Nicholas E. Lanier. Doctor of Philosophy. (Physics) University of Wisconsin Madison

Transcription

1 ELECTRON DENSITY FLUCTUATIONS AND FLUCTUATION-INDUCED TRANSPORT IN THE REVERSED-FIELD PINCH by Nicholas E. Lanier A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) at the University of Wisconsin Madison 1999

2 i ELECTRON DENSITY FLUCTUATIONS AND FLUCTUATION- INDUCED TRANSPORT IN THE REVERSED-FIELD PINCH Nicholas E. Lanier Under the supervision of Professor Stewart C. Prager At the University of Wisconsin Madison An extensive study on the origin of density fluctuations and their role in particle transport has been investigated in the Madison Symmetric Torus reversed-field pinch. The principal physics goals that motivate this work are: investigating the nature of particle transport in a stochastic field, uncovering the relationship between density fluctuations and magnetic field fluctuations arising from tearing and reconnection, identifying the mechanisms by which a single tearing mode in a stochastic medium can affect particle transport. Following are the primary physics results of this work. Measurements of the radial electron flux profiles indicate that confinement in the core is improved during pulsed poloidal current drive experiments. Correlations between density and magnetic fluctuations demonstrate that the origin of the large amplitude density fluctuations can be directly attributed to the core-resonant tearing modes, and that these fluctuations are advective in the plasma edge; however, these fluctuations appear compressional in the core, provided the nonlinear terms are small. Correlations between density and radial velocity fluctuations indicate that although the fluctuations from the core-resonant modes dominate at the edge, their relative phase is such that they do not cause transport there, consistent with the expectation that core modes do not destroy edge magnetic surfaces. This is not the case in the plasma core, where the density and radial velocity fluctuations are in phase, indicating that

3 ii these fluctuations couple to induce transport. Measurements during PPCD discharges show a large reduction in density fluctuations associated with the core-resonant modes. Furthermore, the phase of these fluctuations in the core changes to be π/2 relative to the radial velocity fluctuations, indicating these fluctuations no longer couple to induce transport.

4 iii Acknowledgements Although my defense was only two hours, it represented the culmination of a long and challenging path. In pursuing my degree, there have been many noteworthy individuals that have offered support and direction, and although I have done the work, they have made this possible, and I wish to acknowledge their efforts. Prior to my graduate career, five individuals stand out as being very influential in my progress in physics. Mr. Larry Dean, my high-school physics teacher who started my formal training in physics, Russ Coverdale, the academic advisor at Purdue, who stuck me in the Honors curriculum and forced me to swim. Still as an undergraduate, my first real world work experience was obtained with Dr. John Molitoris, may he always have a place to sit, and Dr. Paul Springer, who showed the faith in my leadership skills by sending me to Russia to run some great physics experiments. Finally I d like to thank Dr. C. Choi, who introduced me to plasma physics and opened the door to my coming to Wisconsin.

5 iv My years at Wisconsin have been the most enjoyable of my life and the MST group has been a principal reason for that. Faculty such as Sam Hokin, Paul Terry, James Callen, and Chris Hegna (if not he should be) have really worked to expand my plasma physics knowledge. I am especially grateful for the efforts of my advisor Stewart Prager, Cary Forest, and Darren Craig (who will be faculty someday, no doubt about it). MST staff like John Sarff, who introduced me to PPCD, Dan former vacuum man now diversifying into computer repair Den Hartog, Genady come with an envelope leave with a solution Fiksel have really fostered my experimental talents. Not to be underestimated are the benefits gained from working with David the Texan Brower and Yong lip smackin good Jiang. Finally, I thank Dale, Larry, Paul, Mikey, Kay, John, Don and the rest of the MST support crew for helping to turn my ideas into reality. By far the most outstanding aspect of MST life are the graduate students. In my six years here, students like, James Jimbo Chapman, Carl the only man I ve seen argue (and win) with Callen Sovinec, Jay the Mason Anderson, Ted Ironman Biewer, Brett the big lovable vacuum Nazi Chapman, Ching- Shih LT Chaing, Alex BA Hansen, Derek the Bavenator Baver, Paul Wrong glass sir Fontana, Cavendish the Dishman Mckay, Susanna nickname pending Castillo, and of course Neal it ll happen someday Crocker, have made my career here unforgettable. I have no wish to leave such a remarkable set of individuals, but my development as a physicist requires it. Finally I d like to thank those outside my work life, my parents who not so jokingly quote that I was bred for science, my sister Catherine, my friends, Scott

6 Kruger, Paul Ohmann, Brian Totten, others that have been supportive of my efforts here. I have been truly blessed. v In memory of Katherine Nicole Lanier (December 20, 1996)

7 vi Table of Contents Abstract i Acknowledgements iii Table of Contents vi List of Tables List of Figures xii xiii 1 Introduction The Reversed Field Pinch Magnetic Island Formation and Stochasticity Stochastic Transport Fluctuation-Induced Radial Particle Flux Controlling Fluctuations Overview of Thesis References

8 vii 2 The Far-Infrared Laser System Plasma Interferometry Theory The Far-Infrared Laser Interferometer Diagnostic Overview The CO 2 Pumping Laser The Twin Far-Infrared Laser Power Distribution Detection Electronics Digital Phase Extraction Summary References Neutral Hydrogen Density In MST Hydrogen Fueling in MST The Fueling Cycle Franck-Condon Neutrals Neutral Penetration Measuring Neutral Density The H α Array Alignment and Calibration H α Emission

9 viii H α Behavior in Standard Discharges H α Behavior in PPCD Discharges Neutral Particle Density Neutral Particle Profiles in Standard and PPCD Discharges Neutral Particle Losses Neutral Particle Population and CHERS Summary References Impurity Behavior In MST Introduction Atomic Physics Ionization Radiative and Dielectronic Recombination Charge Exchange Recombination Charge State Equilibrium (Coronal or LTE) Electron Impact Excitation and Line Emission The ROSS Filtered Spectrometer Filter Characteristics The Soft X-ray Diodes Diagnostic Geometry and Light Collection

10 ix Deciphering Impurity Line Emission Line Contamination Impurity Effects Impurity Concentration in Standard Discharges Impurity Concentration in PPCD Discharges Electron Sourcing From Impurities Impurity Radiation Estimating Impurity Confinement Times Summary References Radial Electron Flux Profile Measurements Equilibrium Electron Density Behavior Density Profiles in Standard Discharges Density Profiles During PPCD Radial Particle Flux Extracting Radial Particle Flux Radial Particle Flux in Standard and PPCD Discharges Particle Confinement Times Convective Power Loss Summary

11 References x 6 Fluctuations and Fluctuation-Induced Particle Transport Electron Density Fluctuations Chord-Integrated Fluctuation Amplitude Frequency Spectrum Wave Number Content Correlation Between Density and Magnetic Fluctuations Local Density Fluctuation Profiles Origin of Density Fluctuations The Electron Continuity Equation Measurements of the Radial Velocity Fluctuations Nature of Density Fluctuations Fluctuation-Induced Particle Transport Summary References Conclusions 136 A Polarimetry / Interferometry Discussion 140 A.1 Introduction

12 xi A.2 Derivation of Measured Signal Power A.3 Derivation of Reference Power A.4 Digital Extraction of Interferometer Phase A.5 Extracting the Polarimetry Phase References B FIR Density Codes and Analysis Procedures 157 B.1 Introduction B.2 Processing FIR Data B.2.1 General Code Notes B.2.2 The FIR Processing Code B.2.3 Pre-Inspection of Processed Data B.2.4 Inspection Code B.2.5 Manual Removal of Phase Jumps B.2.6 The Manual Processing Code C FIR Polarimety Codes and Analysis Procedures 200 C.1 Introduction C.2 Processing Polarimetry Data C.2.1 The Polarimetry Processing Code C.3 Mesh Calibration

13 xii D H α, CO 2 and other Processing Codes 215 D.1 Introduction D.2 The H α Processing Code D.3 The CO 2 Processing Code E H α Array Components List 227 E.1 The H α Parts List F The SXR Ratio What Does It Really Mean? 228 F.1 Dispelling the Myth Behind the SXR Ratio

14 xiii List of Tables 2.1 FIR Chord Locations The FIR Mesh Geometries Lines Monitored By ROSS Spectrometer ROSS Filter Characteristics E.1 The H α Parts List

15 xiv List of Figures 1.1 The magnetic field configuration of the RFP The RFP q profile Tearing mode island formation Magnetic island overlap in RFP The PPCD circuit Fluctuation reduction during PPCD The Far-Infrared Interferometer The CO 2 pumping laser CO 2 mode of vibration The CO 2 lasing cycle The twin FIR laser FIR beam profile FIR chord locations Preamplifier gain curve Phase resolution histogram

16 xv 2.10 Chord-integrated density for r ~ -24 cm The MST fueling cycle Collision rates for atomic hydrogen The H α detector H α filter transmission Chord-averaged H α trace H α emission over sawtooth crash Radial profile of chord-integrated H α emission Chord-integrated H α in standard and PPCD plasmas Chord-averaged neutral density in standard and PPCD plasmas Neutral density profile in standard discharge Neutral density profile in PPCD discharge Charge exchange cross-sections for CHERS Impurity state density continuity equation Impact ionization cartoon Radiative and dielectronic recombination cartoons Charge exchange recombination cartoon Collision rates for O VII and O VIII Excitation rates for core impurity states of C, Al,and O ROSS filter transmission curves The AXUV-100 diode

17 xvi 4.9 O VII and O VIII densities over sawtooth C V and C VI densities over sawtooth O VII and O VIII emission in PPCD ROSS emission (High energy channel) ROSS emission ( C VI channel) ROSS emission ( C V channel) ROSS emission ( B IV channel) Bolometric vs. radiated power O VIII confinement time Chord-integrated density over crash Electron density profiles over sawtooth crash Chord-integrated density during PPCD Electron density profiles during PPCD Total radial particle flux in standard and PPCD discharges Chord-integrated density fluctuations over sawtooth crash Chord-integrated density fluctuation profiles Chord-integrated density fluctuation frequency spectrum Density fluctuation m behavior Average toroidal mode spectrum Toriodal mode spectrum Density fluctuation coherence with core-resonant modes

18 xvii 6.8 Radial density fluctuation profiles Computed C V and He II profiles Coherence between density and radial velocity of He II Coherence between density and radial velocity of C V Coherence profile between density and radial velocity of He II Coherence phase profile in standard and PPCD discharges B.1 Example of a phase jump missed by FIR processing code B.2 Example of incorrect offsetting of the FIR data B.3 Graphic interface of MAN_FIX_FAST.PRO B.4 Missed phase jump B.5 Zoomed in view of phase jump B.6 Example of a GOOD density trace F.1 The SXR ratio vs. Plasma Current F.2 The transmission curves of the BE_1 And BE_2 foils

19 1 1: Introduction Three physics goals motivate this thesis. They include: investigating the nature of particle transport in a stochastic magnetic field, uncovering the relationship between density fluctuations and magnetic field fluctuations arising from tearing and reconnection, identifying the mechanisms by which a single tearing mode in a stochastic medium can affect particle transport. These issues are particularly relevant to the reversed-field pinch 1 (RFP) because improving confinement continues to be the primary obstacle in advancing the RFP as a fusion concept. Recent theoretical understanding predicts that large magnetic tearing modes resonant in the core are responsible for particle and energy transport 2 in the RFP, and has led to the idea that confinement can be improved by reducing these fluctuations. Magneto- Hydrodynamics (MHD) modeling indicates that these tearing modes are driven by gradients in the parallel current density gradient, and can be reduced through auxiliary current drive. 3 These predictions are supported by recent experimental evidence showing that during pulsed poloidal current drive

20 2 (PPCD), which in an experiment designed to flatten the edge parallel current density gradient, can halve the magnetic fluctuations while increasing the global energy confinement fivefold. 4 Understanding fluctuations and their role in confinement continues to be a primary research focus of the MST group. Past experiments, limited to the extreme plasma edge, have explored both magnetic and electrostatic fluctuationinduced particle 5,6 and energy 7 transport. These experiments led to two conclusions about transport in the RFP. The fluctuation-induced particle transport experiments showed that electrostatic transport dominates over the magnetic component in the edge, but further in; the magnetic fluctuations play a larger role. The second conclusion was that although particle transport from magnetic fluctuations was small, energy transport was not. This work aims to improve our understanding of the transport processes over the entire RFP plasma cross section. This is conducted in two parts: by quantitatively investigating the equilibrium particle transport through simultaneous measurement of the electron density and source profiles (from both hydrogen and impurities), and exploring the fluctuations and fluctuationinduced particle transport by examining the relationship between electron density fluctuations and radial velocity fluctuations. Five experimental tools enabled this study in the MST 8 reversed-field pinch. They include a fast multichord far-infrared laser interferometer to measure equilibrium and fluctuating electron density throughout the plasma, a multi-chord H α radiation diagnostic to quantify the electron sourcing from ionization of neutral hydrogen, a thin-film multi-foil diode spectrometer to estimate the electron source from impurities, a fast Doppler spectrometer to monitor impurity ion radial velocity fluctuations,

21 and inductive current profile control (known as PPCD) to alter the fluctuation and particle transport characteristics. 3 This work reports three primary conclusions. First, through measurements of the radial electron flux profile, we have determined that pulsed poloidal current drive, or PPCD, experiments improve particle confinement in the reversed-field pinch (RFP) core. Second, most of the large amplitude density fluctuations are directly attributed to the core-resonant tearing modes, and that these density fluctuations are compressional in the core and advective (i.e. resulting from the radial motion of the equilibrium density gradient) in the edge. Finally, we demonstrate for standard discharges, that the density fluctuations associated with the core-resonant tearing modes do cause particle transport in the core but do not cause transport in the RFP edge, but when magnetic fluctuations are reduced (during PPCD), particle transport from these core-resonant modes also drops. In this introductory section we revisit some basic principles of the MST RFP as well as a heuristic description of magnetic tearing modes and their relevance to particle transport. We also briefly discuss the inductive current profile control capability that has proved very useful in examining the relationship between magnetic fluctuations and confinement in the RFP. In the final section we present an overview of the thesis. 1.1 The Reversed-Field Pinch (RFP) The RFP is a toroidally axisymmetric current-carrying plasma where the toroidal magnetic field amplitude is of the same order as the poloidal magnetic field. An interesting feature of the RFP is that upon startup the plasma

22 4 naturally relaxes to its preferred state where the toroidal field reverses direction, hence the name reversed -field pinch (figure 1.1). This relaxation mechanism, sometimes referred to as the Dynamo, is responsible for the sustainment of the RFP discharge; however, in carrying out this task, the dynamo degrades the particle and energy confinement of the plasma. Conducting Shell Surrounding Plasma B T B P r B BT Small & Reversed at Edge Figure 1.1 The magnetic field configuration of the RFP. The toroidal field is about the same magnitude as the poloidal field and reverses direction near the plasma edge. The preferred RFP state was first derived by Taylor 9 in 1974 and was based on the conjecture that the magnetic helicity ( K o ) integrated over the entire plasma volume would be conserved. d dt K o = d dt A B dv 0 (1.1) V By minimizing the magnetic energy with respect to the magnetic helicity, Taylor arrived at a preferred magnetic configuration described by B = λb, (1.2)

23 where λ is a constant. Equation 1.2 describes the RFP minimum energy state in which the dynamo works to maintain. 5 The dynamo mechanism has been the subject of a number of exhaustive studies. In 1998, spectroscopic measurements performed by Chapman 10 reported that the correlated cross product between the magnetic and velocity fluctuations ( v b ) was sufficient to balance parallel ohm s law in the RFP core and sustain the RFP discharge. More recently, the measurements of Fontana 11 reached a similar conclusion about parallel ohm s law balance in the RFP edge, confirming the earlier Langmuir probe results measured by Ji 12 in The magnetic field fluctuations ( b ) that contribute to the dynamo term result from resistive tearing instabilities within the plasma. Unlike the tokamak, the low toroidal field of the RFP leads to a safety factor (q = ab T R o B P ) that is much less than 1.0, where q monotonically decreases and changes sign where the toroidal field reverses (figure 1.2). As a consequence, this magnetic configuration has a large number of closely packed low-order resonant surfaces. Resonant surfaces occur at radial locations where q is rational, or in other words, q = mn (1.3) where m and n are integers. Rational surfaces are undesirable because magnetic field tearing and reconnection is permitted at these radial locations, making them susceptible to the formation of magnetic islands.

24 6 q(r) Tokamak Dominant Resonant Surfaces RFP ~1 ~ radius, r a Figure 1.2 The q profile of the RFP has many low-order, closely packed resonant surfaces. These surfaces are susceptible to tearing mode formation. 1.2 Magnetic Island Formation and Stochasticity With tearing and reconnection permitted at a rational surface, magnetic islands can form (figure 1.3). These islands, often referred to as modes, are undesirable because they allow heat and particles to rapidly traverse the radial extent of the island and thereby degrade confinement.

25 7 q=m/n W ~ B r / B resonant surface magnetic island Figure 1.3 Rational surfaces permit tearing and reconnection of the magnetic field to occur, allowing islands to form. Magnetic islands degrade confinement by allowing rapid transport across the island s width. The situation outlined above is compounded in the RFP because as islands form and begin to grow on the many closely packed rational surfaces, they can overlap. When islands overlap, the magnetic field becomes stochastic, and the field lines can wander freely throughout the overlap region. If a large number of islands are overlapping, large stochastic regions can form in the plasma, and instead of rapidly transporting heat and particles just across an island width, the confinement is degraded over the entire stochastic region (figure 1.4).

26 8 q(r) 1,5 (m,n) 1,6 typical island width 1,7 magnetic stochasticity Figure 1.4 If a large number of magnetic islands overlap, a large area of the plasma can become stochastic, further enhancing the particle and energy transport. 1.3 Stochastic Transport Rechester and Rosenbluth, 13 who modeled electron heat transport via parallel conduction along wandering field lines, addressed the fusion relevance of transport in a stochastic magnetic field in They conjectured that the stochastic diffusion coefficient ( D st ) would take the form, b D st π r B o L A + 1 λ mfp, (1.4) where b r B o is the fluctuation to mean field ratio for the magnetic field, λ mfp is the electron collision mean free path, and L A is the autocorrelation length. In MST, b r B o is typically about 1-2% and the collisional mean free path is long, on the order of tens of meters. The autocorrelation is basically a fudge-factor and for MST is about a meter and therefore D st m. The critical aspect

27 behind this loss mechanism is that the diffusion loss rate will be proportional to the particle s parallel velocity leading to 9 D D st v. (1.5) Loss The implications of a velocity dependent diffusion rate are far reaching in that by preferentially transporting particles of higher energy, one leads to the possibility of current or momentum diffusion and non-maxwellian distribution functions. It was the idea of current diffusion that lead Jacobson and Moses 14,15 (1984) to propose the kinetic dynamo theory (KDT) as a means for sustaining the RFP discharge; however, this mechanism has yet to be observed (although one might argue we haven t looked very hard). In defense of the MHD dynamo, selfconsistent calculations conducted by Terry and Diamond 16 (1990), indicate that the current transport from the KDT is insufficient to explain the dynamo. The concept of stochastic diffusion was applied to particle transport by Harvey 17 (1981), who proposed that if particle diffusion were weighted by parallel velocity, the electrons would be transported more rapidly inducing an ambipolar radial electric field. Assuming that the local distribution functions did not deviate substantially from Maxwellian, the radial particle flux would be described as Γ r = 2 π D st v T n 1 n n r + 1 T 2T r + ee A T, (1.6) where v T is the electron thermal velocity, n and T are the electron density and temperature, E A is the ambipolar electric field, and D st is the stochastic diffusion coefficient described in equation 1.4. The result is that particle diffusion is not driven solely by gradient in density as predicted in the Fick s Law case, but that

28 10 gradients in electron temperature and the ambipolar electric field would also be important. In this report, we do not address the validity of Harvey s suppositions or apply equation 1.6 to our radial particle flux measurements. However, in chapter 5, we compare our measured total radial particle flux with the particle transport modeling conducted for RFX discharges, 18 and equation 1.6 is vital to those results. With the profile measuring capabilities of the FIR interferometer, Thomson Scattering system, and Heavy-Ion Beam Probe (HIBP), it is hoped that experiments to validate equation 1.6 will be undertaken by MST. 1.4 Fluctuation-Induced Radial Particle Flux Experimentally, we extract Γ from the electron continuity equation by simultaneously measuring the electron density and source. In this section, we expand Γ to isolate the fluctuation-induced particle flux term, and identify the measurable quantities. The equilibrium particle flux (Γ ) is defined in the electron continuity equation in the balancing term between the change in electron density and the electron source, n e t + Γ =S e, (1.7) where Γ=n e v. Expanding Γ into its equilibrium and fluctuating components, we see that ( ) v o + v Γ= n o + n ( )=n o v o + n v +n o v + n v o. (1.8)

29 11 Imposing toroidal axisymmetry on the equilibrium quantities and averaging over a flux surface, the two cross terms integrate to zero leaving the radial particle flux as Γ r = n o v or + n v r = Γ equilibrium + Γ fluctuation induced (1.9) With the classical E B inward pinch velocity small and assuming no anomalous pinch effects, the equilibrium radial velocity is negligible (v 0 or ), leaving the fluctuation-induced transport term solely responsible for the overall radial particle flux. The fluctuation-induced particle flux is defined as Γ fluctuation induced = n v r = γ n Amp v r Amp cos( δ nv ), (1.10) where and are the amplitudes of the density and radial velocity n Amp v ramp fluctuations respectively, and γ and δnv are the coherence amplitude and phase between the density and velocity fluctuations. In the linear ideal magnetohydrodynamics (MHD) description, the velocity fluctuations that cause fluctuation-induced particle transport are directly linked to the magnetic fluctuations. 1.5 Controlling Fluctuations As mentioned earlier, the large magnetic fluctuations are a result of the plasma attempting to fluctuate itself back to its preferred energy state. Although this process sustains the RFP discharge, the magnetic fluctuations degrade confinement. One of the principal research goals of MST has been to develop ways to control magnetic fluctuations in the RFP; pulsed poloidal current drive (PPCD) has been very successful at accomplishing this.

30 12 PPCD is based on the premise that any work done to aid the plasma in reaching its preferred state, means that less work is required of the magnetic r fluctuations. The plasma desires a flat parallel current density profile ( J B r B 2 ), but the ohmic heating applied to MST is very inefficient at driving parallel current in the plasma edge. As a result, gradients in the parallel current density profile form and resistive tearing modes (magnetic islands) become unstable and begin to grow. As the modes grow, they flatten the current density profile but also degrade confinement. PPCD is designed to drive current in the RFP edge, thereby reducing the need for the magnetic fluctuations. The experimental setup is elegantly simple (figure 1.5). Current is driven poloidally around the conducting shell thereby changing the toroidal magnetic field. From Faraday s law ( E = B t ), the change in the toroidal magnetic field creates a poloidal electric field that drives poloidal current. As the field at the RFP edge is principally poloidal, the current driven is parallel to the magnetic field and works to flatten the parallel current density gradient. E θ,j θ C1 C2 C3 C4 Figure 1.5 The PPCD circuit. Current driven in the shell changes the toroidal magnetic field, thereby producing a poloidal electric field that works to flatten the edge parallel current density gradient.

31 13 The results from PPCD have been very encouraging. Measurements to date have shown that the magnetic fluctuations are halved and that global energy confinement increases fivefold. 4 Shown in figure 1.6, are the poloidal electric field pulses and the subsequent reduction in magnetic fluctuation amplitude. E θ (a) (V/m) b rms 3 B 2 (%) 1 0 PPCD Time (ms) MST 25 Figure 1.6 The poloidal electric field (top) and the magnetic fluctuations (bottom). Note the substantial reduction in fluctuation percentage. Beyond obtaining overall confinement improvements, PPCD has proven to be invaluable in studying the RFP. PPCD offers the ability to turn the fluctuation levels in MST up or down, allowing a more complete investigation of the role of magnetic fluctuations in particle and energy confinement in the RFP. 1.6 Overview of Thesis In this work we have, measured the radial particle flux profile in both standard and PPCD discharges, characterized and quantified the large-scale

32 14 density fluctuations over the entire plasma cross section, and measured (qualitatively in the core, quantitatively in the edge) the fluctuation-induced particle flux from the global core-resonant tearing modes. The chapters that discuss this work are organized as follows. Chapter 2 introduces the Far- Infrared (FIR) Laser Interferometer * system that was employed to measure both the equilibrium and fluctuating components of the electron density profiles. The discussion focuses on theory of operation, diagnostic hardware, and the phase analysis technique that has greatly expanded the diagnostic s time response. Chapter 3 describes the multi-chord H α detector array used in measuring the electron source for the ionization of neutral hydrogen. This chapter also addresses some very important secondary issues, such as core neutral population and power loss via neutral transport, that have been uncovered during this investigation. The measurements of the electron source from high-z impurities are discussed in chapter 4. We introduce the ROSS multi-foil diode spectrometer used in determining the impurity concentrations of oxygen, carbon and aluminum. Building on the electron source information discussed in chapters 3 and 4, chapter 5 presents the results of the radial particle flux measurements. We also investigate the general behavior of the electron density profiles during standard and PPCD discharges and what their features state about the particle confinement properties of MST. Finally, we address the question of fluctuation-induced transport. In chapter 6 we characterize the large-scale density fluctuations by examining their amplitude, frequency spectra, spectral content, and relation to both magnetic and radial velocity * Developed in collaboration with the University of California at Los Angeles Plasma Diagnostic Group.

33 15 fluctuations. From the measurements reported in chapters 5 and 6, we conclude that, PPCD improves particle confinement in the MST core, the large-scale density fluctuations are directly attributed to the global core-resonant tearing modes and are compressional in the core but advective in the edge, and finally we state that the core-resonant tearing modes do cause transport in the RFP core but not in the edge. REFERENCES 1 H. A. Bodin and A. A. Newton, Nuclear Fusion, 19, 1255 (1980). 2 D. D. Snack, et. al., Proceedings of Fourteenth International Conference on Plasma Physics and Controlled Nuclear Fusion Research, IEIA, Wurzburg, Germany (1992). 3 Y. L. Ho, Nuclear Fusion 31, 341 (1991). 4 J. S. Sarff, N. E. Lanier, S. C. Prager, M. R. Stoneking, Physical Review Letters, 78, 62 (1997). 5 M. R. Stoneking, S. A. Hokin, S. C. Prager, G. Fiksel, H. Ji, and D. J. Den Hartog, Physical Review Letters, 73, 549 (1994). 6 T. D. Rempel, C. W. Spragins, S. C. Prager, S. Assadi, D. J. Den Hartog, and S. Hokin, Physical Review Letters, 67, 1438 (1991). 7 G. Fiksel, S. C. Prager, W. Shen, and M. R. Stoneking. Physical Review Letters, 72, 1028 (1994). 8 R. N. Dexter, D. W. Kerst, T. W. Lovell, S. C. Prager, and J. C. Sprott, Fusion Technology 19, 131 (1991). 9 J. B. Taylor, Physical Review Letters, 33, 1139 (1974). 10 J. T. Chapman, Ph.D. Thesis (1998). 11 P. W. Fontana, Ph.D. Thesis (1999). 12 H. Ji, A. F. Almagri, S. C. Prager, and J. S. Sarff, Physical Review Letters, 73, 668 (1994).

34 13 A. B. Rechester and M. N. Rosenbluth, Physical Review Letters, 40, 38 (1978). 14 A. R. Jacobson and R. W. Moses, Physical Review Letters, 52, 2041 (1984). 15 A. R. Jacobson and R. W. Moses, Physical Review A, 29, 3335 (1984). 16 P. W. Terry and P. Diamond, Physics of Fluids, B2, 428 (1990). 17 R. W. Harvey, M.G. McCoy, J.Y. Hsu, and A. A. Mirin, Physical Review Letters, 47, 102 (1981). 18 D. Gregoratto, L. Garzotti, P. Innocente, S. Martini, A. Canton, Nuclear Fusion, 38, 1199, (1998). 16

35 17 2: The Far-Infrared Laser System In collaboration with the University of California at Los Angeles Plasma Diagnostics Group, we have developed a high time response, multi-chord farinfrared (FIR) laser interferometer 1 to measure the equilibrium and fluctuating density profiles. The vertical viewing heterodyne system is capable of measuring electron density fluctuation behavior, up to 500 khz, simultaneously in eleven chords. 2 Furthermore, the system has recently been upgraded to allow poloidal field measurement capability; 3 however, this work is still in progress and unrelated to the physics goals presented in this report. In this chapter we will describe the far-infrared laser system (FIR), theory of operation (Section 2.1), and principle components (Section 2.2). We also will introduce the digital phase extraction technique (Section 2.3) that has been instrumental in increasing the diagnostic s time response and phase resolution, 4,5 and present some typical data. 2.1 Plasma Interferometry Theory The underlying principle behind plasma interferometry is that an electromagnetic wave will propagate through plasma and air at different speeds.

36 18 The propagation of an electromagnetic wave in plasma is depicted in equation ,7 The index of refraction (μ s, f ) for the slow and fast waves with frequency ω are ( μ s, f ) 2 =1 ω 2 pe ω 2 1 ω 2 ce ω 2 sin 2 θ ( ) ± ω ce ω ω pe ω 2 2 sin 2 θ ( ( ) 1 + ) 12 F ω pe ω 2 1, (2.1) where ω pe and ω ce are the electron plasma and cyclotron frequencies with θ being the angle between the wave propagation vector and the magnetic field in the plasma and F is defined as F = 2ω 1 ω 2 pe cosθ ω 2 sin 2 θ. (2.2) ω ce We can see from the complexity of equations 2.1 and 2.2 that a rigorous solution for a wave propagating through a magnetized plasma, where θ is continually changing, would quickly get frighteningly complicated. As always in plasma physics, we strive to avoid complexity while including the required amount of physics, and this case is no exception. To first order we can examine the special case where the wave propagates perpendicular to the background magnetic field r ( k B r ). With θ = π 2, the index of refraction for the ordinary wave, defined when the electric field vector of the wave in parallel to the background magnetic field r r ( E B ) becomes μ ord = 1 ω 2 pe ω (2.3)

37 r For the extraordinary wave ( E B r ), equation 2.1 simplifies to 19 μ ext = 1 ω 2 ω 2 2 ( ω pe ) ω 2 ω 2 ω 2 ( pe ) ce 2 ω pe 12. (2.4) For MST parameters, ω 2 ce = ( eb m e ) s 2 2 and ω pe = e 2 n e ε o m e s 2. Furthermore, at the laser wavelength of 432 microns, ω s 1 and ω s 2. Given that ω 2 2 ce << ω pe 2 and ω pe << ω 2, a little algebra and a binomial expansion later, equation 2.4 can be simplified, yielding that μ ord μ ext, where μ ord μ ext 1 ω 2 pe ω ω pe. (2.5) 2 ω 2 2 Recalling that k = μω c, and that ω pe = n e e 2 ε o m e where ε o is the free space permittivity and n is the electron density, then the phase difference e ( Φ) between a wave that travels through plasma vs. air will be ( ) Φ= k vac k plasma dz = ω 2 ω pe 2c dz = ω 2 λe 2 n 4πc 2 m e ε e () r o dz. (2.6) Substituting in the relevant MKS values, Φ becomes Φ= λ n e ( r) dz, (2.7) where λ is the FIR laser wavelength, n is the electron density, and e z is the coordinate along the length of the chord through the plasma. From equation 2.7, as the beam passes through the plasma, the presence of electrons along the path length slows the propagation, thus causing its phase to be shifted from that of

38 the reference beam. Thus a measurement of this imparted phase shift is a measure of the number of electrons along the beam s line of sight The Far-Infrared Laser Interferometer We have constructed a multi-chord far-infrared laser interferometer to measure the phase shift described in equation 2.7. The FIR system, outlined in figure 2.1, consists of a high-powered, continuous operation, CO 2 laser, two optically pumped FIR lasers, dielectric waveguide and wire grid mesh assemblies, and twelve independent FIR detector assemblies. In this section we present a general diagnostic overview, detailed descriptions of the principal components, and typical operating parameters for the FIR laser system Diagnostic Overview The FIR system is a vertical viewing heterodyne system that is capable of measuring electron density behavior with a high degree of speed and accuracy. The system functions by using a high-power CO 2 laser to pump the twin FIR cavities producing two independent FIR laser beams. The two cavities are adjusted to operate at slightly different frequencies so that when mixed, produce a modulated signal. The peaks of this modulated signal provide the benchmarks from which a relative phase between chords is measured.

39 21

40 The CO 2 Pumping Laser The heart of the FIR laser system is the continuous power, CO 2 pumping laser (figure 2.2). Designed by Apollo Laser Corporation, the Model 150 is a continuous flow, tunable gas laser that is capable of steady state operation at powers of Watts depending on the line of interest. The laser consists of two water-cooled, gas-filled discharge tubes, a partially reflective (80%) ZnSe output coupler, and a gold coated blazed grating. The grating is grooved at 135 lines per inch blazed for 10.6 μm (Hyperfine part # ML X0.825), and allows the CO 2 laser to be tuned to the appropriate FIR pumping line. For continuous operation the gas mixture of choice is 6 % CO 2, 18 % N 2 and 76 % He. Mirrors Output Coupler Gas Flow Out Cathode (23 kv) Gas Flow Out Grating Monitoring Beam Gas Flow In Anode (Ground) Anode (Ground) Piezo-electric Transducer (PZT) Figure 2.2 The CO 2 pumping laser primarily consists of two colinear discharge tubes, a grating for tunability and a partially reflective mirror (output coupler) that allow continuos operation. Unlike shorter wavelength lasers whose principal transitions are atomic, the CO 2 lasing transitions result from changes between vibrational energy states. 8 The triatomic CO 2 molecule is subject to three types of vibrational excitation symmetric stretching, bending, and asymmetric stretching (figure

41 23 2.3). Vibrational energy is transferred to the CO 2 molecule by collisions resulting in an excited state. When the molecule relaxes to a lower vibrational state, the energy is dissipated as a photon, as is the case for atomic transitions. Although both processes result in the emission of a quantized photon, the vibrational energy levels are more plentiful and closely packed then their low n atomic counterparts. This results in laser emission that is more like a continuum. To obtain the monochromatic emission required for the efficient pumping of the FIR laser, a grating is used to isolate the particular vibrational transition of interest. O C Equilibrium O O C Bending O O C O O C O Symmetric Stretching Asymmetric Stretching Figure 2.3 The CO 2 molecule is subject to three types of vibration: bending, symmetric stretching, and asymmetric stretching. To ensure that the population of vibrationally excited CO 2 molecules in the discharge tubes is sufficient for high-powered lasing, additional gases are introduced to enhance excitation. The process of continually exciting (pumping) and de-exciting (lasing) the CO 2 molecule is displayed in (figure 2.4). Nitrogen, which is diatomic, has only one degree of vibrational freedom (symmetric stretching) and is easily excited by collisions in the discharge tube. Since vibrationally excited N 2 is similar in energy to the CO 2 excited state, N 2 can efficiently transfer its energy to a CO 2 molecule during a collision. Stimulated emission occurs

42 24 and the CO 2 molecule begins to radiate its energy. To minimize the amount of re-absorption, helium is added to enhance the collisional deexcitation of the CO R6 (100) Collisional Transfer of Vibrational Energy Stimulated Emission (020) (010) 10P Collisional De-excitaion (001) Excitation via High Voltage Discharge 1 (000) CO 2 N 2 0 Figure 2.4 The CO 2 lasing cycle. Collisions within the highvoltage discharge tube excite the N 2 molecules. The excited N 2 molecules transfer their energy to CO 2 molecule which then relaxes via stimulated emission. Although not a part of this cycle, Helium is added to enhance the collisionality within the discharge tube The Twin Far-Infrared Laser (FIR) The FIR, displayed in figure 2.5, is an optically pumped system that converts the near 10 micron output of the CO 2 into two semi-independent beams of much longer wavelength. 9 The wavelength of operation can range from 100 microns to several millimeters and is solely governed by the choice of laser gas. On MST, Formic Acid (HCOOH) is used to yield an output wavelength of microns ( 700 GHz); however, the system can be run with methanol (CH 3 OH) or

43 25 difluoromethane (CH 2 F 2 ) which can yield output wavelengths of 119 and 184 microns respectively. Tuning around the Formic Acid transition is achieved with a wire mesh/quartz plate combination that forms a Fabry-Perot etalon that is adjusted to maximize output power. Though the input pumping power is over 100 W, the FIR output is only about 30 mw per laser cavity. Once optimized for power the cavity length mirrors can be positioned independently to vary the interference frequency between the lasers. Wire Mesh (100 LPI) Reflective Coating (10.6 μm) Metallic Corrugated Waveguide CO 2Pumping Beam TPX Output Windows Quartz Etalon Cavity Length Mirrors (Gold Coated) Figure 2.5 The twin FIR laser system. The entire chamber is filled with 200 mt of Formic acid vapor. The CO 2 pumping beam is focused into the corrugated tubes where FIR lasing occurs. Tunability is achieved by adjusting the spacing between the wire mesh and the quartz etalon. The interference frequency between the twin FIR lasers is dictated by the placement of the cavity length mirrors.

44 26 A principal advantage of pumping both FIR cavities with the same CO 2 laser is that any fluctuation in CO 2 power will be equally distributed among the FIR lasers. Issues such as reflections back into the laser cavity (termed laser feedback), vibrations, variations in temperature, and power line noise can cause a laser s output power to fluctuate. However, with this configuration, even if these issues reduce the stability of the CO 2 power and the FIR power fluctuates the modulated signal will still be very stable Power Distribution The output of each FIR laser is focused through a polyethylene planoconvex lens into a dielectric waveguide that carries the beam to the vacuum vessel. The waveguides are air-filled plexi-glass tubes, which have an inner diameter of 3.5 inches, and help channel the beam in a manner that preserves the mode symmetry and reduces power loss. The effectiveness of the waveguide is highly sensitive to the input beam size, so to ensure optimum transmission, a number of lenses were tested to focus the beam into the waveguide entrance. The results show the 120 cm focal length lens was best suited for preserving a small beam through the waveguide (figure 2.6).

45 27 f=120 cm f=100 cm Power (au) Radius (1/8's in.) Figure 2.6 The FIR signal beam profile out of the waveguide, incident on the meshes above the vacuum vessel. The 120 cm focal length lens provides the tightest beam waist of about 2.4 cm. The size of the beam is an important issue for the MST interferometer because the entrance holes in the aluminum tank are drilled separately and deliberately made small to minimize field errors. With an inner diameter of only 3.5 centimeters, a large FIR beam can be greatly attenuated by the small entrance holes, thereby reducing the laser power through the tank. More importantly, especially for polarimetry, a large beam can reflect off the inner walls of the entrance tubes and contaminate the measured phase. To address this latter issue, two sets of threaded inserts were constructed, one set with 48 threads per inch (TPI) and the other with 20 TPI. These inserts are installed in both entrance and exit holes and help ensure that any laser power impacting the inner walls will be scattered as opposed to coherently reflected. The eleven FIR chords are separated into two arrays that are toroidally displaced by five degrees. The chords view impact parameters range from r/a of