0

Br/B0 = ksA||/sB0~0.3A||/sB0

Guttenfelder, APS-DPP 2014, New Orleans LA

2D fluctuation snapshot (in R,Z)C-Mod 1120719014, 1300 ms

• ne/ne0 Br/B0

21Movie: http://w3.pppl.gov/~wgutten/movies/cmod_nebr_sat.mov

Guttenfelder, APS-DPP 2014, New Orleans LA

SYNTHETIC FARADAY ROTATION

22

Guttenfelder, APS-DPP 2014, New Orleans LA

Utilize synthetic diagnostic to examine sensitivity of polarimeter measurement to n, B

• Interested in interferometry, Faraday rotation and Cotton-Mouton effects• int=cint dL(ne) cFR=2.81710-15 m/T, =118m• FR=cFR2 dL(B||ne) cFR=2.63110-13 1/T• CM=cCM3 dL(B

2ne) cCM=2.45610-11 1/mT2

• Equilibrium ne0(R,Z), B0(R,Z) from Thomson Scattering and EFIT• On right is plot of GYRO ne/ne0 and Br/B vs. R (at Z=0)

– Simulations don’t span entire cross-section, at least use what we’ve got– Would be a little more realistic to run a global simulation, still can’t include pedestal

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9−1

−0.5

0

0.5

1x 10

−3

R (m)

GYRO fluctuations, Z≈0

(δne/n

e0)/50

(δBr/B)

23

Guttenfelder, APS-DPP 2014, New Orleans LA

Let’s examine equilibrium first

• Using EFIT (in this case actually .geq from TRANSP plasma state)

• Shown are three polarimeter chords (1,2,4) where data was acquired

24

0.4 0.6 0.8 1−0.6

−0.4

−0.2

0

0.2

0.4

0.6

ψ

0.4 0.6 0.8 1−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Bφ

0.4 0.6 0.8 1−0.6

−0.4

−0.2

0

0.2

0.4

0.6

BR

0.4 0.6 0.8 1−0.6

−0.4

−0.2

0

0.2

0.4

0.6

BZ

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

−6

−5.5

−5

−4.5

−4

−3.5

−3

−2.5

−2

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Guttenfelder, APS-DPP 2014, New Orleans LA

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

5

10

15

20

25

dψ/d

l (de

g/m

)

R (m)

ψfr = 11.7874 (deg) ψ

cm = 3.0974 (deg)

Bφ/10

BR

BZ

B⊥/10

B||

ne

FRCM

Calculated equilibrium Faraday Rotation bigger than Cotton-Mouton effect, matches experimental measurement

• FR=cFR2 dL(B||ne) (cFR=2.63110-13 1/T), =118m• CM=cCM3 dL(B

2ne) (cCM=2.45610-11 1/mT2)

• Quantities along polarimeter chord #2 shown, e.g. B||=(BRdR+BZdZ)/dL

• Relatively flat density profile, differential FR and CM phase shift follows B|| and B

2, respectively

• Integrated phase shift (2d) gives FR=11.8 deg, close to exp. FR=11.3 deg

• Shown previously to work well by Bergerson, RSI (2010), Xu thesis (2013)

25

Chord #2

Guttenfelder, APS-DPP 2014, New Orleans LA

Incorporating GYRO fluctuations by interpolating in lab space

• For each polarimeter chord (R,Z), determine corresponding GYRO (r/a, )• Interpolate ne(r/a,) to obtain ne,pol

• Interpolate A||(r/a,) onto a 5-point stencil in (R,Z)• Calculate BR, BZ from A||(RR,ZZ)

– To lowest order in s/R BR=-B/BA||/dZ, BZ= B/BA||/dR• Project along chord to obtain B||,poldL = (BRdR + BZdZ)

0.5 0.6 0.7 0.8−0.2

−0.1

0

0.1

0.2

δne (1020 m−3)

R (m)

0.5 0.6 0.7 0.8−4

−2

0

2

4x 10

−5 δA|| (Wb/m)

R (m)

chord #1

#2

#4

0.5 0.6 0.7 0.8

−60

−40

−20

0

20

40

R (m)

δB||,pol

(G)

26

Guttenfelder, APS-DPP 2014, New Orleans LA

Predicted Faraday rotation dominated by neB||0,Interferometric signal ~300 bigger than Faraday rotation

• (neB||0)~6(ne0B||)• ne~0.11020 m-3 B||~210-3 T• ne0~2.51020 m-3 B||0~310-1 T

27

0.7 0.8 0.9 1 1.1 1.2−0.1

−0.05

0

0.05

0.1

0.15components of synthetic polarimeter signal

t (ms)

deg

FR

~δn⋅B

~n⋅δB

• int=cint dL(ne)• FRcFR2B||0 dL(ne)• cint ~ 300 cFR2B||0

Will estimate sensitivity of Faraday rotation to interferometric contamination due to non-collinearity of two FIR paths

0.7 0.8 0.9 1 1.1 1.2−40

−20

0

20

40

60

t (ms)

deg

synthetic interferometer signals

chord #1

#2

#4

chord #2

Guttenfelder, APS-DPP 2014, New Orleans LA

Simulated synthetic polarimeter phase predicts Faraday rotation fluctuations ~5x smaller than experiment

• Experimental values averaged over 200 ms polarimeter signal (1250-1450 ms)• RMS amplitude ~5x bigger than synthetic

– rms exp = [0.14, ------ ,0.26] degrees– rms syn = [0.029, 0.037, 0.051] degrees

• Possible sources of error: (i) haven’t matched heat fluxes (possible change in turbulence character) (ii) local, not global, simulations, (iii) not simulating edge and/or near-axis, (iv) contamination from interferometric effects, (v) …

281300 1300.1 1300.2 1300.3 1300.4 1300.5 1300.6

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8polarimeter chord #1 measurement

deg

t (ms)

11.3 degree mean subtracted

100

101

102

103

10−13

10−12

10−11

10−10

10−9

10−8

10−7

10−6

f (kHz)

deg2 /H

z

polarimeter power spectra

chord #1

#2

#4

Simulation + synthetic

experiment

Guttenfelder, APS-DPP 2014, New Orleans LA

Future work

• Complete flux-matching simulations with sufficient resolution– Will MTM become a more significant contributor?

• Clarify discrepancy between measured and synthetic polarimeter signal– If not resolved with local flux-matched simulations consider running global

simulations

• Apply synthetic diagnostics for comparison with other available turbulence data (PCI, TCI and reflectometer)

• Possibly run new experiment in 2015 to obtain ion measurements (planned for 2014)

29