Plasma Theory for Undergraduate Education

Plasma Theory for Undergraduate Education Joseph B. Hakanson 1, Warner Meeks 2, and Dr. Joshua L. Rovey 3 Missouri University of Science and Technology, Rolla, Missouri, 65409 These instructions will discuss both DC plasma theory as well as describe experiments that can be used for undergraduate instruction of DC plasma diagnostics. Experimental breakdown curves and Langmuir Probe curves will be obtained and studied with the use of a DC glow test article. Through the development of these experiments, the Missouri S&T Aerospace Plasma Laboratory (AP Lab) have experimentally achieved data that resembles theoretical models. From this, useful quantities can be obtained, such as breakdown voltage region (lower limit: p*d = 0.2 Torr*cm), electron temperature (T e = 1.4124 ev), etc. The results of the AP Lab have been included in this document for reference. V I R V B p*d T e = voltage = current = resistance = breakdown voltage = pressure-distance parameter = electron temperature (ev) Nomenclature I. Introduction The purpose of this document is to equip undergraduate students with the knowledge to ascertain DC plasma characteristics in a controlled lab setting. Theories included are Paschen Breakdown and determining electron temperature and density with a Langmuir Probe. II. Experimental Test Article The AP Lab has assembled a DC glow discharge similar to that used by the Princeton Plasma Physics Laboratory [1]. The test article is constructed from a 3 ¾ diameter Pyrex tube T-joint, an Edwards Series 3 rough pump, and a Varian V70 turbo pump (see Figure 1). Two electrodes are suspended in a parallel configuration with a variable gap distance. Argon gas or air is used to backfill the chamber to the desired pressure from high vacuum. To control the backfill system, an Alicat Scientific digital flow regulator is used. To power the electric discharge a Glassman High Voltage Inc. 1000V 100mA variable DC power supply is connected to one electrode while grounding the second and is monitored by a Tenima 72-1020 Benchtop Digital Multimeter. For the Langmuir study, a BK Precision 1739 DC Power Supply was used to bias the probe. 1 2 3 Undergraduate Student, Mechanical and Aerospace Engineering, jbhg28@mst.edu Graduate Student, Mechanical and Aerospace Engineering, wcm994@mst.edu Professor, Mechanical and Aerospace Engineering, roveyj@mst.edu 1

Figure 1. Test article setup In addition to the test article, a Langmuir Probe circuit (see Figure 2) should be assembled for the experiment in section IV-B. The probe can be inserted through the same plate as the gas inflow via a Swagelok pass-through whenever the chamber is at atmospheric pressure. Once inserted, the probe position can be adjusted even while the chamber is evacuated. 2

Figure 2. Langmuir Probe circuit setup III. Plasma Theory To understand the observations of this experiment, students must first have a basic understanding of the formation of plasma. A. Electrical Breakdown When a potential difference is applied across a gaseous medium, neutral atoms immediately surrounding the electrodes become ionized. Under low potentials (<100 V), the ionized particles are too infrequent to promote substantial secondary ionization. However, when greater potentials (1000's V) are applied, the free electrons have enough energy to ionize additional atoms via collisions. This cascading effect is called a Thompson avalanche. Once electrical breakdown is achieved, a DC glow can be sustained under reduced voltages until the current is reduced to zero and the glow is extinguished. B. DC Glow Geometry A sustained DC glow has several distinguishable regions that can be explained with sufficient understanding of the driving plasma physics. Upon first observation, the most notable characteristic of a DC glow is how the plasma is separated into two Figure 3. Electric Glow Discharge Schematic distinguishable regions (See Figure 3). The larger of 3

the two regions is composed primarily of the positive column. This region has a positive charge because the much lighter negative electrons have greater mobility than the heavy positive ions. This increased mobility means that the electrons will be more likely to strike the container surface or the electrodes and be removed from the column. The purple/pink light seen in the positive column and the negative glow is created when excited ions release photons so that their excited electrons may be reduced to a stable orbital. Discussion on the other regions that commonly occur in a DC glow discharge may be found in the literature cited [2], [3], & [4]. C. Striations One interesting phenomenon that can be observed with this setup is a striped pattern known as striations in the positive column. Striations are formed under specific conditions related to pressure, gap distance, and voltage. With this test article, the AP Lab was able to achieve striations (See Figure 4). More information about the formation of Striations can be found in literature [5]. This phenomenon always occurs in the positive column, but typically traverses too quickly to be seen. However, under the right conditions a standing wave can be achieved, and this effect can be visualized (See Figure 4). Figure 4. Experimental Striations IV. Plasma Characteristics In using this simple static DC plasma discharge, several fundamental plasma characteristics can be observed. With the correct environment control, the breakdown potential of the plasma can be characterized as a function of electrode gap and pressure. Additionally, if resonance is achieved striations can be observed as standing waves. A. Paschen Curve Breakdown voltage, V B, is the potential difference at which the Thompson Avalanche occurs, and a glow can be sustained. Pressure, electrode gap distance, and gas species all affect the breakdown voltage. However, to usefully characterize breakdown voltage, all variables can be held constant except a pressure-distance parameter, p*d. V B can be shown to have an exponential relationship with p*d through Paschen s law [2]. When graphed, each gas produces a common profile (See Figure 5). The solid lines represent Paschen's law for various gases, while the data points represent example experimental data obtained with this test article. The test was performed in air at a gap distance of 4

3 inches. Paschen Law theory assumes infinite parallel plates are used as electrodes across a region of a static gas. Thus edge effects such as sharp corners as well as fractional gas contaminants (i.e. air in a test of a different gas) will be common sources of error or deviation from theory. Subsequently, only in extremely controlled experiments is the theory realized in full. However using this test article the students can conduct a series of experiments with argon gas or air to achieve a Paschen Curve that approximately resembles those seen in literature [6] (See Figure 5). Figure 5. AP Lab Paschen Curve B. Langmuir Probe Study Electron temperature and density are important characteristic of any plasma study. To determine electron temperature, a Langmuir probe can be inserted into the plasma. The probe may then be biased to known voltages using a variable power supply and the collected current recorded. A characteristic I-V curve can be obtained and an idealized plot of this curve can be found in Figure 6. There are three characteristic regions of this plot: a nearly flat linear region below the floating potential (Region I), an exponential region above the floating potential (Region II), and then a new linear region after the knee (Region III). The floating potential is described as the biased Figure 6. Ideal Langmuir Probe Plot voltage at which zero net current flows through the probe. This floating potential is typically negative because mobile electrons tend to strike the probe more frequently than positive ions. The knee occurs when the probe has been saturated with electrons, causing additional electrons to be repelled. By plotting probe voltage against resulting current, and assuming a Maxwellian distribution, the electron temperature can be determined by taking the log-derivative of the exponential region of the function (Eq. 1). The AP Lab measured an electron temperature of 1.4124 ev. (ev) (Eq. 1) 5

However, as with the Paschen Curve, the idealized Langmuir Curve can be difficult to achieve. In general, Region III will have a slope greater than zero due to an expanding sheath (electron capture boundary) around the probe. You as the undergraduate will conduct an experiment and collect data similar to that plotted in Figure 7. Note how the knee cannot be clearly observed. This is an unfortunate reality of laboratory experiments. Figure 7. AP Lab Langmuir Probe Plot 150 mtorr, 4.63 sccm, 8.5 to 10.2 ma DC discharge, 650V DC discharge V. Student Experiment Guide A. Lab Equipment Checklist To begin this lab, first verify that all necessary equipment has been identified and located: 1) DC Glow Apparatus a) Pair of rounded, polished electrodes for observation b) High-voltage cable Don't Touch 2) Argon Backfill Supply (optional) a) Filled tank of argon b) Bottle and Gauge valves c) Flow regulator 3) Power Supply a) 1000V power Supply b) 30V power supply 4) Pumps a) Rough pump b) Turbo pump (optional) 5) Sensors and Probes a) Digital pressure gauge b) Digital multimeters One to monitor discharge current and probe current and one to monitor discharge voltage c) Langmuir Probe d) Oscilloscope 6

B. Paschen Study This study will allow you to generate a Paschen curve to compare to the ideal case. 1) Start-up Note: Part 1 a-c and e is only necessary for tests using Argon gas. The AP Lab test article was determined to have too much air leakage to satisfactorily perform tests with gases other than air. a) Verify that gauge valve is completely unloaded (counter-clockwise) b) Open the argon bottle valve until the pressure stabilizes (~ ¼ turn) c) Adjust the gauge valve clockwise to increase pressure to about 20 psi d) Turn on power to the cart, rough pump, 1000V supply, and flow meter. Let the experimental equipment warm up for 15 minutes to assure consistent data. e) The chamber should be evacuated to around 20 mtorr or less with the rough pump alone, and then down to 0.05 mtorr with the turbo pump. 2) Monitoring Gas Flow a) Click the mode button b) Select volumetric control (unit: sccm) c) Scroll to the flow settings, and increase the flow until the pressure stabilizes around 40 mtorr (0.1 sccm). Be careful when adjusting the flow controller; it first increases by 0.01 sccm, and then increases by a factor of 10 every few seconds. This means that you can easily over-shoot your target pressure. d) When adjusting the flow at pressures above 99 mtorr, be careful to approach the target slowly by increasing the pressure only. The pressure gauge loses a decimal place, so care must be taken to insure accuracy in your readings. For instance, 9.9*10-2 is ± 0.5 mtorr accurate while 1.0*10-1 is ± 5.0 mtorr accurate. 3) Monitoring Discharge Voltage a) To control the applied voltage, use the black voltage knob on the 1000V DC supply while watching both the digital ammeter and voltmeter (which are monitoring the discharge flow). b) BE CAREFUL WHEN THE CART IS ENERGIZED. All exposed metal should have negligible potential, but avoid unnecessary contact with metal. Try to keep one hand in your pocket. This is good practice whenever working with high voltage. c) Slowly increase the applied potential until breakdown is achieved. This can be noted by a sudden increase in the current from negligible to substantial. d) Once breakdown is achieved, the glow can be sustained at lower voltages. Therefore, if you over shoot the breakdown potential, you will need to fully extinguish the glow and re-approach the breakdown potential slowly. 4) Data Acquisition a) Once the setup has been initially stabilized, note the initial conditions such as the bottle pressure, gauge pressure, evacuated pressure, gap distance, gas species, and any other noteworthy conditions. b) Begin the data acquisition at 40 mtorr and increase by 20 mtorr until the range of the 1000V supply or the digital flow regulator has been exhausted. c) At each data point, note the pressure, breakdown potential, and breakdown current. 5) Data Analysis a) Graph V B vs. p*d in Excel or Matlab and compare to the ideal case. 6) Gathering Additional Data a) If the data acquired does not capture the full region of interest, the electrode gap distance may be adjusted for further experimentation. To adjust the gap distance, first establish a distance of zero by meeting the electrodes. Mark the location on the electrode stem where it enters the chamber with tape. Then increase the distance to the desired amount as measured between the chamber and the tape. b) Make sure that if the gap is adjusted, you take data points that overlap the original data set. This will help you verify the validity of your results. 7

C. Langmuir Study This study will allow you to determine the plasma temperature by generating a Langmuir Curve. 1) Start-up Note: Part 1 a-c and e is only necessary for tests using Argon gas. The AP Lab test article was determined to have too much air leakage to satisfactorily perform tests with gases other than air. a) Verify that gauge valve is completely unloaded (counter-clockwise) b) Open the argon bottle valve until the pressure stabilizes (~ ¼ turn) c) Adjust the gauge valve to about 20 psi d) Turn on power to the cart, rough pump, high voltage supply, low voltage supply, and flow meter. Let the experimental equipment warm up for 15 minutes to assure consistent data. e) The chamber should be evacuated to around 20 mtorr with the rough pump alone, and then down to 0.05 mtorr with the turbo pump. f) Use a digital voltmeter to precisely tune the 1000V supply to the desired potential for the remainder of the experiment. Then the voltmeter can be moved to the Langmuir Probe. g) Use the flow meter controls (as described in section VB2 Monitoring Argon Flow) to establish a flow rate to provide the desired pressure for the remainder of the experiment. This may need to be adjusted periodically. 2) Data Acquisition a) Once the setup has been initially stabilized, note the initial conditions such as the bottle pressure, gauge pressure, evacuated pressure, gap distance, gas species, discharge voltage, chamber pressure, and any other noteworthy conditions. b) To achieve a full spectrum of the Langmuir Study, the full 30V range will need to be swept on both the positive and negative side of the power supply. To change polarity, flip the grounding strap to the other node on the 30V supply and move the banana cable to the other node. c) Collecting Data i. By Hand If you opt to collect data points by hand, simply note the current through the probe for every volt increasing to 30V in both directions. ii. Oscilloscope To quickly acquire data, an oscilloscope can be used to record current as you sweep the voltage across its full range. 3) Data Analysis a) Graph Applied Voltage vs. Probe Current in Excel or Matlab and compare to the ideal case. Note that the Applied Voltage is from the low voltage supply, not the high voltage discharge source. b) Take the log derivative of the exponential region to determine plasma temperature in ev. VI. Conclusion Through these experiments, undergraduate students should gain a richer understanding of the properties and characterization of DC plasma. With a solid grounding in these basics, more complicated applications of plasma technology may be explored. 8

Acknowledgements This report was made possible with the support of the NASA Missouri Space Grant Consortium. References [1] Stephanie A. Wissel, A. Z. (2012). The Use of DC Glow Discharges as Undergraduate Education Tools. Princeton Plasma Physics Laboratory, 1-20. Print. [2] Hutchinson, I. H. Principles of Plasma Diagnostics. 2nd ed. Cambridge: Cambridge UP, 1987. Print. [3] Mott-Smith, H., and Irving Langmuir. "The Theory of Collectors in Gaseous Discharges." Physical Review 28.4 (1926): 727-63. Print. [4] Lieberman, M. A., and Allan J. Lichtenberg. Principles of Plasma Discharges and Materials Processing. Hoboken, NJ: Wiley-Interscience, 2005. Print. [5] Lisovskiy, V. A., V. A. Koval, E. P. Artushenko, and V. D. Yegorenkov. "Validating the Goldstein Wehner Law for the Stratified Positive Column of Dc Discharge in an Undergraduate Laboratory." European Journal of Physics 33.6 (2012): 1537-545. Web. [6] Lieberman, Michael A.; Lichtenberg, Allan J. (2005). Principles of plasma discharges and materials processing (2nd ed.). Hoboken, N.J.: Wiley-Interscience. 546. 9