Lower Hybrid Coupling Experiments

on Alcator C-Mod*

1MIT Plasma Science and Fusion

Center, Cambridge USA2Princeton Plasma Physics

Laboratory, Princeton USA

*Work supported by US DOE awards

DE-FC02-99ER54512 and DE-AC02-

76CH03073.

G.M. Wallace,1 P.T. Bonoli,1 A.E. Hubbard,1 Y. Lin,1 R.R. Parker,1 A.E.

Schmidt,1 C.E. Kessel,2 and J.R. Wilson2

Abstract

The Alcator C-Mod Lower Hybrid launcher couples RF waves at 4.6

GHz via 4 rows of 22 phased waveguides. Directional couplers in the

launcher structure measure forward and reflected power in each

waveguide, while six Langmuir probes mounted to the front of the

antenna grill monitor density at the plasma edge and act as RF probes

for the observation of parametric decay. Parametric decay spectra grow

exponentially with line averaged electron density in the regime ω = 3 -

6 ωlh. Measurements of the coupling of lower hybrid waves have been

performed at power levels approaching 1 MW. Edge density, launched

n|| spectrum, and plasma shape have been adjusted to optimize coupling

in Ohmic and ICRF heated L- and H-mode plasmas. Preliminary results

show that deleterious effects of ICRF on LH coupling are reduced

following boronization, particularly in H-mode. Experimentally

observed coupling results will be compared to simulations from several

coupling codes.

LH System Overview

• f0=4.6 GHz

• 4X22 waveguide

phased array

• Molybdenum

protection limiters

• Langmuir probes

measure plasma

density in front of

LH antenna

Forward and Rear Waveguide Detail

• Power measurements made on transmitter side of final 3 dB splitter

• No direct measurement of forward or reflected power possible in B or C

waveguide rows

LH System Overview - Single Channel

Signals used in

calculation of

net power and

reflection

coefficient

Signals used in

ratio based arc

protection

system

0 2 4 6 8 10

x 1019

−100

0

100

200

300

400

500

600

700

electron density

n ⊥2

Fast and slow wave n⊥2, B=5.4T

n||=1.5

n||=1.7

n||=2.0

Coupling in Slab Geometry

• For n||2>1, wave is

evanescent if

ne<nc=2.6x1017m-3

• Analytic solution in form of

Airy functions for a linear

density gradient( )

2

0

2

2

||||2

2

2

2

2

2

2

0)1(

0

q

mfn

Encx

E

Ec

E

ec

zz

επ

εω

εω

⋅=

=−−∂∂

=⋅−×∇×∇

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 1017

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

electron density

n ⊥2

Fast and slow wave n⊥2, B=5.4T

n||=1.5

n||=1.7

n||=2.0

Measured Probe Density �� Code Density Profiles

∫−=

probe

grill

x

xgrillprobe

probe dxxnxx

n )(1

• No vacuum gap

• Density gradient variable

• Small edge density

• Vacuum gap

• Constant density gradient

• Step density variable

Exponential density profiles are more realistic given

close proximity to limiters

dx

dnx

dx

dnxnxn ≈+= 0)(

Probe measures average density

in region from grill to probe tip

≤−+

<=

xxdx

dnxxn

xx

xngapgap

gap

)(

0

)(0

Density Profiles Compatible with “Grill” Code

Slab Model

• 1-D infinite slab geometry

• Calculates wave reflection

and transmission at each

surface

• Weighted average over

launched n|| spectrum

• Evanescent region at low

density

• Impedance mismatch at high

density

• Minimum reflections ~20%

0 0.005 0.01 0.015 0.020

500

1000

x [m]

k ⊥r [m

−1 ]

0 0.005 0.01 0.015 0.020

50

100

150

x [m]

k ⊥i [m

−1 ]

0 1 2 3 4

x 1018

0.2

0.4

0.6

0.8

nprobe

[cm−3]

Γ2

phase=60o dn/dx=1e20 [m−4] xgap

=0 [m]

“Grill” Coupling Code

• Coupling code calculates reflection coefficients of launched waves based on Airy function solution[1]

• Poloidal variations in density and gradient not included in model

• Linear density profile yields minimum reflections ~5%

• Experimental observations of reflections ~20% more consistent with vacuum gap [2] or constant edge density profiles– Best fit with xgap = 0.5 mm and dn/dx = 1e20 m-4 for vacuum gap model

– Best fit with n0 = 4.0e17 m-3

0 2 4 6 8 10

x 1018

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

nprobe

[m−3]

Γ2

Short Pulse Coupling Data

60o

90o

120o

0 2 4 6 8 10

x 1018

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

nprobe

[m−3]

Γ2

Short Pulse Coupling Data

60o

90o

120o•No vacuum gap

•Density gradient variable

•Small edge density

dx

dnx

dx

dnxnxn ≈+= 0)(

•Vacuum gap

•Constant density gradient

•Step density variable

≤−+

<=

xxdx

dnxxn

xx

xngapgap

gap

)(

0

)(0

TOPLHA Coupling Code

0 2 4 6 8 10

x 1012

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probe Density cm−3

Fra

ctio

n P

ower

Ref

lect

ed

No Vacuum Gap dn/dx=1*1020 m−4

60o

90o

120o

0 2 4 6 8 10

x 1012

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probe Density m−3

Fra

ctio

n P

ower

Ref

lect

ed

No Vacuum Gap dn/dx=1*1020 m−4

TOPLHA1D SlabBrambilla

• Under development at Politecnico di Torino and MIT

• Based on TOPICA code for ICRF antennas[3]

• 3-D model of antenna coupled to plasma response function from FELICE

• Calculates full S-parameter matrix

Dashed = TOPLHA

Solid = “Grill”

Code ComparisonCode Comparison

Finite Element Models

• CST and COMSOL

–Commercial 3-D RF packages

–Calculate S-parameter matrix

–Require small mesh size

• Very computationally intensive for large problems

–CST

• Cold plasma model included as part of simulation package

• Homogenous slabs only

–COMSOL Multiphysics

• Arbitrary dielectric tensor defined as a function of space

Experimental Results: L-Mode

0 2 4 6 8 10

x 1018

0.1

0.2

0.3

0.4

0.5

nprobe

[m−3]

Γ2

Long Pulse Coupling Data 2007

0 2 4 6 8 10

x 1018

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

nprobe

[m−3]

Γ2

Short Pulse Coupling Data

60o

90o

120o

• Low power (~200kW), 10ms pulses to prevent perturbing the

plasma

• High power (500+kW), long (100+ms) pulses show spread in

reflection coefficients, possibly due to modification of density

profile by LH waves

• Reflections are high at low line averaged densities, thus low edge

densities, desirable for efficient current drive

Long Pulse Coupling

• nedge data not directly comparable

from ’06 to ‘07

• Langmuir probes shortened from 3mm to

1.5mm

• Launcher proud of limiter by ~1mm

during 2006 run campaign

• Loss of Langmuir probes due to melting

• Launcher kept >1.5mm behind

limiter during 2007 run campaign

• Higher line average density required

to achieve best coupling with

launcher pulled back 1.5mm

– Lower current drive efficiency at high

density

0 1 2 3 4

x 1018

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

n edge [m−3]

Γ2

Long Pulse Coupling Data 2006

0 2 4 6 8 10

x 1018

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

n edge [m−3]

Γ2

Long Pulse Coupling Data 2007

n|| Spectrum Flexibility

−8 −6 −4 −2 0 2 4 6 80

0.5

1

1.5

2

2.5

n||

F(n

||)2

n|| Spectrum

60o

90o

120o

Peak n|| varied

from 1.5 to 3

without losing

directivity0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

50

100

150

Cou

pled

Pow

er (

kW)

Time (s)

Probe Density and LH Power for Shot 1070329012

60o

90o

120o

60o

90o

120o

0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

2

4

x 1017

Top

Den

sity

[m−

3 ]

Time (s)

0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

2

4

x 1017

Mid

. Den

sity

[m−

3 ]

Time (s)

0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

2

4

x 1017

Bot

. Den

sity

[m−

3 ]

Time (s)

DtopBtop

DmidBmid

Bbot

Launched n||

varied

throughout

single shot

Parametric Decay

4.5 4.55 4.6 4.65 4.7

x 109

−80

−60

−40

−20

0

20

Frequency [Hz]

dBm

4.5 4.55 4.6 4.65 4.7

x 109

−70

−60

−50

−40

−30

−20

−10

0

Frequency [Hz]

dBm

• PDI level increases logarithmically with

line average density up to 1.5e20 m-3

• ω/ωlh = 3 - 6 and Te~Ti indicates decay

into cold LH wave and ion cyclotron wave

or ion cyclotron quasi-mode[4]

2 4 6 8 10 12 14 16

x 1019

−55

−50

−45

−40

−35

−30

−25

−20

−15

−10

ne [m−3]

PD

I lev

el [d

B]

=LHωω

5 4 36

Noise Floor

Symmetric sidebands observed at

78MHz from fundamental during

ICRF

Line Averaged

Parametric Decay

0 0.5 1 1.5 2 2.5 3 3.5 4

x 1020

−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0Run = 1070824

Local ne [m−3]

PD

I lev

el [d

B]

L−Mode

H−Mode 4.3 4.4 4.5 4.6 4.7

x 109

−70

−60

−50

−40

−30

−20

−10

0

Frequency [Hz]

dBm

High Frequency Sweep, Shot 1070824029

0.5 1 1.5 2

x 108

−60

−55

−50

−45

−40

−35

−30

−25

−20

−15

Frequency [Hz]

dBm

Low Frequency Sweep, Shot 1070824029

• PDI level grows exponentially with density

then saturates above 2e20 m-3

• Local density determined from frequency shift

• Distance between peaks in high frequency

sweep matches maxima of low frequency

sweep

32 MHz

∆f=32 MHz

Scanning Probe Measurement

1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10

0.2

0.4

0.6

0.8

1

RF

Pro

be S

igna

l [V

]

Shot = 1070824011

1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10.86

0.88

0.9

0.92

0.94

0.96

Pro

be R

adiu

s [m

]

Time [s]

• Reciprocating RF probe located ~10cm above midplane on A-Port

• One electrode connected through 4.6 GHz bandpass filter to RF diode

• Localization of RF electric field in scrape off layer near R=91cm

A

B

C

D

E

K

J

G

F

H

GH FullLimiter

J ICRF

antenna

AB SplitLimiter

Ip

K midplane

Limiter

D&E ICRF

antennas

LH coupler

Improving Performance

• Poor coupling often caused by too little density at the

antenna during shots with low core density

• Other tokamaks (JET[5], ASDEX[6]) improve coupling

by injecting gas through capillaries magnetically

connected to LH antenna to raise the edge density

• Rerouted two spare NINJA capillaries to C-Port for

upcoming run campaign

• Details about the mechanism of gas ionization near LH

couplers or how to best increase electron density locally

near antenna without increasing global plasma density

still unclear

Coupling with ICRF and H-Mode

−200 −150 −100 −50 0 50 100 150 200−100

−80

−60

−40

−20

0

20

40

60

80

100

φ

θ

Shot 1070817013

LH Ant

D AntE Ant

J Ant

• LH operation with D-Port ICRF antenna unreliable

• E- and J-Port ICRF antennas causes fewer problems

• Langmuir probe data difficult to interpret when D and E antennas are operating due to voltage sheaths produced by ICRF

• Coupling with ICRF better during H-modes

0 1 2 3 4 5 6 7 8 9

x 1018

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

nprobe

[m−3]

Γ2

ICRF and H−Mode Coupling

LSN H−ModeUSN L−Mode

90o105o

*+

Conclusions and Future Work

• LHCD system successfully operated during ‘07 campaign

with ICRF and H-mode

• Parametric Decay observed

– Have not reached “density limit”

• Several codes under development to simulate coupling in

complex geometry with arbitrary density profiles

• Simple gas injection system installed for upcoming ’08

campaign

• New antenna for FY09

– X-mode reflectometer

• Measures density profile

• Not affected by ICRF sheaths

– 2nd generation gas injection system

References and Poster Download

[1] M. Brambilla. Nuc. Fus., 16(1):47-54, January 1976.

[2] J. Stevens, et al. Nuc. Fus., 21(10):1259-1264, October 1981.

[3] TP8.00138, TO4.00006, BP8.00068

[4] M. Porkolab. Physics of Fluids, 20, 2058, (1977).

[5] A. Ekedahl, et al., Nuc. Fus. 45, (2005).

[6] F. Leuterer, et al., Plasma Phys. and Cont. Fus. 33, (1991).

To download a copy of this poster, go to:

http://www.psfc.mit.edu/research/alcator/pubs/APS/APS2007/orlando2007index.htm

or

http://www.mit.edu/~wallaceg/wallace_aps_07.pdf