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In its basic form, phase contrast imaging (PCI) provides line-integrated measurements of electron density fluctuations in plasmas. As turbulent fluctuations in magnetically confined plasmas have wave vectors almost perpendicular to the background magnetic field, the signals scattered by fluctuations from different parts of the PCI line-of-sight (LoS) are spatially separated in focal planes of the plasma. This allows localized PCI measurements by placing a mask in such a plane, to only permit signals from specific parts of the LoS to reach the PCI detectors. The present paper describes modeling and design of localization masks for the PCI system at the Wendelstein 7-X (W7-X) stellarator as well as the first results obtained using the masks in the recent long-pulse W7-X experimental campaign. During this project, we have extended the theory describing the mask response within the Fraunhofer diffraction model. As a novel development, we show from first principles that the mask response is determined by the fraction of power of the scattered beam spots that passes the mask. These insights have been used to select the W7-X mask design, consisting of a circular cutout, allowing the unscattered beam spot to pass the mask, with wedges covering a fixed angular range outside the central cutout. In the recent W7-X experimental campaign, the masks have verified the location of the main turbulence features observed by the PCI system and provided new information about the location of short-wavelength magnetohydrodynamic modes. [ABSTRACT FROM AUTHOR]

This work describes a novel optical heterodyne detection scheme that significantly extends the frequency response of the phase contrast imaging method to detect electron density fluctuations in tens of megahertz frequency range. The system employs a variable frequency electro-optic modulator to allow operation at any frequency in the range 10–40 MHz without the need to realign the system. The frequency coverage of the system makes it suitable to measure the radial structure of the electron density component of ion cyclotron emission on devices having confining magnetic field of a few tesla, thus extending the purely temporal measurements provided so far by magnetic probes. [ABSTRACT FROM AUTHOR]

Mode conversion of fast waves in the ion cyclotron range of frequencies (ICRF) is known to result in current drive and flow drive under optimised conditions, which may be utilized to control plasma profiles and improve fusion plasma performance. To describe these processes accurately in a realistic toroidal geometry, numerical simulations are essential. Quantitative comparison of these simulations and the actual experimental measurements is important to validate their predictions and to evaluate their limitations. The phase contrast imaging (PCI) diagnostic has been used to directly detect the ICRF waves in the Alcator C-Mod tokamak. The measurements have been compared with full-wave simulations through a synthetic diagnostic technique. Recently, the frequency response of the PCI detector array on Alcator C-Mod was recalibrated, which greatly improved the comparison between the measurements and the simulations. In this study, mode converted waves for D-3He and D-H plasmas with various ion species compositions were re-analyzed with the new calibration. For the minority heating cases, self-consistent electric fields and a minority ion distribution function were simulated by iterating a full-wave code and a Fokker-Planck code. The simulated mode converted wave intensity was in quite reasonable agreement with the measurements close to the antenna, but discrepancies remain for comparison at larger distances. [ABSTRACT FROM AUTHOR]

For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness. [ABSTRACT FROM AUTHOR]

We present an experimental and numerical study of hydrodynamic and magnetohydrodynamic free shear layers and their stability. We first examine the experimental measurement of globally unstable hydrodynamic shear layers in the presence of rotation and their range of instability. These are compared to numerical simulations, which are used to explain the modification of the shear layer, and thus the critical Rossby number for stability. Magnetic fields are then applied to these scenarios and globally unstable magnetohydrodynamic shear layers generated. These too are compared to numerical simulations showing behavior consistent with the hydrodynamic case and previously reported measurements. [ABSTRACT FROM AUTHOR]

Reversed shear Alfvén eigenmodes (RSAEs) have been observed with the phase contrast imaging diagnostic and Mirnov coils during the sawtooth cycle in Alcator C-mod [M. Greenwald et al., Nucl. Fusion 45, S109 (2005)] plasmas with minority ion-cyclotron resonance heating. Both down-chirping RSAEs and up-chirping RSAEs have been observed during the sawtooth cycle. Experimental measurements of the spatial structure of the RSAEs are compared to theoretical models based on the code NOVA [C. Z. Cheng and M. S. Chance, J. Comput. Phys. 71, 124 (1987)] and used to derive constraints on the q profile. It is shown that the observed RSAEs can be understood by assuming a reversed shear q profile (up chirping) or a q profile with a local maximum (down chirping) with q≈1. [ABSTRACT FROM AUTHOR]

Recent advances in gyrokinetic simulation of core turbulence and associated transport requires an intensified experimental effort to validate these codes using state of the art synthetic diagnostics to compare simulations with experimental data. A phase contrast imaging (PCI) diagnostic [M. Porkolab, J. C. Rost, N. Basse et al., IEEE Trans. Plasma Sci. 34, 229 (2006)] is used to study H-mode plasmas in Alcator C-Mod [M. Greenwald, D. Andelin, N. Basse et al., Nucl. Fusion 45, S109 (2005)]. The PCI system is capable of measuring density fluctuations with high temporal (2 kHz–5 MHz) and wavenumber (0.5–55 cm-1) resolution. Recent upgrades have enabled PCI to localize the short wavelength turbulence in the electron temperature gradient range and resolve the direction of propagation (i.e., electron versus ion diamagnetic direction) of the longer wavelength turbulence in the ion temperature gradient (ITG) and trapped electron mode range. The studies focus on plasmas before and during internal transport barrier formation in an enhanced Dα H-mode plasma assisted with ion cyclotron resonance frequency heating. Nonlinear GYRO simulations have also been performed [J. Candy and R. E. Waltz, Phys. Rev. Lett. 91, 045001 (2003)] and the predicted fluctuation is compared against experimental measurements through a synthetic PCI diagnostic method. The simulated fluctuations from GYRO agree with experimental measurements in the ITG regime. GYRO also shows good agreement in transport predictions with experimental measurements after reducing the ion temperature gradient (∼15%) and adding E×B shear suppression, all within the experimental uncertainty. [ABSTRACT FROM AUTHOR]

The recently upgraded phase-contrast imaging (PCI) diagnostic is used to characterize the transition from the low (L) to the enhanced Dα (EDA) high (H) confinement mode in Alcator C-Mod [I. H. Hutchinson, R. Boivin, F. Bombarda et al., Phys. Plasmas 1, 1511 (1994)] plasmas. PCI yields information on line integrated density fluctuations along vertical chords. The number of channels has been increased from 12 to 32 and the sampling rate from 1 MHz to 10 MHz. This expansion of diagnostic capabilities is used to study broadband turbulence in L and EDA H mode and to analyze the quasicoherent (QC) mode associated with EDA H mode. Changes in broadband turbulence at the transition from L to EDA H mode can be interpreted as an effect of the Doppler rotation of the bulk plasma. Additional fluctuation measurements of Dα light and the poloidal magnetic field show features correlated with PCI in two different frequency ranges at the transition. The backtransition from EDA H to L mode, the so-called enhanced neutron (EN) mode, is investigated by new high frequency (132 and 140 GHz) reflectometer channels operating in the ordinary (O) mode. This additional hardware has been installed in an effort to study localized turbulence associated with internal transport barriers (ITBs). The EN mode is a suitable candidate for this study, since an ITB exists transiently as the outer density decreases much faster than the core density in this mode. The fact that the density decays from the outside inward allows us to study fluctuations progressing towards the plasma core. Our results mark the first localized observation of the QC mode at medium density: 2.2×1020 m-3 (132 GHz). Correlating the reflectometry measurements with other fluctuating quantities provides some insight regarding the causality of the EN-mode development. [ABSTRACT FROM AUTHOR]

Phase contrast imaging (PCI) diagnostic has been used to study mode conversion physics of ion cyclotron range of frequency waves [E. Nelson-Melby et al., Phys. Rev. Lett. 90, 155004 (2003)], plasma turbulence [A. Mazurenko et al., Phys. Rev. Lett. 89, 225004 (2002); N. Basse et al., Phys. Plasmas 12, 052512 (2005)], and Alfvén Cascades [M. Porkolab et al., IEEE Trans. Plasma Sci. 34, 229 (2006)] in Alcator C-Mod. The C-Mod PCI system measures line integrated electron density fluctuations along 32 vertical chords with a sampling frequency of 10 MHz and wavenumber resolution up to 30 cm-1. Although PCI normally lacks localization along the chords, the vertical variation of the magnetic field pitch angle allows for localized measurements for large k⊥ fluctuations. A system consisting of a partially masked phase plate on a rotatable stage has been installed and quasicoherent modes with wave number ∼5 cm-1 associated with the enhanced DαH mode at the top and bottom of the plasma have been differentiated. In future experiments, for k∼30 cm-1, a spatial resolution of r/a∼0.3 can be achieved under ideal conditions. [ABSTRACT FROM AUTHOR]

A phase contrast imaging (PCI) diagnostic has been developed for the Wendelstein 7-X (W7-X) stellarator. This diagnostic, funded by the U.S. Department of Energy through the Office of Fusion Energy Sciences, is a collaboration between the Max Planck Institute for Plasmaphysics, MIT, and SUNY Cortland. The primary motivation for the development of the PCI diagnostic is measurement of turbulent fluctuations, such as the ion temperature gradient, electron temperature gradient, and the trapped electron mode instabilities. Understanding how the magnetic geometry and other externally controllable parameters, such as the fueling method and heating scheme, modify the amplitude and spectrum of turbulence is important for finding operational scenarios that can lead to improved performance at fusion-relevant temperatures and densities. The PCI system is also sensitive to coherent fluctuations, as may arise from Alfvén eigenmodes or other MHD activity, for example. The PCI method creates an image of line-integrated variations in the index of refraction. For a plasma, the image created is proportional to the line-integral of electron density fluctuations. This paper provides an overview of some key features of the hardware and the optical system and presents two examples of recent measurements from the W7-X OP1.2a experimental campaign.