Line-integrated Density Research Articles

Density Profiles in the Levitated Dipole Experiment

A multi-chord interferometer (center frequency 60 GHz) has been constructed to measure the electron density profiles of plasmas in the Levitated Dipole Experiment (LDX). Theoretical considerations suggest that the density of a dipole-confined plasma will vary with radius as 1/r4. Measurements have been made for LDX plasmas, where the dipole-field was produced by a coil that was not levitating but rather suspended from a central column by thin supports. A ray-tracing code has been written to fit the chord data, which are line-integrated densities, to azimuthally-symmetric electron density profiles ne(r, t). Initial analysis has focused on the model \(n_e(r, t) = A(t)(r-r_0)^{-\alpha(t)}\), where A(t) and α(t) are free parameters; α(t) is referred to as the “steepness exponent.” The density profiles are observed to exhibit dynamics due to ECR heating and neutral-gas fueling. The model-fit, meant only to serve as a rough approximation, suggests that LDX plasmas have steepness exponents in the range of 1.5–4. The density at the location of the 2.45 GHz ECRH resonance is reconstructed and found to be of the same order of magnitude as the heating cut-off \(n_e \sim n_c =7.4\times10^{10}\,{\rm cm}^{-3}\).

Electron Density Measurement by Using a Multi-Channel Interferometer System in the Tandem Mirror GAMMA 10

Fluctuation in the plasma is important to be measured for studying the improvement of the plasma confinement by the formation of the plasma confinement potential. Density fluctuation is observed using microwaves, such as interferometer, reflectometry and Fraunhofer diffraction method. We have constructed a new multi-channel microwave interferometer for measuring the plasma density and fluctuation radial profiles in a single plasma shot. In order to study higher density plasma operation, we have started sub-millimeter hydrogen ice pellet injection experiments into the potential confined plasma. We successfully measured the time dependent density and line-integrated density fluctuation radial profiles in the pellet injection experiments using the multi-channel microwave interferometer.

A Multi-Reflection Type Visible-Laser Interferometer for High Density Plasma Measurements

In order to measure a high density plasma more than 1020 m-3 in the vicinity of a magneto-plasma-dynamic arcjet (MPDA), a visible-laser interferometer is fabricated using a He-Ne laser (λ = 632.8 nm). As it doesn't have enough phase shift when the light passes through the MPDA plasma once, we adopt a multi-reflection optical system in this interferometer to improve the phase sensitivity. We measured a plasma density by the interferometer and estimated the maximum value of line-integrated density of 4 × 1019 m-2 . These experimental results are consistent with that of electrostatic probe measurement in the downstream region.

Application of differential phase method to interferometry

The differential phase (DP) method was applied to microwave interferometry for the first time. Its advantage over standard interferometry is that the greatly reduced phase shift enables the unique determination of phase. Such a system was implemented on the Tokyo Spherical Tokamak-2 (TST-2), and demonstrated that the correct phase shift can be obtained even when the probing frequency is close to the cutoff density, and that very fast time evolutions of the line-integrated density can be measured.

Simultaneous Cotton-Mouton and Faraday rotation angle measurements on JET

The change in the ellipticity of a laser beam that passes through plasma due to the Cotton-Mouton effect can provide additional information on the plasma density. This approach, complementary to the more traditional interferometric methods, has been implemented recently using the JET interferometer-polarimeter with a new setup. Routine Cotton-Mouton phase shift measurements are made on the vertical central chords simultaneously with the Faraday rotation angle data. These new data are used to provide robust line-integrated density measurements in difficult plasma scenarios, with strong Edge Localized Modes (ELMs) or pellets. These always affect interferometry, causing fringe jumps and preventing good control of the plasma density. A comparison of line-integrated density from polarimetry and interferometry measurements shows an agreement within 10%. Moreover, in JET the measurements can be performed close to a reactor relevant range of parameters, in particular, at high densities and temperatures. This provides a unique opportunity to assess the quality of the Faraday rotation and Cotton-Mouton phase shift measurements where both effects are strong and mutual nonlinear interaction between the two effects takes place.

Upgraded two-dimensional phase contrast imaging system for fluctuation profile measurement on LHD

The two-dimensional (2D) phase contrast imaging system on LHD can measure the k spectrum of line-integrated density fluctuations (k∼0.2–3mm−1 and k⊥ρi∼0.1–1.5) with modest spatial resolution (Δρ∼0.1) along a line of sight passing close to the magnetic axis, sensitive to radial fluctuations in the core and poloidal fluctuations in the edge. The spatial resolution is attained using a 6×8 2D detector array taking advantage of the strong magnetic shear in LHD. The system can be configured with different magnification factors to investigate different ranges of k (in “overview” mode from 0.2to0.6mm−1, characteristic of ITG/TEM scale turbulence; and “zoom” mode from 1to3mm−1, which may access to the lower limit of the ETG range). Zoom mode additionally employs cylindrical optics to stretch the image by a factor of 4 in order to provide better spatial resolution for high k fluctuations within a narrow spatial region. The highest detected value of k in zoom mode, for which the signal-to-noise ratio is better than 1, is 2.5mm−1 (at around 1.5MHz).

Electron density fluctuation measurements using a multichannel microwave interferometer in GAMMA 10

Measurement of fluctuation in plasma is important for studying the improvement in plasma confinement by the formation of the plasma confinement potential. The density fluctuation is observed by microwaves by methods such as interferometry, reflectometry and Fraunhofer diffraction method. We have constructed a new multichannel microwave interferometer to measure the plasma density and fluctuation radial profiles in a single plasma shot. We successfully measured the time-dependent density and line-integrated density fluctuation radial profiles in a single plasma shot using the multichannel microwave interferometer. Thus, we have developed a useful tool for studying the improvement in plasma confinement by the formation of plasma confinement potential.

Real-time recovery of the electron density from interferometric measurements affected by fringe jumps

Optical interferometers are normally used in magnetically confined plasmas to measure the refractive index of the plasma by comparing the phase shift variation between a reference and a probe laser beam, from which the line-integrated electron density can be derived. Unfortunately, interferometric measurements are affected by fringe jumps, which are basically the erroneous phase difference determination due to the loss of signals or a phase difference bigger than 2π. The multiple causes include the refraction, wavelength of the laser radiation used, sensitivity, and time resolution of the measurements. On the other hand, the plasma density has become an essential piece of information for many real-time control schemes, which can therefore be completely jeopardized by fringe jumps. To overcome this problem at JET two main approaches can be adopted. The first approach consists of performing a real-time correction of the affected chords, eliminating the spurious effect of the fringe jumps, and providing a corrected line integral of acceptable quality. This is done at JET by complex algorithms that have inputs of various interferometry and polarimetry measurements. A second approach can be adopted based on the observation that, for many real-time experiments, an approximate estimate of the density profile is sufficient. In JET, it was demonstrated that the density profile of the vast majority of configurations could be determined with sufficient accuracy by using only the line-integrated density profile provided by two chords; one external and one internal. The various solutions were tested and results compared in order to verify the most suitable one for the various plasma configurations and operational scenarios. A “general purpose” version of the correction algorithm was implemented and is now normally running during JET operation.

A 1 mm interferometer for time and space resolved electron density measurements on pulsed plasmas

A quasi-optical interferometer operating at the frequency f = 274.2 GHz has been employed for measuring electron densities of pulsed plasmas in a wide range. Line-integrated densities down to nearly 1014 m−2 can be measured with temporal and spatial resolutions of 1 µs and less than 10 mm, respectively. A wavelength of about 1 mm requires a quasi-optical set-up making use of grid and dielectric beam splitters as well as elliptic mirrors for focussing the probing and reference beams. Due to the Michelson-like set-up, the probing beam traverses the plasma twice thus doubling the sensitivity as compared with the Mach–Zehnder configuration. The large difference between the probing and reference paths enables one to shift the phase by varying the frequency in a narrow band. When the detector output signal of the interferometer is recorded thereby shifting the phase stepwise, one obtains a cosine function for each sample time from which the phase shift by the plasma and, thus, the electron density, is deduced. The performance of the interferometer is demonstrated on a pulsed high-density helicon discharge as well as the large-volume plasma in a diffusion chamber connected with the helicon source.

Diocotron instability in non-neutral plasmas with a stationary point in the rotation frequency profile

A new analytical solution to the problem of the l=1 diocotron mode instability in a hollow density non-neutral plasma column with finite lenght is presented. The starting point of the analysis is the paper of Finn et al. [J. M. Finn, D. del-Castillo-Negrete, and D. C. Barnes, Phys. Plasmas 6, 3744 (1999)], where the instability mechanism involves compression of the plasma in the direction parallel to the magnetic field, with conservation of its line-integrated density. In the limit of small curvature of the plasma end-fronts, the method presented here provides both eigenvalue and eigenfunction for the unstable l=1 “extreme mode.”

Thermo-optical effect in zinc selenide windows for two-color interferometer for fusion plasma diagnostics

After some improvements in the two-color interferometer for plasma density measurements in the TJII fusion device, an effect, which we attribute to the thermo-optical characteristics of zinc selenide windows, has been put in evidence. Part of the 53.2 GHz mm radiation, used to heat the plasma, heats the windows and produces an optical path length difference between the two laser beams of 10.6 and 0.633μm wavelength. The effect induces a deformation of the line integral density measured by the interferometer. It is important in shots with high plasma reflectivity at the electron cyclotron resonance heating (ECRH) frequency. Some experiments and calculations have been done. The effect is explained and its order of magnitude is justified on the basis of some approximations. Several ways to avoid the effect including a correction procedure are discussed. Other possible heating sources are also discussed. The observed effect could be very relevant for experiments where ECRH is the main heating mechanism.

Two-dimensional diagnostic of edge plasma structure using a lithium beam probe in a compact helical system

A neutral lithium beam probe for two-dimensional diagnosis of edge plasmas has been designed and installed on the compact helical system. A lithium beam with an energy of 15keV and a current of 0.1mA is used. The spatial resolution is about 10mm, and the time response is about 10ms. The beam penetration depth is expressed in terms of the line integral density ⟨nel⟩, which is about 2×1018m−2. The beam injection angle can be varied and the observation point covers the edge and separatrix region of the helical diverter configuration. Two-dimensional electron density profiles for electron cyclotron heating and neutral beam injection (NBI) heated plasmas are obtained near and outside the last closed flux surface (LCFS). Analysis for two-dimensional density profile reconstruction indicates that significant amounts of surface plasma are confined outside the LCFS for NBI plasmas even though the ergodic layer is cut by the vacuum chamber wall (inboard limiter configuration). The usefullness of this new two-dimensional diagnostic in the edge region is demonstrated.

A new method for the inversion of interferometry data using basis functions derived from singular value decomposition of local measurements in tokamak plasmas

A novel method for inverting time-resolved line-integrated interferometric plasma density measurements is described. The method uses singular value decomposition of local density profiles from Thomson scattering measurements obtained at low sampling rates in the same or equivalent plasmas to determine a set of orthogonal spatial basis functions which is well adapted to the physical processes under investigation. The sought-for density profile is expanded into a limited series of these functions and a solution is calculated by using a simple least-squares fit method. The new method overcomes the difficulties encountered with other methods, such as regularization methods, which smoothen gradients and depend on the availability of accurate measurements in the plasma edge region. The small number of computations required provides for a fast algorithm. This method, which combines the high bandwidth of interferometer systems with the spatial accuracy of Thomson scattering, is applied to invert interferometer measurements in a wide variety of operational regimes in the Tokamak à Configuration Variable and Joint European Torus (JET) tokamaks. In particular, the collisionality dependence of density peaking observed in ASDEX Upgrade is confirmed in JET H-modes using this method.

Fizeau interferometer for measurement of plasma electron current

A high-resolution, vertically viewing far-infrared polarimeter-interferometer system is currently used on the Madison symmetric torus (MST) reversed-field pinch (RFP) to measure the plasma electron density and toroidal current density via Faraday rotation. In this article, we propose a scheme to measure the well-known Fizeau effect, whereby through modest modification of the existing apparatus, the line-integrated poloidal current density can also be directly measured. This parameter is important, since the RFP toroidal magnetic field is largely determined by currents flowing within the plasma. The Fizeau effect is a phase shift of an electromagnetic wave associated with movement of a dielectric medium. This motion can be related directly to the plasma electron current. Determining the Fizeau effect involves measurement of the phase shift between two collinear, orthogonally polarized, counterpropagating laser beams. Estimates indicate a phase shift of ∼2° is expected for typical MST parameters, well within the existing system resolution.

High resolution CO2 interferometry on the TJ-II stellarator by using an ADC-based phase meter

A 10 MSample/s analog-to-digital converter has been used to analyze the signals from the double wavelength heterodyne interferometer (CO2 10.6 μm, HeNe 0.63 μm) in the TJ-II stellarator. The phase difference between the two interferometers has been calculated using a new algorithm in Labview environment. A systematic study of the 1 MHz intermediate frequency has been done using our software and Labview tools. Different sources of noise and nonlinear effects have been analyzed. Crosstalk (from the reference path) has been detected and corrected by software. The complete system (single channel double pass) has been routinely working during the complete TJ-II autumn experimental campaign, providing the plasma line integral density in scenarious with average densities ranging from few 1018 m−3 to more than 5×1019 m−3. The results have been compared with those from a 2 mm interferometer, obtaining an excellent agreement. Working with a final bandwidth of 4 kHz, a one pass line integral error level about ±−2×1017 m−2 has been achieved.

Asymmetry of collapse of density pedestal by type I ELM in JT-60U

The edge plasma density at the high-field side (HFS) and low-field side (LFS) was measured using a FIR interferometer and an O-mode reflectometer simultaneously in order to study the asymmetry of collapse of the density pedestal by type I ELM. From fast time series analysis using the same digitizer system for the reflectometer, Dα intensity, interferometer and magnetic probe, experimental evidence for poloidal asymmetry of the collapse was clearly observed in JT-60U ELMy H-mode discharges for the first time. The collapse of the pedestal density is manifested as a fast inward displacement of the cutoff layer at the LFS, the increase of Dα intensity and large magnetic oscillations. No immediate response, however, was observed in the line-integrated density at the HFS of the plasma (FIR-U1). Instead, the signal showed a small reduction after a time delay of about L∥/Cs, which was attributed to the parallel flow from the inside to outside in order to fill the density gap as a result of localized particle expulsion from the LFS. Furthermore, no density increase in the HFS scrape-off layer (SOL) was observed during the horizontal plasma sweep experiments corresponding to particles expelled from the HFS midplane to the SOL directly, at the onset of density collapse and before the increase of Dα intensity. Together, these results indicate that the collapse of the density pedestal during type I ELMs is localized at the LFS midplane.

Real time safety factor profile determination in JET

In this paper, we present the recent implementation at joint european torus (JET) of a real-time system to calculate the electron density and the safety factor profiles directly from the line-integrated density (LID) and the calibrated Faraday angle (FAR) measurements. Current density, electron temperature and density profiles are now available in real time using magnetic, interfero-polarimeter and electron cyclotron emission data, thus allowing real-time feedback control of these profiles with the heating and current drive actuators available at JET.

Real-time fringe correction algorithm for the JET interferometer

On the JET facility, the line-integrated electron density is measured by a multichannel far-infrared (FIR) interferometer. The basic source of radiation is a deuterium cyanide laser (λ=195 μm) measuring the density along four vertical and four nearly horizontal (lateral) channels. During high-density discharges the system suffers from fringe jumps that are manually partially corrected by an off-line program. This intermittent phenomenon prevents reliable usage of the measured line-integrated density in a real-time feedback controller. To solve this problem we have developed a method to correct the fringe jumps on the lateral channels in real time. The method uses the additional methyl alcohol laser (λ=118.8 μm) interferometer present on the lateral channels to compensate the vibrations. The method has been successfully tested with off-line test data, before implementation on a VERSA Module Eurocard system for the real-time control of the JET discharges.

Gas density measurements with heavy ion beams

High current discharge channels are a promising option for the final stage of beam transport in a heavy ion fusion reactor. The creation and the properties of the channel are studied at the Gesellschaft fuer Schwerionenforschung accelerator facility. This article discusses a diagnostic technique to determine the neutral gas density channel created by a laser in a neutral gas. The concept is to measure the spreading of an ion beamlet due to collisional scattering with the gas, and thereby deduce the average line-integrated gas density. The results show a density reduction near the axis, which compares favorably with one-dimensional code calculations.

First results from the multichannel interferometer system on HSX

Measuring the equilibrium electron density distribution and its response to perturbations provides important information to magnetically confined plasma research. A multichannel interferometer system is now routinely operating on the new quasihelically symmetric stellator (HSX) to measure the equilibrium profile and electron density dynamics. The interferometer system has nine viewing chords with 1.5 cm spacing. The source is a bias-tuned Gunn diode at 96 GHz with passive solid-state tripler providing output at 288 GHz (8 mW). The HSX plasma is produced by 28 GHz electron cyclotron resonance heating and first results of the interferometer measurement are reported. The density spatial distribution is reconstructed from the measured line-integrated density. At high density [n̄e>2×1012 cm−3], an m=1 density oscillation with frequency of 1–2 kHz is observed. Plans to determine the radial particle flux and transport coefficients will be discussed.