LIF Signal Measurements and Analysis in ANU Experiment, Papers of Art

Download LIF Signal Measurements and Analysis in ANU Experiment and more Papers Art in PDF only on Docsity! Neutral Density Profiles in Argon Helicon Plasmas Amy M. Keesee Dissertation submitted to the College of Arts and Sciences at West Virginia University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Plasma Physics Earl Scime, PhD., Chair Manfred Boehm, PhD. Fred L. King, PhD. Mark. E. Koepke, PhD. John E. Littleton, PhD. Department of Physics Morgantown, West Virginia 2006 Keywords: helicon source, laser-induced fluorescence, neutral density, collisional- radiative, Abel inversion Copyright 2006 Amy M. Keesee Abstract Neutral Density Profiles in Argon Helicon Plasmas Amy M. Keesee A diode laser-based laser-induced fluorescence (LIF) diagnostic has been developed that can measure three species; argon neutrals, argon ions, and helium neutrals. This diagnostic has been combined with passive emission spectroscopy and a neutral argon collisional-radiative (CR) model to measure ground state radial density profiles of argon atoms in a helicon source. We have found the ground state neutral argon atoms to have a 60% on-axis depletion for a typical helicon mode case, yielding a 28% ionization fraction. The depletion decreases to 20% with a 9.8% ionization fraction for a second helicon mode case, indicating that slight changes in plasma parameters can lead to a significant difference in RF power coupling and gas ionization. In a series of experiments in a low density helicon source, measurements of argon ion flow through a double layer with the LIF diagnostic confirmed predictions of a Monte-Carlo particle-in- cell model of double layer formation in expanding helicon plasmas. Additionally, the LIF diagnostic has been used to measure argon neutral flow velocities, argon ion flow velocities, and argon neutral density and temperature evolution during a plasma pulse. v Chapter 6: Measurements of Radial Profiles, Temperatures and Flows in HELIX........ 112 6.1 Parameter Set A (6 mTorr Helicon mode)............................................................ 113 6.2 Parameter Set B (Capacitive mode)...................................................................... 117 6.3 Parameter Set C (5 mTorr Helicon mode) ............................................................ 121 6.4 Neutral and ion flow measurements ..................................................................... 125 6.5 Pulsed plasma measurements................................................................................ 131 References................................................................................................................... 134 Chapter 7: Comparison of CR Model and Measurements .............................................. 135 7.1 Parameter Set A (6 mTorr Helicon mode)............................................................ 136 7.2 Parameter Set B (Capacitive mode)...................................................................... 139 7.3 Parameter Set C (5 mTorr Helicon mode) ............................................................ 155 References................................................................................................................... 158 Chapter 8: Summary ....................................................................................................... 159 References................................................................................................................... 163 Appendix A: Pressure Calibration Data.......................................................................... 164 Appendix B: Iodine Cell Fluorescence Data .................................................................. 167 Appendix C: International Equipment Transit................................................................ 178 Appendix D: Collisional-Radiative Model Code............................................................ 183 1 Chapter 1: Introduction Helicon source plasmas are used for plasma processing, space simulation, space propulsion, and basic plasma physics studies. While plasma physics typically focuses on the dynamics of ions and electrons in the plasma, the neutral gas that is present in all plasmas can play a significant role in radiation losses, diffusion, momentum transport, and cooling. To understand the role of neutrals in helicon plasmas, accurate and precise measurements of neutral atom spatial distribution, temperature, density, and flow speed are required. In this work, it will be shown how laser-induced fluorescence (LIF) and passive emission spectroscopy provide non-perturbative measurements of these neutral atom properties in argon helicon source plasmas. Because both of these optical diagnostic methods probe an excited neutral state, a collisional-radiative (CR) model is also needed to relate the measured excited state properties to those of the neutral ground state. Thus, LIF measurements of excited state radial profiles and a CR model relating the excited state density to the ground state density yield a measurement of the ground state radial profile. The atomic physics of the CR model, i.e., the rate of excitation and depopulation of the excited neutral states, is primarily controlled by the electron energy distribution function. Therefore, Langmuir probe measurements of electron temperature and density are an important input to the CR model and are also reported in this work for a series of helicon source configurations. Since different excited neutral states are investigated with LIF and passive emission spectroscopy, the possible existence of an electron beam (an 2 important topic in helicon plasma source research) will also be considered in light of the experimental measurements and CR model results. After reviewing some background information in the remainder of this chapter and then relevant experimental apparatus and diagnostic methods in Chapters 2 and 3, respectively, the review of experimental measurements in this work begins in Chapter 4 with measurements of the acceleration of argon ions through a spontaneously forming double layer (DL) in experiments at the Australian National University (ANU). The portable LIF diagnostic used to measure the neutral argon velocity distribution is also capable of measuring the velocity distribution of argon ions and neutral helium. In addition to providing confirmation of the existence of the DL in the ANU experiment, the initial argon ion LIF measurements demonstrated that satisfactory LIF signal to noise could be obtained at target species densities of as little as 109 cm-3 and that the heated iodine cell used for absolute flow velocity reference could be reliably used for a wide range of experimental conditions. Details of the collisional-radiative model are discussed in Chapter 5, and the experimental measurements of neutral spatial distribution, neutral density, neutral temperature, neutral flow, and ion flow, are presented in Chapter 6. Interpretation of the experimental measurements in light of the collisional-radiative model results is presented in Chapter 7, and a summary of the key results of this work are given in Chapter 8. 1.1 Neutral atoms in helicon sources In a number of helicon source investigations, the absolute density and spatial distribution of neutral atoms in the source chamber remains an important and unanswered question. For example, plasma processing applications typically require plasma 5 model of plasma density and electron temperature. In the model, they assumed that neutrals were completely depleted from the center of the discharge during the “high- current phase” of the pulse. Their model yielded current densities that agreed with experimental measurements in their modeled helicon source.7 In previous work on ion heating and ion flows in the WVU helicon source,8,9,10 ion-neutral and electron-neutral collisions have been shown to be important mechanisms for wave damping, flow thermalization, and ion heating. In fact, edge ion heating in cylindrically symmetric plasmas (which is often observed in our experiments and believed to be evidence of damping of edge-localized slow waves in the helicon source11,12) can also result from the thermalization of ion flow by charge-exchange collisions.13 Therefore, although poorly understood, the spatial distribution, temperature, and flow of neutral atoms in helicon sources are important to understanding the physics of helicon sources. 1.2 Electron beams in helicon sources There has been much debate among those in the helicon source community about whether or not an energetic electron beam exists in helicon plasmas. That the efficient ionization of helicon source plasma is due to linear Landau damping by energetic electrons was originally hypothesized by Chen.14 However, Chen and Blackwell later discarded this hypothesis because the predicted density of 50 eV electrons would only account for 10% of the observed ionization, though they do not deny the possible existence of these electrons.15 Molvik et al. measured 20 eV electrons using a gridded- energy analyzer.16 In this work, we measure the electron population using Langmuir 6 probes with RF compensation that prohibits the measurement of any RF-phased pulses of electrons.15 To avoid this problem, Chen and Hershkowitz used uncompensated Langmuir probes, and reported measuring electron beams with energies corresponding to phase velocities of multimode helicon waves.17 Blackwell and Chen argue that the Chen and Hershkowitz results were still affected by RF potentials, so they made measurements using a time-resolved energy analyzer and reconstructed typical Langmuir probe traces for different phases in the RF cycle.18 They reported no evidence of energetic electrons using this method. Recently, Lieberman et al. suggested that an energetic electron beam of 20% density is required for an electric double layer to form, as has been observed in several helicon source plasmas.19 In addition to directly measuring the electrons, the presence of energetic electrons will manifest itself through interactions with the ions and neutrals. Ellingboe et al. found argon ion line emission in a helicon plasma to be modulated at the RF excitation frequency and postulated that the emission modulation was due to pulses of electrons accelerated under the antenna.20 They also found that peaks in the emission propagated in phase with the magnetic field. Scharer et al. performed similar experiments, arguing that the measured argon ion line emission could only be present due to 20-45 eV energetic electrons exciting ions into the relevant upper state.21 Because the excited states of the neutral atoms are populated by collisions with electrons, the electron dynamics, including the presence of an electron beam, will affect the relative densities of these states. By measuring different excited states, as we are doing with laser-induced fluorescence and passive emission spectroscopy in these experiments, we would expect to see evidence of an electron beam. If the energy of the electron beam were between the energies of the 7 two measured states, we would see increased density in the only the lower state, spatially localized similar to the beam. Additionally, for any beam energy, we would expect an electron beam to increase the metastable density, which would increase the density of the nearby states through collisions. 1.3 Flows and double layers in helicon sources Flows are a common phenomenon found in all types of plasmas and can be exhibited by all species, including neutrals. Ions and electrons typically flow along the magnetic field lines. Flow and flow shear can provide an energy source for instabilities and lead to increased particle transport. Ion flow (along the magnetic field) and shear in the ion flow have been measured in the WVU helicon source.22 Theoretical studies suggest such flow shear in the presence of plasmas with thermal anisotropy (as is observed in helicon plasmas23) may drive ion acoustic and ion cyclotron instabilities in helicon and other laboratory plasmas.24,25,26,27,28,29 Hardin et al. have measured bulk rotation about the helicon source axis due to ExB forces as well as radial diffusion using 3-D LIF measurements.30 The bulk rotation of the plasma slows towards the outer edge, which could drive Kelvin-Helmholtz or other perpendicular shear-driven instabilities. These previous studies have focused on the measurement of ion flows. The flows, both radial and rotational, of the neutrals may also drive instabilities, transport, and particle heating. Thus, direct measurements of neutral flows could be important for understanding helicon source physics. Enhanced axial flows are also of great interest for applications such as thrusters. Recent experiments by a number of groups have demonstrated that electric double layers 10 and by charge-exchange collisions was observed. Downstream of the DL, a high-energy ion population accelerated through the DL was observed. The roughly 14 eV potential drop across a DL with a width of a few tens of Debye lengths was obtained in the simulation for an argon plasma at a pressure of 0.5 mTorr, an electron density of 6.5 x 108 cm-3, and an electron temperature of 7.2 eV. The total ion acceleration occurred over roughly an ion mean-free path. The hybrid simulation results were consistent with retarding field energy analyzer (RFEA) probe measurements in the Chi-Kung helicon plasma source60 that indicated a sharp discontinuity in the plasma potential at the location of rapid plasma expansion31 (current-free DL of strength ~3kTe/e) and the existence of an energetic ion beam downstream of the expansion point (vbeam ~ 2vsound) with a density of ~109 cm-3 at low neutral pressures in the source.33 Independent experiments in the Magnetic Nozzle Experiment (MNX) reported similar plasma behavior: formation of an energetic, supersonic ion beam below a threshold neutral pressure for a helicon plasma expanding in a divergent magnetic field.34 1.4 Diagnostic development To investigate particle flows, heating, and density non-invasively, a multi-species laser-induced fluorescence (LIF) diagnostic was developed at WVU. With the development of diode lasers with adequate power output (see Section 3.1.1) and an Ar II LIF scheme compatible with an existing diode laser wavelength range,61 Scime and Boivin proposed a diode laser-based diagnostic that could probe Ar II, Ar I, and He I. Compared to a tunable dye laser-based system, the diode laser-based diagnostic is less 11 expensive, easier to operate, and portable. To accomplish three different LIF schemes with one diode laser, the schemes for Ar I and He I had to be somewhat unconventional. The Ar I scheme does not begin with a metastable state, as most LIF schemes do, to ensure an adequate state population for the diagnostic. Thus, the initial state must be populated by collisions. The He I scheme requires a collisional transfer after the laser excitation to yield fluorescence at a wavelength that can be easily detected. Thus, both of these schemes require higher plasma pressures to provide the necessary collisions. Boivin reproduced the Ar II scheme with the diode laser in the plasma chamber at WVU. He also successfully performed initial measurements with the He I scheme.62 My contribution to the development of diode laser-based LIF measurements in argon was to successfully demonstrate the Ar I scheme,63 satisfying the intended measurement objectives of our diagnostic. The portability of the diagnostic was demonstrated during experiments on the Magnetic Nozzle Experiment at Princeton Plasma Physics Lab34 and the Chi-Kung Experiment at Australian National University.64 1.5 Neutral argon line structure To use optical spectroscopy diagnostics, the energy level structure of the target species must be understood. While most energy levels can be described by understanding Russell-Saunders coupling of the electrons, there are other coupling mechanisms that yield more complex level-naming systems. For Ar I, jj-coupling must be used to describe the sublevels because the interaction between the spin of the outermost electron and its own orbit is greater than the interactions between the spins of the electron and parent ion 12 and between the orbits of the electron and parent ion. The most common interaction between two electrons is Russell-Saunders coupling, also called L-S coupling. Each electron has an orbital angular momentum li and a spin angular momentum si. The interaction energy of the spins of each electron and that of the orbital momenta is greater than the interaction energy between an electron’s spin and its orbital momentum, so that the si’s combine to create the total spin momentum S, where |s1-s2| ≤ S ≤ s1+s2 and the li’s combine to create the total orbital momentum L, where |l1-l2| ≤ L ≤ l1+l2. The total angular momentum J is then obtained from combining L and S, where |L-S| ≤ J ≤ L+S. While the interaction energy between the spins is generally thought of as due to the magnetic moments of the electrons, it is actually due to a phenomenon known as the Heisenberg-Dirac resonance caused by the charges of the electrons.65 The interaction between the orbital momenta is strong because the orbits of the electrons overlap, causing them to perturb each other. There are additional ways for electrons to interact with each other besides L-S coupling. One of these possibilities is j-j coupling. In this case, the interaction energy between the spin and orbital momenta of an electron is greater than that between the spins of the two electrons. In this case, the li and si combine to form a ji, where |li-si| ≤ ji ≤ li+si. The total angular momentum J, is then obtained by combining the ji’s, with |j1-j2| ≤ J ≤ j1+j2. The vector models for L-S and j-j coupling are shown in Figure 1.1.66 The vector magnitude J* is given by ( 1)J J + , and similarly for the other vectors. For L-S coupling, the li’s and si’s precess about their resultant L and S, respectively. The L and S, then precess around the resultant J. For j-j coupling, the li and si precess about their resultant ji, and the ji’s precess about the resultant J. 15 Figure 1.2 Vector model for L-S (left) and j-j (right) coupling in a weak magnetic field. The vector magnitudes are given by * ( 1)J J J= + . Because most excited states of the noble gases don’t follow L-S coupling, the usual notation, 2S+1LJ cannot be used. Several types of notation can be found describing the states of noble gases, including Paschen notation, Racah notation, and j-j notation. When Paschen studied the spectrum of neon, he found that he could arrange the lines into four series of s terms, ten series of p terms, twelve series of d terms, and twelve series of f terms using Rydberg’s formulas.66 Further understanding of the atomic structure and Rydberg formula indicated that a series corresponds to all radiative transitions to a single energy state. Thus, there are four s states (i.e. the outermost electron is in an s state), ten p states, etc. The four s states are the first excited states and are notated 1s2, 1s3, 1s4, 1s5. The next excited states are p states, notated 2p1 through 2p10. The notation continues in this manner for higher excited states. The ground state is notated 1p0 because all six electrons in the outer shell are p electrons. This notation can J* L* l2* l1* s2* s1* S* J* j2* l2* s2* s1* l1* j1* Mg H H Mg 16 be extended to the other noble gases, including argon. Racah notation has the format nl[K]J where n is the principal quantum number of the outer electron, l is the orbital angular momentum quantum number of the outer electron, K is the sum of l and the total angular momentum of the parent ion, and J is the total angular momentum of the atom obtained by adding K and S.67 The prime indicates that the parent ion has a total angular momentum of ½. It is also possible to find the states written with a notation that explicitly indicates the j-j coupling. This notation is in the form (j1 j2)J where each term is defined as in the description of j-j coupling above.66 The ground state of argon is given by 1s22s22p63s23p6 1S0. Because argon contains a complete p-group, as do all noble gases, singly ionized argon yields an inverted 2P doublet.66 For an excited argon atom, the outer electron couples with the parent ion via Russell-Saunders coupling if it is in one of the lower s states. If the outer electron is in a higher state, it couples with the parent ion according to j-j coupling.65 Table 1.1 shows the different notation schemes for the first 15 states of argon neutrals and their energies. For the work described here, we will use Racah notation to describe the excited argon neutral states. 17 Table 1.1 Argon state notation and energies Paschen J-L Coupling (Racah) L-S Coupling Energy (eV) 1p0 1S0 Ground 1s5 4s[3/2]°2 3P2 11.55 Metastable 1s4 4s[3/2]°1 3P1 11.62 1s3 4s’[1/2]°0 3P0 11.72 Metastable 1s2 4s’[1/2]°1 1P1 11.82 2p10 4p[1/2]1 12.91 2p9 4p[5/2]3 13.08 2p8 4p[5/2]2 13.10 2p7 4p[3/2]1 13.15 2p6 4p[3/2]2 13.17 2p5 4p[1/2]0 13.27 2p4 4p’[3/2]1 13.28 2p3 4p’[3/2]2 13.30 2p2 4p’[1/2]1 13.33 2p1 4p’[1/2]0 13.48 20 Chapter 2: Experimental Setup The combination of the Hot hELIcon eXperiment (HELIX) and the Large Experiment on Instabilities and Anisotropies (LEIA) was originally designed to study magnetospherically relevant plasmas. The plasma is created in the HELIX plasma source and flows into the larger LEIA chamber where the magnetic field is weaker, allowing for high beta ( 20Bnk T Bβ µ= ) plasmas. The geometry of the system also enables studies relevant to plasma processing and space propulsion. A picture of HELIX and LEIA is shown in Figure 2.1. Figure 2.1 HELIX (foreground) and LEIA combined system. HELIX is enclosed in a copper Faraday cage. 21 The experimental hardware used in this work is described in this chapter. All the measurements (except those described in Chapter 4) were performed in HELIX, while LEIA parameters were held fixed. Additional descriptions of the experimental apparatus can be found in Refs. [1,2]. 2.1 Plasma chamber The HELIX vacuum chamber is a 61 cm long, Pyrex tube 10 cm in diameter connected to a 91 cm long, 15 cm diameter, stainless steel chamber. The chamber has one set of four 6” Conflat™ crossing ports in the center of the chamber and four sets of four 2 ¾” Conflat™ crossing ports on either side that are used for diagnostic access. The four 6” crossing ports are fitted with 4” viewports for optical diagnostics. The end of the stainless steel chamber is connected to LEIA, a 1.8 m diameter, 4.4 m long space chamber. The end of the LEIA chamber is connected to a pumping station. At the opposite end, the HELIX chamber is connected to a glass tee with each branch terminated by the pumping station, ion gauge, and 12” stainless steel flange fitted with a 4” viewport, respectively. A schematic of the HELIX and LEIA system is shown in Figure 2.2. The z-axis is measured from the junction of the HELIX chamber and glass tee. 22 Figure 2.2 Schematic diagram of the HELIX and LEIA chambers. The locations of the A) Baratron gauge (z = 80 cm), B) Langmuir probe (z = 95 cm), and C) optical diagnostics (z = 110 cm) collection are shown. At location C (the 6” crossing ports) in Figure 2.2, a scanning stage for optical diagnostics collection is mounted to the chamber. A schematic of the stage is shown in Figure 2.3. The stage consists of two Velmex motor driven Unislide rail assemblies, one horizontal and one vertical. A set of collection optics is attached to each rail. The computer controlled stepping motor allows for precise positioning of the optics and scanning of the optics across the viewport. Typically, the optics on the vertical scanning stage are collimated while the optics attached to the horizontal scanning stage are focused such that the focal point intersects the line of sight of the collimated optics. When scanning vertically, the entire stage moves, such that the focal point always intersects the line of sight of the collimated optics. The viewing area is an 8 cm x 8 cm plane perpendicular to the chamber axis, limited primarily by the size of the viewports. 25 turned off, and a puff of argon gas (flow of 5 sccm for a short time) was introduced into the chamber. The gas was allowed to equilibrate and the pressure was assumed to be uniform throughout the entire system. Then readings from the front (HELIX) Balzers, Baratron located at z = 220 cm (at the second large port in LEIA), and back (LEIA) Balzers gauges were recorded. Compton and Biloiu gradually increased the pressure by introducing additional gas puffs. Calibration curves measured by Compton and Biloiu with no plasma discharge are shown in Figure 2.4 and Figure 2.5. There are different calibration curves for P < 4 mTorr and P > 4 mTorr due to the switching of the Balzers gauge from cold cathode to Pirani gauge. (There may have been some confusion in pressure conversion that resulted in the choice of 4 mTorr as a breakpoint. The Balzers gauge reading and actual pressure agree at 4 x 10-3 mbar, with differing characteristics above and below this value due to the different gauges.3 4 x 10-3 mbar is equivalent to a pressure of ~3 mTorr, which probably should have been the breakpoint used for the calibration data.) 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 Argon (<4mTorr) y = -0.13957 + 1.2618x R= 0.99591 Ba ra tro n (m To rr) Front Balzer Gauge (mTorr) (a) 0 5 10 15 20 25 30 2 4 6 8 10 12 14 16 18 Argon (>4mTorr) y = -1.1846 + 1.8056x R= 0.99878 Ba ra tro n (m To rr) Front BalzerGauge (mTorr) (b) Figure 2.4 Pressure gauge calibration for front (HELIX) Balzers gauge using Baratron gauge for pressures a) < 4 mTorr and b) > 4 mTorr. The linear fit shown is used to convert the gauge pressure reading to actual pressure. 26 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 4 Argon (<4 mTorr) y = -0.27024 + 1.2032x R= 0.99537 Ba ra tro n (m To rr) Back Balzer Gauge (mTorr) (a) 5 10 15 20 25 30 4 6 8 10 12 14 16 18 20 Argon (>4mTorr) y = -1.4454 + 1.6218x R= 0.99873 Ba ra tro n (m To rr) Back Balzer Gauge (mTorr) (b) Figure 2.5 Pressure gauge calibration for back (LEIA) Balzers gauge using Baratron gauge for pressures a) < 4 mTorr and b) > 4 mTorr. The linear fit shown is used to convert the gauge pressure reading to actual pressure. Compton and Biloiu also determined the pressure at z = 80 cm and z = 220 cm as a function of Balzer gauge readings with a typical pressure gradient present when the pumps are on (with no plasma discharge) by placing the Baratron gauge at each location. This was done by again introducing increasing amounts of argon gas into the chamber and recording readings of each gauge. See Appendix A for data and graphs of these measurements. The data acquisition code uses the following equations to determine the pressure at z = 80 cm given the front gauge pressure reading PG (unconverted): 0.02 0.5 , 4 0.3 0.8 , 4 . G G G G P P P mTorr P P P mTorr = + × < = − + × > (2.1) Similar measurements for helium, a gas not used in this work, are shown in Appendix A. 2.3 Magnetic field Ten electromagnets produce a steady state axial magnetic field of 0-1300 Gauss in 27 HELIX. Each magnet has 46 internal copper windings with a resistance of 17 mΩ and an inductance of 1.2 mH. The magnets are water-cooled, and their axial positions are adjustable along a set of rails. Two Xantrex 200 Amp power supplies configured in parallel provide current to the electromagnets. These power supplies are different from those used previously1 to eliminate fluctuations that were discovered in the old MacroAmp power supply. The LEIA magnetic field is created by a set of seven custom-built, 9’ diameter electromagnets. Each magnet consists of five sets of aluminum tubing wound into two pancakes of four layers each, for a total of 40 turns. The 0.5” x 0.5” tubing is hollow and wrapped in an insulating paper. The magnets are water-cooled by a closed system with a Neslab HX-300 chiller. These magnets are upgraded versions of those used in previous experiments.1 In these new electromagnets the larger size aluminum tubing and increased number of turns allow us to achieve a higher magnetic field strength. Additionally, the inner hole of the new tubing is circular, rather than rectangular, allowing for a much better attachment of the water connections. A magnetic field of 0-130 Gauss can be created using a 200 Amp DC EMHP power supply; an ~85 % increase over the original magnets. Upon completion of LEIA magnet building and installation of the new HELIX power supplies, several measurements of the axial (at r = 0) magnetic field were made (shown in Figures 2.6-2.7). 30 2.5 Plasma parameters The plasma can be operated in pulsed or steady state mode over a wide range of plasma parameters. For these experiments the plasma was typically operated steady state, at a RF frequency of 9.5 MHz, and a HELIX magnetic field of 750 Gauss. The LEIA magnetic field was set to zero because a non-zero field tended to cause the core, central bright plasma region, to be off-axis. The parameters that were varied include gas fill pressure and RF power. Additional typical parameters are shown in Table 2.1. Table 2.1 Typical plasma parameters in HELIX. Plasma Parameter Typical Value in HELIX Gas species argon, helium Base pressure < 2 x 10-7 mTorr Operating pressure 0.1 to 100 mTorr Magnetic field < 1300 Gauss RF power 0 to 2 kW Operating frequency 9.5 MHz (6-18 MHz) Density ~ 1012 cm-3 Electron temperature ~ 5 eV Ion temperature < 1 eV Electron gyroradius ~ 0.04 mm Ion gyroradius ~ 2.7 mm 31 For the collisional-radiative model, a measurement of the neutral pressure at the edge is needed. For the experiments reported in this work, I chose to use the measured fill pressure in the absence of the discharge obtained with the Baratron gauge located at position A (z = 80 cm) in Figure 2.2. When the plasma discharge was turned on, the Balzers gauge reading increased while the Baratron gauge reading at z = 80 cm decreased. This may be an effect of RF noise, though Tynan has reported a similar decrease in the edge neutral pressure upon initiation of the discharge measured by a capacitance manometer.4 He finds the same results occur whether the gauge is attached to the chamber wall or inserted into a radially scannable tube. Hanna and Watts also report a decrease in edge neutral pressure at discharge initiation using a thermocouple gauge.5 Table 2.2 shows a comparison of pressure gauge reading with and without discharge for various gas flow settings. As described by the table, with no plasma discharge, the Balzers gauge in the glass tee measures a higher pressure than does the Baratron located at the edge of the HELIX chamber. This is an expected pressure gradient due to the gas inlet located in the glass tee and the pumping configuration. Upon initiation of the plasma discharge, the Balzers pressure increases while the Baratron pressure decreases. This indicates that the actual pressure at the edge of the main plasma column is much lower than that upstream of the plasma column. Therefore, relying on pressures measured away from the plasma column could yield inaccurate results. A valve was used to separate the Baratron gauge from the plasma during operation to protect it from extended exposure to hot plasma. 32 Table 2.2 Pressure gauge reading comparison. Flow (sccm) HELIX Balzers reading (mTorr) Balzers conversion (mTorr) Baratron reading (mTorr) z = 80 cm Discharge status 80 5.4 8.6 4.1 Off 80 5.7 9.1 3.8 On 90 6.2 10.0 4.6 Off 90 8.2 13.6 2.1 On (P=350W) 90 9.7 16.3 0.3 On (P=750W) 102 6.4 10.4 5.1 Off 102 8.7 14.5 2.3 On 114 7.3 12.0 6.0 Off 114 10 16.9 3.2 On 35 modern physics as the personal computer.” - J.C. Camparo6 The diode laser was actually invented before the dye laser; however the nonlinearity of intensity versus injection current, unstable spatial profile, requirement of liquid nitrogen temperatures, and widely spread cavity modes made them less desirable.6 As these problems have been overcome and diode lasers have become commercially available, they have been used in many scientific applications; particularly in atomic physics. Bölger and Diels conducted the first atomic physics experiment with a diode laser, observing photon echoes in a cesium vapor.7 Diode lasers currently available have several advantages over dye lasers: they are comparatively inexpensive and do not require high voltage power and water cooling, making them accessible to more research groups. They are capable of gigahertz modulation; they are smaller in size, allowing for better portability; and they are available from ultraviolet to infrared wavelengths. A diode laser consists of several semiconductor layers. An injection current is sent through the active region between the n- and p-type layers. The electrons and holes created by the current recombine and emit photons to produce the laser light. The laser wavelength region is determined by the band gap of the semiconductor. Lasers that emit in the region of 670 nm are made from an InGaAlP semiconductor. The semiconductors are doped to achieve the wavelength range desired. The optical path length of the cavity and the wavelength dependence of the gain curve both depend on temperature; thus laser tuning can be achieved by varying the temperature. The shifting of the gain curve as the temperature changes will cause jumps in wavelength from one longitudinal cavity mode to another.8 Figure 3.1 shows laser wavelength versus laser temperature for a Sacher 36 Lasertechnik SAL-665-10 diode (the type of diode laser used in this work), in which the cavity mode jumps appear as large shifts in laser wavelength for small changes in temperature. The injection current also changes the wavelength, primarily by changing the laser temperature via Joule heating, but also by changing the index of refraction through changes in the charge carrier density.8 Since laser power also depends on laser current, injection current modification is not a practical means of wavelength tuning for our application. Varying the ambient pressure and applied magnetic field strength are alternative diode laser tuning methods.6 Figure 3.1 SAL-665-10 Laser wavelength versus temperature with laser piezo voltage at 50.0 V. Diode lasers can be configured in several ways to narrow the linewidth and control the central frequency.8 One option is to use an antireflection coating on the diode with external optics to create the laser resonator. This is known as an external cavity. A pseudo-external cavity setup has a diode with only one facet that has antireflection 37 coating. Two types of pseudo-external cavity setups are the Littman/Metcalf 9 and Littrow10 configurations. In the Littman/Metcalf configuration (shown in Figure 3.2), output from the diode is directed toward a grating at grazing incidence. The diffracted light reflects off the tuning mirror and back to the grating. Wavelength tuning is achieved by rotating the tuning mirror. Figure 3.2 Littman/Metcalf configuration11 In the Littrow configuration, the grating is placed at the Littrow angle, defined such that the first-order diffracted beam is coincident with the input beam. The zeroth-order beam reflects off the grating and is directed out of the cavity. Wavelength tuning is achieved by changing the incidence angle of the beam upon the grating. The Littrow configuration is shown in Figure 3.3. Figure 3.3 Littrow configuration11 The power output of the Littrow configuration is much greater than that of the Littman/Metcalf configuration because the zeroth-order beam is lost for Littman/Metcalf. However, the mode-hop-free tuning range in the Littrow configuration is smaller. Because laser power is critical to achieve significant LIF signal, the Littrow configuration 40 668.4 668.5 668.6 668.7 668.8 668.9 0 20 40 60 80 100 W av el en gt h (n m ) Piezo voltage (V) Figure 3.6 Laser wavelength versus piezo voltage for a laser temperature of 21 ºC 668.55 668.60 668.65 668.70 668.75 668.80 16 18 20 22 24 26 W av el en gt h (n m ) Temperature (ºC) Figure 3.7 Laser wavelength versus laser temperature for a piezo voltage of 50.0 V 41 The destruction of the laser diode by the EMP reflects the extreme sensitivity of these diode lasers to environmental conditions. Precautions that can be taken to reduce diode destruction include plugging the laser controller into an Uninterruptible Power Supply, turning the laser current on and off in gradual steps, and wearing a wrist grounding strap attached to the laser table. Special care should be taken when low humidity conditions could cause static buildup on the optical table or on personnel. Frequency (wavelength) scanning is accomplished by varying the voltage on the piezoelectric-controlled grating located within the laser cavity. A National Instruments I/O card provides the voltage ramp to scan the laser frequency. The custom LabWindowsTM code used to create the voltage ramp includes a conversion factor to create a voltage ramp that provides the desired frequency range. This conversion factor is a unique characteristic of each diode used. For the SAL-670-15 used in these experiments, the conversion factor is 1.73 GHz/V. The linearly polarized laser is mounted on a vibration-isolated platform to decrease drift in the laser frequency. The laser light is directed through an iodine cell, into a wavemeter, and into the plasma through a viewport at location C in Figure 2.2 with a series of mirrors and beam splitters mounted on the vacuum chamber and the laser table. 42 Figure 3.8 Diagnostic Configuration: 1. Laser head; 2. Iodine cell heater and photodiode detector; 3. Power meter; 4. Wavemeter; 5. Optical chopper; 6. Laser to plasma; 7. Light from collection optics in fiber; 8. Bandpass filter and PMT or infrared detector; 9. Lock-in amplifier; 10. I/O board; 11. Laser controller A tightly focused set of optics, mounted on the horizontal arm of the scanning stage, collects the fluorescence light perpendicular to the injected beam and sends the light through a fiber optic cable to a filtered (1 nm wide bandpass) Hamamatsu photomultiplier tube (PMT) for argon ions or Hamamatsu infrared detector for argon neutrals. The PMT/detector signal is composed of fluorescence radiation, electron impact induced radiation and electronic noise. A mechanical chopper operating at a few kHz is used to modulate the laser beam before it enters the vacuum chamber, and a Stanford Research Systems SR830 lock-in amplifier is used to eliminate all non-correlated signals. Lock-in amplification is indispensable since the electron-impact induced emission is several orders of magnitude larger than the fluorescence signal. The laser wavelength is 5 1 2 3 4 6 7 8 9 10 11 45 know the linewidth in terms of frequency, ν∆ . Using E hν= and Equation (3.2), Equation (3.1) becomes 1 . 2ij im jnm i n j A Aν π < <   ∆ = +    ∑ ∑ (3.3) For the Ar II LIF scheme, the linewidth of the 668.6139 nm transition from the 3d 4F7/2 state to the 4p 4D05/2 state will only depend on the transition probabilities of the transitions out of the upper state, because the lower state is metastable, such that the transition probabilities out of that state are negligible. The transitions out of the upper state and the respective transition probabilities are given in Table 3.1.16 Using these values and Equation (3.3), the linewidth is ν∆ = 2.13 MHz. Since this is larger than the laser linewidth, the natural linewidth limits the spectral resolution of the LIF diagnostic. Table 3.1 Transition probabilities for calculating the linewidth of the Ar II LIF scheme absorption transition. Upper State Lower State A (108 s-1) 4p 4D05/2 3d 4F3/2 0.002 4p 4D05/2 3d 4F5/2 0.025 4p 4D05/2 3d 4F7/2 0.107 For the Ar I LIF scheme, the linewidth of the 667.9126 nm transition from the 4s[3/2]°1 state to the 4p’[1/2]0 state will depend on transitions out of both states since the lower state is not metastable. The transitions out of these states and the respective transition probabilities are given in Table 3.2.17 Using these values and Equation (3.3), the linewidth is ν∆ = 26.5 MHz. Since this is much larger than the laser linewidth, the natural linewidth also limits the spectral resolution of the Ar I LIF measurement. 46 Table 3.2 Transition probabilities for calculating the linewidth of the Ar I LIF scheme absorption transition. Upper State Lower State A (108 s-1) 4s[3/2]°1 1S0 (ground) 1.19 4p’[1/2]0 4s[3/2]°1 0.00241 4p’[1/2]0 4s’[1/2]°1 0.472 To obtain reasonable Ar I LIF signal-to-noise, the source was operated at pressures above 10.5 mTorr (operating pressure). Optimal signal-noise was achieved for neutral pressures of approximately 17 mTorr (operating pressure). These relatively high neutral pressures provide the collision rates necessary to populate the initial 4s[3/2]°1 state. A typical Ar I LIF measurement is shown in Figure 3.10. 0 0 .1 0 .2 0 .3 0 .4 0 .5 -4 .0 -2 .0 0 .0 2 .0 4 .0 LI F In te ns ity (a rb . u ni ts ) F req u en cy (ν − ν o ) (G H z) T A r I = 0 .0 3 eV Figure 3.10 Typical Ar I LIF signal versus laser frequency and Maxwellian fit to the distribution (solid line). The LIF signal for a three-level LIF scheme is directly proportional to the density of the initial state (i) in the collection volume:18 47 ( ) ( ),3 3, ,0( , ) , , ,4 4 m i m f i m i BdI A d x d vN x v d L v W xν ν ν π π ∞Ω∝ ∫ ∫ ∫ (3.4) where dΩ is the detector’s solid angle, Am,f is the Einstein transition coefficient from the middle (m) to final (f) state (fluorescence transition), Ni is the phase space density of the initial state, Bm,i is the Einstein absorption coefficient from the initial to middle state, Lm,i is the absorption line shape of the initial to middle state transition, and W is the laser intensity line shape. As mentioned above, the laser linewidth is on the order of a megahertz. For typical helicon source argon plasma parameters, the total absorption lineshape is a convolution of thermal (Doppler) broadening and Zeeman splitting. Because the Doppler width and Zeeman splittings are on the order of a gigahertz, other effects such as the natural linewidth of the line and Stark broadening are ignorable.19 Thus, the total absorption lineshape consists of a number of Zeeman split components that are Doppler broadened. These components include π transitions ( ∆ M = 0; M is the magnetic orbital quantum number) and σ transitions (half for ∆ M = +1, half for ∆ M = -1). The relative intensities of the Zeeman components obey Iπ = 2 Iσ. When the polarization axis of the laser is oriented parallel to the axial magnetic field (laser injection perpendicular to the chamber axis), only the π transition is pumped. For parallel laser injection, the σ transitions are pumped. Insertion of a quarter-wavelength retarder in the laser path creates circularly polarized light and enables pumping of either the ∆ M = +1 or ∆ M = -1 transitions for parallel laser injection. Each Zeeman component of the measured LIF intensity can be integrated over the essentially delta function laser lineshape to yield a LIF intensity that is proportional to the bulk flow-shifted Maxwellian distribution of the interrogated species: 20 50 For this transition, the LIF signal is linear with laser power up the highest diode laser powers available. Thus, laser powers up to 11 mW do not saturate the Ar II pump state. A similar plot for the Ar II LIF scheme at x = 4 cm, near the edge of the plasma, is shown in Figure 3.12. 0 0.01 0.02 0.03 0.04 0.05 0.06 5 6 7 8 9 10 11 LI F S ig na l A re a (a rb . u ni ts ) Laser Power (mW) Figure 3.12 LIF signal versus laser power for Ar II LIF at x = 4 cm To determine if the initial state for the Ar I scheme is saturated, similar experiments were performed. The results are shown in Figure 3.13 for x = 0 and in Figure 3.14 for x = 3 cm. These measurements indicate a linear dependence of LIF signal on laser power (albeit with a much smaller slope than for the Ar II scheme), confirming that the initial state is not saturated for laser powers up to 11 mW. 51 0 0.01 0.02 0.03 0.04 0.05 6.5 7 7.5 8 8.5 9 9.5 10 10.5 LI F Si gn al A re a (a rb . u ni ts ) Laser Power (mW) Figure 3.13 LIF signal versus laser power for Ar I LIF at x = 0 cm 0 0.01 0.02 0.03 0.04 0.05 6.5 7 7.5 8 8.5 9 9.5 10 10.5 LI F S ig na l A re a (a rb . u ni ts ) Laser Power (mW) Figure 3.14 LIF signal versus laser power for Ar I LIF at x = 3 cm 52 When measuring across the diameter of the plasma by scanning the collection optics, the incident light on the PMT can vary with radius, generally increasing toward the center. For optimal signal levels, the PMT voltage can be adjusted during the radial scan. Because the LIF measurements are not automatically normalized with respect to PMT voltage, the data must be corrected by hand after the radial scan is performed. Each time the PMT voltage required adjustment, a measurement was taken at the same radial position with both the old and new PMT voltage level. A conversion factor for the PMT voltage change was calculated by dividing the area of the curve measured at higher PMT voltage by the area of the curve measured at lower PMT voltage. All measurements across the diameter of the plasma were then normalized to a single PMT voltage using these conversion factors. For the complete radial profiles presented in this work, the PMT voltage was constant across the plasma diameter, eliminating the need for this calibration. 3.1.3 Iodine cell The shift of the measured velocity distribution from the LIF absorption frequency (wavelength) is used to determine the bulk flow of the interrogated species for all three LIF schemes. A particle, atom or ion, moving towards the laser will see the frequency higher than that of the actual frequency. Thus, the laser will excite the particle at a lower laser frequency (higher wavelength) than if the particle were at rest. Measurements of fluorescence spectrum from an iodine cell during the frequency scan of the laser provide an absolute measurement of laser wavelength. Thus, the absolute shift in the absorption line is measured during each LIF measurement. Because the weak absorption lines of molecular iodine in the wavelength range of all three LIF schemes are difficult to fluoresce in commercially available iodine cells, a 55 The absolute wavelengths of each fluorescence peak were determined with the Burleigh wavemeter (with an absolute accuracy of ± .00003 nm according to the manufacturer and an observed statistical uncertainty of ± .0004 nm). The temperature of the heated iodine cell was kept at 69.3 ± 0.4 °C. None of these very weak iodine peaks (all of Figure 3.16) appear in the standard iodine tables. The spacing in GHz between the LIF peak and the nearest iodine cell peak is -0.40, -2.02, and +2.28 for Ar II, He I, and Ar I, respectively. Figure 3.17 shows a 120 GHz-wide scan of the iodine fluorescence spectrum for the Ar II sequence with the Ar II pump line indicated by a vertical line at zero GHz. As in Figure 3 of Ref. [14], the location of molecular iodine absorption lines in the published atlas23 are indicated by solid circles. Note that most of the molecular iodine fluorescence lines do not appear in the standard atlas of absorption lines. This discrepancy is not restricted to only weak lines as a number of the fluorescence lines that are missing from the absorption atlas are “stronger” than those that do correspond to absorption lines in the atlas. A possible explanation for this could be that additional vibrational modes are excited by heating the iodine cell. 56 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -60 -40 -20 0 20 40 60 668.55668.6668.65668.7 Io di ne F lu or es ce nc e (a rb . u ni ts ) Frequency (ν-ν 0 ) (GHz) Wavelength (nm) Figure 3.17 Iodine fluorescence spectrum for 60 GHz on either side of the Ar II pump line. The vertical line at zero GHz indicates the Ar II pump line. The solid dots indicate iodine absorption lines in the published line atlas.23 Recently, my iodine cell heater design was reproduced and similar measurements were made by Woo et al.24 They measured an iodine fluorescence pattern that matches Figure 3.16a, but found the wavelengths of the peaks to be shifted by -0.002 nm. It is possible that the calibration of our wavemeter is incorrect, which calls into question the exact location for the unshifted LIF absorption lines with respect to the iodine fluorescence spectrum. To determine this location for use in Ref. [14], G. Severn simultaneously measured etalon fringes and the iodine fluorescence as he scanned his diode laser (see Figure 3.18).25 The peaks in Severn’s iodine fluorescence spectrum were matched with those calculated using a program based on calculations by Gerstenkorn and Luc26 and provided to NIST (National Institute of Standards and Technology) by S. 57 Gerstenkorn (see Table 3.3 below; original communication shown in Figure B.1). Severn then created a set of linear equations based on the simultaneous measurements which he solved to find an approximate location for the unshifted line. His result is indicated in Figure 3.18. The absolute wavelength values determined by the Severn result are closer to those of Woo et al. than ours (see Fig. 4 of Ref. [24]). Therefore, our absolute flow velocity calculations could be incorrect by as much as 0.002 nm. A shift of 0.002 nm corresponds to an absolute velocity error of approximately 900 m/s. Figure 3.18 Iodine fluorescence versus etalon bin number as measured by G. Severn. Bin numbers of selected peaks are indicated as well as the calculated location of the unshifted (v = 0) Ar II LIF absorption line. The iodine reference cell proved to be indispensable in the portability and 60 where Tλ is the transmission factor of the detection system, and Ψλ is the sensitivity of the CCD. The sensitivity (measured in counts per Watt) is written as ,G hλ λη νΨ = (3.10) where ηλ is the quantum efficiency of the CCD at wavelength λ and G is the gain of the detector. 3.2.1 Spectroscopy diagnostic apparatus Measurements of spontaneous emission by excited neutral atoms used in this work were obtained from three different transitions: the 4p’[1/2]0 to 4s[3/2]°1 transition at 667.9126 nm, the 4p’[1/2]0 to the 4s’[1/2]°1 transition at 750.5934 nm, and the 4p[1/2]0 to 4s’[1/2]°1 transition at 751.6720 nm. These transitions are shown in Figure 3.19. Figure 3.19 Diagram of the transitions used for passive emission spectroscopy. Light emitted by spontaneous de-excitation is collected by a set of collimated optics, mounted on the vertical Velmex stage, which focuses it into a fiber optic cable 750.5934 nm 667.9126 nm 751.6720 nm 61 attached to a McPhersonTM Model 209 scanning monochromator. A fiber optics adapter is used to match the light from the fiber into the monochromator aperture.28 The monochromator consists of a two mirror, plane grating optical system, known as a Czerny-Turner system, with a 1.3 meter focal length. To select the desired detection wavelength, the grating is rotated while the mirrors and slits remain fixed. A CCD camera is attached to the exit slit for image capture. Relevant parameters of the monochromator are given in Table 3.4.29 Table 3.4 McPherson Model 209 scanning monochromator parameters. Parameter Value n – grating groove density 1200 gr/mm F – focal length 1330 mm f-number 11.6 (small grating) D – dispersion 0362 nm/mm GA – grating area 102 x 102 mm2 The resolution of the spectrometer diagnostic is given by the full width at half maximum (FWHM) of a spectral line emitted by cold atoms measured with the smallest slit width that does not diffract the incoming light. This can be done by sending light from an argon calibration lamp through the fiber optic used for the diagnostic into the monochromator. The slit width is decreased until distortion in the measured spectral line can be seen. The resolution for the 667.9 and 750.6 nm lines was measured to be approximately 0.13 nm. This corresponds to a width in frequency of 88 GHz, considerably larger than the ~ few MHz resolution of the LIF diagnostic. 62 3.2.2 Abel inversion Abel inversion is a technique that can be used to find the radially dependent value of a cylindrically symmetric quantity at a given point from measurements that are average values of the quantity along chords through the plasma. Figure 3.20 Geometry of cylinder of radius a with chord of length c at distance y from the center. The measured value, F(y), can be written in terms of the cylindrically symmetric quantity, f(r), as follows. 2 2 2 2 ( ) ( ) a y a y F y f r dx − − − = ∫ (3.11) Since 2 2 2x y r+ = , a change of variables in the integral gives 2 2 2 2 ( ) ( ) 2 ( ) , a a a y rdr rdrF y f r f r r y r y− = = − − ∫ ∫ (3.12) known as the Abel transform. In order to find f(r) from F(y) measurements, the inverse Abel transform is needed. Since f(r) is zero for r > a, it is equivalent to extend the integral bound to infinity. 65 [ [ ] / ] 0 [ 1, 100, , [ ] * /100; [ ] (1/ ) '[ [ ] [ ]] [ ] ; ]. ArcCos r j a For j j j r j a j e j N Pi ff r j Sec Sec dθ θ θ = < + + =  = −  ∫ This method yields an array, e[j], corresponding to the radially dependent f(r). Unfortunately, this method has several disadvantages. Any radial structure information inherent in the deviations of the measurements from the fit polynomial is lost, i.e., the polynomial fitting method forces the assumption of a source profile that is monotonically increasing toward the center of the plasma. After presenting results using the above method at a conference, R.E. Bell suggested a matrix inversion method (method 2b) that preserves detailed radial structure information. This method involves dividing the viewing region of the plasma into several segments and determining, geometrically, how much each region contributes to a given line of sight measurement.31 The measured plasma cross-section was divided into concentric circles such that each circle is considered to be an “emission zone” where the emission is the same from anywhere in that zone. A length matrix, L, can then be created where each element Lij describes the length of line of sight i that passes through emission zone j. The measured quantity, F, will then be related to the quantity, f, emitted by each emission zone by .i ij j j F L f=∑ (3.22) The desired quantity, f, can then be determined by inverting matrix L and calculating 1 .i ij j j f L F−=∑ (3.23) The k emission zones, where k is the number of measurements made from the 66 center to edge of the plasma, are created such that the radius of zone i lies halfway between the line of sight of measurement i and measurement i+1, as shown in Figure 3.21 for k = 5. If yi is the position of each line of sight measurement, then the radius of each emission zone circle is defined by ( )1 2,i i ir y y += + (3.24) and rk = Rmax. Figure 3.21 The plasma cylinder is divided into emission zones that are concentric circles such that the radius rj of zone j lies halfway between lines of sight j and j+1. The line of sight i is located yi from the center. The elements of the length matrix can be calculated by finding the length of a chord c across a circle of radius a at a distance y from the center of the circle. As shown in Figure 3.20, these are related by 2 22c a y= − . The matrix elements are then given by if ,j ir y> and i = j, 2 22 ,ij j iL r y= − if ,j ir y> and i ≠ j, 2 2 2 2 12 2 ,ij j i j iL r y r y−= − − − (3.25) if ,j ir y< 0.ijL = r3 y3 line of sight, i emission zone, j 1 2 1 3 4 5 2 3 4 5 67 For our experiments, k = 15 and Rmax = 3.625 cm is set by the diameter of the window through which the measurements are performed. The radius of the plasma is actually larger than 3.625 cm, but this value of Rmax is chosen so that the width of the outermost emission zone used in the inversion is the same width as the other zones. Since the viewport size limits our emission collection much beyond Rmax in the vertical direction, it is impossible to include the contribution from that region in the calculation. However, emission from outside Rmax does contribute along each horizontal line of sight that includes plasma radii larger than Rmax. Therefore, the outermost emission zone includes contributions that are not correctly weighted, i.e., if the emission intensity was constant across the plasma cross section, even after accounting for the longer line of sight through the outer emission zones, the measured emission from the outermost zone would be higher than the emission from the inner zones because of the additional contributions from plasma beyond Rmax. A Matlab® code was used to calculate the matrix and perform the inversion. A comparison of the two methods and the collisional-radiative model profile to be matched is shown in Figure 3.22, where the inversion results have been normalized to the model output. The advantage of the matrix inversion method’s ability to yield non-monotonically increasing results can be seen at r = 1.5. 70 for current is that of current flowing out of the probe. The locations of floating and plasma potentials, and ion and electron saturation currents are indicated. Figure 3.23 Langmuir probe I-V trace.33 To determine plasma parameters from the I-V trace, the electrons are assumed to be Maxwellian. The total electrical current from the probe is given by 1 2 1 2 01 2 1exp exp , 2 2 e i s e p i e e p T m eV AI n eA m m T Aπ         = − −                  (3.26) where n is the plasma density, Ap is the surface area of the probe, Te is the electron temperature, V0 is the voltage seen by the plasma (applied voltage minus plasma potential, pV V− ), and As is the area of the sheath surface. 32 The second term in the brackets is the ion saturation current, Isi, which, for an unmagnetized plasma, is given by 0.61 .si i e p e iI eJ en A T m= − = − (3.27) The slope of the I-V trace is given by ( ) 0 0 .sisi e dI e dII I dV T dV = − + (3.28) 71 As can be seen in the I-V trace, 0 0sidI dV dI dV$ , so that Te can be approximated by ( ) 0 .e si dIT e I I dV = − (3.29) Experimentally, a line is fit to ln siI I− versus V0 in order to determine the slope which is the inverse of Te. Once Te is known, Equation 3.27 can be used to determine the plasma density, ne. Because of the high densities in helicon sources, Langmuir probes are typically not driven into the electron saturation current region because the probe would not have a sufficiently negative potential to form a sheath and the high heat flux could destroy the probe.32 Without the electron saturation current measurement, we are unable to measure the plasma potential directly. The voltage V0 ( 0 pV V V= − ) must then be approximated by the applied voltage in the above calculations. Since the plasma potential is constant, the slope measured will not be affected by this approximation, yielding the same measurement of electron temperature.5 Because ions and electrons gyrate around magnetic field lines, the cross-field motion of the particles will be restricted, affecting the amount of particles reaching a Langmuir probe in a magnetized plasma. The effect will be determined by the relationship between the gyro-radius of each species and the size of the probe. Because the electrons have a smaller gyro-radius than the ions, the motion of the electrons will be reduced with respect to the ions, which will decrease the electron saturation current. However, since we do not drive the probe into the electron saturation current region, the probe remains significantly negative such that the electron dynamics can be treated as described above.32 The ion gyro-radius in HELIX with a 1000 G magnetic field and an 72 ion temperature of 0.3 eV is approximately 3.5 mm.5 Since this is on the order of the probe tip length of 2.0 mm, we must consider the effects of the magnetic field on the ions. The magnetic field reduces the number of ions reaching the probe, such that Equation 3.27 becomes32 0.49 .si e p e iI en A T m= − (3.30) The RF fields in helicon source plasmas will also affect Langmuir probe measurements. The fields will accelerate and decelerate the electrons toward the probe when the probe potential is near the floating potential, yielding an error in floating potential measurement.34 Sudit and Chen developed a method of RF compensation for Langmuir probes35 which we use in our probe design. A floating electrode is exposed to the plasma potential fluctuations and is connected to the probe tip by a large capacitor, which lowers the sheath impedance such that the probe tip will follow the plasma potential oscillations. Additionally, a chain of RF chokes is connected to the probe tip which increases the impedance of the circuit at the RF frequency. A schematic drawing of the Langmuir probe design is shown in Figure 3.24. The probe tip is 0.5 mm diameter graphite (mechanical pencil material) inserted into a 0.6 mm diameter alumina shaft and attached by a set screw to a copper base. A 10 nF capacitor is also connected to the copper base. This assembly is placed inside a boron nitride (BN) cap such that the probe tip extends into the plasma through a hole in the BN cap, and the opposite leg of the capacitor remains within the head so that it is not directly exposed to the plasma. The threaded BN cap attaches to the stainless steel probe shaft. The chain of RF chokes is attached to the copper base. The RF chokes are ¼ Watt shielded inductors, each specially designed to shield a certain RF frequency, from Lenox-Fugle International, 75 References 1 R.A. Stern and J.A. Johnson, Phys. Rev. Lett. 34, 1548 (1975). 2 H.C. Meng and H.-J. Kunze, Phys. Fluids 22, 1082 (1979). 3 D.N. Hill, S. Fornaca, and M.G. Wickham, Rev. Sci. Instrum. 54, 309 (1983). 4 M.M. Balkey, Optimization of a Helicon Plasma Source for Maximum Density with Minimal Ion Heating, Ph.D. Dissertation, West Virginia University, Morgantown (2000). 5 J.L. Kline, Slow Wave Ion Heating and Parametric Instabilities in the HELIX Helicon Source , Ph.D. Dissertation, West Virginia University, Morgantown (2002). 6 J.C. Camparo, Contemp. Phys. 26, 443 (1985). 7 B. Bölger and J.C. Diels, Phys. Lett. A 28, 401 (1968). 8 C.E. Wieman and L. Holberg, Rev. Sci. Instrum. 62, 1 (1991). 9 M.G. Littman and J. Metcalf, Appl. Opt. 17, 2224 (1978). 10 M. Born and E. Wolf, Principles of Optics (Cambridge U.P., Cambridge, 1959). 11 http://www.sacher-laser.com/ar_diode.php. 12 R.F. Boivin and E.E. Scime, Rev. Sci. Instrum. 74, 4352 (2003). 13 J. Sacher, private communication, 27 July 2005. 14 G.D. Severn, D.A. Edrich, and R. McWilliams, Rev. Sci. Instrum. 69, 10 (1998). 15 Sacher Lasertechnik LLC, Instruction Manual, Hannah Arendt Str. 3-7 D35037 Marburg/Lahn Germany (2000). 16 http://physics.nist.gov/PhysRefData/ASD/index.html 17 W.L. Wiese, M.W. Smith, and B.M. Glennon, Atomic Transition Probabilities, NSRDS-NBS (1966). 18 M.J. Goeckner and J. Goree, J. Vac. Sci. Technol. A 7, 977 (1989). 19 R.F. Boivin, “Study of the Different Line Broadening Mechanisms for the Laser Induced Fluorescence Diagnostic for the HELIX and LEIA Plasmas,” PL-039 (1998). 20 R.F. Boivin, “Zeeman Splitting for LIF Transitions and De-convolution Technique to Extract Ion Temperature,” PL-050, EPAPS-E-PHPAEN-10-003306 (2001). 21 L. Pauling and S. Goudsmit, The Structure of Line Spectra (McGraw-Hill, New York, 1930). 22 G. Marr, Plasma Spectroscopy, (Elsevier, 1968). 23 S. Gerstenkorn and P. Luc, Atlas Du Spectre D’absorption De La Molecule D’iode, Editions DuCentre National De La Recherche Scientifique (1978). 24 H.-J. Woo et al., Journal of the Korean Physical Society 48, 260 (2006). 25 G. Severn, private communication. 26 S. Gerstenkorn and P. Luc, J. Physique 46, 867 (1985). 27 W. Lochte-Holtgreven, Plasma Diagnostics, (American Institute of Physics, New York, 1995). 28 R.F. Boivin, “Spectroscopy System and Basic Spectroscopy Diagnostics for the HELIX and LEIA Plasma Devices,” PL-046 (2000). 29 McPherson, Instruction Manual for the Model 209 1.33 Meter Scanning Monochromator (1998). 30 R.N. Bracewell, The Fourier Transform and Its Applications, (McGraw-Hill, New York, 1978). 31 R.E. Bell, Rev. Sci. Instrum. 66, 558 (1995). 32 I.H. Hutchinson, Principles of Plasma Diagnostics, (Cambridge U.P., Cambridge, 1987). 33 P.A. Keiter et al., Phys. Plasmas 7, 779 (2000). 34 N.A. Krall and A.W. Trivelpiece, Principles of Plasma Physics, (San Francisco Press, San Francisco, 1986). 35 I.D. Sudit and F.F. Chen, Plasma Sour. Sci. Technol. 3, 162 (1994). 36 Lenox-Fugle International, Inc. 1071 N. Grand Ave. #115, Nogales, AZ 85621. (520) 287-5847. 37 P.A. Keiter, Experimental Investigation of Ion Temperature Anisotropy Driven Instabilities in a High Beta Plasma, Ph.D. Dissertation, West Virginia University, Morgantown (1999). 76 Chapter 4: ANU Experiments 4.1 Introduction To better compare the double layer (DL) measurements performed using LIF on HELIX/LEIA at WVU and MNX at PPPL with those using the retarding field energy analyzer (RFEA) on Chi-Kung at ANU, we were interested in performing LIF measurements on Chi-Kung. Additionally, the RFEA measurements are limited in spatial resolution (the RFEA can only be placed at discrete locations along the axis of the experiment). There was also a strong possibility that the grounded RFEA significantly perturbed the plasma during the measurement, whereas LIF could provide non- perturbative, spatially resolved measurements of the ion velocity distribution function in the Chi-Kung plasma. I was awarded funding through the East Asia and Pacific Summer Institute (EAPSI) Program sponsored by the National Science Foundation and the Australian Academy of Science to travel to Australia and perform these measurements. The portability of the diode laser LIF diagnostic was essential to this collaboration. (For more information on International Equipment Transit, see Appendix C.) Typical normalized RFEA ion energy distribution function (IEDF) measurements in the Chi-Kung plasma downstream of the region of diverging magnetic field are shown in Figure 4.1. The two ion populations evident in Figure 4.1 (the two peaks in the IEDF) are the fast ion beam flowing away from the source and the stationary ion population trapped downstream by the strong plasma potential gradient of the DL.1 The trapped ion population appears in the grounded RFEA measurement at an energy equal to the local plasma potential while the ion beam appears at higher energy. 77 Figure 4.1 Normalized IEDFs obtained with the RFEA at P = 250 W and the strong magnetic field case. (a) z = 37 cm (solid line) and z = 50 cm (dashed line) for P = 0.35 mTorr.1 (b) z=37 cm for P = 1 mTorr. The dashed line is a Gaussian fit to each peak. In the Cohen et al. LIF measurements of parallel ion flow speeds in MNX, for a neutral pressure of 0.6 mTorr in the main chamber, an ion beam of energy of 17 eV (corresponding to a beam speed of 9055 m/s) was observed.2 Cohen et al. observed an exponential decrease in the LIF signal from the ion beam as a function of distance from the DL – even though the ion beam energy remained constant or increased slightly with distance from the DL. Analysis of the MNX measurements indicated that the decrease in LIF signal arose from the collisional depletion of the metastable ion states probed in the LIF measurement process, i.e., the beam continued to propagate into the diffusion region but the metastable ions in the beam needed for the LIF measurement were rapidly quenched. 80 ion energy distribution function (IEDF). Two such IEDF measurements are shown in Figure 4.1. The IEDF measured at z = 37 cm (solid line) and z = 50 cm (dashed line) for a pressure of 0.35 mTorr are shown in Figure 4.1a. At z = 37 cm, the ion beam is approximately 9300 m/s faster than the trapped ion population. (RFEA measurements assume that the background population is at rest to calculate the plasma potential. Thus, the beam velocity measurement can only be given relative to the background population.) As the neutral pressure increases, both the energy and density of the ion beam decrease. The normalized IEDF for a pressure of 1.0 mTorr at z = 37 cm is shown in Figure 4.1b. At this higher pressure, the beam is approximately 6200 m/s faster than the background population. According to previous RFEA measurements, collisions reduce the ion beam below the detection threshold by z = 50 cm, as a result of ion-neutral collisions.7 LIF measurements of argon ions in Chi-Kung were performed with the portable diode-laser system. On the Chi-Kung source, the laser enters through a window in the center of the flange at the end of the diffusion chamber. An alternate gas inlet on the end of the source is used as a beam dump to minimize reflections. The fluorescence radiation is collected by a set of focused optics mounted to a rectangular window on the side of the diffusion chamber. (See Figure 4.3 for a picture of the custom optics mount.) The optics mount can be tilted to select the axial position, corresponding to z = 25 - 45 cm along the axis. Based on the core size of fiber optic cable used and magnification of the optics, spatial resolution is approximately 1 cm along the laser beam. 81 Figure 4.3 Chi-Kung tilting LIF optics mount. Since parallel (to the magnetic field) injection is used in these experiments, only the σ transitions are pumped. For the magnetic fields used in this experiment (≤ 150 G) Zeeman broadening can be ignored. Thus, Equation (3.5) can be simplified such that the intensity line shape can be described by a single Doppler shifted and broadened peak: 2 0 o 0 0 ( V / ) ( ) ( )expR R D i v v v c I v I v Tα  − − − =      . (4.1) Fits of Equation 4.1 to the measured LIF intensity as a function of laser frequency yield ion temperatures and ion distribution shifts with average precisions of ± 0.0043 eV and ± 0.27 GHz, respectively. To provide an absolute zero velocity reference for every LIF measurement, the laser is also directed through a heated iodine cell.8 The fluorescence spectrum of the iodine cell is recorded with an amplified photodiode for each LIF laser scan and used to calculate the shift, ν∆ , of the central LIF peak from 0λ = 668.6138 nm. A shift of the center of the LIF peak to lower frequency indicates a bulk flow of the ions towards the 82 laser (away from the source). The parallel ion flow speed is given by v = 0λ ν∆ . The reference spectrum used is shown in Figure 3.17. For most measurements reported here, the molecular iodine fluorescence peak at 668.6196 nm (3.89 GHz from the rest frame Ar II absorption line) was used as a zero- velocity reference for the LIF measurement, e.g., Figure 4.4a. For plasma conditions that yielded higher flow speeds, the molecular iodine fluorescence peak at 668.6318 nm (12.1 GHz from the rest frame Ar II absorption line) was used, e.g. Figure 4.4b. The absolute wavelengths of the iodine cell peaks were measured with an accuracy of ± 0.0004 nm (according to the stated wavemeter accuracy), yielding an error in the absolute bulk ion flow speed determination of ± 180 m/s. This systematic error is combined with the statistical error in determining the center of LIF peak (approximately ± 20 m/s on average) for the total parallel ion flow speed error shown in Figure 4.8 and Figure 4.9 (typically ± 181 m/s). If we include the overall shift in the iodine line wavelengths suggested by the recent Woo et al. measurements, the ion flow speeds reported here would decrease by approximately 900 m/s (approximately 10% - 20% of the measured ion beam velocities). Because low plasma densities (~109 cm-3 in the diffusion chamber) required long lock-in integration times (~ 1 s) to differentiate background plasma emission from the laser induced fluorescence, at least five one-minute laser frequency scans were needed to obtain adequate signal-to-noise. RF powers greater than 400 W were required to obtain LIF signal and RF powers > 750 W were problematic given the need to operate the source long enough to acquire a complete LIF scan (at RF powers greater than 750 W the matching circuit and RF antenna would overheat during the measurement). Therefore, 85 Figure 4.5 LIF signal versus parallel argon ion flow speed (away from the source) and axial position for (a) P = 1.3mTorr, weak magnetic field case, (b) P = 0.55 mTorr, strong magnetic field case, and (c) P = 0.37 mTorr, strong magnetic field case. RF power is 740 W in all cases. 86 For lower neutral pressures (< 1 mTorr) and for the strong magnetic field case, useful LIF signal was only achieved between axial positions z = 25 - 32 cm. Below neutral pressures of 0.35 mTorr, LIF measurements were not possible anywhere along the axis of the experiment – most likely due to significantly reduced plasma densities downstream of the DL at low neutral pressure. Figure 4.5b and Figure 4.5c show the log of LIF signal versus parallel ion flow speed and axial position for neutral pressures of 0.55 mTorr and 0.37 mTorr, respectively. Note that the ion flow speed upstream of the DL increases as the pressure decreases, indicating a larger potential difference across the DL for lower pressures. For P = 0.55 mTorr and P = 0.37 mTorr, the maximum ion speeds measured by LIF were approximately 7000 m/s and 7300 m/s (corresponding to ion beam energies of 10.1 eV and 11.0 eV), respectively. Based on the measured downstream electron temperatures of 7 eV and 8 eV, respectively, the ion flow speeds are clearly supersonic compared to ion sound speeds of 5300 m/s for 0.55 mTorr and 5700 m/s for 0.33 mTorr. Since the LIF signal was lost near the DL, the final ion flow speeds could not be measured with LIF. We expect that additional ion acceleration up to similar energies as measured by the RFEA occurred in the DL – which would be consistent with the RFEA probe measured ion beam energies downstream of the DL at z = 37 cm: 13.4 eV at 0.55 mTorr (obtained at a RF power of 250 W and not the 740 W used here) and 15.2 eV at 0.33 mTorr. These spatially resolved LIF measurements of the ion velocity distribution function (IVDF) also show that as the neutral pressure decreases, the DL forms further inside the diffusion chamber (based on the ion beam acceleration continuing further downstream for higher pressures). 87 The LIF intensity of the ion beam population measured in Figure 4.5a decreases rapidly with distance downstream of the DL. The amplitude of the LIF signal for the ion beam population is shown as a function of distance downstream of the DL in Figure 4.6. An exponential fit to the measurements yields a 1/e folding distance of 3.6 cm. Assuming that the decrease is due to a rapidly decreasing population of metastable ions in the beam and the rapidly expanding magnetic field (decreasing plasma density), the 1/e folding distance provides a measure of the quenching rate of the metastable ions. The 1/e folding distance for the ion beam signal obtained in these measurements is inconsistent with what was observed in MNX (1.6 cm for a pressure of 0.135 mTorr)2 and other argon LIF experiments.9 Using the 1/e folding distance obtained by Cohen et al.,2 one would expect to find a 1/e folding distance of 0.4 cm for a pressure of 1.3 mTorr in Chi-Kung, assuming the same collisional quenching-cross-section for the metastable state. In other words, the LIF signal persists much further downstream of the DL in Chi-Kung then expected. The very low pressure MNX experimental configuration included a physical aperture that limited plasma flow and therefore plasma production downstream of the DL. The Chi-Kung experiment has no aperture and we hypothesize that the longer 1/e folding distance results from additional metastable production by high energy electrons throughout the measurement region in this higher pressure plasma. As noted above, at lower neutral pressures the LIF signal decreases much more rapidly downstream of the DL. 90 useful LIF emission. That the ion beam energy scales as 1/Po2 with the neutral pressure, suggests that the double layer strength also scales with 1/Po2. 0 1000 2000 3000 4000 5000 6000 7000 0.0 0.5 1.0 1.5 2.0 2.5 Pa ra lle l I on F lo w S pe ed (m /s ) Pressure (mTorr) Figure 4.8 Parallel ion flow speed versus neutral pressure at z = 25 cm, RF power = 740 W, and for the strong magnetic field case. The solid line is given by vio = (1267/Po + 2156) m/s. In Figure 4.9a, the parallel ion flow speed is shown as a function of magnetic field strength for the same current in both coils. In Figure 4.9b, the ion flow speed measurements are for the case where the top coil (furthest from the diffusion chamber) was held at 6 Amps while the current through the bottom coil was varied. Note that a current of 6 Amps in both coils yields the strong magnetic field case geometry shown in Figure 4.2b. Because Figure 4.9a indicates that as the magnetic field strength increases the ions flow into the diffusion chamber faster, it would be natural to assume that the increased ion flow arises from magnetic moment conservation leading to increased conversion of perpendicular thermal energy into directed parallel ion flow. However, the measurements shown in Figure 4.9b demonstrate that it is the coil furthest from the 91 diffusion chamber that has the most influence over the ion flow speed into the diffusion chamber. Thus, the strength of the double layer is controlled by the plasma source parameters (i.e., the magnetic field strength in the source), and the high speed ion flows result from acceleration in the spontaneously formed DL and not any magnetic moment conservation process in the diverging magnetic field. The dependence of the potential drop across the DL on the coil furthest from the diffusion chamber is confirmed by RFEA measurements.11 Figure 4.9 Parallel ion flow speed versus magnet coil current (magnetic field) for (a) equal currents in both coils and (b) top coil held at 6 Amps while current through bottom coil was varied. RF power of 740 W, P = 0.55 mTorr, and z = 25 cm. 92 4.4 Discussion The high spatial and velocity resolution of the LIF IVDF measurements shown in Figure 4.5 provide a unique opportunity for comparison with numerical predictions of the structure and magnitude of DL formation in expanding, current-free plasmas. A recently developed one-dimensional Monte-Carlo Collision12 Particle-in-Cell13 (MCC-PIC) plasma computer code was used to confirm that DLs could form in current-free expanding plasmas.14 The PIC simulation consisted of a bounded plasma with a floating left wall and a grounded right wall. The system was separated into two regions: the source region and the diffusion chamber. In the source region, the electrons are heated up by a uniform RF electric field of 10 MHz perpendicular to the axis of the simulation. In the diffusion chamber, the diffusion of the plasma in the diverging magnetic field was modeled with a loss mechanism (see Figure 4.10). Figure 4.10 Spatial dependence of electron heating and loss rate used in PIC model of plasma expansion. The ion velocity distribution in phase-space, where the abscissa represents the position and the ordinate the ion velocity, predicted by the PIC code is shown in Figure 4.11 for a simulation neutral pressure of 1 mTorr. Throughout the simulation, a low energy population of ions is observed which corresponds to the ions which are created by