| | MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAL OF STANDAROS - 1963 £a rā: "… : :"…: … ." - ** is * > * Y*, r**w-TEKart: **:re:::::::::::::::: :* * *T*: £ *g 5:…" $ Č'2/YA- 4 727/2%-/ *N. ELECTRON-TEMPERATURE WARIATION INDUCED EFFECTs" s "T"---------------------.......---- ...------- * . .4-4-2 ...* * * * * : * ~ * : *- : * * *---* --- **** ~ - ** f ***, * for o * . - AND LANDAU DAMPING OF ION-ACOUSTIC WAVES : CFSTI PRICES I. Alexeff and W. D. Jones - . . . - . . 4. Oak Ridge National Laboratory H.C. s. 5.0% MN 4 < –== and w- |- RELEASED FOR ANNOUNCEMENT . * * David Montgomery ENCE ABSTRActs University of Iowa IR NUCLEAR SCI * *- I. INTRODUCTION Ion-acoustic W8 VeS 8.X'e * compression waves in a plasma which are quite analogous to sound waves in a gas. However, in the plasma, most Of the momentum is supplied by the ions, while most of the restoring force is supplied by the thermal pressure of the electrons. The electron and the ion fluids are con- strained to move in phase by the 3 squirement that the plasma should be charge-neutral. Ionic-sound W8 VeS Wel"e presisted theoretically by Tonks and Langur: Probably the first clear-cut observation Of tha Waves was in gaseous assense tubeS by Revans 2 Recently, theoretical discussions by Fried and by Gould have predicted * Landau damping of the waves by the ions: Experiments in which the Landau * was observed were made by Wong, Motley, and D'Angelo: using a thermally-produced cesium plasma. Observations of the waves in cylindrical gaseous discharge tubes have been made by Hatta and Saito, by Crawford and self # and by Barrett and Little 7 The waves have been observed in magnetically-supported arcs by Alexeff and Relatea' Observations of the cut-off of wave propagation at high frequencies in relatively &N simple geometries have been made by Sessler : Tanaca, Koganei, and Hirosé: and Jones and Alexeff." with somewhat conflicting results. * . . * Ion-acoustic waves Offer the opportunity Of studying a relatively simple plasma - cooperative-effect In an easily accessible, low-frequency range. The frequencies used seldom exceed one megacycle per second. The phenomena can be studied in quite simple - systems, in the absence of a magnetic field. - s - - # s -w - - t t Research sponsored by the U. S. Atomic Energy Commission . . . under contract with the Union Carbide Corporation. *-** * *-** *** **** - r *xrt --" " "we- - - - - - * * * * * --->u-*- II. EXPERIMENTAL APPARATUS USED For the past few years, We have been observing the propagation of ion-acoustic waves in a very simple discharge tube. The basic apparatus and earlier experiments have been described in a paper given at the Conference on Ionization Phenomena in Gases held in Belgrade, Yugoslavis' and papers published elsewhere /2, /3 As a review, first we discuss the experimental apparatus, which is shown in Fig. 1. In this apparatus, plane is contained in a large, glass sphere. The object of using a spherical vessel is to place the walls far from the region being studied - to minimize wall effects. * is created in the discharge tube by injecting high energy electrons - say 500 V at 150 mA - from the elementary electron gun shown. The gun is simply a hot, tungsten wire surrounded by a gridded anode. The electrons are not emitted in **** ********** * * ******* a beam, but enter the plasma in a relatively random fashion. In this manner , we hope to avoid the instabilities produced by beam-plasma interactions. Plasma is produced when the injected electrons ionize a low pressure gas present in the discharge tube. The gases generally used are argon and xenon, at a pressure of about 3 x 10" torr. At this pressure, the collision rate between ions in the plasma and background gas atoms should not strongly affect our ion acoustic wave studies. As a by-product of using the gases argon and xenon, the collision rate between the plane electrons and the * atoms is sufficiently low that it may be ignored. This occurs because the average energy of the plasma electrons, about l electron volt, places them in the region of Ramsauer transmission, and they simply pass through the gas atoms. - Experimentally, we find that or plasma is very quiet and stable as long as ve keep the discharge voltage high, the cathode emission limited, and the discharge current below a relatively poorly-defined threshold of about 200 mA. We suspéct 4) ***** **********************, *r-s:... . . . . . . . . ........ "...--, -,-,-,-------. ---": "... . ..." -a-...----------......… . . . ...: that keeping the anode close to the cathode and keeping the cathode emission limited break up an instability mechanism caused by plasma density fluctuations changin' the discharge current. This mechanism has been experimentally observed by us previously. Above this limiting current threshold the plasma exhibits strong, narrow band oscillations near the plasma-electron frequency, and shows a brighter glow resembling that produced by r.f. excitation. Still higher currents result in violent low- frequency oscillations. When the discharge tube is operating in the quiescent fashion, we find that the noise picked w 'by a negatively-biased probe placed in the plasma is less than about *O / W, peak to peak. The plasma density profile is smooth and rather spherically symmetric l "The thermalization of electrons confined in this plasma can be quite slow.” , /7 This plasma appears to be ideal for basic studies. III. TECHNIQUE FOR OBSERVING ION-ACOUSTIC WAVES Ion-acoustic waves are studied in the plasma by a simple, time-of-flight tech- nique. The waves are generated by perturbing the potential on a negatively-biased transmitting electrode. As transmitting signals, we use delta functions, step functions , and sine-wave bursts. The waves are generally detected by observing the perturbation they induce in the ion current flowing to a negatively-biased receiving electrode. Other, more sensitive detectors are a negatively-biased electron-emitting probe, and a positively-biased, electron-collecting probe t 3. However, to avoid possibly perturbing the plasma, ion collection to a negatively-biased probe is usually used. Typical experimental results are shown in the oscillograms of Fig. 2. The upper part of Fig. 2 shows the ion waves produced by negative and positive step functions. Note that a step function of opposite polarity produces ion waves of opposite ..polarity, * t as is expected. The oscillograms of Fig. 2 demonstrate why a time-of-flight technique is necessary. The transmitting signal causes a direct-coupled signal in the receiver that is much stronger than the ion-wave signal. However, by using a time-of-flight technique, rather than a continuous transmission technique , one can separate the direct-coupled signal from the ion-wave signal. From the oscillograms such as shown in Fig. 2, we extract the ion-wave velocity in the following fashion. Given an experiment performed at a known electrode spacing, we determine the time at which the received signal just commences to appear. This time corresponds to the signal velocity in the medium. We then change the electrode spacing and repeat the experiment. In this manner, we obtain a series of time vs. distance points that we plot as is shown in Fig. 5. Plotting distance vertically and time horizontally produces a curve the slope of which gives the i. n-wave velocity. If our plot corresponds to the peak of the ion-wave response pulse, a curve With the S&MS slope is obtained, showing that in this experiment, dispersion effects are not present. Other experiments that demonstrate that in our experiments non-dispersive waves are being studied are discussed in Reference l. The lack of scatter of the experimental points from the straight line demonstrates that the experimental system is remarkably stable in time. The experimentally-obtained ion-wave velocities can be compared with the theore- tical formula” v - (y *..)"/","/: Here V is the wave velocity (cm sec”), 7 is a dimensionless number near unity, k is Boltzmann's constant (erg per °k) , T is the electron temperature (°K), and m: is the ion mass (gm). This equation is valid when the electron temperature is much higher than the ion temperature, and when the frequency components being transmitted 8.I'ê lower than the ion plasma frequency? In comparing the formula with experimental velocity, we use "e as measured by a Langmuir probe. The ion mass, mi is known." The value of y has been experimentally shown to be unity.” IV. TECHNIQUE FOR WARYING THE ELECTRON TEMPERATURE In comparing the experi'ental and the theoretical values for the ion-wave velocity, we had earlier been able to change mi by using different gases in the t discharge tube. Typical results of changing £1 are shown in Fig. 5. However, until. recently, We had been unable to vary the electron temperature Te. Changing the voltage or the current to the discharge only resulted in changing the plasma density - the electron temperature remained stubbornly fixed. Fortunately an experimental technique has recently been developed in which the electron temperature in our discharge tube can be varied downward from its initial value of a few electron volts to a lower limit of about 0.1 electron volt ls. The technique works in the following fashion. Normally, the electrons in the dis- charge tube maintain their remarkably high temperature - one electron volt, ox: ll ,600°K - because they are insulated from the walls of the discharge tube by being electrostatically confined in a positive potential well. However, if we place in the plasma a *tal plate that can be heated to emit electrons, this plate also approaches the positive plasma potential. Unier this condition of operation, hot plasma electrons can reach the plate and be lost, while they are replaced by rela- tively cool, thermionically-emitted electrons. Thus, the electron-emitting plate is an effective heat sink for the plasma electrons. By increasing the electron emission from the plate, the plasma electrons can be cooled in a controllable fashion from their initial temperature of a few electron volts down to almost the surface tempera- ture of the plate: With oxide-coated plates, we have reduced the electron temperature to about 0.1 eV. With pure tungsten emitters, we generally cannot reduce the tempera- ture below 0.2 eV. However , we prefer to use pure tungsten emitters, as they do not evolve gas, as the oxide-coated surfaces often do. The experimental apparatus for L E G A L NOT ICE varying electron temperature is shown in Fig. * * * ****"…a…:... "...a. " States, nor the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accu- | * * * privately owned rights; or t racy, completeness, or usefulness of the information contained in this report, or that the use : of any information, apparatus, method, or process disclosed in this report may not infringe |f B. Assuraes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or proceds disclosed in this report As used in the above, "person acting on behalf of the Commission” includes any em- ployee or coatractor of the Commission, or empt of such oontractor, to the extent that such employee or contractor of the Commission, or employee of such contractor prepares, disseminates, or provides access to, any information pursuant to his employment or contract with the Commission, or his employment with such contractor, Typical experimental results demonstrating that the electron temperature C&I) be changed in our discharge tube are shown in Fig. 5. Here are shown two Langmuir probe graphs. Wertically is plotted the logarithm of the electron current to the s probe, horizontally is plotted probe potential. The two curves. £hown axe displaced 'norizontally to avoid overlap. The electron temperature is inversely proportional to the slope of the curves. Note how these curves show that the electron temperature was changed by about a factor of five solely by changing the surface temperature Of the emitting electrode in the plasma. W. ION-WAVE VELOCITY AS A FUNCTION OF ELECTRON TEMPERATURE If we make several sets of measurements on the ion wave velocity in the plasma, each set being at a different electron temperature, we get the family of curves seen in Fig. 7. Note that as the electron temperature is reduced, the velocity of the ion acoustic wave decreases. Although we are drastically changing the electron temp- erature, the scatter of each set of points from its given line still remains small, so the plasma system seems to be quite stable. If we extrapolate each line to zero time, we find a finite probe species. This means that the probes are covered by thick sheaths through which the signal penetrates very rapidly. Two problems with these sheaths are, first, they are 10 to 20 times larger than the expected Debye sheaths, and second, they do not appear to vary in thickness with electron tempera- ture as the Debye shaaths do. Our ion-wave sheath is a puzzle to be explored at a later date. If we plot the velocities obtained from the graphs in Fig. 7, as a function of electron temperature, we get the curve shown on Fig. 8. We find, as predicted, that the velocity of the ion acoustic wave does depend approximately on the square root of the electron temperature. However, at very low electron temperatures, the points - begin to de late from the *::/2 line. In this case, the ion temperature component Of the plasma is beginning to make itself evident. A theoretical curve that fits the data is produced if a 5 kT, ion pressure term is added to the kre electron pressure term. This extra term can be obtained from the precise theory of Fried and Goula: Their mathematical results reduce to the formula shown when the ion temperature is low compared to the electron terrerature. We can also show by directly calculating the velocity from the exact theory, that the equation con- taining the ioli temperature * in Fig. 7 actually gives almost the correct velocity in the region where T - Ti. To make this equation fit the experimental data, we are forced to choose an ion temperature that, within a factor of better than 2, is 1/50 eV. Thus, our experimental velocity measurements for the ion acoustic waves give us a technique for measuring the ion temperature in the bulk of the plasma. Such ion temperature measurements have riot been possible with common Langmuir probe techniques. As a cross check on this ion temperature of 1/50 eV. Obtained from the velocity measurements, we have four other independent methods of estimating the ion temperature. These other methods also give about 1/50 eV. These methods are as follows: First, measuring the ion Landau damping of the ion-acoustic waves. Second, * the damping of the wave due to ion-neutral collisions. Third, measuring the radial drift of the plasma to the discharge tube wall by means of a Doppler shift in the radial ion Wave velocity" Fourth, by estimating the relaxation time required for the energy in the electrons to be transferred to the ions. Thus, at low electron temperatures, we have verified a predicted deviation of the ion-wave velocity from the simple *::/ dependence, and as a by-product, have developed an ion wave thermometer. WI. LANDAU DAMPING AS A FUNCTION OF ELECTRON TEMPERATURE e * f * t Another experiment performed by lowering the electron temperature is to observe the onset of Landau damping of the ion acoustic waves. In this Landau damping experiment, the wave is propagating through the plasma at the same velocity as some of the ions. . Under this condition, a travelling wave-tube type of interaction €X- tracts energy from the wave and transfers it to the ions. In our ion wave experiments, the wave velocity depends primarily on the electron temperature. Since the electra temperature is high, the ion acoustic waves move about ten times faster than the most probable velocity of the ions. However, if we reduce the electron temperature, the ion acoustic waves slow down until the velocity of these waves begins to match the velocity of some high-energy ions. Under this condition of operation, Landau damping is expected. Experimentally this form of Landau damping has been demonstrated by wons , D'Angelo, and Motley: - e Experimental observation of the Landau damping Of the iOn acoustic waves is shown in Fig. 8. Fig. 8 is composed of three pairs of ion acoustic wave signals. The upper trace in each pair corresponds to ion acoustic waves propagating in a plasma in which the electrons are about 1 eV in temperature. The lower trace in each pair corresponds to ion acoustic waves propagating in the identical system, except that the electron temperature has been reduced to approximately 0.2 eV. Looking at the top- most pair in Fig. 8, we find that at short distances the ion wave signal for both the l, eV and the O.2 eV plasma are approximately the same in amplitude and shape. For the middle pair of traces, which correspond to the detecting and transmitting electrodes being further apart, we find that the ion wave in the lower temperature plasma is re- duced in emplitude compared to that in the higher temperature plasma. Also, the ion acoustic signal in the lower temperature plasma is spreading. This spreading is a predicted result of Landau damping, because Landau damping tends preferentially to attenuate the high frequency components in a wave packet. For the bottom pair of traces, the transmitting and receiving electrodes are separated still further. The relative attenuation and spreading of the wave packet in the lower temperature plasma iS even more accentuated. Thus, this damping and spreading of the wave packet for the lower temperature plasma is occurring in Space. One further observation is that the * : **-*.*.*.*.*.*.*.*.*.*, *. wave packet in the colder plasma arrives much later in time. Thus, one observes that the ion acoustic waves move more slowly in a placma with a lower electron temperature. • - - A second set of data which yield information on Landau damping, is shown in Fig. 9. Here we show the amplitude of the received signal as a function of electron temperature. The transmitting and receivine electrose were kept at constant separa- tion for this experiment. The reason that the data were not taken as a funcuion of distance is that the electron temperature was reduced to lower values than in the previous experiment. * i s As a consequence of the experimental technique used, we could not reproduce precisely the same electron temperature from run to run. Thus, we could not take a set Of data for different probe spacings at the same electron temperature. Observing the data in Fig. 9, we see that as the electron temperature is lowered there is first a region in which the amplitude of the received signal decreases gradually. Second, at approximatel. 0.2 eV, there is a change of slope in the aroli- tude vs. electron temperature curve. . Third, at electron temperatures 'below 0.2 eV, we see that the received signal decreases very rapidly with decreasing electron temperature. To interpret this data in terms of the conventional Landau damping formula: We fit, the theoretical curve to one experimental point, because the ampli- tudes which are measured are relative. We discover that the conventional Landau damping theory predicts, first, the slope in the severely attenuated low temperature region, and second, the change-of-slope point at 0.2 eV. The conventional Landau damping theory, however, does not predict the gradually sloping region above 0.2 eV. We think that in this relatively high temperature region the coupling between the transmitting and receiving probes and the plasma varies with the electron temperature. However, we feel that this data does present some evidence for Landau damping. * f t •. . * * * * .---------- **-****** * **-* ..., J.O VII. LANDAU DAMPING PRODUCED BY A LIGHT CONTAMINANT Although we apparently have been able to observe the onset of Landau damping as we lowered the electron temperature, this experiment is not satisfactory for several reasons. First, as we very the electron temperature , the velocity of the ion-acoustic waves changes. The change in the wave velocity might produce other damping mechanisms. For example , as the wave slows, there is more time for iOn- neutral collisions to damp the wave. Also, as is shown in Fig. 9, there appears to be a residual amplitude variation at high electron temperatures not attributable to Landau damping. - One way of avoiding the above difficulties is to demonstrate Landau damping in a system in which the bulk properties of the plasma do not change. We have been able to accomplish this by adding a light contaminant to a plasma of heavy ions. For example, in a plasma of xenon ions and with an electron temperature of l eV, the average thermal velocity of helium ions is approximately the same as that of the ion acoustic W8 VeS . - Although the helium ions are very cola t" having a temperature of only 1/50 eV - the helium ions are also very light. Therefore, these cold, light contaminant ions move at the same velocity as the iOn acoustic Waves. The reason that a trace of helium ions in the xenon plasma provides strong Landau damping can be seen from Fig. 10. In Fig. 10, we plot the fraction of xenon ions at 8, given velocity relative to those at zero velocity. Only about one xenon ion in lo" is moving at the same velocity as the ion acoustic wave. However, for only 5 percent helium ions in the xenon plasma, approximately 10 times as many helium ions are pre- sent as xenon ions at the ion-wave velocity. Thus, only 5 percent helium ions in the Re11CI1 plasma can provide much more Landau damping than can the xenon ions. The exact mathematical equation for the contamination-induced Landau damping is in the appendix of this paper. - * ll. An experimental demonstration that traces of a light contaminent can produce Landau damping is given in Fig. ll. In Fig. ll are shown the four 3received ion acoustic wave signals in a xenon plasma as 8. function Of helium contamination . The topmost trace of the four corresponds to a xenon plasma containing no helium. As - we gradually add helium, we see that the ion acoustic wave * to damp as is shown in the Second trace. Still more helium produces severe damping and the testmins of wave packet spreading, as is shown in the third trace. As discussed earlier, the spreading of the wave packet is due to the preferential attenuation of high-frequency signal components. The fourth, lowest trace, shows what happens with even more helium added. In this case, the ion acoustic wave begins to increase in velocity * the signal appears at a shorter time. This increase in velocity occurs because there is enough helium present to reduce the ion mass appearing in the velocity equation. Since the wave is now moving faster, the coupling between the wave and the thermal helium ions is less. Thus, although there are more helium ions present the fourth trace shows that the damping is actually reduced. To verify that the bulk properties of the plasma electron temperature and plasma density did not vary, we also took a Langmuir probe trace for each ion wave trace. A typical Langmuir probe trace is shown below the four ion acoustic wave traces. Thus, in this experiment we believe we have demon- strated Landau damping of ion acoustic waves without changing the bulk properties of the plasma. VIII. SUMMARY In conclusion, we have been able to generate quite quiescent plasmas in a very simple spherical discharge tube. In these plasmas we propagate ion acoustic waves. We can observe the velocity of the waves as a function of the electron temperature with the aid of a simple device. We observe both the ion temperature contribution - t 12 to the wave velocity * the onset of Landa damping as the electron temperature is *. * As a second demonstration of the Landau damping, We add a light contaminant . to the plasma and observe aspins without * the bulk properties of the plasma. As a by-product of this study, ve have developed 8, * device for producing a quiescent plasma in which the electron temperature can be varied over a very wide range. - - d 12. l3. 14. l5. REFERENCES L. Tonks and I. Langmuir, Phys. Rev. 55, 195 (1929). R. W. Revens , Phys. Rev. lilt, 798 (1955). B. D. Fried and R. W. Gould, Phys. Fluids l, 159 (1961). R. W. Goula, Phys. Rev. 136, A991 (1961). A. Y. Wong, R. W. Motley, and N. D'Angelo, Phys. Rev. 155, Alij6 (1964). Y. Hatta and N. Saito, Ionization Phenomena in Gases, edited by H. Maecker (North Holland Publishing Company, Amsterdam, 1962), Vol. 1, p.178. T. W. Crawford and S. A. Self, p. 129, VI Conference Internationale sur les Phenomenes d' Ionisation dans les Gay. vol. III, Paris, SER MA, 1965. P. J. Barrett and P. T. Little, Phys. Rev. Letters ll, 556 (1965). I. Alexeff and R. v. Neidigh, Phys. Rev. 129, 516 (1963). G. M. Sessler, Phys. Rev. Letters 17, 215 (1966). H. Tanaca, M. Koganei and A. Hirose, Phys. Rev. Letters 16, 1079 (1966). W. D. Jones and I. Alexeff, Proceedings of the VII International Conferences on Phenomena in Ionized Gases, Belgrade, Yugoslavia, Aug. 1965 (to be **) o I. Alexeff and W. D. Jones, Pye. Rev. Letters 15, 286 (1965). - I. Alexeff and W. D. Jones, Physics Letters 20, 269 (1966). I. Alexeff, W. D. Jones, and John Lohr, Phys. Fluids 9, 11:05 (1966). I. Alexeff and W. D. Jones, Applied Physics Letters 9, 77 (1966). Fig. l Q-> Fig. 5 - Fig. 1: - FIGURES Schematic of Discharge Tube. Typical Ion-Acoustic Wave Signals. The upper trace in the upper picture shows the received signal as a function of time. The lower trace represents the transmitter voltage. At zero time, a downward step function is applied to the transmitting electrode. 60 pisec later, the ion acoustic wave is detected. At 100 pisec, an upward step function is transmitted. 160 usec later, the ion acoustic wave is detected with the opposite polarity. The gas is xenon. The lower trace in the lower picture corresponds to a sine wave burst applied to the transmitting electrode. The upper trace corresponds to the signal received. Note the strong direct-coupled signal near zero time. The time scale is 20 "sec/cm. The gas is xenon. . . Typical Time vs. Distance Graphs. Horizontally is plotted time; vertically, distance. The slope of each curve corresponds to the ion-wave velocity. The electron temperature for all gases but helium was about i eV, helium being about 10 eV. Thus, for gases other than helium, the velocity Of the iOn Waves * * function of ion mass is here directly displayed. - schematic of the Device for Varying Electron Temperature. In this figure, the ion-wave transmitting and receiving electrodes would be above and below the plane of the paper, respectively. *-*-- *----- *** ********** | * Fig. 5 * Fig. 6 - Fig. 7 Q- Fig. 8 * 'Typical Langmuir Probe Curves Showing a change in Electron Temperature. The gas used here was helium. The two curves from left to right re- present electron temperatures of 1.9 eV and 0.58 eV, respectively. A pure tungsten auxiliary electrode was used. 'Typical Time vs. Distance Plots Showing the Ion-Wave Velocity Dependence on Electron Temperature. In this case, the gas used was xenon. The Ion-Wave Velocity in Xenon as a Function of Electron Temperature. Note thet at low electron temperatures, the effect of the ion temperature becomes visible. The scatter of the experimental points at higher electron temperatures is due to the discharge tube's being operated in a noisy re- gime that was used to get unusually high electron temperatures. Evidence for Landau Damping Produced. When "e *> Ti in Ion Acoustic Waves. Here we show the propagation of pulses in a xenon plasma for three successively larger spacings between the transmitter and receiving electrodes. In each pair of traces, the upper trace corresponds to Te= l eV and the lower to Te- O.2 eV. In the top pair of traces, for an electron separation of 2 cm, both signals have about the same amplitude, although the lower one arrives later in time. In the central pair of traces, for an electrode separation of 6 cm, the lower pulse is much smaller than the upper, showing that spatial damping is occurring. Note also that the lower pulse is getting broader showing that high frequencies are being preferentially attenuated. In the lower pair of traces, for an electrode separation of 8 cm, the relative attenuation is even more pronounced, as is also the spreading. The time scale is 20 usec/large division. The gas is xenon. Fig. 9 Q- Fig.10 © Fig.ll. • The Experimentally Observed Variation in Amplitude as a Function of Electron Temperature. All other plasma parameters were kept constant. Note that the theoretical curve predicts the severe damping at low electron temperatures and the change-of-slope at about 0.2 ev. The theoretical curve does not predict the slow variation of amplitude with electron temperature above o.2 ev. in The Relative Proportion of Helium and Xenon Ions Responsible for Landau Damping. The xenon curve shows the relative number of xenon ions moving normal to an ion-wave front as a function of velocity. At the wave velocity, only about 10-7 ions (relative to those at zero velocity) can couple to the ion wave. The helium curve shows the number of helium ions moving normal to the ion-wave front for a 5% helium ion contamination in the xenon ion plasma. Note that at the ion-wave velocity, about 10" more helium ions are present than xenon ions. The Landau Damping of Jon Waves in Xenon as Helium is Added. Top - No helium ana - Trace of helium - damping appears. 3rd - More helium - maximum damping. About 2% of helium is present. Bottom - Still more helium. The wave speeds up (appears at shorter times), and the damping decreases. The time scale is 20 usec/large division. The curve beneath the ion-wave traces is an example of a Langmuir probe curve made to monitor the properties of the plasma. A Langmuir probe curve was taken on each ion-wave picture. APPENDIX Using the approach of Fried and Gould, the temporal damping decrement y, is produced by a fractional contamination e of a light ion m2 in a plasma of heavy ions ml. 2 4. ... * * :- (*= * {# * me 2 ml * E. Here K is the wave number of the disturbance, k is Boltzmann's constant, T. is the electron temperature, Ti is the ion temperature, ml is the heavier ion mass and mo &: * is the lighter ion mass. To the extent that y spatial = y temporal/phase velocity, we find that kT. 5/2 m * m- T 7 spatial * _s kV. ( ) ( : T ) :- exp --à- #- 2 /2 i “2 * 2 k + | # [. i §§ T – —|| LL C O 2 %. Ż - n * 6. X I. L 4 H- + * 2 % [. de- O t- | | | | | | | | 40 60 80 100 120 140 160 PROPAGATION TIME (usec) —- 48O ORNL-DWG 66–4976. -- To AUTOMATIC LANGMUIR / £- -\ . & PROBE CURVE PLOTTER LANGMUIR PROBE ANODE - J •- To FILAMENT -: l F-> TRANSFORMER LARGE, HOT ELECTRON . . EMITTER (CONTROLS ELECTRON TEMP.) 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