A heterodyne detection scheme is combined with a 10.59 μm CO2 laser dispersion interferometer for the first time to allow large bandwidth measurements in the 10-100 MHz range. The approach employed utilizes a 40 MHz acousto-optic cell operating on the frequency doubled CO2 beam which is obtained using a high 2nd harmonic conversion efficiency orientation patterned gallium arsenide crystal. The measured standard deviation of the line integrated electron density equivalent phase resolution obtained with digital phase demodulation technique, is 4 × 1017 m−2. Air flow was found to significantly affect the baseline of the phase signal, which an optical table cover was able to reduce considerably. The heterodyne dispersion interferometer (DI) approach is found to be robustly insensitive to motion, with measured phase shifts below baseline drifts even in the presence of several centimeters of retroreflector induced path length variations. Plasma induced dispersion was simulated with a wedged ZnSe plate and the measured DI phase shifts are consistent with expectations.

Interferometry is a common method employed to measure the electron density of plasmas. The measured phase shift ϕ of a probe beam is determined by changes in the optical path length, which is the line integral of the electron density (ne) dependent refractive index N of the optical medium (in this case plasma),

ϕ=2πλ0L1Ndl=2πλ0L11ωpe2ω2dl=2πλ0L11e2ω2ϵ0menedl.
(1)

Here, λ is the wavelength of the probe beam, L is the physical path length, ωpe is the plasma frequency, ω is the frequency of the probe beam, e is the elementary charge, ϵ0 is the permittivity, and me is the mass of the electron. The line-integrated electron density can be determined from ϕ1 as follows, supposing ωpeω:

ϕπλe2ω2ϵ0me0Lnedl=e2λ4πc2ϵ0me0Lnedl,
(2)
0Lnedl=4πc2ϵ0mee2λϕ.
(3)

Mechanical vibrations, especially parallel to the beam path, cause additional phase shifts through physical changes in L (which are often much larger than the plasma induced phase shift of interest and result in measurement errors). Three successful approaches used to deal with this in the past include: vibration isolation systems such as a pneumatically suspended system,2,3 two-color interferometers in which two co-linear, separate wavelength interferometers are employed,4–7 and the dispersion interferometer8,9 approach which is discussed further here.

While a dispersion interferometer (DI)10 is basically a type of two-color interferometer, it is intrinsically less sensitive to the mechanical vibrations. This is because the DI measures the phase shift which is related only to the dispersive component in a medium—such as that from the plasma induced optical path length difference. Even if L changes in the air due to the vibrations, the resultant phase shift measured with an ideal DI system is quite small, making it particularly attractive when vibration isolation is difficult.11 The DI is also able to provide useful measurements even if the air pressure along the beam path changes significantly.12,13 Although it is the focus of this work, plasma density measurements by the DI approach are not limited to fusion plasmas, they find significant utility in the measurement of atmospheric pressure plasmas as well. Generally speaking, it is difficult to measure the electron density of atmospheric pressure plasmas with high resolution using a conventional interferometer. This is because the plasma heats the surrounding gas and the resulting expansion of the gas causes changes in the refractive index of air Nair which leads to an additional phase shift in a conventional interferometer. The additional phase signal is much larger than that induced by the plasma. On the other hand, since the dispersion of a dry gas is quite small, the DI is insensitive to this effect and can be used to measure the electron density despite changes in Nair.

To date, several DIs have been installed and operated successfully on fusion plasma devices worldwide.10,11,14–17 Despite the presence of significant vibration, all were shown to allow accurate plasma density measurements. One of the shortcomings of the simplest DI approach, however, is that it is basically a homodyne configuration. The measured interference signal I is given by

I=I1+I2+2I1I2cos3/2ϕ+ϕ0,
(4)

where I1, I2 are detected intensities of two second harmonic laser beams and ϕ0 is the initial phase. Since I1 and I2 are necessary to extract ϕ, they are measured by a calibration experiment without plasmas. If I1 and I2 vary during plasma operation, the variations lead to measurement errors. On fusion devices, I1 and I2 can vary due to alignment changes, refraction of the laser beams in plasmas, and due to instabilities of laser oscillation. In addition to this problem, ne cannot be determined uniquely when the range of ϕ is larger than π. This means that the dynamic range of the density measurement is limited.

In order to overcome these problems, several different approaches have been tested, namely, phase modulation11,17 and quadrature detection.15 These approaches reduce the measurement errors caused by intensity variations and increase the dynamic range. On the Large Helical Device (LHD), a photoelastic modulator (PEM) is used for phase modulation.11 Since the PEM is a resonant modulator, drive frequency noise and jitter are small and high density resolution measurements are possible. However, the present upper limit of the PEM modulation frequency is 50 kHz at most. Whereas this temporal resolution is sufficient for density control, it is not sufficient to measure density fluctuations of interest which can have frequencies extending into the MHz range for typical fusion device configurations.

In this paper, a large bandwidth heterodyne DI utilizing a 40 MHz acousto-optic cell and a high efficiency orientation patterned gallium arsenide (OP-GaAs) crystal21 is described. In Sec. II, the principle of the heterodyne DI operation is described. The optical system and results of the proof of principle experiments are shown in the Secs. III and IV, respectively. Sec. V gives a summary and discusses future work.

A schematic view of the heterodyne DI is shown in Fig. 1. After generating the second harmonic component with a nonlinear crystal, the fundamental and the second harmonic components are separated by a beam splitter. An acousto-optic modulator (AOM) is used to shift the frequency of the transmitted component by Δω. The two components are then recombined again and the mixed beam is used as a probe beam. After passing through a plasma, another second harmonic component is generated from the fundamental component. The electric fields of the second harmonic components E1 and E2, which are generated before and after the plasma, are given as follows, respectively,

E1=E1,0sin2ω+Δωt+ϕ/2+2πΔl/λ/2,
(5)
E2=E2,0sin2ωt+ϕ+2πΔl/λ,
(6)

where ω is the angular frequency of the laser source, ϕ is the phase shift caused by the plasma, Δl is the change in the path length due to the mechanical vibrations, and λ is the wavelength. In order to detect the interference signal between two second harmonic components, a filter that blocks the fundamental component is used. The detected interference signal Ip is shown below,

Ip=E1+E22=E1,02+E2,02/2+E1,0E2,0cosΔωt3/2ϕ=I1+I2+2I1I2cosΔωt3/2ϕ,I1=E1,02/2,I2=E2,02/2.
(7)

Compared with the reference signal cosΔωt from a driver of the AOM, the phase shift ϕ, which is proportional to the line integrated electron density, can be obtained. In the same way as the conventional heterodyne interferometer, the heterodyne DI is not an amplitude based measurement and hence is less affected by the intensity variations. As a further refinement, an optical local oscillator could be formed with a third crystal instead of the electronic reference signal. The recombined laser beams would be divided into two (probe and reference chords) immediately after the AO cell. In the case of an analog phase comparator,4 the temporal resolution is determined by the frequency Δω of the interference signal. Generally speaking, the frequency shift given by the AO cell can be selected from approximately 10–100 MHz and is sufficient for high-frequency density fluctuations caused by Alfvén eigenmodes18 and even possibly ion cyclotron range of instabilities (several tens MHz).19 A digital phase comparator can further improve both the temporal and obtainable density resolutions.20 Compared with a PEM based DI, whose maximum modulation frequency capability is 50 kHz,11 the heterodyne DI is capable of three orders of magnitude faster temporal resolution. Further, these phase extraction methods are the same as those used for conventional interferometers. Hence phase comparators which are used in the conventional interferometer are available without any modifications.

FIG. 1.

Principle of the heterodyne dispersion interferometer.

FIG. 1.

Principle of the heterodyne dispersion interferometer.

Close modal

An advantage of using a frequency doubling crystal is that the two colors are almost aligned and co-linear with each other. For example, the displacement of the two wavelengths is about 0.1 mm, which is caused by walk-off in a nonlinear crystal AgGaSe2. For example, since the beam diameters of 10.59 and 5.3 μm laser light are typically larger than several mm, a displacement of 0.1 mm will be almost negligible. In the technique described here, the second harmonic beam must be separated from the fundamental beam in order to direct it through the AO cell. This destroys the alignment between the two beams that must be re-established. The phase resolution is affected by the accuracy of combination of the fundamental and the second harmonic beams after the phase shift with the AO cell. The phase shifts caused by the vibrations are cancelled by superimposing two beams. If the co-linearity and wavefronts of the two probing beams, or in the final stage, the two second harmonic components are not matched, the vibration components will not be cancelled and the residual phase shift will show up as noise on the density measurement. Hence careful beam alignment is necessary to obtain good phase (density) resolution. It is noted, however, that it is basically impossible to perfectly match the wavefronts in all DI applications due to the difference in wavelength, dispersive optics, etc. In that context, reflective optics should be used in the DI instead of the transmissive optics such as a lens. An exception is a vacuum window which must be transmissive to both wavelengths.

Figures 2(a) and 2(b) are an illustration and a picture of the optical system, respectively, for proof-of-principle experiments. The light source is a continuous-wave and RF-excited Coherent GEM Select 50 CO2 laser, which is operated with an output power and a wavelength of 7 W and 10.59 μm, respectively. A nonlinear optical material OP-GaAs21 is used for the second harmonic generation. The advantage of the OP-GaAs is its high conversion efficiency. The OP-GaAs is put into an oven and operated at a temperature of 60 °C to be the maximum conversion efficiency. Considering laser absorption (Pabs = P0 (1 − exp(−αt)) = 7 (W) ∗ (1 − exp(0.01(cm−1) ∗ 3(cm))) = 0.2 (W)), the temperature is gradually increased for about 1 h to be thermal equilibrium. As for thermal lensing, which limits the injection power to some crystals, it will be negligible for OP-GaAs because the thermal conductivity of GaAs is higher than other crystals (like AgGaSe2 and ZnGeP2) and the gradient of the refractivity (caused by the temperature gradient) is expected to be small. At 7 W incident 10.59 μm power, the generated second harmonic power is 3 mW, which is about 60 times higher than that generated with an AgGaSe2.11 As mentioned above, accurate beam alignment is necessary for good density resolution. Hence a second harmonic beam power, which is sufficient to visualize the spot with a luminescent plate or an IR camera, is required: practically about 1 mW. In principle, the heterodyne technique is possible even for a DI using a conventional lower conversion efficiency crystal, however, an OP-GaAs based system is significantly simplified, from the viewpoint of beam alignment, due to the higher second harmonic power.

FIG. 2.

An illustration (a) and a photograph (b) of the optical system for the proof-of-principle experiments. Size of the optical table is 120 × 180 cm. The path length from the laser output to the detector is 5.3 m.

FIG. 2.

An illustration (a) and a photograph (b) of the optical system for the proof-of-principle experiments. Size of the optical table is 120 × 180 cm. The path length from the laser output to the detector is 5.3 m.

Close modal

A ZnSe beam splitter with a custom coating reflects the second harmonic component and passes the fundamental, after which, the frequency of the second harmonic is shifted by 40 MHz upon exiting the AO cell. In principle, either the fundamental or second harmonic components could be frequency shifted. Here, we chose to shift the second harmonic because the AO cell is not 100% efficient (only about 60%–75% of the incident beam is frequency shifted by 40 MHz). Since the conversion in the frequency doubling crystals is proportional to squared power, a reduction in second harmonic power results in a larger signal on the final detector than the same fraction reduction in fundamental power at the AO cell stage. After combining the fundamental and the second harmonic components again, the laser beam is expanded with a beam expander and sent to a corner cube mirror (CCM), which, in a plasma measurement application would be installed on the other side of the plasma.

A plasma is simulated with a wedged ZnSe plate, which is scanned perpendicularly to the beam path to shift the phase. The laser beam is then focused at another OP-GaAs crystal in which some of the fundamental is again converted into frequency-unshifted second harmonic radiation. The fundamental component is removed with another ZnSe harmonic separator and a sapphire plate (that acts as an optical filter), which 10.59 μm component cannot transmit. Then the interference signal between two second harmonic components is detected. The total path length from the laser output to the detector is 5.3 m. The detector is an uncooled HgCdTe VIGO PVMI-8 with a high gain DC coupled pre-amplifier built by Palomar Scientific Instruments. DC coupling aids alignment significantly. The 40 MHz interference and the reference signals are then sent to a phase demodulator or are digitized directly with an oscilloscope to apply digital phase demodulation offline.

The detected interference signals are shown in Figs. 3(a) and 3(b). The signals are digitized with a sampling frequency of 500 MHz and offline digital phase demodulation20 is applied to the digitized signals. As shown in Fig. 3(a), the beat amplitude is constant. The calculated phase difference with different bandwidths of the bandpass filter applied to each signal is shown in Fig. 3(c) and the standard deviation as a function of the bandwidth for 1 s is shown in Fig. 3(d). When the bandwidth is 10 MHz, the standard deviation of the line integrated electron density is about 4 × 1017 m−2. This bandwidth is sufficient for fluctuation measurements, and fast transient events such as pellet and massive gas jet injection. Alfvén eigenmodes (AEs), whose frequency is typically lower than 500 kHz, are easily detected. If this dispersion interferometer is applied to a radial double pass view on DIII-D with a path length in a plasma L of about 2.6 m and an electron density of 1.6 × 1019 m−3, a standard deviation of 4 × 1017 m−2 would be better than 1% line-averaged density resolution.

FIG. 3.

(a) Detected interference signal. (b) Expanded interference and reference signals. (c) Phase difference between the interference and reference signals by offline digital phase demodulation with different bandwidth Δf of the bandpass filter. (d) Standard deviation as a function of Δf.

FIG. 3.

(a) Detected interference signal. (b) Expanded interference and reference signals. (c) Phase difference between the interference and reference signals by offline digital phase demodulation with different bandwidth Δf of the bandpass filter. (d) Standard deviation as a function of Δf.

Close modal

For application to long pulse discharges, such as those expected in ITER and future fusion devices, long time scale baseline drifts must be minimized. Recently, LHD and Experimental Advanced Superconducting Tokamak (EAST) achieved 48 min-long22 and 400 s-long discharges,23 respectively. WEST24 and JT-60SA25 are also planning steady-state discharges, 1000 s and 100 s, respectively. Figure 4 shows 100 s baseline drift data for three separate records obtained using a digital phase comparator.26 These data were digitized in the same condition and the differences in drift are due to, as of yet, unknown factors. The worst case drift observed over a 100 s interval was approximately 20°, which corresponds to a line density of 8 × 1018 m−2, at a maximum. On the other hand, the standard deviation of the phase signal for 1 s is 1°, which corresponds to 4 × 1017 m−2. Hence the obtainable density resolution for long pulse discharges, in this particular case, would be determined by the baseline drifts. These were the first data obtained in this configuration and it is expected that these drifts can be reduced significantly. Several factors contribute to these drifts, for instance, the temperature of the OP-GaAs crystals was observed to change in time. The temperature variations change not only the conversion efficiency, but also add uncompensated optical path length changes. Also, air flow, which means inhomogeneous, is a large factor because the refractive index of the air depends on the partial pressure of H2O, the temperature, and the density of the air. During the bench tests described here, the optical table was covered to avoid the largest perturbations caused by air conditioning in the room. Figure 5 shows changes in the baseline drift when the optical table cover is opened or closed during periods when the air conditioner is on. It is obvious that both the noise and slower drift are larger after the cover is opened.

FIG. 4.

The baseline phase drifts for three separate 100 s intervals, overlaid on the same time axis.

FIG. 4.

The baseline phase drifts for three separate 100 s intervals, overlaid on the same time axis.

Close modal
FIG. 5.

The baseline phase data with the optical table cover closed (t < 50 s) and open (t > 50 s).

FIG. 5.

The baseline phase data with the optical table cover closed (t < 50 s) and open (t > 50 s).

Close modal

The phase shifts due to mechanical vibrations and the air are largely cancelled along the optical path where the fundamental and the second harmonic components overlap. The heterodyne dispersion interferometer, however, has a portion of the optical system where the fundamental and second harmonic probing beams do not share a common path; the region where the frequency shift is introduced by the AO cell. If the density of the air varies in this region or there are vibrations of any of these components, uncompensated phase shifts and baseline drifts can result. For reduction of the impact of air perturbations in this region, the optical system around the AO cell should be made as compact as possible. In addition, a special cover made to thermally insulate the optical system around the AO cell may be effective at reducing gradual uncompensated changes of the phase, such as the drifts shown in Fig. 4. Enclosing the optics under a moderate vacuum might also be effective. Another option to ameliorate the impact of the non-common path portion of the heterodyne DI is to split off a portion of the two beams and introduce a third frequency doubling crystal and detector system before the beams are sent to the plasma (or wedge). This detector can then serve as the 40 MHz reference signal as opposed to the AO drive signal. In this way, an optical local oscillator is formed and any uncompensated phase can be removed from the final detector signal.

Several tests of the heterodyne DI’s ability to cancel vibration were carried out. The most compelling of which was the translation of the CCM through distances of several centimeters. In this test, the CCM was linearly translated in the direction of beam propagation back and forth by approximately 12 mm (the arrow in Fig. 2(a) indicates the direction) and no noticeable impact on the noise floor was observed. This is quantified in Fig. 6. The phase shifts caused by the CCM translation are not recognizable and are smaller than the baseline drifts. Figure 7 shows the cancellation of the mechanical vibrations as different optical components are tapped periodically with an impact tool to simulate high frequency vibrations similar with the ones occurring during disruptions, for example. The tapping experiment can easily simulate the system response to large impulsive and high frequency vibration components up to about ∼1 kHz. Similar instantaneous physical impacts possibly occur at the excitation of a central solenoid and at the disruptions. When the mirror next to the AO cell is tapped, the phase shift changes by approximately ±300° as shown in Figure 7. As mentioned, this is expected since the fundamental and second harmonic components are not common path at this point. When the same procedure is carried out after the beams are recombined, however, the vibration induced phase variation is well cancelled. When the CCM is tapped, very little leakage is observed. When the mirror after the CCM incident angle 45° is tapped, the amplitude of the vibrations is reduced to about 5% of that when the beams are not overlapping. A possible reason of this difference and any vibration leakage in general, is as follows. Vibrations of the mirror with a 45° angle of incidence cause displacements of the beam spot perpendicular to the beam path, those of the CCM cause displacements parallel to the beam path. If the wavefronts of the combined two beams are not superposed completely or have different curvature, perpendicular motion will cause uncompensated phase variations. This effect highlights the importance of a careful beam alignment as well as optimization of the optical setup such that the two different color beams are similar in size and have similar divergence.

FIG. 6.

The phase signal when the CCM is translated back and forth approximately 12 mm several times during data sampling.

FIG. 6.

The phase signal when the CCM is translated back and forth approximately 12 mm several times during data sampling.

Close modal
FIG. 7.

Simulation of vibrations by tapping various DI mirrors with a tool. Mirrors and the CCM are tapped every 10 s.

FIG. 7.

Simulation of vibrations by tapping various DI mirrors with a tool. Mirrors and the CCM are tapped every 10 s.

Close modal

In order to introduce dispersion and simulate the impact of a plasma, a wedged ZnSe plate is scanned perpendicular to the beam path. The change in the phase ϕs is given by the following expression:

ϕS=4πdtanθλ(n2ωnω),
(8)

where d is the scanned distance, θ is the wedged angle, and nω and n are the refractive indexes at the fundamental and the second harmonic components, respectively. The evaluated wedged angle with the dispersion interferometer on LHD is 0.236°11 (specification of fabrication: 0.25° ± 0.05°) and the expected phase shift is 7.21° mm−1. The wedge plate was moved back and forth by 20 mm for 20 s and the measured phase shift is shown in Fig. 8. The evaluated phase shift is 7.17° mm−1 which is in good agreement with the expectation, showing not only is vibration effectively cancelled but the heterodyne DI produces quality measurements of dispersion.

FIG. 8.

Data showing the DI measured phase shift as a ZnSe wedge is translated back and forth across the beam path.

FIG. 8.

Data showing the DI measured phase shift as a ZnSe wedge is translated back and forth across the beam path.

Close modal

This paper presented the design and initial results from a CO2 laser based heterodyne dispersion interferometer. This interferometer type can reduce measurement errors caused by the mechanical vibrations, which is one of the disadvantages of a conventional interferometer. Previous dispersion interferometer implementations suffer from the detected intensity variations and limited temporal resolution. The heterodyne dispersion interferometer described here, with a beat frequency of 40 MHz, can realize sufficient temporal resolution for large bandwidth density fluctuation measurements as well as fast transients and, is insensitive to the variations of the detected intensities. An OP-GaAs frequency doubling crystal, which has a high second harmonic generation efficiency, is used for precise beam alignment of the second harmonic component relative to the fundamental and also for excellent signal to noise. A second harmonic power of 3 mW is successfully generated from a fundamental power of 7 W.

The standard deviation of the line-integrated electron density for 1 s converted from the measured phase signal is 4 × 1017 m−2 with a bandwidth of 10 MHz. For long time measurements, which will be required on ITER and other long pulse devices, slow baseline drifts limit the line density resolution to approximately 8 × 1018 m−2 for 100 s during this first setup. It is noted, this is with very little optimization of the setup and climate control. The drifts are inferred to be caused by the air flow around the optical system where the fundamental and the second harmonic components are transmitted separately as well as temperature drifts in transmissive components such as the AO cell and frequency doubling crystals. Mechanical motion, especially parallel to the beam path, is well cancelled, and measurements of dispersion introduced by a wedged ZnSe plate were shown.

Future application to large fusion devices, such as ITER, will require long beam path lengths ∼100 m. Although vibrations and the air flow along the beam path where the fundamental and second harmonic components are superposed should to first order not affect the measurement, this should be proven and will be the subject of future work. Accurate alignment of the system, particularly at the frequency doubling crystal, is particularly important and for long beam paths, active feedback control will be indispensable. This is because small vibrations cause large displacements after long beam transmission and displacements of the optical system caused by device temperature changes will be non-negligible. Being equipped with the long beam transmission and the active feedback control, demonstration of plasma measurements on actual fusion plasma devices and achievements of acceptable resolutions are also indispensable for application to future large devices.

This work was supported by Japan/U.S. Cooperation in Fusion Research and Development (No. FP5-3, 2015), as well as U.S. DOE under DE-FC02-06ER54875 and DE-FC02-08ER54972. The authors appreciate the engineering and administration staff at General Atomics for their kind support for this collaborative work. The authors also appreciate several useful discussions with Dr. Douglas J. Bamford of Physical Sciences, Inc. about their proprietary OP-GaAs frequency doubling crystals.

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