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Imaging and Probe Techniques for Wave Dispersion Estimates in Magnetized Plasmas

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Imaging and Probe Techniques for Wave Dispersion Estimates in Magnetized Plasmas Imaging and Probe Techniques for Wave Dispersion Estimates in Magnetized Plasmas by A. D. Light B.A./B.S., Case Western Reserve University, 2005 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Physics 2013 This thesis entitled: Imaging and Probe Techniques for Wave Dispersion Estimates in Magnetized Plasmas written by A. D. Light has been approved for the Department of Physics Prof. Tobin Munsat Prof. Martin Goldman Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. Light, A. D. (Ph.D., Physics) Imaging and Probe Techniques for Wave Dispersion Estimates in Magnetized Plasmas Thesis directed by Prof. Tobin Munsat Fluctuations in magnetized laboratory plasmas are ubiquitous and complex. In addition to deleterious effects, like increasing heat and particle transport in magnetic fusion energy devices, fluctuations also provide a diagnostic opportunity. Identification of a fluctuation with a particular wave or instability gives detailed information about the properties of the underlying plasma. In this work, diagnostics and spectral analysis techniques for fluctuations are developed and applied to two different laboratory plasma experiments. The first part of this dissertation discusses imaging measurements of coherent waves in the Controlled Shear Decorrelation Experiment (CSDX) at the University of California, San Diego. Visible light from ArII line emission is collected at high frame rates using an intensified digital camera. A cross-spectral phase technique allows direct visualization of dominant phase structures as a function of frequency, as well as identification of azimuthal asymmetries present in the sys- tem. Experimental dispersion estimates are constructed from imaging data alone. Drift-like waves are identified by comparison with theoretical dispersion curves, and a tentative match of a low- frequency spectral feature to Kelvin-Helmholtz-driven waves is presented. Imaging measurements are consistent with previous results, and provide non-invasive, single-shot measurements across the entire plasma cross-section. Relationships between imaging and electrostatic probe measurements are explored. The second part of this dissertation discusses the design and construction of diagnostics for the Colorado Field-Reversed Configuration (CFRC), as well as preliminary results. A triple probe, a Mach probe, a multi-chord heterodyne interferometer, Rogowski coils, a single-point, three-axis magnetic probe, and a 16-point, three-axis magnetic probe have been constructed. Each diagnostic is designed for fluctuation measurements up to the data acquisition Nyquist frequency of 20MHz. iv A histogram cross-spectral analysis technique allows experimental dispersion estimates to be made from multi-channel magnetic measurements. Hints of waves in the range of ion-cyclotron frequency harmonics are observed, but lack of global information about the plasma objects formed in CFRC prevents definitive interpretation. Dedication To anyone who might find this work useful, and to the taxpayers who funded it. vi Acknowledgements You know who you are. Contents Chapter 1 Introduction and General Background 1 1.1 Overview and Organization of Dissertation . ............ 1 1.2 SpectralDensityEstimation. ......... 2 1.2.1 Overview ...................................... 2 1.2.2 SpectralDensity ............................... ... 3 1.2.3 TheTwo-PointTechnique . .... 4 1.2.4 Two-dimensional Fourier Transform Technique . ........... 6 2 Imaging Measurements of Fluctuations in the Controlled Shear Decorrelation Experiment 7 2.1 Motivation ...................................... ... 7 2.2 TheoreticalBackground . ....... 8 2.2.1 Instabilities in a Linear, Magnetized Plasma Column . ............. 8 2.3 CSDX-UDevice.................................... 16 2.3.1 Overview ...................................... 16 2.3.2 DeviceHardware ................................ 17 2.4 ImagingMeasurementsofCoherentModes. .......... 24 2.4.1 Cross-spectral-density Phase Mapping . .......... 24 2.4.2 Dispersionestimatesfromintensity . .......... 28 2.4.3 ImplicationsforDynamics. ...... 35 viii 2.4.4 DiscussionofImagingResults. ....... 38 2.5 Relationship between Probe and Imaging Measurements . .............. 39 2.5.1 IntensityasaProxyforDensity . ...... 39 2.5.2 Correlations Between Intensity and Electrostatic Quantities . 40 3 The Colorado FRC Experiment 51 3.1 MotivationandOverview . ...... 51 3.2 TheoreticalBackground . ....... 53 3.2.1 The Spheromak and the Woltjer-Taylor Relaxation Paradigm ......... 53 3.2.2 The Field-Reversed Configuration - High β ................... 55 3.3 DeviceandDiagnostics. ....... 61 3.3.1 PlasmaGuns .................................... 62 3.3.2 DischargeDiagnostics . ..... 67 3.3.3 PlasmaDiagnostics. 69 3.3.4 CFRC Plasma Properties and Machine Status. ........ 89 3.4 Wave Measurements Using High-Resolution Magnetics . ..............109 Bibliography 118 ix Tables Table 2.1 Comparison of partial derivatives of with respect to normalized electron temperature fluctuation amplitude. If the dynamics are adiabatic (V n ), the high sensitiv- p ∼ e ity of Vˆ Vˆ to the temperature fluctuation level should make it obvious when f − p temperature fluctuations cannot be neglected. .......... 48 Figures Figure 2.1 Illustration of the drift wave mechanism. (a) Initial conditions: An ion perturbation in the presence of a background magnetic field and density gradient. (b) The accom- panying potential perturbation generates a local E B circulation. (c) The E B × × brings higher density towards one side of the perturbation and lower density to the other. (d) Thus the density perturbation propagates in the electron diamagnetic direction. ......................................... 10 2.2 An annotated copy of Fig. 2 of Ref. 53, showing the points used for computation of the b parameter. A parabola fit to these points is used to extrapolate b values beyond m =5. ....................................... 12 2.3 Time average profiles for plasma parameters. (a) Electron density and temperature profiles. The black solid line is a Gaussian fit to the density data (gray dots). (b) Measured plasma potential and resulting azimuthal E B velocity. 17 × 2.4 Technical drawing of the CSDX device. Labeled distances are as follows: (a) Length of experimental section. (b) Axial distance from z = 0 to location of 4-tip probe. (c) Axial distance from location of 4-tip probe to end window (optical path length from the camera focal plane to the window). (d) Magnet spacing. (e) Diameter of experimentalsection.. ..... 18 xi 2.5 Background axial magnetic field properties. (a) Axial profile of background magnetic field at Imag = 330A. (b) Calibration data for background magnetic field as a function of coil current. Uncertainties in measured values are within the size of the datamarkersforboth(a)and(b). ..... 20 2.6 (a) Layout of the electrostatic probe used for measuring fluctuations. The view is end on, from the center of the plasma column. Tips 2, 3, and 4 are in the same (radial) plane while tip 1 protrudes farther into the plasma (darker shading). This geometry allows radial and azimuthal electric fields to be estimated from differences in floating potential. (b) Photograph of the actual probe (side view), including stabilizer disk to ensure that the geometry remains fixed even if the probe stalkdroops. 20 2.7 (a) Raw image example (single frame). White corresponds to zero intensity. (b) Normalized radial profiles of mean I488 (solid black), RMS I488 fluctuation amplitude (dashed black), and mean Is (solidgray). ........................ 23 2.8 Time-average radial profiles of electron density (ne), ion saturation current (Is), and intensity (I488). A Gaussian fit to the density is a convenient and reasonably accurate representationoftheprofileshape. ........ 24 2.9 The average coherence spectrum of the plasma column compared with the average power spectrum. Error bars in the cross-spectral power are statistical uncertainty in the discrete CSD estimate. Note that the power spectrum is plotted on a logarithmic scale. (a)-(d) are the four most prominent peaks, corresponding to the phase maps inFig.2.10. ........................................ 26 2.10 Sample phase maps for the four most prominent coherent modes. Vertical bars in Fig. 2.9 highlight the frequency component corresponding to each map, (a), (b), (c) and(d). .......................................... 26 2.11 Standard-deviation maps (Eq. 1.6) corresponding to Fig. 2.10. Note that particularly asymmetric parts of the phase maps seem to coincide with high uncertainty. 26 xii 2.12 (a) Time-average frame. (b) RMS frame. (c) Azimuthal variation at r = 3cm for time-average (mean) I488, RMS I488, and the radial gradient (negative) of I488. Intensity is normalized to its maximum value in the image sequence. ......... 28 2.13 Normalized spectral density and measured dispersion relations at r = 3cm from (a) 2D auto-spectral density of image data, (b) average of 32 two-point estimates from pixel data, (c) two-point floating-potential data (probe), and (d) two-point pixel data. The color scale for each plot indicates the power relative to the total spectral power at the given radius. White circles represent the maxima of the k-spectra for frequencies where the total spectral power is more than
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