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Transport in a Field Aligned Magnetized Plasma

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Transport in a Field Aligned Magnetized Plasma University of California Los Angeles Transport in a field aligned magnetized plasma/neutral gas boundary: the end of the plasma A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Christopher Michael Cooper 2012 c Copyright by Christopher Michael Cooper 2012 Abstract of the Dissertation Transport in a field aligned magnetized plasma/neutral gas boundary: the end of the plasma by Christopher Michael Cooper Doctor of Philosophy in Physics University of California, Los Angeles, 2012 Professor Walter Gekelman, Chair The objective of this dissertation is to characterize the physics of a boundary layer be- tween a magnetized plasma and a neutral gas along the direction of a confining magnetic field. A series of experiments are performed at the Enormous Toroidal Plasma Device (ETPD) at UCLA to study this field aligned Neutral Boundary Layer (NBL) at the end of the plasma. A Lanthanum Hexaboride (LaB6) cathode and semi-transparent anode creates a magnetized, current-free helium plasma which terminates on a neutral helium gas without touching any walls. Probes are inserted into the plasma to measure the basic plasma parameters and study the transport in the NBL. The experiment is performed in the weakly ionized limit where the plasma density (ne) is much less than the neutral density (nn) such that ne=nn < 5%. The NBL is characterized by a field-aligned electric field which begins at the point where the plasma pressure equilibrates with the neutral gas pressure. Beyond the pressure equi- libration point the electrons and ions lose their momentum by collisions with the neutral gas and come to rest. An electric field is established self consistently to maintain a current- free termination through equilibration of the different species' stopping rates in the neutral gas. The electric field resembles a collisional quasineutral sheath with a length 10 times the electron-ion collision length, 100 times the neutral collision length, and 10,000 times the ii Debye length. Collisions with the neutral gas dominate the losses in the system. The measured plasma density loss rates are above the classical cross-field current-free ambipolar rate, but below the anomalous Bohm diffusion rate. The electron temperature is below the ionization threshold of the gas, 2.2 eV in helium. The ions are in thermal equilibrium with the neutral gas. A generalized theory of plasma termination in a Neutral Boundary Layer is applied to this case using a two-fluid, current-free, weakly ionized transport model. The electron and ion momentum equations along the field are combined in a generalized Ohm's law which predicts the axial electric field required to maintain a current-free termination. The pressure balance criteria for termination and the predicted electric field are confirmed over a scaling of plasma parameters. The experiment and the model are relevant for studying NBLs in other systems, such as the atmospheric termination of the aurora or detached gaseous divertors. A steady state modified ambipolar system is measured in the ETPD NBL. The drift speeds associated with these currents are a small fraction of the plasma flow speeds and the problem is treated as a perturbation to the termination model. The current-free condition on the model is relaxed to explain the presence of the divergence free current. iii The dissertation of Christopher Michael Cooper is approved. Christopher Russell George Morales Troy Carter Walter Gekelman, Committee Chair University of California, Los Angeles 2012 iv To my parents . who always knew when to push me and when to hug me, and my wife who mostly hugged me v Table of Contents 1 Introduction :::::::::::::::::::::::::::::::::::::: 1 1.1 Motivation . 1 1.2 Observations in Nature . 1 1.3 Laboratory Experiments . 3 1.4 The Physics of Weakly Ionized Plasmas . 5 1.5 Summary of Observations in the Experiment . 8 2 Experimental Methods ::::::::::::::::::::::::::::::: 12 2.1 The Enormous Toroidal Plasma Device . 12 2.1.1 Description of the LaB6 cathode . 13 2.1.2 The ETPD plasma . 15 2.2 Plasma Termination on a Neutral Gas . 18 2.2.1 Experimental setup . 18 2.3 Diagnostics . 22 2.3.1 Langmuir and Mach probe . 25 2.3.2 Emissive probe . 28 2.3.3 Magnetic probe . 30 2.3.4 Electrostatic flux probe . 34 2.4 Data Acquisition and Analysis . 34 2.5 The Role of Primary Electrons in the Neutral Boundary . 35 2.6 Turbulence in the ETPD Plasma . 36 3 Plasma Termination on a Neutral gas :::::::::::::::::::::: 40 vi 3.1 Outline . 40 3.2 Model for Plasma Termination on a Neutral Gas . 41 3.3 The Three Regions of the ETPD Plasma . 46 3.3.1 The ionization region . 47 3.3.2 The loss region . 50 3.3.3 The Neutral Boundary Layer region . 51 3.4 Axial Profiles of the Neutral Boundary Layer . 52 3.4.1 Radial Profiles of the Neutral Boundary Layer . 56 3.5 Zone A: The Pre-NBL Plasma . 56 3.6 Zone B: The Stopping Plasma . 60 3.6.1 The difference between momentum and temperature loss . 60 3.6.2 Stopping the plasma . 62 3.6.3 Estimation of the electric field from the NBL model . 63 3.7 Zone C: Ionization in the NBL . 65 3.8 Plasma Pressure and Flux in NBL . 67 3.9 Kinetic Effects . 69 3.10 Scaling . 70 4 Modified Ambipolar Flow ::::::::::::::::::::::::::::: 77 4.1 Radial pressure Balance and Generalized Ohm's Law . 78 4.2 Types of current in ETPD plasma . 79 4.3 The system of closure currents . 81 4.4 applying the ambipolar model to ETPD . 81 4.5 Measurement of current in ETPD NBL . 84 4.6 Possible closure mechanisms for return currents . 86 vii 5 Conclusion ::::::::::::::::::::::::::::::::::::::: 90 5.1 Summary of Results . 90 5.2 Future Work . 92 A Appendix A: Calibration of magnetic field probe ::::::::::::::: 94 A.1 Testing the probe . 94 A.1.1 Continuity . 94 A.1.2 Coil Identification . 95 A.2 Calibration . 96 A.2.1 Setup . 96 A.2.2 Typical Calibration . 97 A.3 Using calibration on real data . 97 viii List of Figures 1.1 A plot of the production rate (solid, left axis) and cross section (dashed, right axis) for electrons to ionize helium gas. The plots are generated using fits from Janev (1987). 7 1.2 A colormap of the plasma potential measured in the Neutral Boundary Layer in the ETPD. White arrows show the electric field. The parallel component of the electric field is multiplied by 10 accentuate the field aligned electric field terminating the plasma. 9 2.1 (top) A top view of the ETPD. Here, the plasma ends before completing a lap. The toroidal confining magnetic field lines follow the machine walls in a circle and the vertical field is out of the page. The outlines of the four data planes examined are shown in yellow. A linear representation of the plasma with the LaB6 source at the near end and the Neutral Boundary Layer at the far end is shown at the bottom of the diagram . 14 2.2 Time trace of the discharge current in the ETPD . 17 2.3 Pictures of the visible light from the plasma for three different plasma condi- tions. In all cases, the fill gas was helium, the toroidal magnetic field was 250 G and the discharge current was 200 A. The discharge voltage and neutral fill pressure changed in each case - (left) 400 V, 2.0 mTorr (center) 300 V, 2.7 mTorr (right) 210 V, 3.6 mTorr. The pictures were taken with a digital camera and are integrated over the whole shot. 19 2.4 A cartoon of the coordinate system in the ETPD. The cylindrical coordinate system (blue) is rotated about the radial axis r by and angle φtilt creating the tilted coordinate system (black) to match the magnetic field (purple). 21 ix 2.5 Cartoon of a dataplane along the magnetic field. The gridding of area sub- tended by the probe is shown in blue with each intersection corresponding to a data point. This data is interpolated onto toroidal coordinates shown in red. 23 2.6 A sample I-V trace from a Langmuir probe in the center of the plasma. The knee region fit to an exponential plus an offset is shown in blue, the floating voltage is shown in green, and the plasma potential is shown in red. The electron temperature was 2.2 eV in this trace. 27 2.7 (top) A picture of the emissive probe showing the tungsten filament and spot welded tantalum wire pushed out of the protective slot in the alumina, which was blackened by graphite and (bottom) the potential of the emissive probe tip which equilibrates after 10 ms, averaged over 20 shots . 31 2.8 (top) The raw EMF of the B-dot probe and (bottom) the integrated and calibrated value of the magnetic field as a function of discharge time, averaged over 20 shots . 33 2.9 (top) Electron temperature and (bottom) plasma density scaling near the neutral boundary layer for different input powers. Changing the input power by changing the discharge voltage is shown in black and changing the discharge current is shown in red. Below 45 kW the two lines overlap and the makeup of the input power (voltage and current) does not affect plasma parameters, above 50 kW it does. The experiment was run at 43 kW. 37 2.10 (top) Moving probe Isat - stationary probe Isat correlation plane showing an m=1 drift mode and (bottom) a radial cut of the moving probe Isat - vertical electric field cross phase.
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