Microwave probe diagnostic for the lower hybrid four-way ...€¦ · l=0.001 m l=0.005 m l=0.010 m l=0.015 m l=0.020 m l=0.025 m l=0.050 m l=0.100 m Quickly scan the antenna phasing.

Microwave probe diagnostic for the lower hybridfour-way-splitter antenna on Alcator C-Mod

O. Meneghini, I. Faust, D. Johnson, R. Parker, S. Shiraiwa,D. Terry, R. Vieira, G. Wallace, S. Wukitch

MIT-PSFC

June 24, 2010

* Work supported by USDOE awards DE-FC02-99ER54512 and DE-AC02-76CH03073

O. Meneghini (MIT-PSFC) EPS 37th Plasma Conference 2010 - Dublin June 24, 2010 1 / 18

Abstract

The new lower hybrid launcher (LH2) of the Alcator C-Mod tokamak is based on anovel 4-way-splitter concept. A diagnostic based on the microwave probes concept[Jacquet et al. 1997] has been installed to verify the LH2 design and study thephysics of LH wave coupling. A total of 32 dedicated probes measure the forwardand reflected power in a carefully selected set of the active and passive waveguidesof the LH2 grill. A new technique which relies only on the microwave probes formeasuring the edge density profile in front of the launcher is proposed.


Lower Hybrid current drive (LHCD)

• Slow wave branch with n‖ > 1 forωci << ω << ωce

• Highly efficient non-inductivecurrent drive and current profilecontrol

• LH waves are well described by:• Cold plasma wave theory

(governs wave propagation)• Electron Landau Damping

(governs wave damping)

• n‖ is the control nob• Accessibility ↑ as n‖ ↑• ηELD ↑ as n‖ ↑• ηCD ↑ as n‖ ↓

Slow waveFast wave

ncutoff

Density [1E18 m-3]

N||=1.4

N||=1.5

N||=1.3

N2

Dispersion relation of fast (dashed) and slow (solid)waves in a cold plasma for Alcator C-Mod plasmaparameters


C-Mod LH2

4.6 GHz, 16x4 grill (60x7mm WGs), based on 4-way-splitter concept

RF probes

ReflectometerLangmuir probes

• Design goals:• Increase transmission

efficiency• Improve wave coupling• Lower breakdown probability

• Several diagnostics installed

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8

9

10

Ver

PLT

Asdex

Alcator-A

FT

PBX-M

Alcator-C

TSJET

C-Mod LH1 C-Mod LH2(10 200kW Klystrons)

C-Mod LH2(16 200kW Klystrons)

f2b (GHz cm)

Power Flux (kW/cm2)

Hard conditioning limit

Soft conditioning limit


C-Mod LH2


4-way-splitter concept

• Power splitting at front end of thelauncher

• Simplified low loss feeding network(WR187, copper)

• Input impedance is resilient touneven poloidal plasma load

• Flexible N‖ spectrum

• Directivity is almost independentof plasma load


4-way-splitter simulated performances

0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

Density at grill [1E18 m-3]

% average reflection coefficient

N||=1.6

N||=1.9

N||=2.2

-6 -4 -2 0 2 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Normalized power spectrum

N||

N||=1.6 , ne=0.5E18 [m-3]

N||=1.6 , ne=1.25E18 [m-3]

N||=1.9 , ne=0.5E18 [m-3]

N||=1.6 , ne=1.25E18 [m-3]

N||=2.2 , ne=1.25E18 [m-3]

||=2.2 , ne=0.5E18 [m-3]N

More power is coupled through the rowswhich have more favorable density.


Microwave probe diagnostic

• Two probes displaced by ∆ = λg/4sense the total wave field in thewaveguide

• Forward and reflected wave canthen be deduced

Einc =−(EAe−iK∆ + EB)e−iK(∆+L)

1− e−2iK∆

Eref =−(EAeiK∆ + EB)eiK(∆+L)

1− e2iK∆

Probes arrangement:

AD A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 ADBD B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15 B16 BDCD C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 CDDD D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16 DD

Probes mounted on modules fed directly by a klystronProbes mounted on modules fed by a split klystronProbes mounted on dummy columnsUnused probes housings

e-, current drive direction


Microwave probe diagnostic

• Coupling of ≈ −65 ± 2 dB:• Microwaves coupled through

small circular hole• Central conductor is welded to

the opposite side of the housing

• Silicon-Dioxide (SiO2) cables areused in-vessel to ensure:

• Stability of phase with respectto temperature variations

• Low losses

• Phase and amplitude are measuredby off-the-shelf homodyne IQdetectors

• 250 KHz digitization rate


Measuring the edge density profile

Common practice to use the ambiguity of the edge density profile to makecoupling simulations fit to the experimental measurements

0 2 4 6 8 10

x 1018

0

0.2

0.4

0.6

0.8

1

Probe Density [m−3

]

Γ2

λ = 40000 [m−1

]

n||=1.5

n||=2.3

n||=3.1

Simulation vs experimental measurements for LH1, G. Wallace

Detail of langmuir probes and reflectometer horns on LH2

Necessity to eliminate free parameters:

• Self-consistent validation of LHcoupling codes

• Optimize design of future antennas forspecific plasma profiles

Measurement of density profile is on LH2:

• SOL X-mode reflectometer at threepoloidal locations

• Langmuir probes of different length(1 mm and 2 mm) estimate edgedensity and gradient

• Phase scan method, a new techniqueto fit a model density profile using linearcoupling theory


Phase scan method - General idea

Reflection coefficient strongly dependson the N‖ of the launched wave (i.e.antenna phasing)

0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

phase

Γ

Γ as a function of phasing (ne0

=4E17[m−3

])

λ=0.001 m

λ=0.005 m

λ=0.010 m

λ=0.015 m

λ=0.020 m

λ=0.025 m

λ=0.050 m

λ=0.100 m

• Quickly scan the antenna phasing.Assuming that linear theory holdstrue, the density profile can beinferred by the least square fittingof the measured reflectioncoefficients to the ones predictedby linear coupling theory

• LH grill antenna as a edge densityprofile diagnostic

• Average antenna reflectioncoefficient Average density profile

• On LH2, microwave probes allowdensity measurement at each row

• On LH2, X-mode reflectometer willbe used to validate this method


Phase scan method - Example

• E.g. Assume linear densityprofile in the experimentne0 = 9E17 [m−3] andλ = 15E−3 [mm] was to bemeasured

• Least square with fit twovariables linear density model:ne0 and λ

• ALOHA1D code, in the range1.2× 1017 < ne0 < 30× 1017

m−3 and 0.1 < λ < 100 mm• RMS error of the density

profile fitting procedure, for a50 to 145 degrees phase scan(to keep experimental Γ2

within acceptable limits)

5 10 15 20 25 30

10

20

30

40

50

60

70

80

90

100

RMS error for ne0

and λ fit

ne0

[10−17

m]

λ [10

−3 m

]


Microwave probes and LH2 calibration

Probes calibration done in two stages:

• Probe assembly (invessel, passive):probes, SiO2 cables, feedtrhough

Relative: Obsorber loads in each of thefingers of a 4-way-splitter andmeasure coupling of incidentwave from each of the probes.

Absolute: Measure true amplitude andphase of the incident wave withOdaptor

• IQ detector assembly: IQ detectors,

amplifiers, attenuators, filters, DC breaks

• Back-mapping procedure(compensates for IQnon-linearities). Proven to beresilient to temperaturevariations. Assumes constantamplitude LO signal.

Obsorber: ECCOSORB 117 piramids comb (-30 dB

simulated, -27 dB measured) 1.5cm insertion depth

Odaptor: reduced waveguide to WR187 adaptor with

low insertion loss (-30 dB simulated, -20 dB

measured) at 4.6 GHz


1D simulation of grill antenna

The LH grill antenna theory gives analytic equations for the electric field and theplasma surface impedance for the linear density profile [1,2].Simulation results were tested against those Airy function based expressions,showing very good agreement.

N ||

-14 -12 -10 -8 -6 -4 -2 0

1.5

1.0

0.5

0

Z

Gamma

3000

2000

1000

0

Anal

ytic

eq.

is in

valid

[1]M. Brambilla, Nulear Fusion,16, 47 (1976)

[2]S. F. Knowlton and M. Porkolab, Nulear Fusion, 29, 1543 (1989)O. Meneghini (MIT-PSFC) EPS 37th Plasma Conference 2010 - Dublin June 24, 2010 14 / 18

2D model of Grill antenna

The modeling of cold plasma + collisions can be done in a straightforward manner.The following grill antenna simulation shows the well-known resonant conepropagation [P. Bellan and M. Porkolab, PRL 34 (1975) 124 ].

• Port boundary conditions (specify the forward power at the wave guide)

• Radiative boundary implemented by collisions

• Cold plasma dielectric εr

• Collisions are introduced by imaginary part of mass

Phasing

WG ports

Pla

sma


S matrix shows good agreement with TOPLHA

Comparison with TOPLHA (a LH antenna code based on the boundary elementmethod) shows good agreement with FEM model.

ne

ne0 =0.5×1018m-3

dne/dx=1.0×20m-4

ne0 =0.5×1018m-3

dne/dx=2.5×20m-4

ne0 =2.0×1018m-3

dne/dx=1.0×20m-4

WG# WG# WG#

• Thick lines : TOPLHA

• Thin lines : 2D FEMdne/dr

ne0

r

LH grill

Vgap


3D cold plasma modeling with FEM

The remaining difference between COMSOL and TOPLHA motivated the 3Dsimulation of the grill antenna.

3D antenna model of the traditional grill

COMSOLTOPLHA

Comparison of the waveguide reflectivitycalculated by COMSOL and TOPLHA

Coupling shows good agreement between between COMSOL, TOPLHA andALOHA-2D (not shown here).


3D FEM simulation shows better agreement

ne0 =0.5×1018m-3, dne/dx=1.0×20m-4

ne0 =0.5×1018m-3, dne/dx=2.5×20m-4

2D COMSOL and TOPLHA 3D COMSOL and TOPLHA


Microwave probe diagnostic for the lower hybrid four-way ...€¦ · l=0.001 m l=0.005 m l=0.010 m l=0.015 m l=0.020 m l=0.025 m l=0.050 m l=0.100 m Quickly scan the antenna phasing.

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