CURRENT VOLTAGE CHARACTERISTIC OF PLANAR LANGMUIR PROBE IN IONOSPHERIC MAXWELLIAN PLASMA

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1 Scinc CURRENT VOLTAGE CHARACTERSTC OF PLANAR LANGMUR PROBE N ONOSPHERC MAXWELLAN PLASMA Shankar Bhattarai *1, Lkha Nath Mishra 2 1 MSc Physics, Dpartmnt of Physics, Patan Multipl Campus, Tribhuvan Univrsity, Lalitpur, Npal 2 Assoc. Prof., Dpartmnt of Physics, Patan Multipl Campus, Tribhuvan Univrsity, Lalitpur, Npal DO: Abstract Frquntly usd gomtris of Langmuir probs ar planar, sphrical, and cylindrical shaps. Th gomtry is chosn dpnding on th purpos of th masurmnts and th platform configuration. Planar Langmuir Probs hav bn installd on satllits and sounding rockts to obsrv th gnral charactristics of thrmal plasma in th ionosphr for mor than fiv dcads. Bcaus of its simplicity and convninc, th Langmuir prob is on of th most frquntly installd scintific instrumnts on spaccraft. Th Planar Langmuir Prob is th ky plasma diagnostic usd by scintists intrstd in plasma charactrization to masur th intrnal paramtrs of th bulk of th plasma. This rsarch xplors th thortical study of Planar Langmuir Prob -V Charactristics. Th rlationship btwn first drivativ of currnt vrss applid prob voltag is also computd. With th hlp of th (volt ampr curvs) of Planar Langmuir probs, th diffrnt paramtrs of plasma can b dtrmind such as plasma potntial, floating potntial, prob currnts in diffrnt prob voltag and so on. Planar Langmuir prob gomtry is asy to construct and qually suitabl for plasma charactrization. Kywords: Planar Prob; Plasma Paramtrs; -V Charactristic; Maxwllian Plasma. Cit This Articl: Shankar Bhattarai, and Lkha Nath Mishra. (2017). CURRENT VOLTAGE CHARACTERSTC OF PLANAR LANGMUR PROBE N ONOSPHERC MAXWELLAN PLASMA. ntrnational Journal of Rsarch - Granthaalayah, 5(4), ntroduction Th lctromagntic forc is gnrally obsrvd to crat structur:.g., stabl atoms and molculs, crystallin solids. n fact, th most widly studid consquncs of th lctromagntic forc form th subjct mattr of Chmistry and Solid-Stat Physics, which ar both disciplins dvlopd to undrstand ssntially static structurs. Structurd systms hav ntrnational Journal of Rsarch - GRANTHAALAYAH [228]

2 binding nrgis largr than th ambint thrmal nrgy. Placd in a sufficintly hot nvironmnt, thy dcompos:.g., crystals mlt, molculs disassociat. At tmpraturs nar or xcding atomic ionization nrgis, atoms similarly dcompos into ngativly chargd lctrons and positivly chargd ions. Ths chargd particls ar by no mans fr: in fact, thy ar strongly affctd by ach othr s lctromagntic filds. Nvrthlss, bcaus th chargs ar no longr bound, thir assmblag bcoms capabl of collctiv motions of grat vigor and complxity. Such an assmblag is trmd a plasma. Th Czch mdical scintist, Johanns Evanglista Purkinj introducd us of th Grk word plasma (maning formd or moldd ) in th mid-19 th cntury, to dnot th clar fluid which rmains aftr rmoval of all th corpuscular matrial in blood. Th Nobl Priz winning Amrican chmist rving Langmuir first usd this trm to dscrib an ionizd gas in 1927 [1]. Th trm plasma mans somthing moldd or fabricatd and coms from Grk. As th tmpratur of th matrial is raisd, its stat changs from solid to liquid and thn liquid to gas. f th tmpratur is incrasd furthr-mor, th molcul will dissociat into atoms and ultimatly som of thir lctrons bcom so nrgtic that th atom ionizs. At ths high tmpraturs, th gas bcoms a mixtur of oppositly chargd particls and nutral atoms. Thus, a gas which contains larg numbr of ionizd particls and nutral atoms which show quasinutrality and collctiv bhavior ar calld plasma. n short, Plasma is a quasi-nutral gas of chargd and nutral particls which xhibits collctiv bhavior. Elctric probs, such as th Langmuir prob, ar th most widly usd plasma diagnostic tools [2]. Othr mthods includ passiv rmot snsing mthods, which dtcts radiation or particls mittd spontanously by th plasma, such as studying plasma phnomna rlatd to th sun activ non-contact mthods, whr radiations or particls producd by xtrnal sourcs, such as th study of th absorption and scattring of lctromagntic radiation by th plasma [3]. Langmuir probing dtrmins th proprtis of a plasma with xcllnt spatial rsolution, nabling th rconstruction of th crossing point of th particl [4]. Additionally, this mthod succssfully dscribs th plasma s paramtrs in a varity of situations, such as low-prssur plasmas for matrial procssing, dg plasmas in fusion dvics, and ionosphric plasma and it aids th dsign of ion sourcs and nw plasma chambrs. Th simplst application of a Langmuir Prob involvs insrting th prob into th plasma rgion of intrst and applying a voltag V with rspct to th mtallic chambr that contains th plasma. Svral configurations ar commonly usd, including singl, doubl, and tripl probs [5]. Ths variations allow for simplifications in th control systm or in th analysis of masurmnts. Th bias voltag is typically swpt at a spcifid frquncy ovr a rang that is comparabl to th lctron tmpratur to dtrmin th currnt-voltag (-V) charactristic for th local plasma. Th plasma paramtrs ar xtractd during a post-procssing stp, whr softwar can b usd to fit th -V charactristics. Th Langmuir prob tchniqu involvs applying a voltag to a mtallic conductor immrsd in plasma and obsrving th collctd currnt. Th obsrvd total currnt,, is a summation of various currnts such as lctron and ion thrmal currnts, photolctron currnt, scondary lctron currnts, tc [6]. Th bnfits of th simplicity of this tchniqu, howvr, ar offst by th complxity of th thory rquird to analyz th obtaind currnt vs. potntial, or -V, curvs. ntrnational Journal of Rsarch - GRANTHAALAYAH [229]

3 Thr is no gnral thory of Langmuir probs which is applicabl to all masurmnt conditions, bcaus it dpnds on th prob siz and gomtry, plasma dnsity and tmpratur, platform vlocity, and othr factors. Th actual dsign of th prob is usually dtrmind by considring th rlationship btwn th prob dimnsions and th Dby lngth of th plasma. n gnral, two approximations ar usd to xprss th currnt on th prob in th plasma: 1) orbital motion limitd (OML) and 2) shath ara limitd (SAL). OML thory can b adoptd whn th prob radius is smallr than th thicknss of th shath surrounding th prob, whil it must b qual to or largr than th shath thicknss in th cas of SAL thory [7]. Figur1: Planar prob installd on Japans Akbono satllit. Langmuir probs may hav diffrnt lctrod shaps, such as cylindrical, sphrical and planar. Planar Langmuir probs ar not that common. Th main disadvantag of thm is that it is not asy to nglct boundary ffcts, in ordr to modl thm as an infinit planar conductor. This could b don by making th prob larg nough, compard to th Dby lngth. Nvrthlss, this approach is not always accptabl in laboratory and industrial plasmas, as it would most likly caus an qually larg prturbation in th plasma that is to b diagnosd, which is an undsirabl ffct. Howvr, thr ar situations whr this gomtry may com in handy,. g. probs dsignd to b mountd on divrtr plats in fusion dvics, whr th prob has to ovrcom hug hat fluxs. Anyway, fusion dvics ar not th only plac whr planar probs ar usd [8]. 2. Currnt-Voltag Charactristics of Langmuir Prob Th xact shap of th currnt to voltag ( V) charactristic curv of a Langmuir prob, dpnds on th proprtis of th plasma whr it is bing usd, as wll as on th gomtry and othr attributs of th prob itslf. Nvrthlss, th V charactristic curv of any Langmuir prob can b qualitativly dscribd as th on that appars in Fig. blow. Th diagnosis of a plasma is basd on th comparison of th currnt, in on zon or point of th V charactristic curv, with th prdiction of a particular thortical modl. n this way, th currnt and biasing voltag of th prob ar corrlatd to proprtis of th plasma, as th lctron dnsity or tmpratur [9]. ntrnational Journal of Rsarch - GRANTHAALAYAH [230]

4 Figur 2: Currnt-voltag charactristics of Langmuir prob. Th typical trac of currnt-voltag charactristics with th us of Langmuir prob is shown in Fig. 2. t can b analyzd by considring thr diffrnt rgions as follows: Th rgion-1 is corrsponding to th valus of th potntial lss than V f whr floating potntial V f is dfind as th potntial at which th lctron and ion flux towards th prob coms in an quilibrium and hnc th nt currnt from th plasma is zro. Du to larg mass of ions this currnt is gnrally small and ngativ. Th drawn currnt is mainly contributd by positiv ions and givs ion dnsity in plasma. Th rgion-2 is corrsponding to valus of potntial btwn V f and V p, whr V p is th plasma potntial or spac potntial. At th bginning of this rgion from V p, th lctrons ar initially attractd to th positiv potntial of th prob and hnc form a shath in ordr to shild th lctric fild producd. Aftr th formation of shath, th prob surfac bcoms ngativly chargd so it will start attracting th positiv ions and rpls th lctrons to prsrv th quasi nutrality of th plasma. Sinc th lctrons ar mainly rtardd thrfor this rgion is calld lctron rtardation rgion. Th rtardation procss continus until th ion and lctron fluxs bcom qual at floating potntial [1]. Th rgion-3 dscribs th situation whr th potntial is positiv and gratr than V p. Thrfor, th lctrons will b acclratd and positiv ions will b rplld from th prob. ncrasing th bias will yild th lctron saturation currnt such that incras in voltag dos not incras th currnt [10]. ntrnational Journal of Rsarch - GRANTHAALAYAH [231]

5 3. Thory of Planar Langmuir Prob Although many plasma diagnostic mthods hav bn dvlopd sinc th original work of rving Langmuir, th Langmuir prob is still on of th most powrful plasma diagnostic tools du to its simplicity, low cost, adaptability, ability to dtrmin th fundamntal charactristics of a plasma. A Langmuir prob may hav any gomtry, but cylindrical, sphrical, and planar probs ar usually mployd bcaus of thir symmtry [11]. Th basis for T masurmnts is th convntional Langmuir prob thory of Mott-Smith and Langmuir, assuming a Maxwllian nrgy distribution F(E) givn by, E F( E) E xp (1) kt Whr k is th Boltzmann constant. Thus, in a Maxwllian plasma, whn th prob to plasma potntial, V, is drivn ngativ, dcrass xponntially. Th gnral formula of currnt in a charg plan conductor is givn as, planar V 1 (2) T For V < 0, And i V o xp KT io V xp1 KTi Whil for V > 0, V o xp1 KT And V i io xp KTi (3) (4) (5) (6) Hr th various currnts ar givn as, o KT An 2 m 1 2 (7) ntrnational Journal of Rsarch - GRANTHAALAYAH [232]

6 Whr o is th random lctron currnt, is th lctron charg, m is lctron mass, and A is th prob ara. This quation for what is known as th lctron rtarding rgion in a Maxwllian plasma is th sam for all prob gomtris. io KT i An 2 mi 1 2 (8) 1/2 KT V An xp 2 m KT (9) And for Planar Langmuir prob, A=2πr 2 1/2 KT V 2 2 r n xp 2 m KT (10) For a Maxwllian plasma, all thr prob gomtris ar suitabl for th masurmnt of T. Howvr, th lctron saturation rgions diffr gratly with collctor gomtry. Th lctron saturation rgion of th cylindrical prob is narly indpndnt of T, whras this rgion is highly tmpratur dpndnt for th planar and sphrical probs. Th cylindrical and sphrical probs hav th advantag of producing larg saturation currnts for th sam dnsity, an advantag for masurmnts in rgions of vry low dnsity. 4. Rsults and Discussions Th Langmuir prob tchniqu for in situ masurmnt of plasma paramtrs has bn around for ight dcads, driving th paramtrs with accuracy from th data acquird by a Langmuir prob immrsd in spac plasma is still a challnging task. n th prsnt rsarch work, thortical study of Planar Langmuir Prob in Maxwllian plasma ar studid. This work is typically basd on th -V charactristic of Planar Langmuir Prob. Th main propos of this work is to study th Currnt-Voltag charactristic of Planar Langmuir prob with diffrnt low ionosphric plasma tmpraturs. Th mthodology of our study includs th thortical drivation of th rlationships btwn various paramtrs and thn plotting th paramtrs in suitabl rang from a mathmatical softwar (hr MATLAB is mployd). 5. Th Variation of Planar Langmuir Prob -V Curv with Tmpraturs Th -V charactristic is a fundamntal part of dagnosis of plasma paramtrs. So, it is dpictd in th following figurs. n th prsnt study, th ionosphr paramtrs (lctron tmpratur, ion tmpratur, lctron dnsity and ion dnsity) ar modlld. For this purpos, it is assumd that for dnsity N =10 12 m -3, radius of planar prob (r p =2.5mm).Ths figurs illustrat th ffct of T on th width of th lctron rtradation rgions. ntrnational Journal of Rsarch - GRANTHAALAYAH [233]

7 Hr, Fig.3 dpicts that th Planar Langmuir prob curvs computd for a Maxwllian plasma illustrat th ffct of Tmpraturs (i.. 1V, 2V and 3V) rspctivly on th width of th rtarding rgion. n ordr to obtain th -V curv th prob bias voltag is swpt ovr a spcifid rang (-10 V to +10 V in this simulation) that ncompasss th plasma potntial. Th lctron and ion currnts collctd by th prob will chang dpnding on th applid bias voltag. Figur 3: Th Planar Langmuir Prob -V curvs computd for a Maxwllian plasma illustrat th ffct of T on th width of th rtarding rgion. Th amplitud of th lctron saturation currnt varis gratly with T. Whn th plasma tmpratur is 1V th kn of th curv is sharp and is a good masur of V s. Th Floating Potntial V f is narly -2 volt. This floating potntial is typically ngativ bcaus mobil lctrons tnd to strik th prob mor frquntly than positiv ions. Whn th plasma tmpratur is 2V, th Floating Potntial V f is narly -6volt. Th kn occurs littl bit sharpr, whn th prob has bn saturatd with lctrons, causing additional lctrons to b rplld. Plasma Potntial V s is gratr than 1 volt. At 3V, th Floating Potntial V f is narly -10 volts. For prob potntial is gratr than plasma potntial (V p >V s ), lctron saturation currnt is apparing constant du to an incras in shath thicknss. n th Transition Rgion, th ion currnt is ngligibl, and th lctrons ar partially rplld by th ngativ potntial V p V s. n a Maxwllian plasma, this part of th curv is xponntial as shown in abov figur. 6. Drivativ of -V charactristics of Planar Langmuir Prob Th Figur blow shows th first drivativ of -V charactristics of planar Langmuir prob in Maxwllian plasma. All thr graphs shows th rlation btwn drivativ of currnt vrsus bias voltag and prob currnt vrss applid prob voltag. ntrnational Journal of Rsarch - GRANTHAALAYAH [234]

8 Figur 4: Th Planar Langmuir Prob -V curv computd for a Maxwllian plasma with first drivativ at T= 1 V. n Fig. 4, th first drivativ of th prob lctron currnt vrsus th prob voltag V p provids a pak valu of 1V, which corrsponds to th spac potntial (plasma potntial) whn th lctron tmpratur is 1V(11600K). Th ngativ ions and positiv ions saturation currnts ar comparabl, with such charactristic th plasma potntial is asily dtrmind as th voltag at which th first drivativ is maximum. Figur 5: Th Planar Langmuir Prob -V curv computd for a Maxwllian plasma with first drivativ at T= 2 V. ntrnational Journal of Rsarch - GRANTHAALAYAH [235]

9 Hr in Fig.5 shows that, whn th lctron tmpratur is 2V(23200K), th point of inflction of -V charactristics i..d/dv is maximum corrsponds to 1V plasma potntial. So hr th plasma potntial is 1V, which is xpctd rsult and also that th charactristics is roughly symmtric about 8 ma. Figur 6: Th Planar Langmuir Prob -V curv computd for a Maxwllian plasma with first drivativ at T= 3 V. Finally, th graph shown in Fig.4, Fig.5, and Fig.6 ar outcoms of th plot -V curvs and its first drivativ with prob voltag and first drivativ shows th plasma potntial. n all thr graphs th plot of drivativ is rprsntd by th puls sn distinctly. Th -V curvs wr plottd at diffrnt valu of plasma potntial with rmaining ion or lctron tmpratur constant. 7. Conclusion This rsarch has attmptd to improv th application of planar Langmuir probs to unmagntizd collisionlss plasma. Th physical conditions undr which th prsntd modl is valid and can b applid hav bn discussd. Th -V charactristic of th Planar Langmuir Prob in th Maxwllian Spac plasma at diffrnt tmpratur rang ar plottd in graph by using th mathmatical softwar by putting th suitabl rangs for various paramtrs. All lmntary procsss wr xtnsivly discussd and most of information has bn prsntd. With th hlp of th (volt ampr curvs) of Planar Probs, th diffrnt paramtrs of plasma can b dtrmind such as plasma potntial, floating potntial, prob currnts in diffrnt prob voltag and so on. And th ffct of tmpratur T on th width of th lctron rtardation rgions ar clarly studid in this rsarch. Thus, masurd plasma paramtrs, and th rlationship btwn th dnsity of th plasma on prob currnt, ffct of tmpratur on -V curv, ar of fundamntal importanc for rsarch on laboratory plasma, ionosphr trrstrial ntrnational Journal of Rsarch - GRANTHAALAYAH [236]

10 plasma and industrial application. Th first drivativ of currnt voltag charactristic is suitabl for to dtrmin th plasma potntial. Rfrncs [1] Langmuir, and H.M. Mott-Smith, "Th thory of collctors in Gasous Dischargs," Physical Rviw, vol. 20, p. 727, [2] F. F. Chn, "Elctric Probs," Plasma Diagnostic Tchniqus, pp , [3] T. N. Acadmis, Plasma Scinc: From Fundamntal Rsarch to Tchnological Applications, National Acadmy Prss, [4] mpdansltd, Plasma Managmnt to Undrstand and Control th Futur, probs, [5] J. G. Laframbois, "Thory of sphrical and cylindrical Langmuir probs in a collisionlss, Maxwllian plasma at rst," UTAS, [6] J. G. Laframbois, Thory of Sphrical and Cylindrical Langmuir Probs in a Collisionlss, Maxwllian Plasma at Rst, Toronto: UTAS Rport No.100 Univrsity of Toronto, [7] L. Cond, An introduction of Langmuir prob diagnostics of plasmas, Madrid: Univrsidad Politcnica d Madrid, [8] D. Bohm, E. H. S. Burhop, and H. S. W. Massy, Th Charactristics of Elctrical Dischargs in Magntic Filds, Nw York: McGraw Hill, Nw York, [9] Pil, M. Hirt, and C. T. Stigis, "Plasma diagnostics with Langmuir probs in th quatorial ionosphr:. Th influnc of surfaccontamination," J. Phys. D: Appl. Phys., vol. 34, no. 17, pp , [10] W.E. Amatucci, P. W. Schuck, D. N. Walkr, P. M. Kintnr, S. Powll, B. Holback, and D. Lonhardt, "Contamination fr sounding rockt Langmuir prob," Rv. Sci. nstrum., vol. 72, no. 4, p. 2052, [11] V.N. Rai, M. Shukla, H.C. Pant and D.D. Bhawalkar, "High Spd Plasma Diagnostics for lasr plasma intraction and fusion studis," Sudhana, vol. 24, p. 513, [12] P. M. Bllan, Fundamntals of Plasma Physics, Cambridg: Cambridg Univrsity Prss, *Corrsponding author. addrss: oshobhattarai2@gmail.com ntrnational Journal of Rsarch - GRANTHAALAYAH [237]