Two-color Interferometer Research Articles

Measurement of electron and neutral particle densities using a two-color optical fiber interferometer.

A two-color homodyne Mach-Zehnder optical fiber interferometer is developed for the measurement of electron and neutral particle densities in a high-density capsule θ-pinch device. The interferometer leverages the disparate contributions of distinct particles to the refractive index across two discrete wavelengths of 1310 and 1550nm and incorporates the contributions of both electron and neutral particle densities to the phase shift in the plasma. The temporal evolutions of line-integrated electron and neutral argon densities are successfully measured by the interferometer. Comparing the electron density waveforms under various working gas pressures as well as the results obtained using the monochromatic and two-color measurements, it is inferred that the influence of neutral particle density can be neglected when measuring the electron density using a long-wavelength laser. Moreover, the maximum electron density is linearly correlated with the capacitor bank voltage for the θ-pinch device (5-9kV). Overall, the proposed interferometer is capable of simultaneously measuring the electron and neutral particle densities.

Real-time processing system of a two-color CO2 laser interferometer for density feedback control in JT-60SA.

A real-time processing system for the two-color CO2 laser interferometer on the JT-60SA has been developed for density feedback control. The system has a novel feature that can detect fringe jumps due to off-normal events, such as loss detection due to displacement of the beam axis and changes in the laser wavelengths. Because a phase change due to the JT-60SA plasma is smaller than π/2, corresponding to the line-integral electron density NL of ∼6×1019 m-2 in a short interval of 500ns, the threshold of the fringe jump detection is decided to be π/2. Hence, off-normal events can be detected from a fringe jump, leading to the abort of the real-time feedback control. In the density feedback control of the JT-60SA plasma, the system is employed as a density monitor, with NL being successfully controlled at 16.8% ± 6.6% lower than the reference.

Development of the upgraded single crystal dispersion interferometer (SCDI-U) and its first measurements of the line integrated electron densities in KSTAR during shattered pellet injections

Dispersion interferometers (DI) are widely used to measure line integrated electron densities in many fusion devices. A recent development of a heterodyne single crystal DI (SCDI) with a laser wavelength of 1064 nm (Lee et al 2021 Rev. Sci. Instrum. 92 033536) allows an easier and simpler optical setup by using only one, instead of two, nonlinear crystal. It is found that the reported heterodyne SCDI with an acoustic-optical modulator (AOM) has different beam paths between the frequency-shifted, via the AOM, fundamental and second harmonics which act as the reference beams. Such a separation of the reference beams inevitably produces non-removable phase shifts associated with mechanical vibrations, resulting in a reduction of the removing efficiency of the mechanical vibrations that DI systems can provide. By utilizing the fact that the diffraction angle due to the AOM is inversely proportional to the frequency of the laser beam and linearly proportional to an order of the frequency-shift, the SCDI-Upgrade (SCDI-U), which has complete overlap of the optical paths for both probing and reference beams from the laser source to the detectors, is proposed in this work. Its first measurements in KSTAR during shattered pellet injections are reported, and results obtained by the SCDI-U are compared with those from the existing two-color interferometer (TCI) in KSTAR. It is found that the SCDI-U measures the electron density more reliably during such an abrupt and large density change than the TCI does. Qualitative analyses on the effects of different injection schemes of the shattered pellets and possible application of the SCDI-U for ITER are also discussed.

Conceptual design and demonstration of a three-color laser interferometer for noise reduction in fusion plasma measurements.

A three-color laser interferometer consisting of three Mach-Zehnder-type, one-color laser interferometers with heterodyne detection and coaxial laser beams is demonstrated. The three-color laser interferometer is considered as three sets of a two-color laser interferometer. From the two sets of the two-color laser interferometer, the value consisting only of the noise floor can be assessed. The noise floor can be reduced by subtracting the value consisting only of the noise floor from the measurement value obtained with the other two-color laser interferometer. In the case of the three lasers with wavelengths 9.25 μm, 10.59 μm, and 532nm, a 15% noise reduction was obtained compared to the two sets of the two-color laser interferometers contained in the three-color laser interferometer. The 100-Hz noise reduction by 53% was achieved, and the other frequency noises were equal to or less than the smallest noise achieved by the two-color laser interferometers. The 100-Hz noise floor is caused by the vibration noise, which remains because of the non-coaxiality of the three beams.

A multi-chord, two-color interferometer using Hilbert transform phase detection for measuring electron density in spheromak plasmas.

A new, four-chord, CO2/He-Ne heterodyne interferometer has been designed and built for measuring line-averaged plasma density in the HIT-SI3 and subsequent HIT-SIU sustained spheromak devices. The two-color system successfully eliminates vibration-induced errors caused by mirrors that are secured to the vacuum chamber and is able to resolve electron densities ne in the full operating range of 1018-1020m-3 in both experiments with an integrated error of 4.7 × 1017m-2. Data are presented from high toroidal current plasma discharges, showing the time evolution of electron densities ne and jϕ/ne along multiple chords.

Self-correction of air refractive index in distance measurement using two-color sinusoidal phase modulating interferometry

A two-color sinusoidal phase modulating (SPM) interferometer based on electro-optic modulator (EOM) is devised for self-correction of air refractive index in distance measurement. Two laser sources with high frequency stability and close wavelengths (633 nm and 782 nm) are used in this scheme. High-accuracy phase demodulation was realized using phase generated carrier (PGC) demodulation techniques with an FPGA-based signal processing board. Experimental results of nanometer displacement measurements show that the resolution and accuracy of PGC demodulation is better than 1°, and the nonlinear error is less than 0.2°. Performance tests of two-color SPM interferometer compared with one-color interferometers under dynamic environment were implemented with an arm length difference of 4 m. The results show that, the measured distance of one-color interferometer drifts 4.8 μm in 600 s, which is caused by the deviation between the measured value of air refractive index and the actual value along the laser propagation path, and this drift reduces to ±1.5 μm using two-color interferometer without environmental sensing.

Long-time measurements of line-integrated plasma electron density using a two-color homodyne optical fiber interferometer

A two-color homodyne Mach-Zehnder (M-Z) optical fiber interferometer with wavelengths of 1.55 and 1.31 µm was developed for long-time measurement of line-integrated plasma electron density. A novel phase difference demodulation algorithm based on a single 3 × 3 optical coupler was implemented in a two-color optical fiber interferometer scheme for the first time. Our laboratory tests showed that this new optical fiber interferometer could determine the phase shift due to the low-frequency ambient vibration and could maintain high phase resolution measurement. The resolution of the new interferometer was less than 0.04rad in 1000s, corresponding to a line-averaged electron density of less than 1.0 × 1019m-2. Actual plasma discharge experiments performed on KTX-CTI, which is a new compact torus injector (CTI) constructed at the Keda Torus eXperiment (KTX), showed that this interferometer has excellent several-second stability.

Two-color interferometer for study of dense low-ionized plasma on the target in high-power pulse linear accelerator.

A two-color infrared interferometer has been developed for the investigation of high-density weakly ionized tantalum plasma in x-ray complexes based on linear induction accelerators (1.6 kA electron beam current, 4.6MeV energy, and 100ns pulse duration). Simultaneous probing at two different wavelengths makes it possible to independently measure the density of neutral and electron components. The interferometer uses wavelength values of 1.064 µm (Nd:YAG laser) and 10.6 µm (CO2 laser). To attenuate the effect of sample beam refraction in inhomogeneous plasma, the interferometer used a refraction suppression scheme composed of spherical mirrors focusing the object beam into the region occupied by the plasma. In addition, the power of the sample beam transmitted through the plasma was controlled in order to analyze whether there was a distortion of the interference pattern because of strong sample beam refraction and absorption in the plasma cloud. To calibrate the initial phase shift of the probe radiation, a movable mirror mounted on a piezoelectric element and oscillating according to a harmonic law with amplitude greater than the laser wavelengths was used. In initial experiments, the parameters of target plasma registered by this interferometer are as follows: the linear density of neutrals reached 1.5 · 1017cm-2, and the degree of ionization was of the order of 10-2. The target plasma expansion velocity is determined as ∼6 km/s.

Multi-chord IR-visible two-color interferometer on KSTAR.

Major parts of an IR-visible two-color interferometer (TCI) on KSTAR have been upgraded for the multi-chord operation: (1) a diode-pumped-solid-state (DPSS) laser (660nm) replacing the former HeNe laser (633nm), (2) vacuum-compatible vibration isolator with titanium retro-reflectors, and (3) full digital phase comparator for multi-chord real-time density signals. The commercial compact DPSS laser suits the multiple chord configuration with its strong beam power (500 mW) and long coherent length (>100 m). Ti retro-reflectors are mounted on vacuum-compatible vibration isolators. The isolators are essential for the visible beams to avoid any fringe skips due to their short wavelength, considering the speed of the mechanical vibration (up to hundreds of μm). Field-programmable-gate-array (FPGA) modules count the entire fringes fast enough with a signal output rate up to 1.25MHz, solving the fringe skip issues. The FPGA module enables the full digital processing of the phase comparator with a CORDIC algorithm after the sampling rate of 160 MS/s for the 40MHz intermediate frequency of each beam. The full digital signals are transferred to the main plasma control system in real-time. Stable single-input-single-output operation of the KSTAR density control was demonstrated with the TCI. The real-time density profile control is also promising in the near future, with multiple actuators such as pellets and gas puffings.

In Situ Sub-50-Attosecond Active Stabilization of the Delay Between Infrared and Extreme-Ultraviolet Light Pulses

The blooming of attosecond science (1 as = $10^{-18}$ s) has raised the need to exquisitely control the delay between two ultrashort light pulses, one of them being intense and in the visible spectral range, while the second is weak and in the Extreme Ultra-Violet spectral range. Here we introduce a robust technique, named LIZARD (Laser-dressed IoniZation for the Adjustment of the pump-pRobe Delay), allowing an active stabilization of this pump-probe delay. The originality of the method lies in an error signal calculated from a two-photon photoelectron signal obtained by photoionizing a gas target in an electronic spectrometer with the two superimposed beams. The modulation of sidebands in phase quadrature allows us to perform an \textit{in situ} measurement of the pump-probe phase, and to compensate for fluctuations with an uniform noise sensitivity over a large range of delays. Despite an interferometer length of several meters, we achieved a long term stability of 28 as RMS over hours. This method could be applied to the stabilization of other types of two-color interferometers, provided that one of the propagating beams is capable of photoionizing a target.

Self-calibration of the secondary laser source in two-color Linnik interferometer

The imaging Linnik interferometer equipped with two lasers of different colors is under development and metrological study at National Metrology Institute of Brazil (INMETRO). This work reports the self-referenced method for practical calibration of the secondary laser wavelength. The method is based on accurate digitalization and comparison of the waveforms for both reference He-Ne stabilized laser at 633 nm and secondary laser diode at 488 nm. The process makes use of multiple step phase-shifting technique for waveform measurement and multi-parameter fit for wavelength extraction. The advantage of the method is that no extra hardware of realignment of interferometer is required to perform the calibration.

The new single crystal dispersion interferometer installed on KSTAR and its first measurement.

Dispersion interferometers have been used to measure line integrated electron densities from many fusion devices. To optically suppress noise due to mechanical vibrations, a conventional dispersion interferometer typically uses two nonlinear crystals located before and after the plasma along the laser beam path. Due to the long beam path, it can be difficult to overlap the fundamental and second harmonic laser beams for a heterodyne dispersion interferometer and to focus the beams on the second nonlinear crystal located after the plasma, especially when the aperture of the nonlinear crystal is small, i.e., of the order of mm. To overcome such difficulties, a new concept of a heterodyne dispersion interferometer, a single crystal dispersion interferometer (SCDI), is developed and installed on KSTAR with the laser wavelength of 1064nm. The concept and the optical setup of the KSTAR SCDI are discussed, as well as its first measurement during a shattered pellet injection that produces abrupt and large changes in the electron density. To demonstrate feasibility, the KSTAR SCDI measurements are also compared with those from the existing two-color interferometer.

Combining laser interferometry and plasma spectroscopy for spatially resolved high-sensitivity plasma density measurements in discharge capillaries.

Precise characterization and tailoring of the spatial and temporal evolution of plasma density within plasma sources are critical for realizing high-quality accelerated beams in plasma wakefield accelerators. The simultaneous use of two independent diagnostics allowed the temporally and spatially resolved detection of plasma density with unprecedented sensitivity and enabled the characterization of the plasma temperature in discharge capillaries for times later than 0.5 µs after the initiation of the discharge, at which point the plasma is at local thermodynamic equilibrium. A common-path two-color laser interferometer for obtaining the average plasma density with a sensitivity of 2 × 1015 cm-2 was developed together with a plasma emission spectrometer for analyzing spectral line broadening profiles with a resolution of 5 × 1015cm-3. Both diagnostics show good agreement when applying the spectral line broadening analysis methodology of Gigosos and Cardeñoso in the temperature range of 0.5 eV-5.0eV. For plasma with densities of 0.5-2.5 × 1017 cm-3, temperatures of 1 eV-7eV were indirectly measured by combining the diagnostic information. Measured longitudinally resolved plasma density profiles exhibit a clear temporal evolution from an initial flat-top to a Gaussian-like shape in the first microseconds as material is ejected out from the capillary. These measurements pave the way for highly detailed parameter tuning in plasma sources for particle accelerators and beam optics.

A heterodyne dispersion interferometer for wide bandwidth density measurements on DIII-D.

In order to improve both the density and particularly the temporal resolution beyond previous dispersion interferometers (DIs), a heterodyne technique based on an acousto-optic (AO) cell has been added to the DI. A 40 MHz drive frequency for the AO cell allows density fluctuation measurements into the MHz range. A CO2 laser-based heterodyne DI (HDI) installed on DIII-D has demonstrated that the HDI is capable of tracking the density evolution throughout DIII-D discharges, including disruption events and other rapid transient phenomena. The data also show good agreement with independent density measurements obtained with the existing DIII-D two-color interferometer. The HDI line-integrated density resolution sampled over a 1 s interval is ∼9 × 1017 m-2. Density fluctuations induced by MHD instabilities are also successfully measured by the HDI.

Density characterization of discharged gas-filled capillaries through common-path two-color spectral-domain interferometry.

Electrically discharged plasma structures, typically several centimeters in length and sub-millimeter in diameter, have been applied to guide laser pulses in laser plasma accelerators and to focus ion and relativistic electron beams in compact, radially symmetric transport configurations. Knowledge of the on-axis plasma density is critical. Traditional density interferometry has been ineffective for these laser-machined structures, while group velocity delay (GVD) techniques involve combining two laser paths with corresponding alignment complexities and stability sensitivities. Here the GVD technique is advanced to a common-path two-color interferometer configuration performed in the spectral domain of a broad-bandwidth femtosecond laser. Multi-shot tracking of the phase is not required, and the common path assures improved stability. This in situ technique was validated on 15mm long plasma structures, measuring electron densities of 1017-1018 cm-3 for various fill pressures.

EPICS data acquisition system for FPGA-based plasma electron density measurement on KSTAR

The Korea Superconducting Tokamak Advanced Research (KSTAR) has several diagnostics devices, including a millimeter-wave interferometer (MMWI), far-infrared interferometer (FIR), two-color interferometer, etc., for measuring plasma electron densities. The MMWI diagnostic device measures the electron density of the plasma from the phase difference generated by transmitting a 1 mm (280 GHz) electromagnetic wave into it. The FIR device is similar to the MMWI, but uses a far-infrared (119 um) laser as its electromagnetic wave source. The MMWI is the primary plasma density measurement system in KSTAR. However, its signal contains significant noise and hundreds of fringe-jump events from the phase comparator circuit. The original analogue circuit of the phase comparator is limited in noise handling since it needs to average the raw IF signal to be treated in analogue circuit with limited bandwidth. To handle noise with more flexibility and to reduce occurrence of fringe-jump errors, we developed a new data acquisition (DAQ) system using a high-speed FPGA-based digitizer. The MMWI signal resembles a 10 MHz sine wave. We acquired data at 100 MSPS using a new digitizer. The phase difference per sample was 36°, which lead to inaccurate results due to noise. To increase the accuracy, the new DAQ system has interpolation logic within the FPGA that increases the phase resolution. In addition, the phase comparative value is transmitted to two channels by inverting the signal. The signal that does not travel through the plasma has a phase difference of 180°. The FPGA-based system was constructed using the same algorithm as existing phase comparator circuit [2]. The detected phase was averaged to obtain a phase value, and the result was transmitted as 1280 phase values per msec. In the EPICS Input/Output Controller (IOC), the density is calculated using data received from the direct memory access (DMA) via peripheral component interconnect (PCI) Express. The above FPGA logic was successfully used for real-time feedback control in the ITER CODAC environment. This paper introduces a new, detailed MMWI DAQ system design concept using FPGA, and its operational results.

Tests of a two-color interferometer and polarimeter for ITER density measurements

A full-scale 120 m path length ITER toroidal interferometer and polarimeter (TIP) prototype, including an active feedback alignment system, has been constructed and undergone initial testing at General Atomics. In the TIP prototype, two-color interferometry is carried out at 10.59 μm and 5.22 μm using a CO2 and quantum cascade laser (QCL) respectively while a separate polarimetry measurement of the plasma induced Faraday effect is made at 10.59 μm. The polarimeter system uses co-linear right and left-hand circularly polarized beams upshifted by 40 and 44 MHz acousto-optic cells respectively, to generate the necessary beat signal for heterodyne phase detection, while interferometry measurements are carried out at both 40 MHz and 44 MHz for the CO2 laser and 40 MHz for the QCL. The high-resolution phase information is obtained using an all-digital FPGA based phase demodulation scheme and precision clock source. The TIP prototype is equipped with a piezo tip/tilt stage active feedback alignment system responsible for minimizing noise in the measurement and keeping the TIP diagnostic aligned indefinitely on its 120 m beam path including as the ITER vessel is brought from ambient to operating temperatures. The prototype beam path incorporates translation stages to simulate ITER motion through a bake cycle as well as other sources of motion or misalignment. Even in the presence of significant motion, the TIP prototype is able to meet ITER’s density measurement requirements over 1000 s shot durations with demonstrated phase resolution of 0.06° and 1.5° for the polarimeter and vibration compensated interferometer respectively. TIP vibration compensated interferometer measurements of a plasma have also been made in a pulsed radio frequency device and show a line-integrated density resolution of m−2.

Two-color heterodyne laser interferometry for long-distance stage measurement with correction of uncertainties in measured optical distances

We designed a new system that eliminates deviations by correcting uncertainty in optical distance measurements in the laser two-color heterodyne interferometer. In simulations, eliminating the uncertainty from the atmosphere, the deviation in the uncertainty of the optical distance was 50 times greater with the two-color method than with the one-color method. Adding a correction arm reduces the deviation caused by the uncertainties in measured optical distances. The uncertainty in the measured path length is reduced to 20 nm over a path length of 1500 mm, giving a relative uncertainty of 1.34 × 10−8.

A simple and versatile phase detector for heterodyne interferometers.

The measurement of the relative phase of two sinusoidal electrical signals is a frequently encountered task in heterodyne interferometry, but also occurs in many other applications. Especially in interferometry, multi-radian detectors are often required, which track the temporal evolution of the phase difference and are able to register phase changes that exceed 2π. While a large variety of solutions to this problem is already known, we present an alternative approach, which pre-processes the signals with simple analog circuitry and digitizes two resulting voltages with an analog-to-digital converter (ADC), whose sampling frequency can be far below the frequency of the sinusoidal signals. Phase reconstruction is finally carried out by software. The main advantage of this approach is its simplicity, using only few low-cost hardware components and a standard 2-channel ADC with low performance requirements. We present an application on the two-color interferometer of the ASDEX Upgrade tokamak, where the relative phase of 40 MHz sinusoids is measured.

The design of two color interferometer system for the 3-dimensional analysis of plasma density evolution on KSTAR

A 5-channel two color interferometer (TCI) system has been designed on KSTAR. TCI system is designed for tangential beam paths, which will combine with two existing interferometer systems of vertical and radial beam paths, so that it will provide 3-dimensional measurement of electron density evolution. TCI system uses wavelengths of 10.6μm by a CO2 laser and 0.633μm by a HeNe laser. The system compensates the vibrational noise by using two colors and avoids refraction by short wavelengths. The main purpose of the TCI is to generate routine measurement of the line integrated plasma density for the real time density control on KSTAR. The 5-channels will provide profile data for the density. Time resolution of the system is expected to be 500kHz or higher in order to measure 3-dimensional density fluctuations for ELMs and other MHD activities including TAE modes. The system is planned to be working on KSTAR 2016 campaign with 1–2 channels.