Slow wave measurement using the WVU 300 GHz collective scattering diagnosticRobert Hardin, Earl Scime, Alex Hansen Department of Physics, West Virginia University

Recent experiments in helicon plasma sources by Krämer et al. [2006] and Kwak et al. [2006] have employed mm-wave technology to investigate electron densities in a pulsed source and density fluctuations due to ion -acoustic waves, respectively. Measurement of the temporal and spatially resolved electron densities by Kramer was accomplished with a mm-wave interferometer. The ion -acoustic waves measured by Kwak employed a collective scattering system with a heterodyne detection scheme. The WVU 300 GHz quasi-optical collective scattering diagnostic, uses a homodyne detection method similar to the interferometer, designed to measure the “slow” wave. Experimental parameters observed to heat ions in the plasma edge in conjunction with theoretically calculated wave numbers associated with the slow wave, as seen in Kline et al. [2002], were examined for evidence of the slow wave using the mm-scattering diagnostic. Here we present initial wave number spectrum measurements of the slow wave in a helicon plasma source.

M. Krämer, B. Clarenbach, and W. Kaiser, Plasma Sources Sci. Technol. 15, 332 (2006).J.G. Kwak, S.J. Wang, S.K. Kim, and S. Cho, Phys. Plasmas 13, 074503 (2006).J.L. Kline, E.E. Scime, R.F. Boivin, A.M. Keesee, and X. Sun, Pl asma Sources Sci. Technol. 11, 413 (2002).

Abstract - Motivation

Wave number predictions based on the dispersion relation developed by S. Cho [Phys. Plasmas 7, 417 (2000)].

Aluminum alignment wedges cut to simulate scattering angles of 6 0, 70, 80, and 90 degrees were employed to evaluate the spatial coverage and angular resolution of the collection optics. With the collection mirror aligned to the appropriate radial location and scattering angle, the alignment wedge was moved to different locations in the incident beam across the vacuum vessel to determine the angular resolution. The measured 1/e2 folding width for the collection optics is comparable to the ZEMAX optical design predictions.

0

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-6 -4 -2 0 2 4 6

90 o Scattering Angle

80o Scattering Angle

70 o Scattering Angle

60o Scattering Angle

Co

llect

ion

Mir

ror

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catio

n [c

m]

Plasma Radius [cm]

0

1 10 -6

2 10 -6

3 10 -6

4 10 -6

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-8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0

Scattered Angle = 80o

Sca

tter

ed P

ow

er [W

att]

Plasma Radius [cm]

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1

2

1

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Angular Resolution and Spatial Localization of Collection Optics Homodyne detection scheme proof-of-principle

A technique for bench -marking the homodyne detection scheme is the insertion of a rotating aluminum wheel to create a Doppler frequency shift of the incident beam similar to that reported by J. Choi et al. [Rev. Sci. Instrum 76, 023109 (2005)]. The use of a solid rotating wheel allows for a continuous signal as well as greater ease in alignment as compared to a single wire scattering target used in T. Rhodes et al. [Rev. Sci. Instrum. 77, 10E922 (2006)]. The maximum rotation frequency of the wheel is 8000 rpm (~133 Hz) corresponding to a Doppler shift of approximately 190 kHz for a wheel 4.5” in diameter. Initial experiments using homodyne detection yielded no result, so the reference leg was removed and the source was chirped at 3 MHz to simulate an intermediate freq uency. Doppler shifts were observed in this configuration but at approximately twice the wheel rotation frequency. This is likely due to the entire wheel being a radiator, thus leading us to attempt the ro tating wire technique. With Doppler shifts up to only 240 Hz, the homodyne scheme may have worked, but with such low frequencies the signal would have been well below the noise.

300 GHz Detector Issues

• The 300 GHz Schottky diode detector is ultra sensitive to any electrostatic discharge. • Since the detector is in such a high RF environment, it is essen tial to protect the detector as

much as possible. The following precautions have been taken to p rotect the detector: • A grounded ¼” thick copper box houses the detector with only a single aperture for the

potter horn, and 2 bulkhead connectors (1 for DC bias in, and 1 for IF signal out).• A RF shielded box for the DC bias supply including a -90 dB line filter in conjunction

with triple shielded SMA cables to the source and detector.• The 60 dB voltage amplifier, powered by batteries, is inside the detector box to help eliminate

RF pickup. However, the amplifier is not currently used in case it was the cause of the detector damage.

• A high pass dichroic plate filter centered @ 300 GHz may be added to help shield the ambient RF from the aperture for the detector potter horn.

( ) 0

58.1

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NrN +

−=

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Kline et al. [2002] originally compared the calculated dispersion relation to experimental data and showed a possible connection between edge ion heating due to Landau damping near the lower hybrid resonance and the existence of the “Slow wave”. Re-evaluating the dispersion relation for current experimental parameters allows us to predict the expected measurable wave number range at a specific spatial location (k⊥ ~ 60 - 90 rad/cm) for the 300 GHz scattering diagnostic. Currently thedispersion relation code assumes a uniform neutral density. However, recent work by Keesee (Poster # JP8-157 this session) demonstrates that HELIX plasmas can have a radially varying neutral density profile. Since neutral collisions are included in the dispersion relation, the addition of a radially dependant neutral density profile modifies the range of possible wave numbers.

Based on the radial ion density profile with N0 = 1x10 13 cm-3 and typical HELIX operating parameters, an example of how the calculated wave numbers vary across the plasma radius are shown in plots A and B. As the plasma density decreases from the central peak, th e magnitude of the wave numbers increase, shift to lower frequency following the lower hybrid resonance (indicated by the black lines), and narrow in the parameter space. As a point of reference, the maximum wave number of 150 rad/cm at a frequency of 11 MHz in plot B corresponds to an ion thermal velocity ~15% of the wave phase velocity. Increases in the perpendicular ion temperature or a decrease in the collisions would cause the Vth/Vφ ratio to allow for greater Landau damping.

R = 1.5 cm R = 4.5 cm

A B

Assumptions used in dispersion relation solver:

•Ion density Profile à

•Ti = 0.2 eV

•Te = 5 eV

•k|| = 0.3 rad/cm

•Neutral Pressure = 6.7 mTorr

•Neutral Temperature = 0.02 eV

Based on the measured angular resolution of the collection optics, we can calculate the centroidof the target measurement location in the plasma for different scattering angles and position of the collection mirror. Since the collection mirror is on a linear translation stage, the spatial location associated with the maximum signal for each scattering measurement corresponds to different locations in the plasma. Even though the “Slow wave” is typically considered to be an edge wave, the measurable wave number spectrum as predicted by the cold plasma dispersion relation, shows that it may be possible to measure the wave through the entire plasma column for certain plasma parameters. For scattering between 60 o and 70 o, the collection coverage is limited to only about half the plasma radius, while collection of scattered microwave signal from 70o up to 90 o can be accomplished for nearly the entire plasma diameter.

With the measurable wave number spectra from 60-90 rad/cm dictated by the vacuum chamber geometry and collection optics, we can use th e dispersion relation to predict the parameters most likely to pro duce measureable wave numbers. Plots C to F illustrate the “radial” density location of the measurable wave numbers for two common RF sourcefrequencies and on axis peak densities. While plots D and E show limited radial locations, C and F exhibit evidence that, for the right conditions, measurable spectra could be present through the entire plasma. Setting the collection mirror to a particular radial location and collection angle, a measurement of the dependence of the wave number spectrum on magnetic field may be accomplished by stepping through differentmagnetic field strengths.

N0

= 1x

1012

cm-3

9.5 MHz 13.5 MHz

C E

D F

N0

= 1x

1013

cm-3

Summary:• First tests of scattering system was applied at parameters believed to exhibit the

existence of the slow wave in Kline et al. was unsuccessful. • A predictive dispersion relation model has been developed to identify the

optimal plasma parameters for generating measurable wave number spectra given the constraints of the diagnostic system.

• A proof-of-principle test of the homodyne detection scheme using a mechanically driven Doppler shift was successful.

• Electrical discharge mitigating procedures have been developed to protect the ultra-sensitive Schottky diode detector.

θ

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0.971.941.830.9460

0.971.471.831.2470

0.971.061.831.7280

0.971.361.831.3490

ZEMAX Div angle [deg]

Divergence angle [deg]

ZEMAX waist [cm]

Measured waist (1/e2

point) [cm]

Scattered Angle [deg]

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2.999900 3.000000 3.000100 3.000200 3.000300

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