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J. Mod. Phys., 2010, 1, 281-289 doi:10.4236/jmp.2010.14039 Published Online October 2010 (http://www.SciRP.org/journal/jmp) Copyright © 2010 SciRes. JMP Study of Propagation of Ion Acoustic Waves in Argon Plasma N. S. Suryanarayana, Jagjeet Kaur, Vikas Dubey Department of Physi cs , Govt. Vishwanath Yadav Tamaskar Post Graduate Autonomous College, DURG (C.G), India E-mail: nssoo2@gmail.com, jsvikasdubey@gmail.com Received June 25, 2010; revised July 22, 2010; accepted August 19, 2010 Abstract The properties of small amplitude acoustic waves (IAW) in unmagnetised plasma have been discussed in detail. An experimental set up to study the propagation of IAW in argon plasma has been descried. The speed of IAW under different conditions of discharge current and pressure has been measured from the time-of flight technique. From these measurements, electron temperatures have been calculated. The results have been compared with those obtained by single probe method, and were found to be in good agreement with each other so IAW speeds can be used to calculate plasma parameters. Keywords: IAW in Argon Plasma, Study of Propagation 1. Introduction Plasma can support a great variety of wave motion. Both high frequency ( pe) and low frequency ( pi) electromagnetic and electrostatic waves may propagate in plasma. The primary emphasis has been placed on the study of electrostatic waves because the ease with which such waves may be excited and detected and because the collision less damping of waves predicted by Landau can be conveniently studied [1-10]. Ion waves are low frequency pressure waves in plasma. If the ion plasma frequency (pi) greatly exceeds the wave frequency, both the electrons and ions oscillate almost in phase. At this stage some of the characteristics of the ion waves are similar to those of the ordinary sound waves. So they are called Ion Acoustic Waves (IAW). The difference between ordinary Acoustic waves and Ion acoustic waves arise from the electric field induced by a slight charge separation. The electron component of the ion acoustic wave tends to propagate faster than the ion component. The electric field retards the electron motion, forcing the two species to propagate together. Ion Acoustic waves were first predicted theoretically by Tonks & Langmuir [11]. They were first observed, in gas discharge plasma by Rewans [12]. Landau damping in plasmas was predicted by Fried & Gould [13] and experimentally demonstrated in a high temperature ce- sium plasma by wong et al. [14]. Ion Acoustic waves were observed in cylindrical discharge tubes by many workers [15-17] and in magnetically supported plasmas by Alesef & Neidgh [18] dispersive effects at high fre- quencies were studied by sessler [19] Tanaca et al. [20] and Jones et al. [21]. Ion Acoustic so lution s were excited and their propagation in plasma was studied by many others [22-28]. Ion acoustic wave propagation in dusty plasmas [29,33] was studied to find charge fluctuation and a new damping mechanism. The possibility of the turbulent development of an Ion Acoustic Wave that yields particle fluxes as well as energy fluxes has been used for characterization of the acoustic wave propaga- tion in presheath region [30]. Dust acoustic solitary waves [31] and nonplaner ion acoustic waves in plasma [32] were studied by many others. In the propagation of these ion acoustic waves (IAW), depending on the details of the velocity distribution function; en ergy may flow from the wave into the ions or in the opposite direction. If the phase velocity of the wave greatly exceeds the average thermal speed of the ions, the interaction is weak and energy exchange is be- tween resonant ions and the electric field of the wave. If the phase velocity of the wave is comparable in magni- tude the average ion speed, the interaction is strong and occurs by phase mixing and also by resonant exchange. The phase velocity of a small amplitude plane ion acous- tic wave propagating along the field lines can be derived N. S. SURYANARAYANA ET AL. Copyright © 2010 SciRes. JMP 282 from the plasma fluid equations [34]. 1/2 1/2 3 ee ii si ee i i kT kT C km kT T m (1) Where the ratio of specific heats, k is the wave number. 1.1. Wave Excitation Electrostatic excitation of low frequency waves by elec- trodes outside the plasma is extremely inefficient be- cause currents on the plasma periphery shield the plasma interior from the applied fields. Excitation by modulation of magnetic field is possib le only if the confining field is weak and only for long wave-lenghths [35]. Various other techniques have also been reported [36,37 ]. In almost all experiments on externally controlled ion waves the grids are placed inside the plasma column with the plane of the grid normal to the axis of the column. This technique was introduced by Hatta et al. [38] and extensively used by wong [39] and others. The transmission of the grid is a function of the applied potential, greater negative po- tentials decrease the transmission. If time varying poten- tials are applied, it would lead to density variations. If pi, finite transit time of ion s through the sheaths around the grid introduces velocity modulation [40]. Grid exci- tation was accomplished at frequencies 0.1 p i (7 to 130 KHz) for all conditions. Detection of ion acoustic waves was done either by another biased grid or with a Langmuir probe. Grid detection generally produces an improved signal-to noise ratio. 1.2. Measuring Techniques Phase and amplitude measurements were made by re- ceiving probe along the plasma column. Phase velocity has been inferred simply by measuring the time of flight of the perturbation between two fixed grids. Capacitive coupling between the grids often presents a pickup prob- lem41, especially if the exciter frequency is > 100 KHz and the grid separation is < 1 cm. Plasma noise is not a problem in wave experiments but to detect extremely faint signals the signal-to-noise ratio should greatly be improved. 1.3. Wave Damping The most significant contribution of the work of wong et al and Alexeff et al., Y.Nakamura et al. [42] and others [43] to the experimental stu dy of ion wav es was the care - ful measurement of wave damping under conditions in which collisional damping of ion waves could be com- pletely neglected. The collisionless damping distance was of the order of a few centimeters or much shorter than the mean free path for ion-neutral charge exchange collisions ( > 1 m).The ion drift between the grids cre- ates a non-negligib le correction to the damping rate. It is convenient to have the average damping constant. Then the characteristics of the observed ion acoustic waves appear to match closely the properties predicted for the ion acoustic wave eigenmodes. Confirmation of these results has b een reported by Sat o [ 44] and others [45,4 6]. 1.4. Effect of Collisions on Ion Acoustic Waves In the works of wong et al. [39] and Aleseff et al it was shown that collisions played no role in the propagation of ion acoustic waves. Collisions between ions and electrons occur frequently 16 310 e x sec but do not affect the ion dynamics unless the electron ion en- ergy equipartion time is comparable to 1 , which does not occur unless 13 3 10ncm 5 ~10 s ec . Heavy particle collisions cannot be neglected. Collisions be- tween ions do not necessarily increase the attenuation of ion waves, in fact for ei TT ion collisions decrease the damping rate because they reduce the resonant in- teraction [47]. Accelerated ions and the background ions would increase rather than decrease the wave damping. The effect of ion-atom collisions on ion waves was extensively studied by Anderson et al. [48]. The ion temperature could be deduced from the drop in ion acoustic wave phase velocity. 1.5. Theoretical Considerations [49,50] A dispersion relation is obtained using fluid approxima- tions and then a useful handy formula for the velocity of ion acoustic wave derived. Langmuir probe I-V charac- teristic have been used to calculate the Te and ne (ni) and hence pe, pi and D. Pe and pi are defined as Electron plasma frequency 1/2 2 4e pe n m (2) Ion plasma frequency 1/2 2 4i pi i n m (3) Since Ion Acoustic Waves propagate only below the ion plasma frequencypi ( << pi) both electrons and ions move together. If Te >> Ti, the ion wave is not strongly damped. Integrating equation of motion for N. S. SURYANARAYANA ET AL. Copyright © 2010 SciRes. JMP 283 electrons, we get the Boltzmann relation. 00 expexp 1 ee e n nekTnekT (4) Ion acoustic perturbation follow 22 4 22 2222 0 ii i sD nn n C txxt (5) Where Cs = (Te/M) 1/2 and 1/2 4 De e Tn is the ion acoustic speed and Debye length. By solving the above equation the disp ersion relation is obtained 22 2 22 1s D Ck k (6) If k2 D2 << 1; phase velocity of IAW equals the cs and is constant and if k2 D2 1 the wave becomes dispersive. The handy f o rmul a for Cs is 1/2 3 ei ei i s kT kTkT T C kmm (7) 1.6. Single Langmuir Probe A small electrode is inserted in to the plasma and the current is measured as a function of the applied voltage. The voltage is measur ed with respect to some convenient reference point, which is often the cathode of the dis- charge. The log I – V characteristic is shown in Figure 2. The plasma potential (Vp) is obtained. Another potential, which is shown as Vf, is the floating potential is also obtained. Let us consider a perfectly reflecting probe. If the electrons have a Maxwellian distribution the Boltz- mann’s relation can be used 0exp ee nneV kT (8) Thus as we approach the probe, electron density de- creases. Let us consider now an absorbing probe. When the mean free path is large compared with the size of the probe, the number hitting the absorbing probe is essen- tially the same. Thus the electron s will mov e to the prob e from regions much further away than the plasma bound- ary without making a collision. But as the probe absorbs the electrons the local electron density is depleted with an absorbing probe the current density is given by 0exp e eV II kT (9) Taking logarithm on both sides, the equation is 0 log loge I IeVkT (10) Thus the slope of the plot of log I (Vs) V shown in Figure 2 gives the electron temperature. Location of the knee of the curve gives the plasma potential. The other handy formulas used to calculate the plasma frequency pe and Debye length De are 1/2 2 4e pe n m 1/2 9000( )sec. p fn or Where n = number of electrons per cm3. 1/2 2 4e De e kT n (11) 1/2 6.9 De Tn (12) 2. Experimental Setup The experimental set up has been shown in Figure 1. The dimensions of the vacuum chamber are 30 cm di- ameter; 50 cm length of stainless steel. First it was evacuated to a pressure of 2 × 10-5 torr. The experiment was performed in the pressure range of 2 × 10-4 to 3 × 10-3 torr. of Argon. Argon was flown continuously for half an hour before the production of plasma. 10 fila- ments of Tungsten (4 cm length and 0.05 cm diameter) were symmetrically distributed and fixed to the two Aluminium supporting rings. First they were heated through supplying heater current ( 1.5 Amp. max. per filament). The discharge was created by applying the voltage between the heated filaments and wall of the chamber. The discharge current was varied between 0.75 Amps. to 0.075 Amps. So the plasma was quiescent. Plasma was spread into the chamber symmetrically. The potential across the filament was 4 V. The discharge voltage was around 60 volts. Figure 1. Photograph of experimental setup. N. S. SURYANARAYANA ET AL. Copyright © 2010 SciRes. JMP 284 Figure 2. Log I–V Curve of langmuir probe. A 1 cm diameter thin aluminium disk was used as the Langmuir probe. The probe voltage was varied between –70 V to + 25 V. The probe current has been measured by a Keithly multimeter. For the launching of Ion Acoustic waves a 30 KHz pulse from the pulse generator was applied to the nega- tively biased transmitting probe. The biasing can also be floating. This probe was situated at the centre of the plasma and normal to the axis of the chamber and it was fixed in the cha mber through a feed through. For collecting the ion acoustic waves, the Langmuir probe was used. It was biased positive to collect the electrons (electron current). The voltage developed at the ends of 1 k resistance was given to the CRO Y1 termi- nal, through a 100 PF capacitor. The pulse, directly from pulse generator was fed to the Y2 of CRO. Both the traces were locked through the adjustment of H. F. sync. and level controls of CRO. The received voltage was in the 20 mV to 50 mV range. While the transmitted volt- age was < 1 V. 3. Observations & Results Table 1 presents a comprehensive list of Te (electron temperature) calculated through (1) Ion Acoustic wave and (2) By single Langmuir probe for various discharge current at various operating pressures. 1) a) Probe current was obtained at different Langmuir probe voltages and discharge currents at three different pressures. b) A sample log I – V characteristic of Langmuir probe has been shown in Figure 2. c) The electron density/ion density, electron tempera- tures, plasma frequency, plasma ion frequency, Debye length were calculated from log I – V characteristics. 2) The traces of the transmitted wave and received ion acoustic wave, appearing on the CRO screen, were care- fully drawn by putting a transparent paper on the CRO screen, at different probe separations, for varying dis- charge currents and pressures. Time taken by ion acous- tic wave to travel from transmitting grid to receiving grid was obtained by the time of the flight techniqu es. Veloc- ity of the IAW was calculated and tabulated . 3) Electron temperature was calculated for different sets of readings. 4) The electron temperature obtained by Langmuir probe method was compared with that obtained from the time of – flight techniques. 4. Discussion and Conclusions 1) The calculation of electron temperature by IAW propagation studies Figure 3 to Figure 8 and by Lang- muir probe techniques Figure 1 indicate that the two values are in fair agreement. However Te calculated from Langmuir probe techniques is slightly more (10 to 15%) than that calculated by IAW propagation speeds. Lang- muir probe suffers from a number of defects such as- a) Laboratory plasma deviates from some of the as- sumptions made, while developing theory, such as Maxwellian distribution of energy and velocity, isotropy of plasma, homogeneity and quasinutrality of plasma. b) Probe Size: It is assumed that the presence of probe does not change the distribution and that the size of the probe is negligible in comparison with reference elec- trode. But finite probe size always as important role and disturbs the distribution. c) Sheath: In general a transition region called sheath appearing around the probe, is assumed to be independ- ent of probe potential. But at strong negative probe po- tentials the central part of the sheath has increased elec- tron density due to the presence of repelled electrons from the probe and incoming electrons to the probe i.e. the energy distribution near the probe may not be equal to that existing in undisturbed plasma. Further, probe current is also affected by secondary emission from probe by the action of photons , ions and m etastable at oms. N. S. SURYANARAYANA ET AL. Copyright © 2010 SciRes. JMP 285 Table 1. A comprehensive list of Te (electron temperature) calculated by (1) Ion Acoustic wave and (2) By single Langmuir probe for various discharge current at various operating pressures. Gas used = Argon Temperature = 306 K S.No. Pressure in torr Discharge Current Amp Velocity of IAW by time–of–flight measurement × 105 cm/sec. Te obtained by velocity of IAW (eV) Te obtained by Langmuir probe (eV) Ion temperature 1 2.5 × 10-4 0.5 2.96 3.65 4.3 2 6.5 × 10-5 0.5 2.34 2.27 - 3 1 × 10-3 0.5 2.14 1.90 2.1 4 6 ×10-4 0.35 2.6 2.84 3.5 5 2.5 × 10-3 0.35 1.95 1.59 - 6 1 × 10-3 0.35 2.03 1.72 - 7 1.5 × 10-4 0.35 2.78 3.23 8 3 × 10-4 0.11 1.82 1.38 1.5 9 7 × 10-4 0.11 1.67 1.16 10 2.5 × 10-3 0.11 1.54 0.99 - 11 3 × 10-3 0.075 1.43 0.85 0.8 12 3 × 10-3 0.2 1.46 0.89 - 13 3 × 10-4 0.2 2.27 2.15 - 14 2.5 × 10-3 0.7 2.83 3.34 - 15 6 × 10-4 0.75 2.84 3.37 - 16 2.5 × 10-4 0.75 2.84 3.37 4.0 800 K Figure 3. Trace for launching pulse and detected pulse by moving probe in various distance (discharge current = 0.5 amp). N. S. SURYANARAYANA ET AL. Copyright © 2010 SciRes. JMP 286 Figure 4. Trace for launching pulse and detected pulse by moving probe in various distance (discharge current = 0.25 amp). Figure 5. Trace for launching pulse and detected pulse by moving probe in various distance (discharge current = 0.11 amp). N. S. SURYANARAYANA ET AL. Copyright © 2010 SciRes. JMP 287 Figure 6. Trace for launching pulse and detected pulse by moving probe in various distance (discharge current = 0.15 amp). Figure 7. Trace for launching pulse and detected pulse by moving probe in various distance (discharge current = 0.075 amp). d) In the measurements: The probe potential as meas- ured by an instrument may not represent the true poten- tial difference between the electrodes and probe. There may be contract potentials. A part of the voltage applied to the probe is drop ped across the sheath and it is an un- known quantity to the experiments. The space potential Vs may vary due to the presence of fluctuations and drift with in the bulk plasma and more intrinsically by the driving probe current through the plasma without infinite conductivity. e) The equivalent plasma resistance, R, between probe and reference electrode plays a significant role on the determination of Te. R in the measuring circuit of the probe depends on both the plasma conductivity and con- figuration of the prob e. f) Probe surface contamination also plays an important N. S. SURYANARAYANA ET AL. Copyright © 2010 SciRes. JMP 288 Figure 8. Trace for launching pulse and detected pulse by moving probe in various distance (discharge current = 0.75 amp). role, which can not be avoided. IAW speed determination involves Time-of-Flight measurements. Each small division on the CRO screen represents 1 s (in present case). Measurement of time can be in an error of 0.5 s i.e. the determination of speed may be in error by about 5 to 10%. Moreover, we have neglected ion temperature in comparison with elec- tron temperature, taking an electron temperature of the order of 30,000 K and 3 T1 of the order of 1500 K. so it also involves an error of 5% we can therefore argue that the determination by the two different techniques are in good agreement. 2) When an IAW is excited by applying a signal, ei- ther a voltage pulse, or sinusoidal wave is applied to the grid, a receiver detects not only a signal of the wave but also a direct coupled signal. This is evident from the various oscillogram presen ted. The coupling was thought to be [54] a capacitive coupling between the transmitter and the detector. In fact Nakamura et al. [42] has shown that it is associated with the change of plasma potential, caused by drawing of electrons by grids and probes. 3) The oscillogram presented in this case shows that the amplitude of IAW goes down or diminishes as it travels longer distances. This is due to damping (colli- sional, non-collisional). 4) Our observations show that when the distance be- tween the transmitting grid and the receiving probe is small, Figure 3 to Figure 8 the speed of IAW is large, which we have neglected in taking th e averag e. It is quite reasonable that when the grid and the receiving probe are close by, the electric field is strong, thereby enhancing the velocity of electrons reaching the probe. This en- hances the electron temperature in the neighborhood of the transmitting grid, wh ich in turn increases th e speed of IAW. 5. References [1] T. H. Stix, “The Theory of Plasma Waves,” McGarw Hill, New York, 1962. [2] V. L. Ginsberg, “The Properties of Electromagnetic Waves in Plasmas,” 2nd Edition, Pergamon, Oxford, 1970. [3] T. J. M. Boyd and J. J. Sanderson, “Plasma Dynamics,” Berns & Nobel, New York, 1969. [4] J. L. Shoket, “The Plasma State,” Academic Press, New York, 1971. [5] N. A. Krall and A. W. 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