Creation of an Undergraduate Plasma Laboratory and an Exploration into Plasma Instabilities

David J. Nyce, Senior from Millbury, Massachusetts
Carl S. Helrich, Professor Emeritus of Physics

An apparatus, given to Goshen College by Princeton Plasma Physics Laboratory, was used to develop experiments to explain the basis for plasma physics. The experiments involving Paschen Law, Langmuir Probes, and Plasma Instabilities all give a good basis of understanding the complexities of plasma. All data gathered in this run of experiments have conformed to previous data. The laboratory manual produced from these experiments may be introduced to Goshen College over the next couple of years.

Introduction

Goshen College received a plasma apparatus from Princeton Plasma Physics Laboratory (PPPL) with a laboratory instruction manual for an entry level graduate course. We have rewritten this laboratory to make it suitable for an undergraduate upper level laboratory course in physics. To do this, we conducted all of the experiments in the PPPL written manual to identify areas where additional explanation had to be included. We carried out experiments of increasing complexity beginning with the formation of the plasma and extending to detailed studies of plasma waves.

The importance of introducing plasma experiments at Goshen College is linked to the present interest nationally and internationally in concept of Fusion Energy. Studying the basic behavior of a laboratory plasma yields information regarding what can happen in the plasma during a fusion reaction. Containment of the hot plasma is a critical problem. Our apparatus is capable of revealing some of less understood plasma characteristics.

We have planned a set of undergraduate experiments for a student at Goshen. The beginning experiments consider the characteristics of plasma generation and the Paschen Curve. The student will then have the opportunity to study light emission from plasmas and the influence of magnetic fields. The axial magnetic field experiments will show the student the importance of understanding the statistical mechanical description of the plasma. We have, therefore, included an overview of plasma theory in the manual. The student will also require this theoretical basis for comprehending the measurements made with Langmuir plasma probes.

Description of Apparatus

The apparatus contains two vacuum tubes in which the plasma can be formed. These are labeled X1 and X2. X1 has a height of 13 cm and a diameter of 6 cm. X2 has a height of 27 cm and a diameter of 10 cm. Both tubes are connected to one vacuum pump which and can each be evacuated separately. But both tubes cannot contain a vacuum simultaneously. The vacuum system is clearly diagrammed in the apparatus

Two gas sources are provided by separate gas bottles. These are helium and neon.

Electrodes are at the top and bottom of the X1 and X2 tubes. The top electrode is connected to a high voltage power source, which is variable from 0 to 3000 V with either positive or negative polarity. The connection from the high voltage supply to the tubes is through a 1 kilo-ohm resistor for measurement of current supplied to the tube. Both current to the tube and voltage across the tube are measured.

The electronics for conducting all the experiments is contained in a standard relay rack. This includes a separate power source for separate magnetic coils, an oscilloscope for Langmuir Probe measurements, which include wave and instability studies.  There are also the required volt and ammeters and low-voltage sources.

Experiments

The experiments we undertook were studies of plasma formation and the Paschen Curve, Single Langmuir Probe, Biased Single Langmuir Probe, Biased Double Langmuir Probe, and plasma oscillations and instabilities leading to a Plasma Pond plot. The Paschen Curve used Neon gas, while the others used Helium gas.

Paschen Curve

In this experiment we used the X1 vacuum tube. We made measurements of the breakdown voltage at which the plasm was formed as a fuction of the plasma pressure. The plot of breakdown voltage against plasma pressure is the Paschen Curve.

We covered a pressure range of 0.2 torr to 8 torr making three measurements of breakdown voltage at each pressure.

Single Langmuir Probe

If the Langmuir Probe is unbiased the tip aquires the plasma potential at the point at which it is located within the plasma. Only the tube X2 has ports for Langmuir Probes.This experiment uses the X2 vacuum tube. We made the measurements of the tip potential using the oscilloscope.

The Langmuir probe enters the tube from a port in the side where it is tightly calmped against an O-ring seal. We began measurements of the plasma potential as a function of plasma pressure at the center of the X2 tube. We held the high voltage constant at 1000 V and began increasing the plasma pressure from 0.3 torr in intervals of 0.1 torr. At 1.2 torr the plasma potential had become high enough that we required a x 10 voltage divider between the probe and the oscilloscope

We also conducted a study of the plasma potential when the high voltage was varied at a fixed plasma pressure. The plasma current was held to under 10 mA in order that the high voltage supply was not damaged.

In a final experiment we made measurements of the plasma potential from the center of the tube to the edge to find the profile of the plasma potential. Between measurements we carefully and slowly pulled out the probe in 1 cm intervals. We accomplished this by first making certain the guard ring was tight so that the probe would not be sucked into the tube, loosening the O-ring collar, easing the probe into the tube and then tightening the O-ring.

Biased Single Langmuir Probe

A biased single Langmuir Probe measures the current from the plasma to the priobe tip. We chose a pressure and connected the Langmuir Probe to a low voltage power source. We made voltage and current measurements using a standard ammeter and voltmeter. [insert MS2010_Plasma_Probe-Biasing-Schematic.tif]

We made measurements at plasma pressures of 0.1 torr, 0.3 torr, and 0.5 torr and high voltages of 1500V, 2000V, and 3000V respectively. In each situation we recorded values of probe voltage and current.

Biased Double Langmuir Probe

As we noted only the X2 tube can accommodate the Langmuir Probe. This is true for both single and double probes. In our studies with the Langmuir Double Probe we located the probe tip at the tube center. We used the same low voltage power source and meters as in the previous experment. In this experiment, however, the two tips of the double probe are at separate voltages. The difference in potential between the tips is supplied by the low voltage supply. The probe floats with respect to ground.

We studied a range of voltages (between the tips) from -40 V to +40 V making measurements of probe current at each voltage. This set up ends up giving a current that the probe draws. For the experiment we have provided in the manual as an example we chose a pressure of .3 torr and the high voltage of 2000V.

Plasma Pond

In this experiment we made measurements using the single Langmuir Probe and the X2 tube. We used the oscilloscope to measure the probe voltage. We had observed oscillations in our previous single probe measurements. In this experiment we returned for a detailed study of these instabilities.

We were able to measure the frequency of the oscillations on the oscilloscope, the tube voltage and the tube current. We held the plasma pressure fixed in each experiment.  This allowed us to obtain voltage and current regions at which various oscillations could be observed and to determine regions in which chaos was evident. This plot of current and voltage covered by regions at which types of oscillations occurred is what may be referred to as a Plasma Pond.

Results

Paschen Curve

We summarized our results for the gas breakdown in a Paschen Curve. There is a large peak at low pressures quickly decreasing to a minimum around 1 torr then slowly increasing again. [insert MS2010_Plasma_paschen-curve-data.jpeg]

Single Langmuir Probe

We plotted our results for the single Langmuir Probe as pressure vs. floating potential, high voltage vs. floating potential, and radial distance vs. floating potential.

At low pressures the floating potential slowly grew until a sudden jump in potential happened at .5 torr. Then at about 1.2 torr there was an instability which made it impossible to give an accurate measure of the potential. [insert MS2010_Plasma_pressure-vs-floating-potential.jpeg]

In the voltage vs. floating potential the voltage increased with the potential i eventually leading to a saturation point at about 900 V. [insert MS2010_Plasma_input-voltage-vs-floating-potential.jpeg]

We found that the potential decreased as the probe was removed to the edge of the tube. [insert MS2010_Plasma_radial-distance-vs-floating-potential.jpeg]

Biased Single Langmuir Probe

All the data we gathered throughout these experiments have followed the same pattern, having a negative saturation current and a positive saturation point. An example is the graph of the current vs. the voltage at pressure .5 torr and a high voltage of 750 V. [insert MS2010_Plasma_single-biased-probe.jpeg]

Biased Double Langmuir Probe

The data we gathered for the double Langmuir Probe produced n almost symmetrical plot. At the upper and lower limits we found what appeared to be limiting current values. [insert MS2010_Plasma_double-probe-data.jpeg]

Plasma Pond

Tour Plasma Pond plot shows regions of stable oscillations and regions of chaotic instability. We used colors to indicate the stable waves and black crosses to indicate chaos. We assume that the white space between the crosses is also chaos. The colors for the dots are as follows (all the periods are in micro seconds): Black = 80, Blue = 100, Green = 110, Red, = 130, Magenta = 140, Orange = 150, Dark Brown = 160, Powder Blue = 170, Baby Blue = 180, Light Green = 200, Banana = 220. The colors were generated by Grapher 8. [insert MS2010_Plasma_Plasma-Pond.jpeg]

Discussion

Paschen Curve

Our results plotted as a Paschen Curve agree with the literatre. The curve follws an empirical relationship

where V is the voltage, p is the pressure, d is the gap between the electrodes, a and b are empirical constants depending on the pressure and the gap between electrodes.

At a certain voltage the electrons create an avalanche in the tube. This happens when an electron gains energy of about 10 eV, which is sufficient to ionize the gas. This collisional energy is lower than the energy required if the electric field alone were to separate the electrons from their atoms, which would be the energy that could be supplied by the field over the dimension of an atom.

Single Langmuir Probe

The single, unbiased Langmuir Probe measures the plasma potential. Our experiment recorded the plasma potential as a function of radial position of the probe tip. The plasma density visibly decreases from the center of the probe toward the wall of the tube.

Our measurements indicate that there is a variation in the plasma potential across the tube. The reasons for this may be complex, although our initial thoughts are that this is related to recombination near the tube walls. The basis for recombination is, however, at this stage of our investigation unknown.

Biased Single Langmuir Probe

When the potential of the Langmuir Probe tip is chosen externally the type of plasma particles providing the measured current in the probe is affected by the dynamic conditions in the plasma. The current is finally a result of the plasma particles collected by the probe tip.

The probe current can be calculated from the principles of kinetic theory as the number of a particular species of plasma particle striking the probe tip per unit time. When the particles are electrons they neutralize ions on the probe tip, which are then replaced by drawing electrons from the tip down the probe. The current is from the voltage supply to the tip. If the particles are ions, they becom neutralized at the tip and become gas atoms. Electrons are supplied by the tip in this process.

This picture is complicated by the details of the occurances at the tip. When we bias the probe negatively positive ions are attracted to the probe and form a sheath around the probe. When we bias the probe positively the electons are attracted to the probe and a sheat of negatively charged electrons forms around the sheath. This sheath is known as the Debye sheath.

The Debye sheath must be accounted for in detailed studies of the probe current. Fortunately our data can be understood based bias potential, plasma potential, plasma density and electron temperature.

Electron temperature is the important single parameter we can obtain from the current vs. voltage plot for the biased single Langmuir probe. The slope of the semi-logarithmic plot of probe current vs. bias voltage is

We can see the ion saturation on the graph. The lower bend on the graph is where the ion saturation current is reached. The upper bend on the far right of the graph is where the electron saturation is reached.

Biased Double Langmuir Probe

We have a fairly complete and consistent theory for the double Langmuir Probe. Our data follow the xpected plot very closely. There is a slight asymmetry in the curve, which is understood in the fact that the areas of the probbe tips are not the same.

We were able to obtain the ion saturation current and the plasma density from biased double probe measurements.

Plasma Pond

We have only just begun working with plasma waves and instabilities. We suspect that these are electron or ion acoustic waves because the Langmuir probe would not be able to record transverse waves. We, however, lack sufficient data at this time to decide of the exact identity. It is also possible that the complex process of ionization may be affecting the character of the waves.

The mixing and chaotic behavior of the waves is also not unexpected bcause the plasam is a highly nonlinear system. To say that, though, does not provide a solution.

Conclusion

We believe that the set of experiments possible with this apparatus provide a systematic introduction to basic plasma physics in a way that can be understaood and appreciated by a Goshen College physics major. An interest in graduate school in general or in plasma physics in particular is not a requirement.

The experiments begin at a rudimentary level as far as conducting them successfully is concerned. The difficulty is always in the understanding and in the interpretation of the data. To conduct and understand the experiments through those on Langmuir Probes could easily form a semester’s experience.

To extend this work any farther into wave motion and the launching of wavescould also fit well into an independent study. Depending on what the student wishes to do this could also become research.

We have also written a manual that not only introduces the experiments and the apparatus, but also provides the vital parts of the theory.