Development of a Space-charge-sensing System

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1 Snsors 7, 7, snsors ISSN by MDPI Full Rsarch Papr Dvlopmnt of a Spac-charg-snsing Systm Ariadi Hazmi, Nobuyuki Takagi, Daohong Wang* and Tiji Watanab Gifu Univrsity of Japan, Gifu, Japan; s: ariadihazmi@yahoo.com, takagi-n@gifu-u.ac.jp, wang@gifu-u.ac.jp. * Author to whom corrspondnc should b addrssd; wang@gifu-u.ac.jp, Tl: , Fax: Rcivd: Octobr 7 / Accptd: 3 Novmbr 7 / Publishd: 4 Dcmbr 7 Abstract: A systm for rmotly masuring th distribution of air spac charg in ral tim is dvlopd. Th systm consists of a loudspakr and an lctric fild antnna. By propagating a burst of dirctional sound wav from th spakr, a modulation in th spac charg and, thrfor, an lctric fild chang at ground is producd. Th distribution of th spac charg dnsity is drivd from th E-fild chang which can b masurd by th E- fild antnna. Th dvlopd systm has bn confirmd by both laboratory and fild xprimnts. Kywords: Spac charg, rmot snsing, thundrcloud, lightning. 1. Introduction Convntionally, spac charg in atmosphr is ithr masurd dirctly at som local prst points or infrrd from masurmnt of potntial diffrnc through balloons, rockts or airplans [.g., Bradly, 1968; Winn and Moor, 1971; Chauzy t al., 1991]. Th lattr has bn widly usd for masuring th charg distribution both insid and bnath a thundrcloud and has providd a lot of valuabl information on lctrical structur of thundrclouds [.g., Soula and Chauzy, 1991; Marshall and Rust, 1993]. Howvr, all convntional mthods ar vry poor in trms of spatial rsolution and thy ar in principl not suitabl for masuring air spac charg distribution in ral tim and in 3- dimnsions. Ral-tim and 3-D information on th charg distribution insid a thundrcloud can not only provid a dirct mans for forcasting imminnt lightning but also hlp to undrstand thundrcloud lctrification mchanism and lightning discharg charactristics. W hav proposd a

2 Snsors 7, mthod which is suitabl for ral tim and 3-D masurmnt of spac charg distribution in atmosphr [Wang t al., 1997]. In this mthod, a burst of dirctional sound wav is usd to modulat th spac charg and to produc an oscillating lctric fild which is masurabl at th ground. Th spac charg location is dtrmind with th tim diffrnc btwn th sound wav and th E-fild variation in combination with th sound wav propagation dirction. Th spac charg amplitud is drivd with th amplitud of th E-fild variation. Th possibility of masuring atmosphric spac charg by us of sound wavs has bn suggstd by Sisco [1971] mor than 3 yars ago. In his mthod, a continuous plan sound wav was usd and th local oscillating lctric filds at th spac charg location had to b masurd. To gt som spatial rsolution, ithr numrous masuring systms ar ndd or th masuring systm has to b movd within air spac charg rgion. Compard to convntional mthods, his mthod in principl has th similar limitation in trms of spatial rsolution. Our mthod is basd on rmot snsing and is capabl of masuring spac charg in ral tim and 3 dimnsions with only a singl stationary systm. To valuat th validity of our proposd mthod, in th prsnt study a prototyp of systm for masuring spac charg has bn dvlopd and tstd in both laboratory and fild conditions. This papr rports th rsults.. Thortical Background Whn a burst of dirctional sound wav propagats in air as shown in Fig. 1, th air dnsity along th sound wav will b modulatd in squncs by th sound wav. Th air dnsity modulatd at a distanc of r from th loud spakr can b calculatd with th following formula (s th dtail in Appndix A). Hight (m) High prssur sound wav High prssur sound wav Low prssur sound wav r r 3 r 1 Prssur (Pa) Spakr E-fild antnna Figur 1. A schmatic illustration of th principl of th dvlopd systm.

3 Snsors 7, 7 36 A αγ j ( ) ( ωt Kr) r t = +, 1 (1) γp whr is th air dnsity in stady stat, with valu of = 1.93 kg m -3 ; A is th amplitud of sound wav (Pa); γ is th ratio of th spcific hat at constant prssur to th spcific hat at constant volum, with valu of γ = 1.4; P is th atmosphric prssur in stady stat, with valu of P = 1.13x1 5 Pa; α is th attnuation constant; ω is th angular frquncy of th sound wav; K is wav numbr whr K = ω/c, c is th sound vlocity. If th spac charg dnsity is in proportion to, which should b tru for most of cass, th spac charg dnsity is modulatd similarly as th air dnsity. Th modulation in can produc an oscillating lctric fild changs at ground. Assum that th sound wav lasts 1.5 priods (or 1.5 wavlngths), th following rlation can b asily drivd (s th dtail in Appndix A). E 3 = 1 sinθ c W 3 ε γp fr π () 8 whr E is th amplitud of th lctric fild chang; ε is th dilctric constant in vacuum; f is th frquncy of th sound wav; r is th propagation distanc of th sound wav; θ is th half angl of th dirctional sound wav; c is th spd of sound; W is th input powr into th spakr. By masuring E, th spac charg dnsity along th propagation of sound wav could b drivd with th abov formula. By changing th dirction and frquncy of th sound wav, it is possibl to obtain 3- dimnsional spac charg distributions in a similar way to typical mtorological radar. 3. Exprimntal St-up Th diagram of th dvlopd systm and also th st-up for laboratory xprimnts ar shown in Fig.. Th xprimnt st-up consists of thr parts: (1) spac charg producing part, () sound wav gnrating part and (3) lctric fild masuring part. As illustratd in Fig., th spac charg producing part is composd of a DC high voltag powr supply and two plat lctrods with on of thm having 15 short ndls on its innr surfac. Th spac charg is gnratd though corona discharging from th ndls. Th rsultant charg dnsity can b adjustd by changing th applid voltags. Th sound wav gnration part consists of an oscillator, a powr amplifir and a loudspakr. Th oscillator outputs a burst sin wav with 1 khz frquncy and 1.5 wavlngths vry scond. Th lctric fild masuring part is composd of a capacitiv lctric fild antnna, a bandpass filtr, a lock-in amplifir and a digital storag oscilloscop. Th lock-in amplifir is usd to rduc nois and to improv th snsitivity of th E-fild masuring systm. Th output of th lock-in amplifir taks th form of intgration of th E-fild variation. Th st-up of fild xprimnts is shown in Fig. 3. In fild xprimnts, th spac charg is producd undr thundrstorm conditions through corona dischargs occurrd from svral ndls which ar mountd on th top of a 14.5 m high groundd towr. In ordr to masur th spac charg in fild nvironmnts, a powrful loudspakr for Dopplr sodar as spcifid in Tabl 1, is usd. All

4 Snsors 7, th othr quipmnts usd in fild ar th sam to that in laboratory and hav alrady bn dscribd abov. Spac charg 3 cm DC high voltag Sound rlatd E-fild rlatd r Powr amplifir Loud Spakr E-fild antnna 1 khz, Band pass filtr + - Oscillator Oscillator 1 DSO Lock in amplifir 1kHz, rfrnc 1kHz, burst sin wav Figur. A schmatic illustration of th stup for masuring spac charg in laboratory. Thundr cloud Sound rlatd E-fild rlatd Spac charg cloud Ndl Wind Dopplr sodar 14.5 m Stl towr E-fild antnna 1 khz, Band pass filtr Powr amplifir R Corona currnt dtction Lock in amplifir Oscillator Oscillator 1 1 khz, burst sin wav DSO 1kHz, rfrnc Figur 3. A schmatic illustration of fild xprimnt stup for masuring spac charg gnratd from ndls on th top of a stl towr.

5 Snsors 7, 7 36 Tabl1. Spcification of Dopplr Sodar AT-9. Frquncy band Bam width Input powr Driv impdanc Hight 15 6 Hz 16 o 9 W 4Ω.1 m 4. Rsults 4.1 Rsults obtaind in laboratory xprimnts Fig. 4 shows an xampl of th burst sound wav and th intgratd lctric fild changs whn th distancs btwn th loud spakr and th bottom of th lctrod ar, rspctivly, 1, 1.5 and mtrs. In th E-fild wavforms, th bginning tim of th E-fild ris and its pak tim ar markd as shown in Fig. 4. Th start of gnrating sound wav is rfrrd as t =. Compard to th sound wav, sinc th travling tim for an lctromagntic wav can b nglctd, th bginning tim of E-fild ris in th E-fild wavforms is th propagation tim for th sound wav front to arriv at th bottom of th spac charg rgion. Multiplication of this tim with th sound spd rsults in th distanc btwn th spakr and th bottom boundary of th spac charg. This distanc, dnotd r, is shown in ach of th bottom thr plats of Fig. 4. Th pak tim corrsponds to th propagation tim for th sound wav to lav th spac charg rgion. Multiplication of this pak tim with th sound spd rsults in th distanc btwn th loud spakr and th top nd of th lctrods, which is quivalnt to r +.7 m. Th distancs calculatd ar in good agrmnt with th masurd distancs with rrors lss than 1%. Also as sn in Fig. 4, th shortr th sparation distancs btwn th spakr and th spac charg, th largr ar th pak valus of th intgratd lctric fild changs. This is also in good agrmnt with quation (). Fig. 5 shows th rlationship btwn th dtctd lctric fild changs and th powrs inputtd to th loud spakr. As sn in Fig. 5, th largr th input powr, th biggr is th amplitud of th lctric fild chang. A thortical curv prdictd by quation () is also includd in Fig. 5. Th xprimntal data ar in rasonably good agrmnt with th thortical curv. From th masurd E-fild changs, th charg dnsity insid th lctrods can b drivd with quation (). Manwhil, in ordr to hav a comparison th spac charg has bn masurd by othr two indpndnt mthods. In th first mthod, rfrrd to as voltag mthod in this papr, th lctric fild E at th insid surfac of th arth plat lctrod and th voltag btwn th two plat lctrods with distanc d ar masurd. Th spac charg dnsity can b stimatd by, ε V = c E (3) d d whr c is spac charg dnsity; E is th lctric fild at th insid surfac of th arthd lctrod; V is th voltag btwn th two lctrods and ε is th dilctric constant in vacuum.

6 Snsors 7, In th scond mthod, rfrrd to as corona currnt mthod in this papr, th total corona currnt flowing to th arth, and th lctric fild on th insid surfac of th arthd plat ar masurd. Th charg dnsity can b stimatd by I = (4) E μs whr I is th corona currnt; E is th lctric fild btwn th two lctrods; μ is mobility of ion, with valu of μ is 1.3x1-4 m s -1 V -1 ; S is th cross sctional ara of th spac charg. Th lctric fild on th insid surfac of th arthd lctrods was masurd with a fild mill. Th corona currnt was masurd through a rsistor. Fig. 6 shows th spac charg dnsitis masurd with thr diffrnt Voltag (V) Sound wavform E-fild (V/m) E-fild (V/m) E-fild (V/m) msc msc msc 6.8 msc 8.1 msc msc Tim (s) Intgratd E-fild Intgratd E-fild Intgratd E-fild r = 1 m r = 1.5 m r = m Figur 4. Intgratd E-filds at various sparation distancs btwn spac charg and th loudspakr.

7 Snsors 7, and indpndnt mthods at various applid DC voltags. As sn in Fig. 6, th largr th applid voltag, th biggr ar th spac charg dnsitis. All thr mthods ar in good agrmnts. Elctric fild chang (V/m) Thory Powr Input (W) Figur 5. Rlationship btwn th E-fild changs and th powr inputtd. Charg dnsity (C/m 3 ) 5.x1-6 4.x1-6 3.x1-6.x1-6 1.x1-6 by voltag mthod by corona currnt mthod by proposd mthod Voltag applid btwn lctrods (kv) Figur 6. Comparison of th spac charg dnsitis masurd with thr indpndnt 4. Rsults obtaind in fild xprimnts Fig. 7 shows an xampl of th sound wav and th intgratd lctric fild dtctd undr a thundrcloud. Basd on ths masurd wavforms, th spac charg distribution can b stimatd by using quation (). Th spac chargs appar to xist in th rgion from 14.9 m to 16 m high abov th ground and hav maximum charg dnsity of 4 nc m -3 as shown in Fig. 8. Th hight of th charg rgion is consistnt with th hight of th groundd towr. Th masurd charg dnsity is about 1

8 Snsors 7, tims as larg as th valu masurd abov a truck farm undr th wintr thundrcloud [Tatsuoka t al., 1991]. Th lctric fild on th top of 14.5 m towr is on avrag mor than 1 tims largr than that abov th truck farm, and this may account for why th charg dnsity masurd by us is largr than Voltag (V) Sound wavform E-fild (V/m) msc 45 msc Tim (s) Figur 7. Intgratd E-fild dtctd undr a thundrcloud. Thundrcloud Hight from th ground (m) Charg dnsity (nc/m 3 ) Spac charg 14.5 m Stl towr.5 m Figur 8. An xampl rsult masurd in fild with th dvlopd systm.

9 Snsors 7, that by Tatsuoka t al. (1991). 5. Concluding Rmarks A systm for rmotly masuring th distribution of air spac charg in ral tim is dvlopd. Th systm consists of a loudspakr and an lctric fild antnna. Th validity of th dvlopd systm has bn confirmd by both laboratory and fild xprimnts. In th futur, in ordr to improv th snsitivity of th systm, not only th nois lvl of th lctric fild antnna should b rducd, but also th output powr of th loudspakr should b incrasd. Acknowldgmnts Th work lading to this papr is supportd in part by th Ministry of Education, Cultur, Sport, Scinc and Tchnology of Japan (Rsarch Grand No ). Appndix A Equations rlating sound wav to lctric fild Th ntir prssur P [Laurn t.al, 198; Fahy, 1989] can b xprssd as αγ j( ωt Kr P = P + A ) (A1) whr P = th ntir prssur (Pa) P = th atmosphric prssur in stady stat (1.13x1 5 Pa) A = amplitud of sound prssur (Pa) γ = th ratio of spcific hat at constant prssur to constant volum (1.4) α = th attnuation constant ω = th angular frquncy of th sound wav K = th wav numbr r = th propagation distanc of th sound wav (m) ω πf π K = = = (A) c c λ whr c = th spd of sound (331.5 m s -1 ) f = th frquncy of th sound wav (Hz) λ = wavlngth (m) P P = γ (A3)

10 Snsors 7, whr = th air dnsity (kg m -3 ) = th air dnsity in stady stat (1.93 kg m -3 ) << 1 (A4) γ = 1 + γ = 1+ γ = P P = 1 P P + γp A αγ j( ωt Kr ) ( r t) = + (A5), 1 (A6) γp Th spac charg dnsity is in proportion to, which should b tru for most of cass; th spac charg dnsity is modulatd similarly as th air dnsity. A αγ j( ωt Kr ) ( r t) = +, 1 (A7) γp whr = spac charg dnsity (C m -3 ) = spac charg dnsity in stady stat (1 nc m -3 ) A = amplitud of sound prssur (Pa) In air, it is plausibl to assum α is zro. Th actual sound prssur is th ral part of (A7), A ( r, t) = 1 + cos( ωt Kr ) (A8) γp On th othr hand, th lctric fild causd by th spac charg shown in Fig.A1 in sphrical coordinat is E' dv = 4πε r (A9) dv = dr rdλ r sin λdφ

11 Snsors 7, E' r = 1 r θ π ( r, t) cos λ r 4πε r sin λdφdθdr (A1) r = 1 θ r sin θ = 4ε ε ( r, t) r1 r cosλ sin λdθdr ( r, t) dr sin θ A ( r r ) { sin( ωt Kr ) sin( ωt Kr )} = 1 4ε γp K 1 (A11) From (A11), lctric fild chang Δ E is sin θ A ΔE = 1 4ε γp K { sin( ωt Kr ) sin( ωt Kr )} sin θ A K K sin 1 r 4ε γp K ( r r ) cos ωt ( r + ) = 1 (A1) (A13) From (A13), amplitud of lctric fild chang is sin θ A K E = sin r 4ε γp K ( r ) 1 (A14) λ λ (A15) ( r r ) = n + ( n 1,, ) 1 = Th sound powr from sound sourc is W A = S I = π sin θ r (A16) c whr W = th sound powr (Watt) S = ara (m ) I = th sound intnsity (Watt m - ) Th sound prssur A is liminatd from quations (A14) - (A16), th amplitud of lctric fild chang can b drivd as follows E 3 = 1 sinθ c W 3 ε γp fr π. (A17) 8

12 Snsors 7, φ r Spac charg dv dr rsinλdφ rdλ r dφ dλ r 1 λ θ Figur A1. An illustration of propagation of th sound wav to th sky. Rfrncs 1. Bradly, W. E. Aircraft soundings of potntial gradint, spac charg and conduction currnt, and thir rlation to prcipitation. J. Atmosphric Scincs 1968, 5, Chauzy, S.; Mdal, J. C.; Priur, S.; Soula, S. Multilvl masurmnts of th lctric fild undrnath a thundrcloud, 1. A nw systm and th associatd data procssing. J. Gophys. Rs. 1991, 96(D1), Fahy, F. J. Sound Intnsity; Elsvir Applid Scinc: London, U.K., Laurn E. K.; Austin R. F.; Alan B. C.; Jams V. S. Fundamntals of acoustics; John Willy & Sons, Nw York, Sisco, G. L. On th possibility of masuring atmosphric spac charg by us of sound wavs. J. Gophys. Rs. 1971, 76(18), Soula, S.; Chauzy, S. Multilvl masurmnts of th lctric fild undrnath a thundrcloud,. Dynamical volution of a ground spac charg layr. J. Gophys. Rs. 1991, 96(D1), Marshall T. C.; Rust, W. D. Two typs of vrtical lctrical structurs in stratiform prcipitation rgions of msoscal convctiv systms. Bull. Amrican Mtor. Soc. 1993, 74,

13 Snsors 7, Tatsuoka K. Elctric fild masurmnt by rockt undr th thundrclouds. In Procdings of th 7th Intrnational Symposium on High Voltag Enginring, Drsdn, Grmany, Aug 6-3, Wang, D.; Morisita, S.; Yoshihasi, H.; Chn, M.; Takagi, N.; Watanab, T. Rmot snsing of spac charg distribution with sound wav and radio wav. National Convntion of th IEE Japan, 1997; Papr No Winn, W. P.; Moor, C. B. Elctric fild masurmnts in thundrclouds. J. Gophys. Rs. 1971, 76(1), by MDPI ( Rproduction is prmittd for noncommrcial purposs.

Principles of active remote sensing: Lidars. 1. Optical interactions of relevance to lasers. Lecture 22

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