1/11

First Measurements of Parallel Wavenumber of Lower Hybrid Waves

S. G. Baek, G. M. Wallace, T. Shinya*, R. R. Parker, S. Shiraiwa, Y. Takase*

MIT Plasma Science and Fusion Center

*University of Tokyo

57th Annual Meeting of the Division of Plasma Physics

Savannah, Georgia

November 17, 2015

2/11

Motivation: Characterizing the LH wave propagation on the first pass is

crucial for predicting LHCD performance in future reactors.

• C-Mod LHCD system at 4.6 GHz operates at reactor-relevant conditions, except temperatures.

• In the strong single-pass damping regime (e.g., in ITER

and future reactors), parasitic loss mechanisms are

expected to be strongly mitigated.

• But, LH wave still needs to propagate across edge/SOL

plasma on the first pass (~ 15 cm in ITER as compared to

~ 2 cm in C-Mod.)

• Goal is to develop a diagnostic to characterize wave

propagation, in particular the parallel refractive index (n|| =

c k|| /ω0) of LH waves.

• With a new magnetic probe array, we carried out the first

proof-of-principle experiment.

See also:

I. Faust (Thu. Afternoon, VI2)

R. Parker (Monday CP12)

S. Shiraiwa (Monday CP12)

B. Mumgaard (Monday CP12)

1Wallace et al, Phys. Plasmas 17, 082508 (2010) 2Shiraiwa et al, RF Conference (2015)

O. Meneghini

MIT Ph.D Thesis S. Takahiro (Monday CP12)

Multi-Pass Regime in C-Mod

3/11

An array of three magnetic probes measures the dominant n|| of LH wave-

fields.

• Top row: 𝐵 ⊥ 𝐵0

• Bottom row: 𝐵 ||𝐵0

• Only the dominant single n|| can be obtained with the

three probes.

• Probe separation distance (Δx) = 6.5 mm: sensitive up to

n|| = 5.5.

1 cm Slit

Shield

Field Line Mapping Magnetic Probe w/ Shield Probe Head

20 cm

Δx = 6.5 mm

• Probe location below the midplane, and 108 deg

toroidally away from the launcher.

• Rprobe = RLCFS + 2~3 cm

108 deg.

1 cm Slit

Shield

4/11

Direct digitization of LH signals at 25 MHz allows performing cross-spectral

analysis.

Fixed LO

@ 275 MHz

CH1

Vari. LO

@ ~ 4.9 GHz

CH2

CH3

Dig

itiz

er

IF=

25 MHz

• Two-step frequency down-conversion from 4600 ± 25 MHz to 25

± 25 MHz.

• Digitizer is triggered every 10 msec at 100 MS/s.

• In each data segment, the data is further divided into 6 segments

to perform a cross spectral analysis.

- auto-power

- dominant n||

- magnitude squared coherence (γ2)

Spectrograms

5/11

In the standard (forward) field configuration, the probes detect coherent

wave-fields from the launcher.

C-Mod Tokamak Top View

Launcher

Probe Head

Location

Forward Field Reverse Field

Peak Power 1.3x10-2 ± 0.004 2.3x10-4 ± 0.0001

n|| 1.5 ± 0.05 1.1 ± 0.39

Coherence 0.94 ± 0.01 0.60 ± 0.10

Ray Trajectory

Ray Path in

Forward Field

Ray Path in

Reverse Field

6/11

Ray-tracing model predicts that wave-fields with low |n||| reach the probe

location.

• Ray have a limited radial penetration with

the decrease in the |n|||.

𝑣𝑔⊥

𝑣𝑔||≈

𝜔0

𝜔𝑝𝑒1 −

1

𝑛||2

ρ < 0.7 ρ > 0.9

Simulation Parameters:

𝑛 𝑒 ≈ 1.1 × 1020 m−3, 𝐼𝑝 = 1.0 MA.

7/11

The phase and amplitude responses as a function of applied n|| suggests that

the probes detects the wave-fields with |n||| ≈ 1.6.

• The dominant n|| is about 1.6, regardless of the

change in the applied peak n|| at the launcher.

Experimental parameters: 𝑛 𝑒 = 1.1 × 1020 m−3

• The decrease in the observed power is consistent

with the change in the antenna spectrum.

Exp.

Power at |n||| = 1.6

in Antenna

Spectrum

• In the applied spectrum from the LH launcher,

the spectral power content at |n|||= 1.6

decreases with the increase in the applied peak

|n|||.

8/11

• Qualitatively consistent with wave

propagation that shows a weaker radial

penetration with the increase in density.

As density increases, the probes detect wave-fields with higher |n||| as the

resonance cone shifts radially outward. .

• Applied peak n|| is fixed at 1.6. 𝑣𝑔⊥

𝑣𝑔||≈

𝜔0

𝜔𝑝𝑒1 −

1

𝑛||2

𝑛 𝑒 = 1.3 × 1020 m−3 𝑛 𝑒 = 1.5 × 1020 m−3

ρ < 0.9 ρ > 0.9

9/11

The observed power decrease correlates with the decrease in the spectral

power content at higher n||.

• The density dependence of the observe

power can be mapped to the n||

dependence.

• At higher density, the decrease in

coherence may implies a possible role of

wave-scattering1, also evidenced by the

broadened frequency spectrum (not

shown here).

1P. Bonoli, Phys. Fluids 25, 359 (1982)

10/11

• These waves1 are excited in front

of, or near the launcher at the

expense of source power at 4.6

GHz.

• The sideband power is lower by

an order of magnitude than the

main signal at 4.6 GHz.

Parametrically excited sideband LH waves are measured with a new

diagnostic.

• The measured n|| at 4.57 GHz tracks the n|| measured at 4.6

GHz.

• High n|| components might have propagated radially inward,

as seen in the previous ray-tracing results.

1M. Porkolab, Phys. Fluids 20, 2058 (1977).

11/11

Summary and Future Work

• The new diagnostic in SOL measures the coherence wave field from the launcher, in line with the ray-tracing

simulations.

• The observed power and n|| dependences is a combined effect of wave propagation and the probe location

being in SOL.

• Spectral broadening mechanisms are observed at high density, and we are continuing to investigate these

experimental results.

A preliminary design of a new

probe array Future Work:

• A new probe system is designed to be placed closer to the LH launcher by

another 36 deg.

• The increased number of probes will allow performing Fourier analysis to

evaluate the n|| spectrum (n|| = [ 0, 1.67, 3.35, 5.01])

12/11

Least Square Fitting

13/11

Dependence of the measured wave power on Ip

14/11

Spectral broadening is observed in the frequency spectra due to wave

scattering effect.

1P. Bonoli, Phys. Fluids 25, 359 (1982)

15/11

Ion cyclotron Sideband @ 4.57 GHz (Ip = 0.8 MA)