Liu, P.

Yang, T.F.

Zu, Q.X.

DSpace@MIT

PFC/JA-94-23Determination of Ion Temperature withSingle and Triple Langmuir ProbesT. F. Yang, Ping Liut and Q. X. ZutPlasma Fusion CenterMassachusetts Institute of TechnologyCambridge, MA 02139Submitted to the Review of Scientiflc InstrumentsAugust 25, 1994This work was supported by NASA under Contract #NAS-9-18372, NASA/JPLunder Contract #958265, AFOSR under Contract #AFOSR-89-0345, and DOEunder grant #DE-FC02-93-ER-54186. Reproduction, translation, publication,use, and disposal, in whole or in part, by or for the US Government is permit-ted.t Southwestern Institute of Physics, Chengdu, Sichuan, China! Institute of Physics, Chinese Academy of Sciences, Beijing, ChinaDetermination of Ion Temperature withSingle and Triple Langmuir ProbesT. F. Yang, Ping Liut and Q. X. Zu:Plasma Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts 02139AbstractThis work discusses a method of determining plasma Ion Temperature using a singleand a triple Langmuir probe in a plasma system having a finite ion temperature. Thetriple probe measures the plasma potential difference between a pair of the floating probesand ion saturation current, Ji , from another pair. The single probe is biased at a positivevoltage higher than the space potential ( corresponding to the bend in the I-V characteristiccurve ) where the electron current approaches a saturation value. It measures the electronsaturation current, Je . The electron temperature, T, , is determined by the plasmapotential difference from the triple probe. However, instead of determining the electrondensity, ne , from the relation Ji = exp (-1/2)en, /k Te/mi and T by neglecting Ti , itis now obtained from J, . It is not needed to make the zero ion temperature assumptionwhich is no longer valid when the ion temperature is finite or higher than the electrontemperature. Taking ne and Te , the ion temperature can now be calculated from therelationship Ti = (m 2/k)(Ji exp (1/2)/ene) 2 - T,.t Southwestern Institute of Physics, Chengdu, Sichuan, Chinat Institute of Physics, Chinese Academy of Sciences, Beijing, China1I. IntroductionIn many plasma systems it is important to be able to measure the ion temperature.There are several techniques which have been used successfully in fusion plasma systemsand few other systems. However, they are either applicable only in a high temperatureregime, too complicated and costly and/or have other limitations. It is desirable to developa technique more suitable in the low temperature regime for small scale laboratories and lowbudget experiments. In a high temperature plasma system like the fusion energy devicesthe ion temperature has been successfully determined by the charge exchange method1 .The charge exchange method is not practical for a small scale laboratory because of itscomplexity as well as the high capital and operational costs. It is difficult to make a spatialscan. Furthermore the method is not suitable for measuring low ion temperature (below 10eV). The grid energy analyzer has been proven useful', but the perturbation of the largeprobe head on the plasma is not known and is very difficult to determine. The plasmatemperature is determined by fitting the data to a Maxwellian distribution function, andcareful post analysis is required to obtain the results. The uncertainty is large when theion temperature is low ( less than 10 eV ). Fine spatial scanning is not practical for a smallplasma system because of the large probe head. The Doppler broadening method1 withthe use of a spectrometer has been tried. It requires a high resolution spectrometer andfrequency scanning system. Optical alignment is critical and spatial scanning is limitedby the optical path. The ion temperature of a hydrogen plasma can only be measuredindirectly through seeding the plasma with helium or other species. Every method has itsown merit, purpose, advantages and limitations. It would be nice if one could put all thesediagnostics on the system so that the plasma properties can be monitored in every aspect.Therefore it is the purpose of this work to examine the possibility of ion temperaturemeasurement by a very simple method: the use of Langmuir probes. It will provide a lowcost, convenient and flexible alternative diagnostics if it is found to be feasible.2In the analysis of the Langmuir probe current signal, the electron temperature isdetermined from the slope of the I-V curve1 '4 . The density is calculated from the ionsaturation current neglecting Ti based on the assumption that the ion temperature is verylow or much lower than electron temperature. This assumption came from the very lowtemperature and low density plasma4 and was used as a convenience to obtain the electrondensity. This is no longer true in high temperature plasma, such as a tokamak or mirrordevice, where the ion temperature could be higher than that of the electrons when theplasma ions are heated by rf power or neutral beams. Even in a low temperature plasma,the ion temperature could be significant and should not be ignored.A triple Langmuir probe measures the plasma potential difference between a pair of theprobes and ion saturation current from another pair. Both pairs share one common probe.Here again the ion temperature is ignored in order to obtain the electron density fromthe ion saturation current. We propose to obtain the electron density from the electronsaturation current of a single Langmuir probe biased at a potential higher than the spacepotential where the electron current approaches saturation. Therefore the ion saturationcurrent can now be used to calculate the ion temperature. There are new uncertainties,such as the error in measurement of the electron saturation current at a fixed probe voltage.However, we gain the accuracy by removing the zero ion temperature assumption.During the course of this study, we have encountered a great deal of difficulty in themeasurement of Triple probe. Section II is devoted to the discussion of the constructionof the triple probe and its circuit. Section III discusses the ion temperature measurement.II. Triple Probe MeasurementMany work, related to Triple Langmuir method, have been previously reported"'6 ,'7 .However, to use the probe successfully in an experiment still takes a lot of trial and error.The learning curve involved is painfully frustrating and time consuming. Principally, all3the electrodes in the probe have to be completely floated and have to be isolated from thedata acquisition system. It is absolutely important that every possible local loop has tobe eliminated or minimized. All conducting material has to be shielded from the plasmaexcept probe tips; otherwise one will obtain false reading or random readings with largepick-ups. After a painstaking work, a dependable probe has been obtained. The detailedprobe configuration and experimental setup are described below.Figure 1 presents the configuration of the probe, vacuum feedthrough and cabling. Theprobe assembly consists of three 0.5 mm tungsten wires. The probe tips are 3 mm in length.Each wire is insulated by ceramic tubing and then shielded by stainless tubing. The probewire, ceramic insulator and stainless steel form a coaxial cable. It would be better to insertthis solid coaxial cable into another ceramic tubing to isolate the stainless outside shieldfrom the plasma. This will greatly increase the over radius of the coaxial tubings and thusthe space between the probes. This will make the probe assembly undesirably large. Tominimize the separation between the probe tips and the overall size of the probe assembly,we gave up the idea of further insulating every probe tubing individually. The stainlesssteel tubings were spot welded together, making certain of good contact lengthwise suchthat local loops were negligibly small. The three probe cable assembly is then enclosed ina quartz glass tube leaving only the probe tips extruding into the plasma. This preventsthe stainless shielding from acting like a floating probe. The probes are isolated from theshaft by a ceramic feedthrough which has four pin conductors. The stainless shieldingtubings are then eclectically connected to the fourth conductor through an insulated wiregrounded at the case of a junction box on the far end of the shaft.The probe wires through the shaft connected to the load resistors must be individuallyshielded and the shielding itself must also be eclectically isolated. The pair of currentcarrying wires should be twisted together. The probe shaft is isolated from the plasmachamber at the entry port. The entry port has a KF-40 flange. The flange clamp and4O-ring are made of insulator.The electric connections are made in the junction box at the end of the shaft. All theconnectors on the junction box and inputs to the amplifier should be isolated. Importantly,the power supply has to be floating and the ground pin on the wall plug should not beused. We use battery packs instead of regular power supply. The physical ground is madeat the junction box.The experiment was carried out on an axisymmetric tandem mirror device which wasbuilt at the MIT Plasma Fusion Center for space plasma propulsion study8,9,10. Thesimplified experimental setup is shown in Figure 2. The plasma discharge was obtainedby back filling the chamber to 8 x 10-5 torr of hydrogen which was broken down withmicrowave power of 500 W at 2.45 GHz. It was further heated with an rf power of 10kW at 3 MHz and at a pulse length of 20 ms. The triple probe and a Langmuir probewere mounted on the midplane of the device at the same radial position but 180 degreesapart, angularly. Their radial position is 5 cm which is one half of the plasma radius.Since the triple probe is in a strong axial magnetic field, we were concerned that themeasurement might be affected by the direction and intensity of the magnetic field due tothe fact that there are three probe tips used to measure two different quantities, the ionsaturation current and the plasma potential difference. To examine this concern a studyhas been made by rotating the probe and moving the probe axially to a stronger andnonuniform field region close to the magnetic mirror point. No distinguishable differencehas been observed beyond the expected uncertainties due to fluctuations, spatial variationsand irreproducible effects between shots. We can say that to the first order the effect ofmagnetic field direction, intensity and uniformity on the triple probe due to its asymmetricstructure is not a concern.The experimental results are presented in Figure 3. Figure 3a is the electron saturationcurrent taken with the single langmuir probe. The plasma potential difference and the ion5current signals taken with the triple probe are shown in Figures 3b and c respectively. Theanalysis is discussed in the next section.III. Ion Temperature CalculationThe theory of a triple probe has been fully developed5 ,6 '7 . We briefly review themethod and formulation of a symmetrical triple probe discussed by Chen and Sekiguchi5in order to present our thinking and the changes to be made for electron density and iontemperature calculations. The current equations for the triple probe are following-I= -SJ exp (-OV1) + Sji(V), (1)I2 = -SJe exp (-OV2 ) + Sji(V2 ), (2)13 = -SJe exp (-bV3 ) + Sji(V3 ), (3)where= e/kTe, (4)andJ= n~e kTe/27rme . (5)Here Je and Ji are the electron and ion saturation current density respectively, S thesurface area of the probe tips, k the Boltzmann constant, and e and m, the charge andmass of an electron, respectively.By assuming the relationships ji(Vi) = ji(V2 ) = Ji(V3 )(= Jj) and eliminating SJ,one obtains the following equations,1, +12 1 - exp (-d2) (6)1, +13 1 - exp (-OVd3)'and1 13 - 12 exp (- OVVd) (7)S 1 - exp (-OVVd)6where V2 = V2 - V1, Vd3 = V 3 - V andVVd = Vd3 -Vd2 = V3 -V 2  (8)Equation (6) determines the value of T directly. The common practice is to use theequationJi ; Jis = exp (-1/2)ene /k Te /Mi. (9)to determine electron density, ne . An assumption of T << T has been made in equation9. This assumption is not universally correct. In many plasma systems, particularly infusion energy devices, the opposite relation T >> T, exists. It is in fact our preferredcondition for plasma propulsion. Therefore it is logical and more accurate to preserve theion temperature term in the ion saturation current relationshipJi e Jis = exp (-1/2)en, y/k(Te + T2)/Mi, (10)Thus T can be determined using the electron density, n, , obtained from equation (5)and the electron saturation current measured with the single Langmuir probe. By forcingprobe P2 to be at floating potential and setting Vd3 at a very large value, equation (6) isreduced to a very simple equationexp (-Vd2) = 1/2. (11)As is mentioned previously the electron saturation current was obtained by setting probe ata biased voltage of 150 V. This voltage was predetermined from the I-V characteristic curvesby sweeping the applied probe voltage. The current signal taken by a DCM Langmuirprobe"' is shown in Figure 4. The voltage is swept from -150 V to +150 V at a frequencyof 1000 Hz. Each peak contains one cycle and gives two I-V curves. A typical I-V curveis shown in Figure 5. The electron saturation current is normally taken to be the valueat the bend. The voltage at this point is 80 V , the plasma space potential. These spacepotentials vary from 50 to 120 volts from the examination of all the I-V curves for the7time scan of the probe signals. In reality the electron current continues to rise slowly andapproaches constant value asymptotically. Here we pick 150 V as the probe bias voltage toassure that the probe measures saturation current for the entire time scan. The maximumerror is I(150) - Ie(50) which amounts to less than 10%. This is much less than the errormade from the assumption that Ti = 0, which can be as high as 35% when Ti = T, '.The deduced electron density would be rendered useless if Ti became larger than T. Theequations used for the determination of Te, n, and Ti are collected and listed as follows,kTe = exp (-1/2)Vd2, (11)andJ ee efk Te/27rme, (5)andJi ~ Jis = exp (--1/2)ene /k(Te + T )/mi. (10)The time scans of the ne, T and Ti are plotted in Figure 6. It is seen that Ti is muchlarger than T, and most of the time the ratio of these two values is more than doubled ortripled. Ignoring Ti in the ion saturation current would miss a very important part of theplasma parameters as well as provide an incorrect value of electron density. One mightargue that the probe crossection should include the sheath thickness. Such correctionto the probe crossection is needed if the probe is spherical and is in a nonmagnetizedplasma. The triple probe is in strongly magnetized plasma and the tips are cylindrical; theprojected current collection area does not change due to presence of the sheath potential.A comparison of the errors risen from the traditional method and the current methodis in order. In the traditional method using equation (9) to calculate n, , the error wouldincreases as the ion temperature increases. For example the errors would increase from44% to 100% when Ti increases from T to 3 T . These errors increase the value of thene and are not real uncertainties in the usual sense. It loses the true meaning when the8value could be more than doubled. Therefore the traditional method would underestimatethe n, value which can be more than a factor of two too small. The error related tothe current method is the uncertainty for obtaining the density n, from equation (6).The uncertainty in the measurement of the electron saturation current is about ±10%.However, the ion temperature is inversely proportional to the square of the density, theuncertainty in Ti is twice the negative value of the uncertainty of ne, i.e., :- 2 0 %. Theerror is physically more meaningful.IV. Concluding DiscussionThis work demonstrates the technique to determine the ion temperature using a singleand a triple Langmuir probe. It provides a valuable plasma parameter, Ti . The uncer-tainty seems better than the usual technique in determining the ne from Ji by neglectingthe ion temperature Ti . This probe set has the advantage of being small in size, low costand simple to fabricate and operate. The results can be displayed almost immediately.Therefore high time resolution measurements of the plasma parameters can be obtained.The error associated with this method seems to be reasonable in value and in physicalmeaning. The single and triple probes can be combined to form a quadruple probe so thatthe measurements can be made at the same spatial location. Great care has to be takento avoid the arcing between probe tips when high voltage is applied to the probe.AcknowledgementThis work is jointly supported by US AFOSR and NASA/JPL and DOE. Valuablediscussions with X. Z. Yao and the technical support of Harvey Lander are acknowledged.9References1. I.H. Hutchinson, "Principles of Plasma Diagnostics", Cambridge University Press, NewYork,1st Ed. (1987)2 T.F. Yang, A.S. Wan and G.S. Luan, J. Nucl. Mater.,172,220(1990)3 A.S. Wan, T.F. Yang, B. Lipschultz, and B. LaBombard, Rev. Sci. Instrum. 57(8),1542(1986)4. O.E. Johnson and L. Malter, Phys. Rev.,80(1),58(1950).5. Sin-Li Chen and T. Sekiguchi, J. Appl. Phys.,36 (8),2363(1965)6. M. Kamitsuma, Sin-Li Chen and Jen-Shih Chang, J. Phys. D: Appl. Phys.,10,1065(1977).7. H. Ji and H. Toyama and K. Yamagishi and S. Shinohara and S. Fujisawa and K.Miyamoto, Rev. Sci. Instrum.,62(10), 2326 (1991)8. F.R. Chang, W.A. Krueger and T.F. Yang", AIAA/DBLR/JSASS 18th Int. Electr.Propul. Conf.,paper AIAA-85-2049, Alexandria,Virginia(1985)9. T.F. Yang and S. Peng and F.R. Chang-Dfaz", AIDAA/AIAA/DGLR/SASS 22ndInt. Electric Propul. Conf.,paper IEPC-91-129, Viareggio, Italy (1991).10. T.F. Yang, and F.R. Chang-Diaz, MIT/PFC Report No. PFC/RR-94-1 (1994)11. T.F. Yang, Ping Liu and Q.X. Zu, submitted to Rev. Sci. Instrum. (1994).10.~ s-i4- ~: -.C.,s-iU*Z -W5-jN75-C.) s-i$wCb.)004a0x0011I0Q~00* -bLJ==0.0QU,0U,ImbJNII0=0~0012-Lz=U,Cq~0120100806040200160 610 615 620 625Time (ms)605605610 615Time (mS)610 615Time (ms)6206202525Figure 3. Time scans of electron saturation current measured by the single Langmuirprobe(a), Potential difference V2 (b) and ion saturation current (b) measuredby the triple probe.13605E)(a)- -0- (b)-0.50.40.30.20.1EU.u .600E0.60.50.40.30.20.10.0600(C)I I I-I I ---66I-I I I I I I I I610 0.615Time (mS)0.620Figure 4. Langmuir probe signal taken prior to the triple experiment for the purpose ofdetermining the probe bias voltage.1420151050EI *I I I I I II I I I -0.600 0.605 0.6250.201510E0-550 -100 -50 0 50VP (volt)Figure 5. An I-V characteristic curve for the single probe.15S----------------------100 1505605 610 615 620Time (mS)OR(b)610 615Time (mS)6 10 615Time (ms)620620Figure 6. Time scans of deduced electron density from electron saturation current mea-sured by the single Langmuir probe(a), ion temperature from the ion saturationcurrent (b) and the electron temperature from the potential difference(c).163210Ez 432is~1(a)1043020CD01060 00605605120 -100-80-60 -40-20-600I I II I I I - I2562

Determination of ion temperature with single and triple Langmuir probes

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Determination of ion temperature with single and triple Langmuir probes

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