Albert E. Chou

Ultrashort‐pulse reflectometry (invited)

Time‐of‐flight radar diagnostics are envisaged as having great potential for determining electron density profiles in next generation tokamaks such as TPX and ITER. Ultrashort‐pulse radar reflectometry is a promising new time‐of‐flight diagnostic capable of making instantaneous density profile determination utilizing a single source and a single set of measurements. A proof‐of‐principle eight channel system has been constructed for use on the CCT tokamak at UCLA, and has undergone extensive testing in the laboratory.

Fundamental investigation of reflectometry as a density fluctuation diagnostic (invited)

Reflectometry is currently used to monitor density fluctuations and turbulent correlation lengths in fusion plasmas. Various models have been used to interpret the experimental data and to determine the regimes of validity of the reflectometer fluctuation measurements. Heretofore, these models have not been validated by direct comparison with experiment. In this paper the first comparison between a controlled laboratory experiment and a one‐dimensional numerical model is presented. It is found that the model is unable to predict the observed high degree of spatial localization and dependence on perturbation wave number. The implications of these disagreements are discussed, together with suggestions for their resolution.

A one‐dimensional numerical study of ultrashort‐pulse reflectometrya)

This article presents a first analysis elucidating theoretical aspects of ultrashort‐pulse reflectometry. It is studied by means of the numerical integration of a one‐dimensional full‐wave equation for ordinary modes propagating in a plasma. The numerical calculations illustrate the potential of using the reflection of ultrashort‐pulse microwaves as an effective probe even in the presence of significant density fluctuations. The difference in time delays of differing frequency components of the microwaves can be used to deduce the density profile. The modification of the reflected pulses in the presence of density fluctuations is examined and can be understood based on considerations of Bragg resonance. A simple and effective profile‐reconstruction algorithm using the zero crossings of the reflected pulse and subsequent Abel inversion is demonstrated. The robustness of the profile reconstruction algorithm in the presence of a sufficiently small amplitude density perturbation is assessed.

The Bragg resonance picture of one‐dimensional fluctuation reflectometry beyond the Born approximationa)

By using HELM1D, a numerical, one‐dimensional Helmholtz equation solver, we have studied the scattering phase shift of S‐polarized O modes in fluctuation reflectometry both within and beyond the Born approximation. Comparisons are made between these numerical results and analytical expressions obtained through the use of the Born approximation. As the fluctuation amplitude increases, various peaks of the phase response evolve with distinct growth rates. This leads to steepening and distortion of the scattering phase shift due to a single wave‐number fluctuation. The simultaneous coexistence of large amplitude fluctuations with nearby wave numbers complicates the task of resolving the response at each wave number.

Reflectometry as a fluctuation diagnostic: A one‐dimensional simulation

Reflectometry is currently employed to characterize turbulence in fusion plasmas worldwide and is expected to be a major diagnostic on the next generation of machines (e.g., ITER). Until recently, little was known about the response of a reflectometer to fluctuations (degree of localization of the signal, sensitivity to fluctuation wave number, dependence on density scale length, etc.). To elucidate these properties, we have been modeling reflectometer behavior with a code based on solution of a one‐dimensional full wave equation. The code models an infinite plane plasma with density gradient in the x direction and solves the full wave equation to find the electric field of the reflectometer’s electromagnetic wave. It can simulate stationary and moving density perturbations with arbitrary waveforms and wave numbers in plasmas with arbitrary density profiles. We present results of test cases comparing computational results to known analytic solutions for linear and 1−α2/x2 plasma density profiles, which sh...

A comparison of the oscillating mirror and Bragg resonance pictures of fluctuation reflectometry in one-dimensional plasmas (abstract)

We have computed the amplitude and phase responses of microwaves scattered from fluctuation wave packets that stream down a density gradient. At various wavelengths and packet sizes and shapes, the dominant scattered signal is either due to reflection from the critical surface or due to Bragg resonance scattering from below the critical density. Depending on the amplitude and wavelength of the fluctuation, one or both of these mechanisms might play a role. The delineation of their relative importance is carried out. Comparisons are made to previous studies within and beyond the Born approximation.1,2 The motivation for this work is a series of well-controlled experiments carried out by the plasma diagnostics group at UC Davis. We will show comparisons of our numerical results, using their experimental parameters, with their measurements of scattered microwave amplitude and phase.3

Studies of the localization paradox of fluctuation reflectometry via multidimensional SOFTSTEP simulations (abstract)

The initial value problem of the scalar wave equation modeling the propagation and scattering of O modes in a fluctuating plasma is solved numerically. Using split operator and FFT techniques, SOFTSTEP codes solve the slow temporal envelope equations that describe fluctuation reflectometry in the presence of space and time varying density profiles. Previous studies have revealed an inexplicable sensitivity of the scattered phase signal to input microwave frequency. This might suggest that the fluctuations that give rise to the scattered signals are highly localized in space, much more so than one might expect on physical grounds. Our simulations attempt to resolve this paradox by demonstrating the existence of additional interference between various signals that contribute to the same measured phase. As the launching and detecting antennas are a few wavelengths wide, the measured phase is an average over their surface areas. This results in added sensitivity and wavelength selectivity which might be overc...

A one‐dimensional numerical study of ultrashort‐pulse reflectometry (abstract)a)

This article presents a first analysis elucidating theoretical aspects of ultrashort‐pulse reflectometry. It is studied by means of the numerical integration of a one‐dimensional full‐wave equation for ordinary modes propagating in a plasma. The numerical calculations illustrate the potential of using the reflection of ultrashort‐pulse microwaves as an effective probe even in the presence of significant density fluctuations. The difference in time delays of differing frequency components of the microwaves can be used to deduce the density profile. The modification of the reflected pulses in the presence of density fluctuations is examined and can be understood based on considerations of Bragg resonance. A simple and effective profile‐reconstruction algorithm using the zero crossings of the reflected pulse and subsequent Abel inversion is demonstrated. The robustness of the profile reconstruction algorithm in the presence of a sufficiently small amplitude density perturbation is assessed.

Bragg resonance picture of one‐dimensional fluctuation reflectometry beyond the Born approximation (abstract)a)

By using HELM1D, a numerical, one‐dimensional Helmholtz equation solver, we have studied the scattering phase shifts of S‐polarized O modes in fluctuation reflectometry both within and beyond the Born approximation. Comparisons are made between these numerical results and analytical expressions obtained through the use of the Born approximation. As the fluctuation amplitude increases, various peaks of the phase response evolve with distinct growth rates. This leads to steepening and distortion of the scattering phase shift due to a single wave‐number fluctuation. The simultaneous coexistence of large amplitude fluctuations with nearby wave numbers complicates the task of resolving the response at each wave number.