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Edge Plasma Phenomena in the Alcator C-Mod Tokamakmeasuredbyhighresolutionx-Ray Imaging Diagnostics by Thomas Sunn Pedersen

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Edge Plasma Phenomena in the Alcator C-Mod Tokamakmeasuredbyhighresolutionx-Ray Imaging Diagnostics by Thomas Sunn Pedersen Edge Plasma Phenomena in the Alcator C-Mod TokamakmeasuredbyHighResolutionX-Ray Imaging Diagnostics by Thomas Sunn Pedersen Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2000 c Massachusetts Institute of Technology 2000. All rights reserved. Author ............................................................. Department of Physics February 16, 2000 Certified by......................................................... Robert S. Granetz Principal Research Scientist Thesis Supervisor Certified by......................................................... Miklos Porkolab Professor of Physics Thesis Supervisor Accepted by ........................................................ Thomas J. Greytak Professor, Associate Department Head for Education Edge Plasma Phenomena in the Alcator C-Mod Tokamak measured by High Resolution X-Ray Imaging Diagnostics by Thomas Sunn Pedersen Submitted to the Department of Physics on February 16, 2000, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract In this thesis high resolution soft x-ray measurements from the Alcator C-Mod plasma edge are presented for a variety of different plasma conditions. These measurements provide radial profiles of the soft x-ray emissivity with 1.5 mm resolution or better, and temporal resolution down to 12 µs. These profiles show a distinct and very narrow pedestal shape in H-mode, indicative of the H-mode transport barrier. The soft x-ray emissivity pedestal at the outboard edge is typically 10 mm inside the last closed flux surface, near the top of the electron density and temperature pedestals. Modelling shows that the inward shift of the x-ray pedestal implies an inward shift of the impurity density pedestal. This inward shift is explained by an inward im- purity pinch located in the region of strong electron density gradient, as predicted by neoclassical impurity transport theory. Calculations using the impurity transport code MIST support the existence of a neoclassical-like inward pinch. Changes in the soft x-ray pedestal width can be interpreted as changes in the edge impurity diffusion coefficient. We find several scaling laws of the edge diffusion coefficient with various plasma parameters in EDA H-mode. A second array views the top of the plasma. The x-ray emissivity measured with this array also shows a distinct and narrow pedestal in H-mode. However, it is located significantly closer to the separatrix and is often narrower. Both of these differences increase with the safety factor at the edge, q95. Thus, there is a significant poloidal asymmetry in the impurity density in the H-mode edge region, which increases with q95. Therefore, the impurity transport in the H-mode edge is highly two-dimensional. The strong poloidal asymmetries measured show some quantitative agreement with theories developed to explain poloidal impurity asymmetries. However, none of the theories are stricly applicable to the Alcator C-Mod edge, and they all significantly underestimate the actual asymmetries that we observe. Thesis Supervisor: Robert S. Granetz Title: Principal Research Scientist 2 Thesis Supervisor: Miklos Porkolab Title: Professor of Physics 3 Acknowledgments This thesis would not have been possible without the help, support and guidance that Ihave received since Iarrived at MIT.First, Iwould like to thank my advisor, Dr. Robert Granetz, for the countless hours he spent with me, teaching me hands- on diagnostic techniques, helping me with everything from the fundamental physics to the secrets of postscript files, as well as constantly inspiring me with his energy, enthusiasm, and always good spirit. Iwould also like to thank him for introducing me to cold water diving off the coast of New England. Iwould like to thank the whole Alcator group, including fellow graduate students, for the constructive criticism and support that I have received. In particular I would like to thank Professor Ian Hutchinson, Dr. Earl Marmar, Dr. John Rice, Dr. Jim Terry, Dr. Steve Wolfe, and Professor Miklos Porkolab, whose ideas, suggestions, and insights Ihave used extensively in my thesis. Iwould also like to acknowledge the financial support Ihave received from the Danish Research Academy and the MIT Alcator Group. Last but not least Iwould like to thank my wife Ann and my son Kasper for their support and patience. 4 Contents 1Introduction 11 1.1 Controlled thermonuclear fusion as a future energy source ...... 11 1.2 The Alcator C-Mod tokamak project .................. 13 1.3 Tokamak transport phenomena ..................... 13 1.3.1 Anomalous transport ....................... 13 1.3.2 L-mode and H-mode ....................... 14 1.3.3 H-mode confinement and ELMs ................. 14 1.4 The importance of high-resolution edge x-ray measurements ..... 16 1.5 Overview of the thesis .......................... 17 2 Description and calibration of the first edge x-ray array 19 2.0.1 Data acquisition .......................... 20 2.1 Calibration of the first edge x-ray array ................. 20 2.1.1 Absolute calibration ....................... 20 2.1.2 Measurement of detector view overlap .............. 24 3Dataanalysis 27 3.1 Inversion .................................. 27 3.1.1 Improved inversion algorithm .................. 30 3.2 H-mode pedestal analysis ......................... 32 3.2.1 Effects of the radial resolution on the pedestal width ..... 33 3.3 Noise reduction .............................. 35 5 4 Measurements made with the first edge x-ray diagnostic 41 4.1 Typical example of soft x-ray data .................... 41 4.1.1 Chord integrated brightness profiles ............... 41 4.1.2 Emissivity profiles ........................ 43 4.2 Evidence for the shadow of the limiter ................. 44 4.3 Pedestal width differences in various H-mode regimes ......... 47 4.4 Pedestal scaling laws ........................... 48 4.4.1 Pedestal width scalings ...................... 48 4.4.2 Pedestal height scalings ..................... 53 4.5 L-mode emissivity profiles ........................ 54 4.6 Edge Localized Modes .......................... 55 4.6.1 The importance of ELMs ..................... 56 4.6.2 Measurements of the soft x-ray emissivity during ELMs .... 57 5 Origin of the edge soft x-ray emission 61 5.1 Origin of the soft x-ray emission in Alcator C-Mod .......... 62 5.1.1 Fluorine .............................. 63 5.1.2 Neon ................................ 68 5.1.3 Oxygen .............................. 72 5.2 Discussion ................................. 74 5.3 Temperature and density profile effects ................. 74 6 One-dimensional theory of impurity transport 79 6.1 Theory of impurity transport ...................... 79 6.1.1 Neoclassical impurity transport ................. 80 6.1.2 Collisional regimes in the Alcator C-Mod transport barrier region 82 6.2 Previous impurity transport studies in tokamaks ............ 84 6.2.1 Results from Alcator C-Mod ................... 85 6.2.2 Results from other diverted tokamak experiments ....... 86 6.2.3 Summary ............................. 87 6 7 Computer modelling of one-dimensional transport 89 7.1 Simulations of edge impurity transport and comparison to experiments 89 7.1.1 Simulation details ......................... 90 7.1.2 Localizing the inward pinch ................... 90 7.1.3 Effects of a neoclassical pinch .................. 101 7.1.4 Correlations between the x-ray and electron density pedestal locations .............................. 105 7.2 Summary of the MIST simulation results ................ 108 7.2.1 Magnetic surface mapping and diagnostic position issues ... 109 7.3 Physics of the x-ray pedestal scaling laws ................ 110 8 Automatic determination of confinement mode 113 8.1 Distinguishing parameters ........................ 114 8.2 Inclusion of Hα measurements ...................... 117 8.3 Examples of mode detection ....................... 117 9 Design and description of the two-array diagnostic 123 9.0.1 Design considerations ....................... 123 9.0.2 Data acquisition .......................... 129 9.1 Absolute calibration of the new two-array edge x-ray diagnostic ... 129 9.1.1 Determination of the absolute position of the top view .... 129 9.1.2 Determination of the absolute position of the outboard mid- plane view ............................. 130 9.2 Relative calibration of the areas of the apertures ............ 131 10 Measurements made with the two-array edge x-ray diagnostic 133 10.1 Description of typical data ........................ 133 10.2 Inversion accuracy revisited ....................... 135 10.2.1 Two examples of simulated data ................. 136 10.2.2 Conclusions ............................ 141 10.3 Systematic pedestal asymmetries .................... 143 7 10.3.1 Position asymmetries ....................... 143 10.3.2 Width asymmetries ........................ 146 10.4 Pedestal character for different types of H-modes ........... 147 10.4.1 Implications ............................ 148 10.5 H to L transitions and ELMs ...................... 151 10.5.1 ELMs ............................... 151 10.5.2 H to L transitions ......................... 151 10.5.3 Implications of the timing difference at the H-L transition .. 155 10.6 Comparison between ohmic and RF heated H-modes ......... 158 10.6.1 Results ............................... 159 10.7 Measurements of impurity injections .................. 161 10.7.1 Transient asymmetries .....................
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