J. Duff

Electron kinetic effects on interferometry, polarimetry and Thomson scattering measurements in burning plasmas (invited)

At anticipated high electron temperatures in ITER, the effects of electron thermal motion on Thomson scattering (TS), toroidal interferometer/polarimeter (TIP), and poloidal polarimeter (PoPola) diagnostics will be significant and must be accurately treated. The precision of the previous lowest order linear in τ = Te/mec(2) model may be insufficient; we present a more precise model with τ(2)-order corrections to satisfy the high accuracy required for ITER TIP and PoPola diagnostics. The linear model is extended from Maxwellian to a more general class of anisotropic electron distributions that allows us to take into account distortions caused by equilibrium current, ECRH, and RF current drive effects. The classical problem of the degree of polarization of incoherent Thomson scattered radiation is solved analytically exactly without any approximations for the full range of incident polarizations, scattering angles, and electron thermal motion from non-relativistic to ultra-relativistic. The results are discussed in the context of the possible use of the polarization properties of Thomson scattered light as a method of Te measurement relevant to ITER operational scenarios.

High-frequency fluctuation measurements by far-infrared laser Faraday-effect polarimetry-interferometry and forward scattering system on MST.

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.

Electron kinetic effects on interferometry and polarimetry in high temperature fusion plasmas

At anticipated high electron temperatures in ITER, the effects of electron thermal motion on phase measurements made by the toroidal interferometer/polarimeter (TIP) and poloidal polarimeter (PoPola) diagnostics will be significant and must be precisely treated or the measurement accuracy will fail to meet the specified requirements for ITER operation. We calculate electron thermal corrections to the interferometric phase and polarization state of an electromagnetic wave propagating along tangential and poloidal chords (Faraday and Cotton?Mouton polarimetry) and incorporate them into the Stokes vector equation for evolution of polarization. Although these corrections are small at electron temperatures Te???1?keV, they become sizable at Te???10?keV. The precision of the previous lowest order linear in the ??=?Te/mec2 model may be insufficient; we present a more precise model with ?2-order corrections to satisfy the high accuracy required for ITER TIP and PoPola diagnostics. Proper treatment of temperature effects will ensure more accurate interpretation of interferometric and polarimetric measurements in fusion devices like ITER and DEMO. The use of precise analytic expressions is especially important for burning plasmas where various interferometric techniques will be used for direct real time feedback control of device operations with time resolution ?1?ms to regulate the rate of the thermonuclear burn and monitor/control the safety factor profile.

Observation of trapped-electron-mode microturbulence in reversed field pinch plasmas

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 ...

Physics and optimization of plasma startup in the RFP

In the tokamak and reversed-field pinch (RFP), inductively driven toroidal plasma current provides the confining poloidal magnetic field and ohmic heating power, but the magnitude and/or duration of this current is limited by the available flux swing in the poloidal field transformer. A portion of this flux is consumed during startup as the current is initiated and ramped to its final target value, and considerable effort has been devoted to understanding startup and minimizing the amount of flux consumed. Flux consumption can be reduced during startup in the RFP by increasing the toroidal magnetic field, Bti, applied to initiate the discharge, but the underlying physics is not yet entirely understood. Toward increasing this understanding, we have for the first time in the RFP employed advanced, non-invasive diagnostics on the Madison Symmetric Torus to measure the evolution of current, magnetic field, and kinetic profiles during startup. Flux consumption during startup is dominantly inductive, but we find that the inductive flux consumption drops as Bti increases. The resistive consumption of flux, while relatively small, apparently increases with Bti due to a smaller electron temperature. However, the ion temperature increases with Bti, exceeding the electron temperature and thus reflecting non-collisional heating. Magnetic fluctuations also increase with Bti, corresponding primarily to low-n modes that emerge sequentially as the safety factor profile evolves from tokamak-like to that of the RFP.

Electron kinetic effects on optical diagnostics in fusion plasmas

At anticipated high electron temperatures in ITER, the effects of electron thermal motion on Thomson scattering (TS), toroidal interferometer/polarimeter (TIP) and poloidal polarimeter (PoPola) diagnostics will be significant and must be accurately treated. We calculate electron thermal corrections to the interferometric phase and polarization state of an EM wave propagating along tangential and poloidal chords (Faraday and Cotton-Mouton polarimetry) and perform analysis of the degree of polarization for incoherent TS. The precision of the previous lowest order linear in τ = Te/mec2 model may be insufficient; we present a more precise model with τ2-order corrections to satisfy the high accuracy required for ITER TIP and PoPola diagnostics. The linear model is extended from Maxwellian to a more general class of anisotropic electron distributions that allows us to take into account distortions caused by equilibrium current, ECRH and RF current drive effects. The classical problem of degree of polarization o...

An upgraded interferometer-polarimeter system for broadband fluctuation measurements

Measuring high-frequency fluctuations (above tearing mode frequencies) is important for diagnosing instabilities and transport phenomena. The Madison Symmetric Torus interferometer-polarimeter system has been upgraded to utilize improved planar-diode mixer technology. The new mixers reduce phase noise and allow more sensitive measurements of fluctuations at high frequency. Typical polarimeter rms phase noise values of 0.05°-0.07° are obtained with 400 kHz bandwidth. The low phase noise enables the resolution of fluctuations up to 250 kHz for polarimetry and 600 kHz for interferometry. The importance of probe beam alignment for polarimetry is also verified; previously reported tolerances of ≤0.1 mm displacement for equilibrium and tearing mode measurements minimize contamination due to spatial misalignment to within acceptable levels for chords near the magnetic axis.

Three dimensional equilibrium solutions for a current-carrying reversed-field pinch plasma with a close-fitting conducting shell

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 MSTs 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.