Search

A new tool for the exploration and diagnosis of the internal magnetic field of plasmas in the DIII-D tokamak in the form of a constraint on the EFIT (Equilibrium Fitting) Grad–Shafranov code based on the Faraday-effect Radial Interferometer-Polarimeter (RIP) diagnostic is presented, including description, verification, and sample application. The physics underlying the diagnostic and its implementation into EFIT are discussed, and the results showing the verification of the model are given, and the model’s limitations are discussed. The influence of the diagnostic’s input on the resulting equilibrium parameters is characterized. The effect of electron density profile refinement is evaluated and found to be negligible. A sample application of the diagnostic is shown, indicating that the RIP constraint has similar effects on the equilibrium as motional Stark effect constraints do.

Vertical position stability plays a crucial role in maintaining safe and reliable plasma operation for long-pulse fusion devices. In general, the vertical position is measured by using inductive magnetic coils installed inside the vacuum vessel; however, the integration drift effects are inherent for steady-state or long-pulse plasma operation. Developing a non-magnetic approach provides a fusion reactor-relevant steady-state solution that avoids the negative impact of integration drift. In this paper, we compare the non-inductively determined vertical position achieved by line-integrated interferometer and polarimeter measurements to that employing an inductive flux loop for a 1056 s discharge recently achieved on EAST (Experimental Advanced Superconducting Tokamak). Experimental results show that the non-inductive measurement is more robust than flux loops after 300 s if the integrator is not reset to suppress integrator drift. Real-time vertical position control using the non-inductive system is proposed for the next EAST experimental campaign.

Toroidal current profile measurements in the tokamak plasma edge are critical for fusion plasma physics research and model validation. A three-wave Faraday-effect polarimeter-interferometer with a sub-centimeter spatial resolution is proposed on the DIII-D tokamak to determine the edge current profile via Abel inversion. By using probe beams with 316 µm wavelength, a low-field-side, vertical-view, single-pass optical layout covering the plasma edge region (R = 2.15–2.27 m) is assessed. Measurements with no greater than 0.1° polarimetric systematic uncertainty, no greater than 0.01° polarimetric root-mean-square noise (1 kHz bandwidth), and a 0.8 cm radial chord spacing are considered feasible based on the achieved performance of existing systems using similar wavelengths on fusion devices. Synthetic diagnostic calculations taking various factors into account, such as diagnostic uncertainty and quality of magnetic flux surfaces, find that the edge current profile can be determined with up to 0.12 MA/m2 uncertainty, or about 10% of the peak current density in the pedestal of an investigated high-confinement plasma.

Internal magnetic fluctuation measurements are utilized to identify turbulence associated with micro-tearing modes (MTM) in the DIII-D Edge-Localized-Mode (ELM)-y H-mode pedestal. Using a Faraday-effect polarimeter, magnetic turbulence (150–500 kHz) is directly observed with a typical line-averaged fluctuation amplitude of ∼0.8 G at peak frequency (250 kHz) and ∼15 G integrated over the spectrum from 150 to 500 kHz. Frequency, poloidal wavenumber, and propagation direction of the magnetic turbulence all serve to identify as MTM. Magnetic turbulence amplitude non-monotonically correlates with collision frequency, peaks off mid-plane, and correlates with electron temperature gradient evolution between ELMs, consistent with MTM features identified from theory and gyro-kinetic simulation. The magnetic turbulence growth correlates with confinement degradation in ELMy H-mode plasmas during a slow density ramp. These internal measurements provide unique constraints toward developing physics understanding and validating models of the H-mode pedestal for future devices.

Magnetic turbulence is directly observed internally in the pedestal of ELMy H-mode tokamak plasmas using a newly developed Faraday-effect polarimetry measurement. Fluctuation amplitude is δ b r ≥ 15 G (150–500 kHz), with a ratio of magnetic to density fluctuation | δ b r / B | / | δ n / n | ≥ 0.15. Magnetic turbulence is identified as resulting from micro-tearing-instability and mode growth accompanied by degraded plasma confinement is observed.

A full-scale ITER toroidal interferometer and polarimeter (TIP) prototype, including an active feedback alignment system, has been installed and tested on the DIII-D tokamak. In the TIP prototype, a two-color interferometry measurement of line-integrated density is carried out at 10.59 μm and 5.22 μm using a CO2 and quantum cascade laser, respectively, while a separate polarimetry measurement of the plasma-induced Faraday effect is made at 10.59 μm. The TIP prototype is equipped with a piezo tip/tilt stage active feedback alignment system that minimizes noise in the measurement and keeps the diagnostic aligned throughout DIII-D discharges. The measured phase resolution for the polarimeter and interferometer is 0.05° (100 Hz bandwidth) and 1.9° (1 kHz bandwidth), respectively. The corresponding line-integrated density resolution for the vibration-compensated interferometer is δnL = 1.5 × 1018 m-2, and the magnetic field-weighted line-integrated density from the polarimeter is δnBL = 1.5 × 1019 Tm-2. Both interferometer and polarimeter measurements during DIII-D discharges compare well with the expectations based on calculations using Thomson scattering measured density profiles and magnetic equilibrium reconstructions. Additionally, larger bandwidth interferometer measurements show that the diagnostic is a sensitive monitor of core density fluctuations with demonstrated measurements of Alfven eigenmodes and tearing modes.

A double-pass radially view 11 chords polarimeter-interferometer system has been operated on the experimental advanced superconducting tokamak and provides important current profile information for plasma control. Stray light originating from spurious reflections along the optical path (unwanted reflections from various optical components/mounts and transmissive optical elements such as windows, waveplates, and lens as well as the detectors) and also direct feedback from the retro-reflector used to realize the double-pass configuration can both contribute to contamination of the Faraday rotation measurement accuracy. Modulation of the Faraday rotation signal due to the interference from multiple reflections is observable when the interferometer phase (plasma density) varies with time. Direct reflection from the detector itself can be suppressed by employing an optical isolator consisting of a λ/4-waveplate and polarizer positioned in front of the mixer. A Faraday angle oscillation during the density ramping up (or down) can be reduced from 5°-10° to 1°-2° by eliminating reflections from the detector. Residual modulation arising from misalignment and stray light from other sources must be minimized to achieve accurate measurements of Faraday rotation.

Density fluctuations in the large-density-gradient region of improved confinement Madison Symmetric Torus reversed field pinch (RFP) plasmas exhibit multiple features that are characteristic of the trapped-electron mode (TEM). Core transport in conventional RFP plasmas is governed by magnetic stochasticity stemming from multiple long-wavelength tearing modes. Using inductive current profile control, these tearing modes are reduced, and global confinement is increased to that expected for comparable tokamak plasmas. Under these conditions, new short-wavelength fluctuations distinct from global tearing modes appear in the spectrum at a frequency of f ∼ 50 kHz, which have normalized perpendicular wavenumbers k⊥ρs≲0.2 and propagate in the electron diamagnetic drift direction. They exhibit a critical-gradient threshold, and the fluctuation amplitude increases with the local electron density gradient. These characteristics are consistent with predictions from gyrokinetic analysis using the Gene code, including ...

Far-infrared laser polarimetry with time response up to ∼1 μs and spatial resolution ∼8 cm has been successfully implemented on the Madison Symmetric Torus reversed-field pinch. Internal magnetic field and current density fluctuations are nonperturbatively measured. This is accomplished by taking parallel polarimetry chords which measure the line-integrated magnetic field fluctuations via Faraday rotation. With suitable analysis we are able to obtain information on spatial profiles of magnetic field fluctuations and current density fluctuations. Coherent interaction between these fluctuations is also measured and observed to generate an electromagnetic fluctuation-induced torque 〈δJ×δB〉.

The current profile and core magnetic field fluctuation amplitudes in a reversed-field pinch are measured by using a high-resolution polarimetry–interferometry system. This paper presents data showing a redistribution of the current during a sawtooth crash. Also, the core magnetic field fluctuation amplitude is observed to increase at a sawtooth crash consistent with the idea of nonlinearly driven dynamo current. In addition, the parallel current density increases in the outer region of the plasma during auxiliary pulsed parallel current drive. This was expected, as the external application of an edge parallel electric field is designed to flatten the current profile providing an equilibrium closer to the minimum energy Taylor state. However, the current density also increases in the core, relative to standard plasmas. This increase can be explained by a reduction of the dynamo (anti)current drive in the core that should accompany the measured reduction of magnetic fluctuations and by a drop in resistivity caused by the increased confinement of fast electrons.

New developments in Faraday rotation polarimetry have provided the first measurements of current density profile and core magnetic fluctuations in the core of a high-temperature reversed field pinch. This has been achieved by a fast-polarimeter system with time response up to 1 μs and phase resolution

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 [ne>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.

The origin of large scale density fluctuations and their role in electron transport has been investigated in the Madison Symmetric Torus reversed-field pinch [R. N. Dexter et al., Fusion Tech. 19, 131 (1991)]. At medium frequencies (10–30 kHz), n is associated with core-resonant magnetic fluctuations having poloidal mode number m=1 and toroidal mode numbers n=6–10. These chord-averaged density fluctuations are shown to be coherent with large scale radial flow fluctuations, permitting fluctuation-induced particle flux of the form 〈nṽr〉 to be studied. In the edge, although amplitudes are large, n and ṽr are out of phase, consistent with advection of the mean density gradient by perturbed magnetic field lines and no electron transport. During improved confinement discharges, produced by inductive current drive, both fluctuation amplitudes and the total radial electron flux are greatly reduced over the entire plasma cross section.The origin of large scale density fluctuations and their role in electron transport has been investigated in the Madison Symmetric Torus reversed-field pinch [R. N. Dexter et al., Fusion Tech. 19, 131 (1991)]. At medium frequencies (10–30 kHz), n is associated with core-resonant magnetic fluctuations having poloidal mode number m=1 and toroidal mode numbers n=6–10. These chord-averaged density fluctuations are shown to be coherent with large scale radial flow fluctuations, permitting fluctuation-induced particle flux of the form 〈nṽr〉 to be studied. In the edge, although amplitudes are large, n and ṽr are out of phase, consistent with advection of the mean density gradient by perturbed magnetic field lines and no electron transport. During improved confinement discharges, produced by inductive current drive, both fluctuation amplitudes and the total radial electron flux are greatly reduced over the entire plasma cross section.

A multichannel millimeter-wave interferometer system has been designed, fabricated and installed on the helically symmetric experiment (HSX), located at the University of Wisconsin, Madison. The interferometer system will view the plasma cross section along nine adjacent chords with 1.5 cm spacing. With this arrangement, coverage will span from the low-field side plasma scrape-off layer to well past the magnetic axis. For the plasma densities anticipated on HSX, a solid-state source operating at 288 GHz will be utilized. At this frequency refraction will be manageable, being less than the channel spacing. The source will be bias-tuned and modulated with a sawtooth wave form at 750 kHz in order to generate the intermediate frequency necessary for the heterodyne detection scheme. The signals will be measured using Schottky-diode corner-cube mixers. The interferometer will have sensitivity nedl≈8×1011 cm−2, being able to measure density changes

A recent study investigating the role of electron density fluctuations in particle transport has been conducted on the Madison Symmetric Torus reversed-field pinch. Four diagnostics enabled this experiment: a high-speed multichord far-infrared laser interferometer, a multichord Hα array, a 64-position magnetic coil array, and a Doppler spectrometer that measured impurity ion flow fluctuations. Correlation analysis is used to elucidate the relationship among density, magnetic, and impurity ion flow fluctuations. We observe that the electron density fluctuations are highly coherent with the magnetic fluctuations resulting from core-resonant resistive tearing modes. Moreover, the fluctuation-induced particle transport, obtained from the correlation between electron density and flow fluctuations, indicates that the core-resonant tearing modes do not drive significant particle transport in the plasma edge. We will address these four primary diagnostics, details of the analysis techniques, and principal results...

As a consequence of recent improvements to the far-infrared (FIR) interferometer time response, from bandwidth of 10 kHz up to 1 MHz, high-frequency density fluctuations can now be resolved on the Madison symmetric torus (MST) reversed-field pinch. The phase measurement allows absolute calibration of the fluctuation amplitude while eleven chords generate information on the spatial distribution. Density fluctuations up to 200 kHz are observed. A unique feature of the MST interferometer is that six chords are toroidally displaced 5° from the remaining five. Hence, besides information on the poloidal structure, i.e., m=1, toroidal information is also available. By computing the cross power, coherence, and cross phase between two toroidally displaced chords, one can determine the toroidal rotation speed, dispersion, and correlation length.

The far-infrared laser interferometer on the Madison Symmetric Torus has recently been upgraded to allow simultaneous interferometry and polarimetry measurements. Centered around a heterodyne laser system that operates at λ≃432 μm, the diagnostic has a frequency response of 1 kHz for the polarimeter and up to 1 MHz for the interferometer. The distribution of laser power through the 11 chord system is managed with wire mesh beamsplitters. Concurrent with the system upgrade to polarimetry, a detailed study of the effect of the wire mesh beamsplitters on beam polarization was conducted. The study shows that the mesh characteristics must be included to extract the polarimetry phase measurement from the raw data. The modifications to the data analysis as well as preliminary five chord polarimetry profile data are presented.

High spatial resolution electron cyclotron emission imaging (ECEI) has been employed on TEXT-U [Texas Experimental Tokamak Upgrade, G. Cima et al., Phys. Plasmas 2, 720 (1995)] to measure turbulent electron temperature fluctuations using an intensity interferometric technique. With the first dispersion relation measurements in the plasma confinement region, a broadband spectral feature is identified at poloidal wave numbers consistent with expectations for electron drift waves.

A novel wide bandwidth, low-cost, 20 channel hybrid Schottky diode mixer array-based imaging system has been developed, tested and implemented for electron cyclotron emission diagnostics on the Texas experimental tokamak upgrade (TEXT-U). The array has been successfully utilized to measure 1D and 2D electron temperature profiles, to study sawteeth and magnetohydrodynamic phenomena, and to make measurements of the poloidal/radial correlation lengths and wave-number spectra of electron temperature fluctuations. Fabrication and laboratory characterization results are presented, together with details and test results from the actual implementation on TEXT-U.

Substantial improvements have been made to increase the frequency bandwidth of the UCLA multichannel interferometer system on TEXT-Upgrade. Recently, a digital phase comparator technique was implemented that has several advantages over the conventional analog phase comparator. The probe and reference wave forms are directly digitized and the phase computed in software using a numerical demodulation algorithm. For the purpose of reducing the data load, aliasing of the laser difference frequency is employed to vary the time response according to experimental demands.

Electron temperature and density fluctuations are measured in the core of the Texas Experimental Tokamak‐Upgrade (TEXT‐U) [P. H. Edmonds, E. R. Solano, and A. J. Wootton, in Proceedings of the 15th Symposium on Fusion Technology, Utrecht (Elsevier Science, Amsterdam, 1989), Vol. 1, p. 342] plasma across the poloidal cross section. The high spatial resolution of the heavy‐ion beam probe (HIBP) and correlation radiometry of electron cyclotron emission (CRECE) reveal that both the density and temperature fluctuations are strongly poloidally asymmetric. Temperature fluctuation measurements indicate a broadband drift wave feature localized near the plasma equatorial plane on both the high‐ and low‐field sides, which is consistent with density fluctuation measurements by far infrared (FIR) scattering. In contrast, the HIBP observes this feature localized only to the low‐field side. Excellent spatial resolution allows us to investigate whether changes in the gradient affect the fluctuation amplitudes. We find that indeed, the temperature fluctuations increase with the electron temperature gradient. Results also link density fluctuations to changes in the density gradient.

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 withi...

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 m...

Neutral beam injection in reversed-field pinch (RFP) plasmas on the Madison Symmetric Torus [Dexter et al., Fusion Sci. Technol. 19, 131 (1991)] drives current redistribution with increased on-axis current density but negligible net current drive. Internal fluctuations correlated with tearing modes are observed on multiple diagnostics; the behavior of tearing mode correlated structures is consistent with flattening of the safety factor profile. The first application of a parametrized model for island flattening to temperature fluctuations in an RFP allows inferrence of rational surface locations for multiple tearing modes. The m = 1, n = 6 mode is observed to shift inward by 1.1 ± 0.6 cm with neutral beam injection. Tearing mode rational surface measurements provide a strong constraint for equilibrium reconstruction, with an estimated reduction of q0 by 5% and an increase in on-axis current density of 8% ± 5%. The inferred on-axis current drive is consistent with estimates of fast ion density using TRANSP...

In order to characterize the Madison Symmetric Torus (MST) reversed-field pinch (RFP) plasmas that bifurcate to a helical equilibrium, the V3FIT equilibrium reconstruction code was modified to include a conducting boundary. RFP plasmas become helical at a high plasma current, which induces large eddy currents in MST's thick aluminum shell. The V3FIT conducting boundary accounts for the contribution from these eddy currents to external magnetic diagnostic coil signals. This implementation of V3FIT was benchmarked against MSTFit, a 2D Grad-Shafranov solver, for axisymmetric plasmas. The two codes both fit Bθ measurement loops around the plasma minor diameter with qualitative agreement between each other and the measured field. Fits in the 3D case converge well, with q-profile and plasma shape agreement between two distinct toroidal locking phases. Greater than 60% of the measured n = 5 component of Bθ at r = a is due to eddy currents in the shell, as calculated by the conducting boundary model.

Electron cyclotron heating (ECH) is used to suppress m=2 magnetohydrodynamic (MHD) oscillations in the Texas Experimental Tokamak (TEXT) [Nucl. Technol. Fusion 1, 479 (1981)]. The location of ECH power deposition is controlled by a movable antenna. The MHD activity is suppressed when the ECH beam is directed close to the q=2 surface. The experiment is simulated using a three‐dimensional resistive MHD code in cylindrical geometry. For fixed plasma current, the saturated m=2 island width is found to depend on the value of the safety factor at the magnetic axis (q0). The simulation suggests that the observed saturated m=2 island in the pre‐ECH plasma, which typically occupies 25% of the minor radius, corresponds to q0∼1.3. The suppression of the island in the presence of ECH is attributed to current profile modification. In some discharges, the m=2 activity does not resume even after the ECH pulse is turned off.

Recent experiments on the Texas Experimental Tokamak (TEXT) [Plasma Phys. Controlled Fusion 27, 1335 (1985)] have focused on identifying the drives and transport significance of the turbulence in the interior of discharges in the neo‐Alcator confinement regime. Far‐infrared (FIR) scattering consistently observes density fluctuations indicative of electron drift waves, i.e., ωk∼ωe*+kθvE, where vE≡−Er/B (the electron diamagnetic frequency Doppler‐shifted by the E×B poloidal plasma rotation) and an amplitude that scales inversely with the density scale length Ln. Although consistent with scattering on the power‐weighted frequency ω, heavy‐ion beam probe (HIBP) data typically indicate kθρs

Modifications to the spectrum and magnitude of turbulent density fluctuations in the Texas Experimental Tokamak (TEXT) [Plasma Phys. Controlled Fusion 27, 1335 (1985)], measured by far‐infrared scattering, are related to changes in plasma profiles (e.g., density and potential) induced by naturally occurring magnetic islands (i.e., m=2) of varying amplitude. The statistical dispersion relation of the microturbulence that propagates in the electron diamagnetic drift direction is observed to be consistent with expectations for electron drift‐wave turbulence when a spectral shift due to E×B plasma rotation is included. Observed spectral widths are several times larger than the linear mode frequency. The fluctuation amplitude is found to scale inversely with the electron density scale length.

A heavy ion beam probe has been used to measure the plasma space potential profiles in the tokamak TEXT [Nucl. Fusion Technol. 1, 479 (1981)]. The Ohmic discharges studied were perturbed by externally produced resonant magnetic fields (an ergodic magnetic limiter or EML). Without these perturbations the plasma central potential is generally consistent with the value calculated from radial ion momentum balance, using experimental values of density and ion temperature and assuming a neoclassical poloidal rotation velocity. Exceptions to the agreement are found when operating with reduced plasma parameters. Possible reasons for this discrepancy are explored, in particular, the effects of intrinsic magnetic field fluctuations, and modifications to the self‐consistent radial electric sheath. With the application of the EML fields the edge electric field and potential increase during periods of magnetic island overlap. A test particle calculation of electron transport shows increases in diffusivity also occur during periods of magnetic island overlap. These calculated changes in diffusivity are interpreted in terms of a stochastic layer width, which is itself used to predict a potential change for comparison with the experimental results.

Experimental evidence for and against drift waves as the origin of the observed fluctuations and anomalous transport in the plasma interior is reviewed. Fluctuation spectra observed by far‐infrared (FIR) scattering and a heavy ion beam probe (HIBP) are compared. The FIR system observes broad S(k,ω), which are spatially resolved at large k and readily identified with electron drift waves. At higher densities a clear ion feature, which may be associated with ion temperature gradient (ITG) modes, appears as well. A quasicoherent feature in the drift wave range of phase velocities is also found at the inner midplane. But interior HIBP measurements using a thallium beam have, by a two‐point correlation method, measured wave numbers far too small (i.e., phase velocities far too high) to be those of drift waves of either variety. Some recent measurements with a cesium beam have produced phase velocities more closely in accord with drift waves at low frequencies. It is suggested that a new mode may be present, which is not drift wavelike. However, the phase velocity and coherence of the HIBP data exhibit qualitative features that suggest possible instrumental effects. Several of these are investigated, which individually do not appear to reconcile the data with a pure drift wave model. They are (1) sample volume size, (2) common mode effects such as cross‐talk or path integrals of beam attenuation, and (3) two‐stream instabilities. Reconciliation of these measurements is important to transport studies. That is, calculated particle and energy fluxes depend sensitively on the frequency and wave‐number spectrum employed. The theoretical considerations about two‐point correlations and possible instrumental effects are also relevant to other diagnostics using this technique.

Anomalous transport in fusion plasmas remains an enigma requiring explanation. A predictive capability is highly desirable if confinement enhancement regimes such as H mode or super shots are to be extrapolated to the next phase in development of the International Fusion program, epitomized, for example in ITER. Therefore, identification of the role that electrostatic turbulence plays in confinement is a critical issue requiring detailed experimental data capable of testing and challenging existing theoretical models. This article presents microturbulence measurements obtained on the DIII‐D and TEXT tokamaks utilizing heterodyne, far‐infrared collective scattering, and reflectometry techniques. The experimental systems are described on both machines and emphasis placed on results obtained during the L‐H transition, ELM activity, and saturated ohmic operation where ion temperature gradient driven (ITGD) turbulence is theoretically predicted to exist.

Diffraction from plasma density irregularities can have significant consequences for the tomographic inversion of line‐of‐sight integrated measurements of the phase disturbance suffered by a probing beam. A new tomographic approach which takes account of diffraction from high‐K refractive index structures is described. The relevance for multichannel interferometry measurements is demonstrated numerically and the technique is applied to the inversion of multichannel TEXT interferometer data.

A far-infrared polarimeter diagnostic has been added to the UCLA multichord heterodyne interferometer system on TEXT-Upgrade. The polarimeter utilizes the phase technique of Rice [Rev. Sci. Instrum. 63, 5002 (1992)] in order to measure the Faraday rotation angle of the incident laser beam upon transmission through the plasma. From these data one derives information on the poloidal magnetic field, current density, and safety factor profiles. Due to the excellent port access and the polarimeter/interferometer scanning capability, the Faraday rotation profile can be measured across the entire plasma cross section.

A magnetic pickup coil diagnostic set is used to measure the position of the plasma column in the Texas Experimental Tokamak Upgrade (TEXT‐U) project. The output from this coil set is used in a digital feedback system to control the plasma position. To provide a fast time response for the feedback system, one complete coil set is located on the interior of the vacuum vessel. Another set with a slower time response is located on the outside of the vessel. To simplify and speed up data processing, the coils are constructed so that the X and Y coordinates of the plasma current centroid are each determined using the signals from only two separate coils. For each coordinate one coil is used to measure a tangential (relative to the coil surface) magnetic field component, while the second coil measures a normal field component. Due to physical constraints, the coils are not continuous around the vacuum vessel. The presence of gaps in the coils causes pickup of the external current flowing in the divertor coil wi...

The first experimental results from the horizontal‐view, multichannel, heterodyne FIR interferometer system on TEXT‐Upgrade are reported. The initial system employs parabolic beam‐expansion optics and a 15 cm array with minimum channel spacing of 1.5 cm. Profiles of the plasma electron density will be presented. In addition, small‐amplitude density perturbations resulting from sawteeth and tearing modes are examined. Due to the double pass of the laser beam through the plasma and the large distance of the detector array (2.5 m) from the plasma, refractive effects can be important. A ray tracing code is developed to correct the measured profiles.

The UCLA far‐infrared scattering/interferometry system on TEXT‐Upgrade has recently been modified to include a two‐dimensional capability. Along with the vertically viewing system, a horizontal view has been added. For interferometric measurements of the plasma density profile, the vertical view consists of a 45 cm array while the horizontal view array spans 15 cm. Density profiles for Text‐Upgrade plasmas will be presented. For collective scattering measurements of electron density fluctuations, cross correlation of scattered signals from the two orthogonal views at the same wave vector will be examined. Finite cross coherence may be used to spatially localize the fluctuation measurements.

Combined polarimetry-interferometry capability permits simultaneous measurement of line-integrated density and Faraday effect with fast time response (∼1 μs) and high sensitivity. Faraday effect fluctuations with phase shift of order 0.05° associated with global tearing modes are resolved with an uncertainty ∼0.01°. For physics investigations, local density fluctuations are obtained by inverting the line-integrated interferometry data. The local magnetic and current density fluctuations are then reconstructed using a parameterized fit of the polarimetry data. Reconstructed 2D images of density and magnetic field fluctuations in a poloidal cross section exhibit significantly different spatial structure. Combined with their relative phase, the magnetic-fluctuation-induced particle transport flux and its spatial distribution are resolved.

Magnetic fluctuation-induced transport driven by global tearing modes has been measured by Faraday-effect polarimetry and interferometry (phase measurements) in the MST reversed field pinch. However, the role of small-scale broadband magnetic and density turbulence in transport remains unknown. In order to investigate broadband magnetic turbulence, we plan to upgrade the existing detector system by using planar-diode fundamental waveguide mixers optimized for high sensitivity. Initial tests indicate these mixers have ×10 sensitivity improvement compared to currently employed corner-cube Schottky-diode mixers and ×5 lower noise. Compact mixer design will allow us to resolve the wavenumbers up to k ∼ 1-2 cm(-1) for beam width w = 1.5 cm and 15 cm(-1) for beam width w = 2 mm. The system can also be used to measure the scattered signal (amplitude measurement) induced by both plasma density and magnetic fluctuations.

The object of this review is to summarize the achievements of research on the Alcator C-Mod tokamak [Hutchinson et al., Phys. Plasmas 1, 1511 (1994) and Marmar, Fusion Sci. Technol. 51, 261 (2007)] and to place that research in the context of the quest for practical fusion energy. C-Mod is a compact, high-field tokamak, whose unique design and operating parameters have produced a wealth of new and important results since it began operation in 1993, contributing data that extends tests of critical physical models into new parameter ranges and into new regimes. Using only high-power radio frequency (RF) waves for heating and current drive with innovative launching structures, C-Mod operates routinely at reactor level power densities and achieves plasma pressures higher than any other toroidal confinement device. C-Mod spearheaded the development of the vertical-target divertor and has always operated with high-Z metal plasma facing components—approaches subsequently adopted for ITER. C-Mod has made ground-breaking discoveries in divertor physics and plasma-material interactions at reactor-like power and particle fluxes and elucidated the critical role of cross-field transport in divertor operation, edge flows and the tokamak density limit. C-Mod developed the I-mode and the Enhanced Dα H-mode regimes, which have high performance without large edge localized modes and with pedestal transport self-regulated by short-wavelength electromagnetic waves. C-Mod has carried out pioneering studies of intrinsic rotation and demonstrated that self-generated flow shear can be strong enough in some cases to significantly modify transport. C-Mod made the first quantitative link between the pedestal temperature and the H-mode's performance, showing that the observed self-similar temperature profiles were consistent with critical-gradient-length theories and followed up with quantitative tests of nonlinear gyrokinetic models. RF research highlights include direct experimental observation of ion cyclotron range of frequency (ICRF) mode-conversion, ICRF flow drive, demonstration of lower-hybrid current drive at ITER-like densities and fields and, using a set of novel diagnostics, extensive validation of advanced RF codes. Disruption studies on C-Mod provided the first observation of non-axisymmetric halo currents and non-axisymmetric radiation in mitigated disruptions. A summary of important achievements and discoveries are included., United States. Dept. of Energy (Cooperative Agreement DE-FC02-99ER54512), United States. Dept. of Energy (Cooperative Agreement DE-FG03-94ER-54241), United States. Dept. of Energy (Cooperative Agreement DE-AC02-78ET- 51013), United States. Dept. of Energy (Cooperative Agreement DE-AC02-09CH11466), United States. Dept. of Energy (Cooperative Agreement DE-FG02-95ER54309), United States. Dept. of Energy (Cooperative Agreement DE-AC02-05CH11231), United States. Dept. of Energy (Cooperative Agreement DE-AC52-07NA27344), United States. Dept. of Energy (Cooperative Agreement DE-FG02- 97ER54392), United States. Dept. of Energy (Cooperative Agreement DE-SC00-02060)

A Far-InfaRed (FIR) three-wave POlarimeter-INTerferometer (POINT) system for measurement current density profile and electron density profile is under development for the EAST tokamak. The FIR beams are transmitted from the laser room to the optical tower adjacent to EAST via ∼20 m overmoded dielectric waveguide and then divided into 5 horizontal chords. The optical arrangement was designed using ZEMAX, which provides information on the beam spot size and energy distribution throughout the optical system. ZEMAX calculations used to optimize the optical layout design are combined with the mechanical design from CATIA, providing a 3D visualization of the entire POINT system.

A multichannel far-infrared laser-based POlarimeter-INTerferometer (POINT) system utilizing the three-wave technique is under development for current density and electron density profile measurements in the EAST tokamak. Novel molybdenum retro-reflectors are mounted in the inside wall for the double-pass optical arrangement. A Digital Phase Detector with 250 kHz bandwidth, which will provide real-time Faraday rotation angle and density phase shift output, have been developed for use on the POINT system. Initial calibration indicates the electron line-integrated density resolution is less than 5 × 10(16) m(-2) (∼2°), and the Faraday rotation angle rms phase noise is0.1°.

This work presents a theoretical and computational analysis of core-localized energetic particle driven modes observed near the magnetic axis in the Madison Symmetric Torus [L. Lin, W. X. Ding, D. L. Brower et al., Phys. Plasmas 20, 030701 (2013)]. Using measured safety factor and plasma pressure profiles as input, the linear ideal MHD code Adaptive EiGenfunction Independent Solution (AEGIS) [L. J. Zheng and M. Kotschenreuther, J. Comput. Phys. 211, 748 (2006)] reveals Alfvenic modes close to the measured frequencies. The AEGIS results together with a reduced analytical model demonstrate that the modes are essentially “cylindrical” and dominated by a single poloidal component (m = 1). The modes are localized at the plasma core where the magnetic shear is weak and continuum damping is minimal. Detailed analysis establishes constraints on the safety factor and plasma pressure, under which two modes can exist simultaneously.

Multiple bursty energetic-particle (EP) driven modes with fishbone-like structure are observed during 1 MW tangential neutral-beam injection in a reversed field pinch (RFP) device. The distinguishing features of the RFP, including large magnetic shear (tending to add stability) and weak toroidal magnetic field (leading to stronger drive), provide a complementary environment to tokamak and stellarator configurations for exploring basic understanding of EP instabilities. Detailed measurements of the EP mode characteristics and temporal-spatial dynamics reveal their influence on fast ion transport. Density fluctuations exhibit a dynamically evolving, inboard-outboard asymmetric spatial structure that peaks in the core where fast ions reside. The measured mode frequencies are close to the computed shear Alfven frequency, a feature consistent with continuum modes destabilized by strong drive. The frequency pattern of the dominant mode depends on the fast-ion species. Multiple frequencies occur with deuterium f...

The effects of pressure gradient on the existence of global Alfven eigenmodes (GAE) in Reversed Field Pinch are studied by numerical calculation. It is found that GAEs near the plasma core can exist when pressure gradient is sufficiently large. The calculated mode frequency and structure are consistent with the experimental results in the Madison Symmetric Torus.

The spatial resolution of small‐angle collective scattering systems is often ambiguous due to the extended length of the scattering volume. By examining two sample volumes at the same wave vector (or scattering angle) that lie along the incident beam, and by varying the separation between these two volumes, one can examine their cross‐correlation through use of simple digital signal processing techniques. As the separation between the two volumes is increased, the signals are observed to decorrelate. Application of this technique on the DIII‐D and TEXT tokamaks shows that when the volumes are located at the plasma edge and core, the two signals are decorrelated indicating that fluctuations in the plasma core can be resolved.

In order to improve the overall output characteristics of far‐infrared (FIR) lasers, recent development at UCLA has concentrated on the use of a metallic overmoded waveguide (smooth bore and corrugated) instead of a conventional smooth‐bore dielectric waveguide. The metallic waveguide has substantially lower propagation losses, especially at frequencies below 500 GHz, and also supports the desired HE11 mode. Laboratory results show a substantial increase in output power using a corrugated metallic waveguide, with 37 mW being obtained at 1.22 mm using 13CH3F (isotopic methyl fluoride) while maintaining the same mode quality and polarization. This represents an improvement of 100% over a smooth‐bore dielectric waveguide. Comparison of far‐infrared output using the three types of waveguide will be made.

High‐resolution interferometry using far‐infrared laser radiation is employed on TEXT‐Upgrade to measure the spatial and temporal evolution of the electron density profile as well as small‐scale perturbations. Perturbations to the electron density induced by naturally occurring sawtooth oscillations or externally imposed gas modulations can be used to ascertain the local particle flux and transport coefficients in the plasma interior. Density islands associated with Mirnov activity can also be resolved, providing detailed information on the density profile at island X and O points. Implementation of a second orthogonal view will allow accurate determination of the density profile in the various asymmetric plasma configurations of TEXT‐Upgrade.

A multichannel, heterodyne, far‐infrared laser interferometer with high spatial and phase resolution is employed on TEXT to characterize the equilibrium density profile for the full range of TEXT discharge parameters. Gaussian and parabolic functional fits with three free parameters are made to the measured profiles and compared. Scaling of the equilibrium density profile shape with plasma current, toroidal magnetic field, and density is clearly observed. By performing a regression analysis on each free parameter for the functional fit, one can construct a set of analytical relations describing the TEXT density profile for steady‐state ohmic discharges. The database used to identify these relations contains 50 different discharge conditions.

A multichannel, heterodyne, far‐infrared laser scattering system is employed on TEXT to determine the spectral and spatial properties of electron density fluctuations. The spatial resolution of this system is demonstrated by utilizing a perturbation to the plasma potential profile induced by an applied resonant field. The perturbation changes the sign of the radial electric field over a certain region of the plasma. Shifts in the density fluctuation frequency spectra can be associated with changes in the radial electric field allowing one to unambiguously resolve fluctuations in the plasma interior and edge.

Internal fluctuations arising from energetic-particle-driven instabilities, including both density and radial magnetic field, are measured in a reversed-field-pinch plasma. The fluctuations peak near the core where fast ions reside and shift outward along the major radius as the instability transits from the n = 5 to n = 4 mode. During this transition, strong nonlinear three-wave interaction among multiple modes accompanied by enhanced fast-ion transport is observed.