Line-integrated Electron Density 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.

Density-profile imaging using a second harmonic dispersion interferometer configured with reflective-beam expanders.

A Second-Harmonic Dispersion Interferometer (SHDI) is assembled to measure the two-dimensional, line-integrated density profile of a pulsed-plasma jet using probe-beam diameters well beyond the 1mm diameters typically used in such instruments. An initial prototype demonstrated the technique using 7mm beam diameters, which are now increased to 35mm diameter using two types of beam expanders: an achromatic-beam expander (ABE) or a reflective-beam expander (RBE). ABEs were found to add a periodic background to the measured-phase image with a magnitude of the order of Δϕ ∼ 2π radians, compared to the background phase noise level in the system configured without beam expanders at Δϕbg ∼ 0.025 radians. Subtraction of the background phase in a sample image reduced the effect of the ABE phase offset to a level of Δϕ ∼ 0.1 radians, enhancing the quality of the density measurements. Reflective-beam expanders (RBEs) did not modify the background phase appreciably and were a significant improvement, allowing the instrument to be used for 2D (r, z) density-profile measurements of a 3cm diameter × 5cm long, pulsed-plasma jet. Variations in the timing parameters for the plasma gun, specifically the gas valve opening time and the gas-injection delay, for a constant discharge current were used to map the plasma gun's performance, indicating a nominal line-integrated electron density of Nedl ≳ 3 × 1015 cm-2 and a volumetric density of Ne ≃ 9 × 1015cm-3. The results obtained for the RBE configuration demonstrate that the 2D-SHDI platform may be scaled to even larger sample areas and a rep-rated system, with the ability to potentially provide for a reproducible, time-resolved (∼1 ns), high resolution (∼100μm) measurement of 2D plasma-density profiles.

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 real-time density feedback control on MAST-U in L-mode

In this paper we report on the development and demonstration of density feedback control for MAST-U. Sinusoidal perturbations are used to measure the frequency response from a deuterium gas valve (actuator) to line-integrated core electron density measured by the interferometer (sensor). In the frequency range relevant for control design, only two system-identification experiments were needed to regress a first-order dynamic model. This control-oriented model informs the offline design of a proportional integral controller with the established loop-shaping controller design method. After offline verification of the controller implementation, control is demonstrated by experimentally tracking a staircase reference for the line-integrated electron density. This paper demonstrates the efficiency of controller design using system-identification and loop-shaping, providing reliable density control for MAST-U.

Electron density measurement by the three boundary channels of HCOOH laser interferometer on the HL-3 tokamak

Far-infrared (FIR) interferometer is widely used to measure the electron density in the magnetically confined fusion plasma devices. A new FIR laser interferometer with a total of 13 channels (8 horizontal channels and 5 oblique channels) is under development on the HL-3 tokamak by using the formic-acid laser (HCOOH, f = 694 GHz). In order to investigate the boundary electron density activity during the divertor discharge, three horizontal interferometry channels located at Z = −97, −76, 76.5 cm have been successfully developed on HL-3 in 2023, and put into operation in recent experimental campaign, with a time resolution of < 1.0 μs and line-integrated electron density resolution of ~ 7.0 × 1016 m−2. This paper mainly focuses on the optical design of the three-channel interferometry system, as well as optical elements and recent experimental result on HL-3.

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.

Interferogram analysis of X-pinch plasmas with a synthetic dark-field Schlieren image

The Mach-Zehnder interferometer and dark-field Schlieren imaging systems are developed to diagnose high electron densities of the X-pinch plasmas. Interferogram analysis can be challenging due to stiff electron density gradients of the X-pinch plasmas. This stiff gradient results in complex fringe patterns which may lead to miscounted indices of the fringes, and even refraction losses. To address these challenges, the geometrical acceptance angle of the imaging system is increased to reduce the refraction losses caused by the X-pinch plasmas. This is achieved by using physically larger optics. Results show that the imaging systems can detect higher line-integrated electron densities. Additionally, to verify the reliability of interferogram analysis results, a synthetic dark-field Schlieren image generated based on the interferogram is qualitatively compared to the measured dark-field Schlieren image which is simultaneously taken with the interferogram. Practicality of the synthetic Schlieren images is examined by comparing them with the measured Schlieren images.

Optimization of power feedback control system for HCN interferometer on EAST Tokamak

The Hydrogen Cyanide (HCN) interferometer stands as an indispensable diagnostic tool, designated to measure the line-integrated electron density on the Experimental Advanced Superconducting Tokamak (EAST), thereby offering essential density feedback signals for EAST operation. The HCN laser used in the interferometer is a continuous glow discharge gas laser. However, owing to variations in external ambient temperature, the HCN laser exhibits output power instability. The current power automatic feedback control system for the HCN laser interferometer exhibits low actuator adjustment precision, thereby limiting its ability to achieve maximum output power. Moreover, the system may cause a temporary power drop to zero during adjustment, while EAST operation requires the HCN laser interferometer to maintain high power continuously. In order to solve the issues, this paper developed an innovative actuator that ingeniously amalgamates the virtues of piezoelectric ceramic and stepper motor. This novel actuator, demonstrating a broad adjustment range and high precision, is intended to replace the present one in the HCN interferometer power control system. While the stepper motor executes coarse adjustment, the piezoelectric ceramic enables precise adjustment, thus enhancing the adjustment accuracy of the automatic power control system to a sub-micrometer level and an adjustment range greater than 5 mm. Accurate determination of the regulator's adjustment direction can significantly improve the efficiency of adjustment. The slope of the laser output power peak decreases as it approaches the maximum value, and increases as it moves away from the maximum value. Therefore, this system replaces the original threshold algorithm with a slope algorithm. By correctly judging the adjustment direction, the efficiency of adjustment is improved. Furthermore, this algorithm can keep the output power stable on a power peak. There will be no instances of zero power output during the adjustment, allowing the power to remain stable above the set threshold for a long time. Currently, this system has been successfully applied to the HCN interferometer, and testing has found that the system can maintain stability for at least 16 hours. Furthermore, even when the laser output power was intentionally reduced to below the set threshold, the system was able to respond quickly and adjust the output, rapidly restoring it to above the predefined threshold. Multiple tests have shown the strong robustness of the system, indicating it meets the stringent demands of the EAST's complex environment.

Development of a dual HCN laser interferometer on a small tokamak device

A dual hydrogen cyanide (HCN) laser interferometer system was designed and developed to measure the electron density of plasma with high temporal resolution. The system comprises two terahertz continuous wave (CW) discharge-pumped HCN lasers, each emitting at a frequency of 0.89 THz and with an output power of up to 100 mW. The intermediate frequency (IF) signal is obtained by adjusting the length of the resonant cavity. The temporal resolution of the interferometer can reach 1 μs when the intermediate frequency is at 1 MHz. The feasibility of the dual HCN laser interferometer system was verified by simulating the plasma using a wedge. Preliminary experimental results were obtained on a small tokamak device, a root mean square error of the dual HCN laser interferometer is approximately 1.5×1017 m-3 when the line-integrated electron density obtained by the dual HCN laser interferometer is about 1.5×1019 m-3.

Systematic design of a multi-input multi-output controller by model-based decoupling: a demonstration on TCV using multi-species gas injection

In this paper, we present the first results of a systematically designed multi-input multi-output gas-injection controller on Tokamak á Configuration Variable (TCV). We demonstrate the simultaneous real-time control of the NII emission front position and line-integrated electron density using nitrogen and deuterium gas injection. Injection of nitrogen and/or deuterium affects both the NII emission front position and line-integrated electron density. This interplay between control loops is termed interaction and, when strongly present, makes designing a controller a significantly more complex problem. Interaction between the control loops can be reduced to an acceptable level by redefining inputs, decoupling the multi-input multi-output control problem to separated single-input single-output problems. We demonstrate how to achieve this by defining virtual control inputs from linear combinations of the actuators available. For the demonstration on TCV, linear combinations of deuterium and nitrogen gas injection are computed from transfer-function models to obtain these virtual inputs. The virtual inputs reduce the interaction in the control-relevant frequency range to a point where control of the NII emission front position and line-integrated electron density can be considered decoupled, allowing for the much simpler design of single-input single-output controllers for each loop. Implementing the controllers with the virtual inputs gives the multi-input multi-output gas-injection controller. This approach is well established in the control community, and is presented here as a demonstration to drive developments of multi-input multi-output control strategies. In particular, the envisioned control of particle- and heat fluxes impacting the divertor targets by injection of multiple gas species.

Digital holographic interferometry for diagnosing the density profile of laser-produced collisionless shock

A digital holographic interferometry based on Fresnel biprism has been developed to measure the electron density profile of laser-produced collisionless shocks in laboratory, which used the Fourier transform method to solve the wrapped phase. The discontinuous surfaces of shocks will produce the break and split of the interference fringes, which cannot be processed by the conventional path-following phase unwrapping algorithm when reconstructing the real phase of the plasma. Therefore, we used a least-squares method to extract the real phase, which is proportional to the line-integrated electron density. We obtained fine density profiles of collisionless shocks in the line-integrated density region around 1018 cm−2 with a density resolution of 3.38 × 1016 cm−2. The shock structure is in well agreement with that measured by the dark-field schlieren methods and that predicted by shock jump condition. Synthetic holograms are used to confirm the effectiveness of our algorithm, and it is shown that correct results can still be obtained even if part of the diagnostic light is refracted out of the optical system by the shock.

Study of plasma parameters in high enthalpy ICP-heated wind tunnel by using single Langmuir probe

In this paper, a single probe (SP) has been designed for study plasma parameters of High enthalpy ICP-heated wind tunnel. It is found that the electron temperature in the core region is about 2.4 eV and that in the edge region is about 3–4 eV. At the maximum power of the High Enthalpy ICP-heated wind tunnel, the electron density reach 4.34 × 1013 cm-3. Meanwhile, the radial electron density distribution of SP is numerically integrated to calculate the line integral density, which is compared with the line integral density measured by 890 GHz HCN laser interferometer. The results show that the probe diagnosis results have the same trend as the laser diagnosis results. The line integral electron density measured by SP is 0.8 times higher than that measured by the HCN interferometer.

A synthetic phase-contrast imaging diagnostic with spatial filtering for gyrokinetic simulations

A Phase-contrast imaging (PCI) diagnostic provides measurements of line-integrated electron density fluctuations. Localisation along the laser beam path can be achieved with a spatial filter that selects the wave-vector directions of the fluctuations contributing to the PCI measurement and is a key feature of the PCI diagnostic installed on the TCV tokamak and also of a similar system planned for JT-60SA. We have developed a synthetic diagnostic that models measurements from PCI taking into account the effect of such a spatial filter. The synthetic tool is based on the principle of integrating over selected diagnostic volumes the electron density fluctuations generated by turbulence simulations, and applying an appropriate spatial filter in wave-vector space. We demonstrate the effect of the filter for a positive and a negative triangularity TCV discharge, and illustrate the potential of the synthetic diagnostic for better understanding the corresponding experimental results. We consider different types of filters and make first-principle estimates of the localisation of the measurement. Finally, using gyrokinetic simulations that include electromagnetic effects, collisions and four kinetic species, we make first predictions of the characteristics of the measurements using the planned set-up of PCI on JT-60SA.

The structure of 3-D collisional magnetized bow shocks in pulsed-power-driven plasma flows

We investigate three-dimensional (3-D) bow shocks in a highly collisional magnetized aluminium plasma, generated during the ablation phase of an exploding wire array on the MAGPIE facility (1.4 MA, 240 ns). Ablation of plasma from the wire array generates radially diverging, supersonic ( $M_S \sim 7$ ), super-Alfvénic ( $M_A &gt; 1$ ) magnetized flows with frozen-in magnetic flux ( $R_M \gg 1$ ). These flows collide with an inductive probe placed in the flow, which serves both as the obstacle that generates the magnetized bow shock, and as a diagnostic of the advected magnetic field. Laser interferometry along two orthogonal lines of sight is used to measure the line-integrated electron density. A detached bow shock forms ahead of the probe, with a larger opening angle in the plane parallel to the magnetic field than in the plane normal to it. Since the resistive diffusion length of the plasma is comparable to the probe size, the magnetic field decouples from the ion fluid at the shock front and generates a hydrodynamic shock, whose structure is determined by the sonic Mach number, rather than the magnetosonic Mach number of the flow. The 3-D simulations performed using the resistive magnetohydrodynamic (MHD) code Gorgon confirm this picture, but under-predict the anisotropy observed in the shape of the experimental bow shock, suggesting that non-MHD mechanisms may be important for modifying the shock structure.

Mm-wave polarimeter and profilometry design study for retrieving plasma density in the PANDORA experiment

In the recent past, the possibility to use a superconducting trap confining a hot and dense plasma as a tool to investigate radioactivity in astrophysical scenarios has been proposed. Making possible these kind of unprecedented measurements is the main aim of the PANDORA (Plasmas for Astrophysics Nuclear Decays Observation and Radiation for Archaeometry) project. In this context, it is planned to build a compact and flexible magnetic plasma trap where plasma reaches an electron density ne ∼ 1011–1013 cm−3, and an electron temperature, in units of kT, kTe ∼ 0.1–30 keV. The setup is conceived to be able to measure, for the first time, nuclear β-decay rates in stellar-like conditions in terms of ionization states. In this paper, the design study of a mm-wave polarimeter for the PANDORA plasma line-integrated electron density measurement is presented. The paper highlights the method of this type of measurements for the first time proposed for a magneto-plasma trap which represents an “intermediate” case between the ultra-compact plasma ion sources and the large-size thermonuclear fusion devices. Preliminary measurements at scaled microwave frequencies have carried out both on a “free-space” setup by using a wire-grid polarizer and a rotable Ka-band OMT + horn antennas system, and on a compact trap (called Flexible Plasma Trap) installed at INFN-LNS and used as PANDORA down-sized testbench are described. The polarimeter technique will support β-decay investigation by simultaneous measurements of the total plasma density, which is crucial to carefully evaluate the decay-constant and to extrapolate the laboratory observed data to the astrophysical scenarios. Moreover, this work proposes to adopt an electromagnetic inverse-scattering-based technique-based method to retrieve the electron density profile along the probing antennas line-of-sight. Numerical results of this so-called “inverse profilometry” are also shown.

Improvement on Faraday rotation measurement affected by the stray lights on the HL-2A tokamak

Formic-acid (HCOOH, λ = 432.5 μm) laser P olarimeter- I nterferomet er ( PIer ) has been developed on the HL-2A tokamak, which provides 4 channels of line-integrated electron densities and 4 channels of Faraday rotation angles, respectively. Affected by the stray lights arising from the reflection of the probe waves in the optical system, the measurement of Faraday rotation angles was drastically contaminated during the HL-2A experiments, showing an obvious oscillation modulation during the electron density ramp-up/down. This paper introduces an effective correction approach used to improve the accuracy of Faraday rotation measurement on the HL-2A tokamak. Based on the method, the deviation term originating from the stray lights can be effectively subtracted from the contaminated Faraday rotation measurement. The preliminary result indicates that the interference amplitude on Faraday rotation angle is reduced by about 80%, and the corrected data is consistent with the experimental measurement by using the optical isolator that consists of a λ/4 wave-plate and polarizer under the similar discharges.

Development of a two color interferometer on a field-reversed configuration device

Two color interferometer adopting short wavelength lasers is one of the most reliable methods to measure the electron density in high density fusion devices, which is immune to mechanical vibration and fringe jump error by using two lasers of different wavelength. Considering the anticipant line-integral electron density of 1020∼1021 m−2, the initial plasma duration of tens of μs, and the expected rotational instability on the order of several μs at the HUST-FRC (HFRC), a single chord two color (CO2/HeNe, 10.6 μm/0.633 μm) heterodyne system is installed in the initial operation stage of HFRC. The modulation frequency is 40 MHz, which is generated by acousto-optic modulator (AOM) and benefits for the future physical research. The experimental results show that the phase noise of the two color interferometer system is within 1.7° and the residual error is less than 1 × 1018 m−2. Based on the results of the single-channel interferometric system, a multi-channel system can be expected in the future.

Development of a combined interferometer using millimeter wave solid state source and a far infrared laser on ENN’s XuanLong-50 (EXL-50)

A millimeter wave solid state source—far infrared laser combined interferometer system (MFCI) consisting of a three-channel 890 GHz hydrogen cyanide (HCN) laser interferometer and a three-channel 340 GHz solid state source interferometer (SSI) is developed for real-time line-integrated electron density feedback and electron density profile of the EXL-50 spherical tokamak device. The interferometer system is a Mach–Zehnder type, with all probe-channels measured vertically, covering the plasma magnetic axis to the outermost closed magnetic plane. The HCN laser interferometer uses an HCN laser with a frequency of 890 GHz as a light source and modulates a 100 kHz beat signal by a rotating grating, giving a temporal resolution of 10 μs. The SSI uses two independent 340 GHz solid-state diode sources as the light source, the frequency of the two sources is adjustable, and the temporal resolution of SSI can reach 1 μs by setting the frequency difference of the two lasers at 1 MHz. The main optical path of the two interferometers is compactly installed on a set of double-layer optical platform directly below EXL-50. Dual optical path design using corner cube reflectors avoids the large support structures. Collinear the probe-beams of two wavelengths, then the phase error caused by vibration can be compensated. At present, the phase noise of the HCN Interferometer is 0.08 rad, corresponding to a line-integrated electron density of 0.88 × 1017 m−2, one channel of measuring result was obtained by the MFCI system, and the highest density measured is about 0.7 × 1019 m−2.

Attosecond dispersion as a diagnostics tool for solid-density laser-generated plasmas

Extreme-ultraviolet pulses can propagate through ionised solid-density targets, unlike optical pulses and, thus, have the potential to probe the interior of such plasmas on sub-femtosecond timescales. We present a synthetic diagnostic method for solid-density laser-generated plasmas based on the dispersion of an extreme-ultraviolet attosecond probe pulse, in a pump–probe scheme. We demonstrate the theoretical feasibility of this approach through calculating the dispersion of an extreme-ultraviolet probe pulse propagating through a laser-generated plasma. The plasma dynamics is calculated using a particle-in-cell simulation, whereas the dispersion of the probe is calculated with an external pseudo-spectral wave solver, allowing for high accuracy when calculating the dispersion. The application of this method is illustrated on thin-film plastic and aluminium targets irradiated by a high-intensity pump pulse. By comparing the dispersion of the probe pulse at different delays relative to the pump pulse, it is possible to follow the evolution of the plasma as it disintegrates. The high-frequency end of the dispersion provides information on the line-integrated electron density, whereas lower frequencies are more affected by the highest density encountered along the path of the probe. In addition, the presence of thin-film interference could be used to study the evolution of the plasma surface.

Optical design of a laser wavefront sensor applicable under strong diffraction effects by irreproducible microscale high-density plasma

Accurate measurements of electron density in irreproducible microscale high-density plasmas are indispensable for improving laser processing and plasma processing technology because the dynamics of these plasmas are strongly influenced by their electron density. Because single-path laser wavefront sensors are capable of acquiring the two-dimensional electron density distribution with a single shot, the electron density of irreproducible millimeter-scale low-density plasmas has been measured by using such sensors. However, the strong diffraction effects caused by the irreproducible microscale high-density plasmas pose challenges for the measurement. In this study, we numerically and experimentally demonstrate a suitable optical configuration of single-path laser wavefront sensors for accurate measurements of irreproducible microscale high-density plasmas with minimal measurement errors. Our Fresnel diffraction-based numerical simulation indicates that the serious measurement errors caused by the strong diffraction effects can be significantly reduced through the use of relay lenses with high magnification and a short-wavelength laser source. In addition, we propose an alignment procedure for the optical setup to minimize the measurement errors and experimentally validated the procedure by measuring a laser wavefront shaped by a spatial light modulator. Finally, we applied the verified laser wavefront sensor to the measurement of a laser-induced plasma with a two-dimensional line-integrated electron density higher than 1 × 1021 m−2 in an approximately 40 × 50 μm region. This study provides a new strategy to rigorously analyze the dynamics of irreproducible microscale high-density plasmas using a laser wavefront sensor.