Optical Pumping of Rubidium

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1 Optical Pumping of Rubidium Janet Chao, Dean Henze, Patrick Smith, Kent Lee April 27, 2013 Abstract 1 INTRODUCTION Irving Langmuir coined the term plasma in a paper in 1928, ushering a whole new and exciting branch of physics. Plasma, the fourth state of matter, consists of charged particles (electrons and ions) and neutral atoms which exhibit collective effects. Plasma is by far the most common phase of ordinary matter in the universe. In space, plasma makes up stars (including our Sun), solar wind, and interstellar, intergalactic, and interplanetary mediums. On earth, plasmas make up some flames, the aurora borealis, and lightning. These are only a few examples of the plethora of plasma that exists naturally in this universe. Through plasma research and technology, scientists have developed plasma displays (including TVs), fluorescent lamps, neon signs, and more. Furthermore, integrated circuits including those within computers, cars, clocks, coffee makers, etc. are also manufactured using plasma processing technology. Plasma physics is not only important because of its application in developing some of our favorite modern gadgets, it could also potentially solve the world s energy problem. For over the last 40 years, a central focus and major area of research in plasma physics has been fusion energy. The harnessing of fusion energy would provide much more energy for a given weight of fuel than any other technology currently in use. This paper will provide some theory and background knowledge on plasma (Section 2), describe the method of creating and perturbing laboratory plasmas for research purposes in the experimental design section (Section 3), our data and results found from these experiments (Section 4), and our concluding interpretation and analysis of these results (Section 5). 2 THEORY Plasmas can be produced by electron bombardment of neutral gas in an evacuated vessel. These electrons can be emitted by a set of filaments when they are excited by an energy greater than the work function of the filament material. These electrons are then accelerated by an external DC electric field (by a discharge potential) with enough energy to ionize the neutral gas. The filament is essentially a cathode that provides electrons, while the vessel s chamber wall acts as an anode, taking back the electrons to complete the circuitry. This will be further explained in the following Experimental Design Section. When experimentally creating plasmas in this manner, there is a balance between plasma particle production and loss. This is a multifaceted and complex balance that relies on many factors. The production of plasma is affected by the density of neutrals, cross section of neutrals, effective path length of the primary electron before lost to the plasma, electron flux, flow of ions, etc. The plasma electrons can also be affected by many variables since they can be lost to the chamber wall, to the recombination of neutrals, to the probes, filament supports, and any other obstacles. Utilizing the Langmuir probe method and the ion acoustic wave method, we attempt to understand the 1

2 relationship between plasma s prominent characteristics. 2.1 Langmuir Probes The Langmuir probe method, developed by Irving Langmuir, allows one to determine the values of ion and electron densities, electron temperature, plasma density, plasma potential, and electron and ion saturation currents. By placing a small Langmuir probe into the plasma, sweeping through a range of potentials in the probe, we can view the current-voltage characteristic to determine the characteristics listed previously. The current collected by the Langmuir probe is calculated by summing all the contributions of the various plasma species I = A i n i q i v i, (1) where A is the collecting surface area of the probe, q i is the charge of species i, n i is the density of species i, and v i is the average velocity of species i. Using statistical mechanics, we can determine that the equilibrium velocity distribution function f will be Maxwellian and use this to determine the average velocity v i = 1 n vfi ( v)d v, where f α ( v) = n( 2πKT α m α ) 3 2 Exp( 1 2 m α v 2 KT α ) (2) is the unnormalized Maxwellian velocity distribution function used to evaluate the average velocity of each species. Assuming that our probe is placed in the yz plane, the probe will only detect a current when a species collides with some x component velocity, v x. Considering just this x component of velocity, we can obtain current as I(v) = nqa v x ( 2πKT α v min m α 1 2 )e ( 2 1 mαv2 x KTα ) dv x. (3) At the electron saturation current, I s, all electrons with v x component toward the Langmuir probe are collected and the saturation cur- Figure 1: Sample Langmuir Probe Current- Voltage Characteristic rent is represented by I s = nq e A v min v x ( 2πKTe 1 2 m e )e ( 1 = nq e A( KTe 2πm e ) 1 2 = 1 4 nq eav e, 2 mev2 x KTe ) dv x (4) 8KT where v e = e πm e. At the ion saturation current, I is, all electrons are repelled by the Langmuir probe, meaning the probe potential, V p must be negative. The ions arriving near the probe sheath accelerate toward the probe with an energy of approximate KT e at the ion saturation current, which is much larger than their own thermal energy of KT i since the ions are so much more massive. The ion saturation current can then be given as I is = nq e A( 2KT e m i 1 2 ). (5) Below the electron saturation current (where the probe voltage, V p, is less than the plasma space potential, V s ), electrons are repelled from the probe and we see from Figure 1 that the probe current should increase exponentially with an increasing probe voltage until the probe voltage reaches the plasma space potential (where the electron saturation current is reached and electrons begin to flow toward the probe). Using Equation 3, and substituting 1 2 m ev 2 min = q e V, where V = V p V s, 2

3 Equation 3 becomes I(v) = I is nq e A( KT e 2πm e ) 1 2 e qe V KTe. (6) At the floating potential, V f, there is no net probe current, meaning the ion and electron currents are equal. Therefore, by solving Equation 5 and Equation 6 when I = 0, we can determine the floating potential to be V f = KT e e ln( m i ) 1 2. (7) 4πm e derivation, we will simply note that the relationship between a perturbation in density, a perturbation in pressure, and a perturbation in velocity do indeed result in a coordinated wave represented in the plasma. However, unlike true acoustic waves such as sound, waves in plasmas do not all travel at the same speed for all frequencies. The ion acoustic waves propagate at the ion acoustic speed ( ω k ) only in a particular range as shown in Figure 2. The electron temperature, T e, can also be determined from Equation 6. By subtracting out the ion saturation current from the probe current measurement and simplifying using Equation 4, we see that the current that can be directly related to T e by I(v) I s e qe V KTe. (8) Then, by rearrangement and differentiation of Equation 8, we find that the electron temperature is obtained by dln I d V = e KT e. (9) Equation 9 shows that by plotting a semi-log I-V characteristic and finding the slope in the V range, we can find T e. By designing an experiment that employs these relations, we can determine experimental values for electron temperature, T e, and plasma electron density, n e. 2.2 Ion Acoustic Waves When Irving Langmuir introduced the concept of plasmas in his 1928 paper, he noted the presence of low frequency oscillations in plasmas such as those of ion acoustic waves and gave an accurate expression for their phase velocity. Since then, ion acoustic wave frequency, wavelength, and phase velocity data have been used as valuable plasma diagnostic measurements. The derivation of the ion acoustic wave dispersion relation has been the basis of all fluid derivations of ion acoustic waves ever since. Although this paper will not go through the Figure 2: A dispersion diagram for ion acoustin waves. Only at the lower frequency, long wavelength linear regime (dashed line) does the plasma behaves acoustically. For a single species plasma, the ion acoustic wave speed (in the long wavelength limit) is given by KTe v = m, (10) where K is Boltzmann s constant, T e is electron temperature, and m is the mass of the ion. 3 EXPERIMENTAL DESIGN 3.1 Langmuir Probes The apparatus used to create the plasma consisted of a large metal vacuum chamber lined with magnets, a filament source, and a Langmuir probe (as initially described in the Theory Section and shown in Figure 3). The filament source emits the primary electrons that are responsible for ionizing the Argon gas molecules, creating the plasma. The multipole magnets (alternating north and south 3

4 3.2 Lockin Amplifier Figure 3: Diagram of the filament-vacuum circuitry responsible for creating the plasma. poles) that line the metal vacuum chamber increase the efficiency of the plasma source by creating a longer primary path length (thereby increasing the production rate of plasma) and reducing the effective surface area of the anode chamber wall (since the electron no longer has a direct path to the anode wall (reducing the loss rate of plasma). This higher percent ionization due to the magnets gives a higher density plasma than without magnets. These primary electrons responsible for ionizing the neutral atoms are accelerated by a DC electric field in order to give the electrons enough energy to ionize the Argon gas. The discharge voltage is responsible for this acceleration and creates a discharge current between the filament and the chamber wall (the effective anode). The Langmuir probe in this steady stade discharge, sweeps through a range of voltages in order to measure the current-voltage characteristic of the plasma. By viewing this current-voltage characteristic at different pressures, discharge currents, and probe distances at fixed plasma producing parameters and using theories listed previously, we are able to calculate electron temperature and electron density (plasma density) for each set of parameters. By evaluating these temperatures for varying pressures, discharge currents, and probe distances, we can gain a better understanding of plasma behaviors and how to create higher density plasmas. The ion acoustive wave experiment was performed using the same vacuum chamber, filament source, and Langmuir probe as in the Langmuir probe experiment. However, we also utilized a grid (with a function generator) and a lockin amplifier (including a reference oscillator and a low pass filter). The grid was used to carry an oscillating potential with a waveform established by a function generator. This oscillating potential caused a perturbation within the plasma, producing ion acoustic wave effects at the long wavelength regime (as described in the Theory Section). A probe picked up the potential oscillations created within the plasma by the grid. The lockin amplifier then takes the signal picked up by the probe and sends it into a mixer that multiplies the waveform created by the grid s function generator with the plasma s waveform. Although this signal would usually be very noisy, we also have a the reference oscillator and phase shifter before a low pass filter. The reference oscillator and phase shifter chop up the signal in order to find the phase of the signal that is in the experiment. The lockin amplifer thereby creates a less noisy signal that can actually be read. When the frequency of the plasma is in pase with the frequency of the grid, we get a strong signal. We can measure the wavelength of the plasma s iona acoustic waves by pulling the probe in and out at different distances, recording the phase shift and voltages of the signal produced, and viewing the probe distances at which we two peaks (an in phase signal). Once we have this wavelength, we simply use the relation v = νλ (11) to determine the ion acoustic wavespeed, where ν is the frequency of the grid s electronic waveform, is the determined ion acoustic wavelength. Then, using Equation 10, we can determine electron temperature T e from this wavespeed. After determine T e using this method, we took a Langmuir probe trace within the same parameters in order to compare the results. 4

5 4 RESULTS 4.1 Langmuir Probes We found that increasing the pressure while keeping all other variables fixed created a decreased in electron temperature as shown in Figure 4. resulted in an electron temperature of 2.4 ev ± 0.6 ev (correlating to an ion acoustic speed of 2400 m/s ± 300 m/s), while the higher pressure of 0.74 mtorr resulted in an electron temperature of 1.8 ev ± 0.8 ev (correlating to an ion acoustic speed of 2100 m/s ± 400 m/s). The trend supported our previous suggestion (from Figure 4) that a higher pressure generates a lower speed ion acoustic wave and lower temperature electrons. 4.2 Ion Acoustic Speeds Figure 4: The effects of varying pressure at otherwise fixed parameters on electron temperature in an Argon plasma. By generating a perturbation in the plasma through the grid and recording the phase shifts that occured at different positions in the plasma, we were able to determine the plasma s oscillating wavelength by finding two probe distances that had the same peak to peak phase shift. Using Equation 11, we then found the ion acoustic wavespeed of the plasma. A frequency Our results for the effects of the discharge current on the electron temperature were less conclusive. The data was quite scattered, but there was a slight trend suggesting that increasing the discharge current resulted in increase in electron temperature as shown in Figure 5. Figure 6: Generated oscillation signal from grid frequency of 100 khz used to determine ion acoustic wavelength (and thus wavespeed). Figure 5: The effects of varying discharge current at otherwise fixed parameters. We also took two Langmuir traces at two different pressures of 0.15 mtorr and 0.74 mtorr, while keeping all other parameters fixed for both traces (V filament = 13.6V, I filament = 10.6A, V discharge = 80V, I discharge = 1.0A). We found that the lower pressure of 0.15 mtorr of 100 khz resulted in a wavelength of m for a wavespeed of 2700 m/s as determined by analysis of Figure 6. This wavespeed correlated with an electron temperature of K or 3.0 ev and an electron density of m 3. A frequency of 150 khz resulted in a wavelength of m for a wavespeed of 2400 m/s as determined by analysis of Figure 7. This wavespeed correlated with an electron temperature of K or 2.4 ev and an electron density of m 3. The trend determined by 5

6 Figure 8: A semilog plot of the Langmuir probe trace Figure 7: Generated oscillation signal from grid frequency of 150 khz used to determine ion acoustic wavelength (and thus wavespeed). analysis of Figure 6 and Figure 7 suggests that higher temperatures create lower density plasmas. The data found through ion acoustic wavespeed analysis was compared to Langmuir probe traces in order to compare the two methods and the relative accuracy of our calculations. A Langmuir probe trace of current due to a voltage sweep by the probe Analysis of our Langmuir probe I-V characteristic plot (Figure 8) and semilog I-V characteristic plot (Figure 9) gave us an electron temperature of K (2.4 ev) corresponding to a wavespeed of 2400 m/s for 100 khz and an electron temperature of K (2.1 ev) corresponding to a wavespeed of 2200 m/s for 150 khz. These values were lower than those found by the wavespeed method but showed a similar trend of the higher frequency produced wave having the lower wavespeed and electron temperature, suggesting that both measurements were relatively accurate. 5 CONCLUSION From our Langmuir probe results, we found that an increase in pressure resulted in a lower electron temperature (colder plasma) and a lower plasma density. Therefore, a high efficiency plasma should be produced at lower temperatures. I m still trying to figure out exactly why this happens... Our data also suggests that an increase in discharge currents produced a higher electron temperature and higher plasma density. This makes some sense with the theory since a higher discharge current means that more electrons are being collected by the anode. We noticed that when we increased the discharge current, the filament voltage also tended to increase along with it. This also makes sense theoretically since more electrons must be sent into the plasma in order to complete the circuitry. When more primary electrons are being sent into the plasma, there is a higher likelihood that the gas will be ionized by these electrons, resulting in a higher plasma density and a hotter temperature. However, considering our data did not show a strong trend for this, other factors could have come into play. In our ion acoustic wavelength determinations, we noticed that there was a significant amount of fluctuation in the theta phase depending on 6

7 the rotation of the probe. Because of this, our wavelengths found had a significant amount of uncertainty. However, our comparison with the Langmuir I-V characteristic analysis showed a similar trend between the two different frequencies, so I believe our electron densities and temperatures were in the correct approximate range. 6 ACKNOWLEDGMENTS References [1] UCLA Department of Physics Plasma Physics Laboratory, Physics 180 E [2] Merlino, Robert L. Understanding Langmuir probe current-voltage characteristics Department of Physics and Astronomy, July 2007, The University of Iowa [3] Hershkowitz, Noah; Ghim, Young-C Probing plasmas with ion acoustic waves Department of Engineering Physics, August 2008, University of Wisconsin at Madison 7

Langmuir Probes as a Diagnostic to Study Plasma Parameter Dependancies, and Ion Acoustic Wave Propogation

Langmuir Probes as a Diagnostic to Study Plasma Parameter Dependancies, and Ion Acoustic Wave Propogation Kent Lee, Dean Henze, Patrick Smith, and Janet Chao University of San Diego (Dated: May 1, 2013)