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VOLUME 78 NUMBER 1 PHYSICAL REVIEW LETTERS 6 JANUARY 1997 Increased Con nement and B by Inductive Poloidal Current Drive in the Reversed Field Pinch I S Sarff N E Lanier S C Prager and M R Stoneking University of Wisconsin Madison Wisconsin 53706 Received 8 October 1996 With the addition of inductive poloidal current drive for current pro le control in the Madison Symmetric Torus MST reversed eld pinch the magnetic uctuation amplitude halves leading to reduced energy and particle transport A four to vefold increase in the energy con nement time to TENS ms with both decreased Ohmic input power and increased stored thermal energy coincides with record low uctuation amplitude and record high electron temperature N600 eV for MST 1 2M5pBa2 increases from 6 to 8 Other improvements include reduced electrostatic edge turbulence and plasma impurity content PACS numbers 5255Hc 5225Fi 5225Gj 5235Py A growing understanding of the turbulence in reversed eld pinch RFP plasmas has inspired recent proposals to reduce magnetic uctuations and associated transport by the application of current density pro le control The ma jority of the energy loss in an RFP plasma occurs through transport in a stochastic magnetic eld generated by mag netic uctuations Most of these uctuations result from several poloidal mode number m 1 toroidal mode num ber n ZRa magnetohydrodynamic MHD tearing in stabilities l resonant in the core of the plasma and driven by the current density gradient Direct measurements of the magnetic uctuationinduced particle 2 and heat 3 losses in the Madison Symmetric Torus MST identify large transport associated with these uctuations In other RFP experiments 4 the estimated magnetic uctuation induced heat ux can account for the observed volume averaged heat ux The uxes measured in MST agree with expectations 5 for stochastic magnetic eld diffu sion except the electron heat loss in the outer region of the plasma occurs at the ion rate 6 Since tearing instability results from the current density gradient the proposals for current pro le control employ auxiliary electrostatic 7 1f 89 or neutral beam 10 current drive in the outer region of the plasma In a conventional RFP plasma the tear ing uctuations drive current in the outer region through a V X B motional emf or dynamo effect 11 establish ing a selfconsistent current pro le The auxiliary current drive aimed to reduce the current density gradient may be viewed as a replacement for dynamo current drive reduc ing the uctuations otherwise essential to sustain the RFP magnetic equilibrium In this Letter we describe the observation of reduced magnetic uctuations and transport resulting from induc tive poloidal current drive in an RFP With poloidal cur rent drive the magnetic uctuation amplitude reaches a record low value for MST The global energy con ne ment time increases four to vefold with both dramati cally decreased Ohmic input power and increased stored thermal energy A record high for MST electron tem perature 600 eV is achieved and the beta value in 62 00319007967816241000 S0031900796020467 creases from 6 to 8 In conventional RFP operation an inductive toroidal electric eld drives the plasma cur rent With the addition of a poloidal component the elec tric eld parallel to B is increased in the outer region of the plasma where the magnetic eld is mostly poloidally directed to facilitate current pro le attening for uctu ation suppression Unlike the proposed electrostatic rf or neutral beam current drive inductive poloidal current drive is inherently transient since it produces a chang ing toroidal ux in the plasma volume The observed improvements last as long as poloidal current drive is present We hereafter refer to this technique as pulsed poloidal current drive PPCD The PPCD experiment is performed in MST 12 a large reversed eld pinch with major radius R 15 m minor radius a 052 m toroidal plasma current 15 S 500 kA and beta 3 2LgpgtBa2 S 10 The wave forms of the toroidal and poloidal components of the elec tric eld E5 V 277R and E5 V527739a measured by loops at the plasma surface the toroidal current 15 the average toroidal magnetic eld 85 CID77112 and the toroidal eld at the surface B a during a PPCD ex periment are shown in Fig l The shaded region indi cates the time during which PPCD is applied In the rst PPCD experiment 13 the E5 drive was a single trian gular shaped pulse Figure 1 illustrates improved PPCD that provides a series of four smaller pulses Improved PPCD drives poloidal current more uniformly through out the PPCD phase and reduces the plasmawall inter action since the peak E5 amplitude of the four pulses is smaller Also PPCD lasts longer maintaining the bene cial effects observed in the rst experiment for a longer period of time Most importantly improved PPCD leads to a greater reduction in the magnetic uctuation ampli tude and an increase of the stored thermal energy en ergy con nement and beta The sharp negative spikes in E5 both before and after PPCD are associated with plasmagenerated toroidal ux in spontaneous sawtooth dynamo events Fig ld The negative E5 spikes rep resent the toroidal eld magnet circuit s inductive back 1996 The American Physical Society VOLUME 78 NUNEER 1 PHYSICAL REVIEW LETTERS 6 JANUARY 1997 sawteeth 1s emdmced thruuh the neauye E sp1ke at ne L 2 115 ms dunng FFcD and by the senes uf geme MM 1kes that 1rnrnea1ate1y fulluw FFcD smun uf the uetu t t ts1uwv ee 1n s lsawr uuth 1n s an rnany1rnpruveu1 FFcD 1 rnas Th1s 1s En pmbably related tu an abrupt hut rnuuest eurren pm l vtmt juSLmEnt assunateu ynth th srna11 sawtuuLh e1ash hut th eurrent e prumueu by an 1rnp1nyeu FFCD 3p ears 1 neeessary as we1 Fenuds ufvery luw uetuauun are nut M uhseryeu when duphcatmg the un1na1 s1n1e p111se E pmg n euetar1su theeunentpen auun1ntu at the p1asnna anuth efure the eurr prumemum eauun quot3m depmd ntheurne anauunufth app1 surfaeee1eetr1e 5 eld 1mpmveu1 FFcD su1teu1 fxu unu1n att ptst upu 1ethe nuu e1e e e1 n 1n a1ue tn the rnaneue e1u rnany antataes shuw F1G 1 Wave rnrrns urthe a surface tumuu e1eetr1e e1u med ms d quot3 F e 91339 391 b surface pa1a1ua1 e1eetr1e ne1u c tnrnuu puma Emmy Vultage 71111 m F1 2 39nm a uaun 1annu1rp ube andd ayerae anu surraee tara1u11nareue ne1u 1 eated ede 1 srna shuws a reuueuun 1n ue s s1rn11 at 1n F1 2a Nute at F1 2a 1s a prueesseu 1rns phtude and F1 20 1s a reaeuuntu dynamu ux ene1auun w1th1n Lheplasmavulr raw m rne 1 eetrustaue uetuauunshay urne and they emf 14 1n a u eunt1ast F CD15 a euntru11eu 1nerease 1n the pu1u1ua1 the edge u ST 1 and uther RFF expenrnents A eurrentthruugn appheauun ufpusmveEg ss1ble eunneeuun hetwee the reuueuu uf rnaneue A resu1tu 1rnpr dFFCD 1s the reuueuun quhe u auuns 1n th ure and e1eetanstaue etuauuns 1 etuauun arnp11tuuetu arecurdluwvalue The edge s an Extmng pm u le euntru1 a rnaneue u lt 21121 mutrmeanrsquzre rna1eue e uetuauun 27m 1 651 urren pr may have a rnure geneml cunsequence than the tareteu turu1u1a1 array uf p1e1rup eu11s un the p1asrna surface 1s shuwn 1n F1 2a nurrna11zeu1 tn the equlhbnum e1u1 stren Ba The aurn1nant waye1enths that cumpuse th1s uetuauun are m 15 10 rnuues a1thuuh the m 1 uetuanun dunn FFcD Befure FFcD 1s app11eu1 the uetuauun amphde e n de 1nthe et13washe1datthe be an sawmuth Er quot ue 1th pmved FFCD e uetuauun 1n surne d1schzrges 11ke that uf F1 2 1s reduced law the s uuth eye1e rn1n1rn a1ue u reeuru luw a1ue Inns3a 03 Dunn these per nuds uf yery 1u etuauun the unpruyernents 1n the plasma are rnust ur e The para11e1 e1eetr1e eld E s B E1 e ured at th asrna surface 1s u l1tude 1s srna11 Althuugh 1are sawteeth are suppressed y F new type uf srna11er saWLuuLh phmumenun 15 e The 1uha1 enery eun nennenturne 7E1ntreases up tu verfuld dunng FFCD w1th huth 1nereaseu stureu there rna1 enery and decreased ohrn1e 1nput puwa Pom The shutrzverzged 17 11ne dens1ty m eentra1 e1eetrun auun 2 71 and H ramauun fur 11m FFcD p1asrnas w1th F1G 2 The a snauu ruutrneansuuare magreue unuman b eu1e uaun Langnux pmbe w1tae and c narr11e1 1n FFCD 1n F1 2e the presenee uf these srna11er FFcD VOLUME 78 NUNEER 1 It 340 er are shuwn tn th 3 The shut averages ame duanutaes her an eunyentaunal RFF plasmas adtal pru le ts assumed e raf An lleehurd tnterferumeter tndteates the denstty pru le ts eentrally pealred but the tem atu nut measured Th te ar e t 5 unal RFF plasmas The sum the measured tetal tnput PHYSICAL REVIEW LETTERS a mum 1997 FFCD plasmas wtth htgher current I AAOkA Wth 7 N l x 10 ml althuugh wtth smaller 5 e 7 but Smllzr 7E 391 5 ms Althuugh the tnerease tn stured thermal energy ts substantial must uf the lntrease ln 7 results 39nm deereased trmspurt tndteatedby deereased Pam Stnee FFCD ts tmnstent aeeutate hmerdepmdmt equlhhnum mudeltng ts redutred tn denye Pam ItVt M r 2 f Blow2m 1 Tu evaluate the vulume lntegated stured magteue ms ergy tn Eq 1 the threeparaneter eyltndneal equlhhr num mudel 18 V x s al e ms r28 gtlt V11 2 g e rate uf ehmge uf st le measurements The paralleletueB eurrent tn Eq 2 ts men ed by shape and amplttude parameters er and A tng th Bred magteue mergy ustng equlhhnum medeltng desenbed tn the nert paragraph Eg plas n thts ensemble ehusen unly uthe same detstty have tnereased 75 m l tet NA ms and tnereased 5 rm a tet 7 7 eetmpared wtth eene ventmnal RFF plasmas at a time near the end uf FFCD 2 e 17 s The pelettdal beta 5 2ynltpgtBga1 a A smaller ensemble uf tnereases sum 6V tu E zs plasmas whteh exhtbtt the exeeptmnally luw mage I h tral betaparameter 5n zquDBi and a pressure pmr l The 512 MU red e assumed tet be py tr 1 e 1 and at 2 parameters ar ad t Ito W2 Etta and 52 medel aeeuraey the predt e 2 mirthMme ts eumpared wtth the tntem ed rm the 755ms and hem 5 9 Tablelsummae nzes tmpruyed FFCD eun nement eutnudent wtth the luwest magneue uetuanun tn 34m kAplasmas An MST reeurd T 515 eV was measured fur stmtlartmpruyed mm WAY thtttr lel u ten no that m z shatayeraged wave turns uf a the centxal chard ltne densty b central eleetran pressure tram Thamstm pawer d meanesquared unumm at The mbmken ltnes are tar b aken ltnes anal are tar emyenu RFP duetmee deny eletdal the plasm wt 1 Elem sured by a l estanun pelettd arr e asymmetxy faetur39 A ts related tn 1 zt2 elfuraetr lar 19 Th p ts enpt a 39 tdmta es equlhhnum medel tnduetaneequotL t whteh tneludes the tetrettdal eld eentrtbutaetntet e magnetae m 5 s t th Atullluslxatethat 22 uf e etae eter tn F tn the l t al eetmpetnent measured by A tbetweenz determtne dbmA mdzt pree gun agreemm t dteted by Eq 2 belsters een dmee tn the calculanun uf Pew The energy een nement tame quated abetye ts de ned as r Tt 4V 7 E a E Pahme 7 it Hum new may msr earnnement parameters thh and thhmt PPcD empared at the same extent and denstty near the end er the Pew phase v w Inpulpwwer Paw 13 MW AAMW Fluetuattm Emma u 2 l 5 cdn nement 5 ms ms VOLUME 78 NLWEER l 5 s New krpnaa 5 m l5 2 25 llmelmsl FIG 4 Nmmahzed mmctmces fax ensemble data uf Flg z Sepsrssrrpl a masalss equh adel prearmms bmxn m Eq 2 Fax hensr l umauan uf m urns ewluuan lhrs campmsm ls Shawn fax x Uh tempm rssaluhmemlzlrssearss Er 10 Althuugh lhermal energy lncreaslng dunng ppcp tends m ar e mere 7 er as mdmced hy reauehems m the tutal radlated pewer me Eludlng vlslble lmpunty lme ramahem and bremsslmhlung raarahem Hl her mar 5 her r lanun mereases u h Emmanun assunat th e Ea lmpmved ppcp dues he require exlx mng m s m the rsllz xpenmmL hemmz unufthe meharrr h h e m summary mauehve pelemal current dnve decreases p 7 Eating uemahms suppresses their assuclated sawreelh mereases the plasma pressure are mereases the errer cun nement tlme fuurr m ver nldlnthe MST RFF The parhele cun nEmEnt lame alsu mereases Fur the rst lame the uemanem zmplltude hel w e between sawmelh erashquot level and the cun nEmEnt am beta lmpmverrrerls m best dunng lhese perm the plasma are d5 uf luw magmas uemahem PHYSICAL REVIEW LETTERS a mum 1997 Althuugh ppcp dues he allmmate tearing uemaaehs sts a elear Eunelanun em between lmpmved cun nemmL pelemal current dnve at h reauehem Ifthe txznspurted energy luss seales e e as acted fur dlffuslu m a sm mappehe eld 5 the e uf the cun nEmEn lame ls EunslsLEnt s Expectanun The amhers are grazelhl ur the asslstznce quhe MST guup Thrs vm k r was supperled hy the U S DOE REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 74 NUMBER 3 MARCH 2003 Direct removal of edgelocalized pollutant emission in a nearinfrared bremsstrahlung measurement J K Anderson P L Andrew B E Chapman D Craig and D J Den Hartog Department of Physics University of Wisconsin 1150 University Avenue Madison Wisconsin 53 706 Presented on 10 July 2002 Visible and nearinfrared electroniion bremsstrahlung measurements in fusion research devices used to determine the effective ionic charge Ze are often plagued by pollutant emission from the cooledge region The primary sources of visible and nearinfrared nonbremsstrahlung continuum emission in the Madison Symmetric Torus arise from electronineutral interactions and the pollutant emission is hence directly proportional to the bulk neutral density Simultaneously monitoring the total emission at 1040 nm and the neutral contaminant via Da emission has enabled an extraction 1 1 of the electroniion and a 1013 cm 3 2003 American Institute ofPhysics I INTRODUCTION The effective ionic charge Zeta is a measure of the plasma contamination from impurities and has broadranging consequences as it determines in part the plasma resistivity ohmic heating ef ciency and total radiated power Continu ous electroniion eii bremsstrahlung emission arising from Coulomb collisions between electrons and ions can be used to measure the effective ionic charge as the emissivity at a given wavelength A is W 1 where T2 is the electron temperature in eV n2 is the elec tron density and if is the freeifree Gaunt factor The effec tive ionic charge is i 2 gffnzzeffe hckkTe e A 1516gtlt10 3 t WE AM 7 2nZ eff EsnsZs n2 2 where n is the density ZS is the charge state and the surn mation is over all ionic species present in the plasma Accurate deduction of Ze is possible with an absolutely calibrated measurement of the emissivity and electron den sity and temperature in a wavelength region where eii bremsstrahlung is the dominant source of light Identi cation of wavelength regions free of atomic lines and other radia tion is challenging but successful bremsstrahlung measure ments have been made on several fusion research devices in the visible range near 523 nml s and 536 nm6397 and in the nearinfrared NIR near 980 nm8 and 1040 nm9 11 These are 39 as molecular 39 7 r and generic recycling light cont ibute to the total emission and are dif cult to quantify and to remove Due to the n dependence of bremsstrahlung the sensitivity to pollutant 2Electronic mail jkandersfacstaffwiscedu bgtCurrent address EURATOMUKAEA Fusion Assoc Culharn Science Centre Abingdon Oxfordshire OX14 3EA United Kingdom 00346748200374321 0743920 00 2107 1 of Ze at p low electron density DOI 101063ll537440 light is magni ed in the typically lowdensity nENl 013 cm 3 Madison Symmetric Torus MST plasmas The expected emission is decreased signi cantly compared to that reported in Refs 2712 with densities in the midto upper 1013 cm 3 range In this work we have identi ed the primary pollutants in the visibletoNIR range and report signi cant emission from electronineutral ein bremsstrah lung in relatively hightemperature fusion research plasmas Emission from dissociation of the deuterium molecule pro hibits a visible bremsstrahlung measurement in MST but direct removal of the contaminant emission from neutrals has enabled a measurement of core NIR bremsstrahlung emis sion in hightemperature T2O N 800 eV MST plasmas The diagnostic used to simultaneously measure the NIR and Da emission is shown in Fig l where 17 poloidal view ing chords accommodate an array of detectors The three lens optical system detailed in the inset samples a cylindrical volume and appropriate lters select the desired wavelength of collection At the focal point of the optics is a silicon photodiode whose output is ampli ed and sampled at 100 kHz A common BK7 microscope slide is used as a partially re ecting surface RS10 directing a small fraction of the incident light onto a Da detector while transmitting the majority of the light onto an NIR detector Calibration of the detectors is performed with optics and a viewing geometry identical to that on the MST Eight viewing chords are out tted with the colinear detector pairs for a modestly resolved pro le diagnostic II POLLUTANT EMISSION The validity of an eii bremsstrahlung measurement hinges on minimization of pollutants Visible brem sstrahlung measurements on MST have proven unsuccessful as the measured continuum shown in Fig 2 overwhelms the bremsstrahlung expected for Ze 2 Emission levels in ap parently linefree regions near 480 or 523 nm are expli cable only by bremsstrahlung with unrealistically high Ze values of 20 to 60 implying that other sources of emission are dominant 2003 American Institute of Physics Downloaded 06 Jan 2005 to 12810422390 Redistribution subject to AIP license or copyright see httprsiaiporglrsilcopyrightjsp 2108 Rev Sci Instrum Vol 74 No 3 March 2003 Long pass colored glass lter BK7 slide Dx Filler f100mm FIG 1 Poloidal cross section of MST showing the viewing chords left and optics lter and detector setup used in simultaneous DEM and NIR emission measurements Emission from the dissociation of the deuterium mol ecule is likely the primary contaminant in visible bremsstrah lung measurements12 During dissociation the upper radiat ing electronic level of D2 is bound and the lower level is unbound on a repulsive molecular potential curve 14 The steep unbound potential curve15 spreads out the radiation over a vast range of wavelengths leading to the observed continuum ranging from below 200 nm to almost 600 nm This is consistent with the results published by Marinar et al where increased levels of broadband visible emission occur with puffs of diatomic molecules D2 or N2 with no corresponding jump in emission for a helium puff7 MST is fueled by introducing molecular deuterium at the plasma boundary puf ng andor wall recycling making the radia tion from its dissociation an unfortunate artifact and render ing impossible a visible bremsstrahlung measurement A study of the MST spectrum indicates that a region well suited for a bremsstrahlung continuum measurement lies in the NIR12 where emission from atomic and molecular deu terium lines recombination and molecular dissociation are all minimal Closely spaced emission lines of helium boron carbon nitrogen oxygen and aluminum barrage the ultra violet and visible spectrum but line radiation at 1040 nm is inconsequential Figure 3 shows the measured NIR spectrum in MST along with the bremsstrahlung expected for Z 652 solid line and the wavelength response of the NIR detectors dashed lines The continuum appears noisy as the measure ment is near the wavelength cutoff of the CCD detector used 100000 g I i g 2 C 5 10000 g E E 1000 8 Z C U 396 100 v I Z I I E E 010 g E Q a K 001 1 1 39 I 440 460 480 500 520 540 560 Wavelength nm FIG 2 The measured spectrum near 500 nm in MST and the bremsstrah lung expected for Zeff2 solid line at the bottom Anderson et al Spectral Radiance pWcm2 sr nm 39 i 980 1000 1 20 1040 1060 1080 1 100 Wavelength nm FIG 3 The measured spectrum near 1040 nm bremsstrahlung expected for Z 632 solid and the wavelength response function of the NIR ltered photodiode detectors dashed Deuterium and helium lines well above the background ob served at both longer 1078 1090 nm and shorter 1003 1009 nm wavelengths indicate that there are no signi cant lines in the collection range although there are allowed tran sitions from C1 N1 and OH low charge state MST impuri ties Other contributors to the continuum mainly due to neutral deuterium and nonfullystripped ions complicate but do not prohibit an NIR bremsstrahlung measurement An electron interacting with a neutral atom leads to con tinuous emission in a fashion similar to e i bremsstrahlung16 As the free electron impinges on the neu tral atom it penetrates the outer electronic cloud is subjected to a partially screened Coulomb force and is accelerated This proves to be a signi cant source of NIR light in MST and makes the measured emissivity inconsistent with reason able Z eff bremsstrahlung The e n bremsstrahlung emissivity is calculated follow ing the developments of Park17 and of Dalgamo and Lane18 The spectral emission coef cient in Wcm3srnm is A i he I davE dv E dE Eein imnone hcAUTKJK EneHOfeinOleaTe where no is the neutral density v is the initial velocity of the electron integration is over the electron energy distribution fE starting at the energy of the photon of interest and dUVEdv is the neutral bremsstrahlung emission cross sec tion It is possible to cast the e n bremsstrahlung emissivity at a given wavelength Eq 3 as the product of memo and a function fenne Te where f9 carries all the relevant in formation of the radiative process Similarly the Da line in tensity is described by he YDQ mnen0ltavgtexcne TeEnen0fDane Te where av exc is the electron impact excitation reaction rate19 It is thus clear that at a given electron density and temperature the Da emission is proportional to e n brems strahlung or Ge ayDa where the proportionality constant is simply feinOIe 3T8 CEOe Te fDaOle 9T9 5 Downloaded 06 Jan 2005 to 12810422390 Redistribution subject to AIP license or copyright see httprsiaiporgrsicopyrightjsp Rev Sci Instrum Vol 74 No 3 March 2003 P 9 co 3 Hm rgt l O 39 o 8MB uWcm2 sr nm 0 N 0 o 500 1000 1500 Da Emission uWcm2 sr FIG 4 Emission at 1040 nm vs DEM emission separated by electron density The data represented by diamonds are for low density average 77 l X 1013 cm 3 while the triangles represent higher density discharges aver age rTe2 X 1013 cm 3 As expected the yintercept is higher for the higher density discharges with a similar slope in each set of data As a is a function of electron density and temperature it will not be constant over the line of sight in a chordintegrated measurement The amount of light collected however is weighted by the neutral density pro le which is measured to be poloidally asymmetric and extremely edgelocalized in the MST Peak values of no are on the order of 1013 cm 3 and the pro le drops by more than an order of magnitude over the rst few centimeters inside the plasma boundary20 Approximating the neutral density as a 6 1nction at the edge n0pN05pa clearly illustrates that the proportion ality of e n bremsstrahlung to Da emission is preserved in the chordintegrated measurement The measured Da emis sion is the line integral of Eq 4 MDQN0neafDaaa 6 the integrated e n bremsstrahlung is similarly found from Eq 3 MeinN0 neafeinaa and the two quantities are again proportional As the continuous NIR emission is the sum of e i and e n bremsstrahlung 61040 594 ayDa a linear relation ship between the measured NIR emission and the measured Da emission is predicted L L M1040 f0 EeiidlC7f0 7Dad132 8 where B and M Dd are the lineintegrated e i bremsstrahlung and Da emission respectively and J aa is the chord averaged proportionality factor The 6 function approxima tion of the neutral density and the assumption of two primary components of NIR emission are consistent with the data Figure 4 shows the expected linear behavior between NIR and Da emission the slope is a and the y intercept is the measured e i bremsstrahlung The data represent line integrated measurements of the emission during a narrow time window with low magnetohydrodynamic MHD ac tivity in a discharge Experiments repeated in helium dis charges con rm that the NIR pollution is proportional to neutral density monitored by a HeI line at 587 nm as op posed to deuterium lines or molecular emission Quantitative prediction of the e n bremsstrahlung emis sivity is possible with measured electron and neutral density Direct removal of edgelocalized pollutant emission 2109 9F 50 81020 uWcm2 sr nm a n Du Emission 04 x I 004 E 0 C A a I g 03 0 E 003 a e N 3 E Q 3 02 O o g 002 3 090039 E g 0 g m 01 f g 001 m a3 00 000 5 1000 2000 3000 0010 0014 0018 0022 0026 Du Emission MWcm2 sr ime 3 FIG 5 a NIR and b DEM signals vs time c NIR vs DEM emission is plotted for time points between t0010 and 0026 s and d the time resolved bremsstrahlung signal with uncertainty upper and lower bounds in dotted lines pro les and tabulated cross sections for deuterium The pre dicted slope assuming e n bremsstrahlung as the only con taminant is about 2gtlt10 5 nm l while measurements are higher but show orderofmagnitude agreement The cause of the higher slope is very likely other sources of emission that are proportional to neutral density continuous emission from freebound interactions leading to negative hydrogen ions21 and deuterium deuteron charge exchange22 are possible in the lowtemperature highneutraldensity region of the plasma The important point is that the emission arises from interactions with neutral particles and is therefore edge 10 calized and proportional to Da emission NIR BREMSSTRAHLUNG MEASUREMENT The e i bremsstrahlung signal is determined by tting a line to the NIR versus Da emission graph and extrapolating to zero neutral density to nd the y intercept Figure 5 shows typical signals from the NIR and Da detectors every varia tion in the Da signal appears in the NIR signal as expected Also shown is a slower 6 kHz plot of the NIR versus Da emission between t 0010 and 0026 s and the deduced e i bremsstrahlung signal Dynamically tting a line to nine data points determines the slope and intercept as functions of time During periods of slowly varying electron density and Z eff 15 ms averaging is inherent in this analysis the inter cept is the e i bremsstrahlung emissivity This signal is typi cally noisy with uncertainty primarily due to error in ex trapolating to zero on the xaxis but is improved by averaging data from many similar discharges The e i bremsstrahlung 002 uWcmZsrnm is only a small fraction of the measured emission 005 02 uWcmZsrnm The signaltopollution ratio thus ranges from about 10 to 40 In enhancedcon nement MST plasmas the neutral particle density and Da emission are greatly reduced the signaltopollution ratio is typically greater than 50 and the extrapolation uncertainty is de Downloaded 06 Jan 2005 to 12810422390 Redistribution subject to AIP license or copyright see httprsiaiporgrsicopyrightjsp 2110 Rev Sci Instrum Vol 74 No 3 March 2003 creased Removal of the neutral contribution to the continu ous emission as described above combines all other un checked contaminants into the eii bremsstrahlung measurement Enhanced bremsstrahlung from neutral and nonfullystripped impurity atoms23 are not separately mea sured but can contribute signi cantly to the emission Fur thermore very dim lines below the resolution of the spec trometer data in Fig 3 from the lowchargestate impurities likely contribute a small amount of light Fortunately these sources of light are limited to the extreme edge region where neutral and singly ionized impurities may exist and are small compared to eii bremsstrahlung in the core of the hot plasma Since the nonneutral contaminant is small com pared to core eii bremsstrahlung it is possible to invert the data to determine the emissivity pro le It is impossible to accurately invert these data without correcting for the ein radiation as the pollutant magnitude is greater often much greater than the core bremsstrahlung and the proportional ity to neutral density makes the emission extremely edge peaked and poloidally asymmetric Wit the measured eii bremsstrahlung and pro les of electron temperature and density Ze is deduced The result in a certain set of MST plasmas T20N800 eV n20 N l X 1013 cm 3 produced without prior boronization of the aluminum vacuum vessel is a core Ze of 46r 07 This result is corroborated by FokkeriPlanck modeling in which the measured xray ux 107100 keV matches the predic tion based on the measured Ze and electron transport properties24 In standardcon nement plasmas with signi cantly lower electron temperature removal of the pollutant emission from neutrals does not lead to a welldetermined Zeff as emission from lowchargestate impurities primarily CI obscures the measurement of eii bremsstrahlung Cur rent work includes investigation of longer wavelengths near 1170 or 1600 nm where carbon lines are completely absent The silicon photodiodes are insensitive to these wavelengths and are replaced with TnGaAs photodiodes having excellent sensitivity at these wavelengths These measurements will proceed following an infrared spectral survey which should identify promising linefree regions IV SUMMARY In summary the consideration of neutral bremsstrahlung and molecular dissociation may shed some light on the dif culties that abound in absolute bremsstrahlung measure ments The dissociating deuterium molecule radiates in the wavelength range of standard visible bremsstrahlung mea surements Emission from electronineutral bremsstrahlung and likely other neutral processes is signi cant in the NTR at low electron density Removal of the neutral emission has enabled an NTR measurement of electroniion bremsstrahlung at electron densities as low as nZNl gtlt10 cm 3 in the MST The line integrated Da emission is proportional to the pollutant emis Anderson et al sion and a fraction of this signal is removed from the total NTR emission from the same sample volume to extract the eii bremsstrahlung Accurate extraction of Ze is limited to the high temperature range of MST as low temperatures al low signi cant populations of lowchargestate impurities that enhance the continuous emission and increase the like lihood of impurity line pollution In MST uncorrected neu tral contamination to eii bremsstrahlung typically leads to an apparent enhancement of Z eff by a factor of 2 to 4 but can brie y be as high as 10 with the high neutral density ob served at large amplitude MHD events In other devices with higher electron density and lower neutral density the en hancement of the deduced Ze due to pollution from neutrals should be smaller but perhaps not negligible ACKNOWLEDGMENTS The authors are indebted to a large group of collabora tors on this project particularly D Whyte and J Lawler for useful discussions of bremsstrahlung and atomic physics Thanks also to T Biewer for leading a fullydiagnosed ex perimental campaign39 and S Castillo and S Gerhardt for development of the diagnostic This work is supported by the US Department of Energy and the Oak Ridge Institute for Science and Education Fusion Energy Science Fellowship Program lK Kadota M Otsuka and J Fujita Nucl Fusion 20 209 1980 ZA T Ramsey and S L Tumer Rev Sci Instrum 58 1211 1987 3M T Fall PhD thesis L Universite Paris xi Orsay 1991 4H Weisen D Pasini A Weller and A W Edwards Rev Sci Instrum 62 1531 1991 5N J Peacock K D Lawson R Bamsley andH Chen Rev Sci Instrum 71 317 1999 6D G Whyte et al Nucl Fusion 38 387 1999 7E S Marrnar R L Boivin R S Granetz J W Hughes and B Lips chultz Rev Sci Instrum 72 940 2001 8B Grek J Bartolick and D Johnson Rev Sci Instrum 63 4627 1992 9H Rohr and K H Steuer Rev Sci Instrum 59 1875 1988 1 J J Rommers R Behn B P Duval S Franke and Z A Pietrzyk Proceedings of the Imemafional Symposium on LaserAided Plasma Di agnostics Doorwerth The Netherlands 1997 pp 2357240 lL Carraro S Costa M E Puiatti F Sattin P Scarin and M Valisa Plasma Phys Controlled Fusion 42 731 2000 12J K Anderson PhD thesis University of WisconsinMadison 2001 13J Lawler private communication ME F McCormack S T Pratt P M Dehmer and J L Dehmer J Chem Phys 98 8370 1993 15T E Sharp Atomic Data 2 119 1971 16G Beke Radiarion Processes in Plasmas Wiley New York 1966 17J Park I Henins H W Herrmann and G S Selwyn Phys Plasmas 7 3141 2000 8A Dalgamo and N F Lane Astrophys J 145 623 1966 19L C Johnson and E Hinnov J Quant Spectrosc Radiat Transf 13 333 1973 ZEIN E Lanier PhD thesis University of WisconsinMadison 1999 21W G Graham Plasma Sources Sci Technol 4 281 1995 22A M Ermolaev A A Mihajlov L M Ignjatovic and M S Dimitrijevic J Phys D 28 1047 1995 23V D Kirillov B A 39Ihsbnikov and S A Trushin Sov J Plasma Phys 1 117 l Z4R O Connell private communication Downloaded 06 Jan 2005 to 12810422390 Redistribution subject to AIP license or copyright see httprsiaiporglrsilcopyrightjsp REVIEW OF SCIENTTFIC INSTRUMENTS VOLUME 74 NUMBER 3 MARCH 2003 Comparison of ion temperature diagnostics on the Madison symmetric torus reversedfield pinch J C Reardonf D Craig D J Den Hartog G Fiksel and S C Prager Department of Physics University of WisconsiniMadison Madison Wisconsin 53 706 Presented on 9 July 2002 There have been three ion temperature diagnostics operating on the Madison symmetric torus MST for the past two years i Chargeexchange recombination spectroscopy CHERS which measures the temperature of fully stripped impurity C6 ions and has a spatial resolution of i1 cm and a time resolution of 3 ms ii Rutherford scattering RS which measures the temperature of the bulk majority D ions and has a spatial resolution of roughly i 7 cm and a time resolution of 30 Ms and iii the ion dynamics spectrometer IDS which measures a chordal average of the temperature of partially stripped impurity C4 ions with a time resolution of 10 Ms The rst two diagnostics use neutral beams while the third is passive The classical ion energy equilibration time T ltl ms between all ion species so we naively expect that all ion temperature measurements should agree in steady state Here we present simultaneous measurements of CHERS and RS pro les in highcurrent burst free pulsed poloidal current drive PPCD discharges CHERS and RS pro les in standard highcurrent discharges and IDS and RS pro les in standard lowcurrent discharges Measurements in standard discharges are made a long time before and after magnetic reconnection events during which there is believed to be a large nonclassical input of energy to the ions RS and CHERS measurements consistently agree IDS measurements are consistently less than RS measurements due to the effect of the C4 emission pro le on the IDS measurements 2003 American Institute afPhysics DOI 10106311538345 I INTRODUCTION Typical Madison symmetric torus MST1 plasma pa rameters are magnetic eld 01 Tlt 3 lt05 T electron den sity n2lt15gtlt1019 m 3 plasma current Ip 500 kA and plasma radius r052 m The majority species is deuterium with carbon aluminum nitrogen oxygen and boron present as impurities The plasma is characterized by large magnetic and electrostatic uctuations as is typical for reversed eld pinches The ion temperature has in the past been measured by passive charge exchange2 and found to be hotter than can be accounted for by electroniion collisions Quantifying the extra input power necessary to keep the ions hot requires accurate measurements of the bulk majority ion temperature which can be made by Rutherford scattering RS3 Since RS has been used only occasionally to diagnose magnetically con ned plasmas on the tokamaks T34 JT 605 and TEXTOR6 and the mirror GDT7 we report a comparison between RS and the two other more wellestablished ion temperature diagnostics currently on MST In addition to RS8 MST features charge exchange recombination spectros copy CHERS9 and passive Doppler spectroscopy the ion dynamics spectrometer IDS1 Each of these measurement techniques yields an ion temperature measurement Are these ion temperature measurements the same Should they be the same 2Electronic mail jcreardonwiscedu 0034674820037431 892420 00 1892 II APPARATUS The RS temperature measurement results from the width of the energy spectrum of He beam atoms that have under gone smallangle Coulomb scattering from plasma ions On MST this energy spectrum is measured by a neutral particle analyzer RS has spatial resolution typically 7 cm formed by the intersection of the analyzer sightline and the He beam Fig l and time resolution of 30 MS within the 3 ms beam duration A temperature pro le is acquired by moving the analyzer between shots CHERS relies on CVI emission at 3434 nm from C plasma ions that have undergone charge exchange with H beam atoms The CHERS signalto background ratio is largest in discharges such as pulsed po loidal current drive PPCD discharges with high T and low neutral densities which allow a substantial population of fully stripped carbon to build up across the plasma pro le CHERS has excellent spatial resolution form ed by the inter section of the neutral beam and a ber viewing chord of i1 cm Fig 2 but a time resolution of only 3 ms since with the current spectrometer the low signaltobackground ratio can be overcome only by averaging many time points A temperature pro le is acquired by moving the viewing ber between shots The IDS measures CV line emission at 2271 nm It produces two independent temperature measurements from two viewing chords throughout a discharge It has ex cellent time resolution of 10 Ms but poor spatial resolution since emission along each viewing chord Fig 2 is inte grated We will assume for now that the IDS measurement is radially localized close to the impact parameter of the IDS viewing chord although this will later be shown to be un 2003 American Institute of Physics Downloaded 04 Feb 2005 to 12810422390 Redistribution subject to AIP license or copyright see httprsiaip0rgrsicopyrightjsp Rev Sci Instrum Vol 74 No 3 March 2003 Analyzer Sightline 2O KeV He Beam FIG 1 Poloidal cross section of the MST vacuum vessel showing the path of the RS beam and the analyzer sightline for a typical analyzer position The cross section of the RS measurement volume is shown in black likely The IDS is most useful as a pro le diagnostic in lowcurrent discharges for which Telt200 eV and there is signi cant CV emission amplitude from the plasma core ralt0511 Plasmas hot enough to produce good CHERS measurements are likely to have very hollow CV emission pro les and therefore produce edgelocalized IDS measure ments the two diagnostics cannot actually be used on the same discharge since they share the same spectrometer and ber bundles Signals from all three diagnostics show dramatic changes at the time of magnetic reconnection events MREs which occur in standard MST discharges The CHERS signal cannot be extracted from the plasma back ground signal which increases by an order of magnitude at a MRE CHERS data at this time are lost The RS signal also I Viewing Chords I 39 I IDSampCHERS I l 1091 lm 30 KeV H Beam CHERS FIG 2 Poloidal cross section of MST vacuum vessel showing the eleven viewing chords used by both CHERS and IDS and the path of the CHERS beam The cross section of the CHERS measurement volume for chord 9 is shown in black measurement volumes for other chords are similar Plasma diagnostics 1893 CHERSRS comporison PPCD 400 1 300 I I J 9 3 200 39 00 39ACHERS 39 ORS O 00 02 04 06 08 10 90 FIG 3 Data from CHERS and RS taken during highcurrent PPCD MST discharge pa values calculated by MSTFIT must compete with increased signal due to highenergy plasma ions expelled at a MRE and with increased noise due to plasma electrostatic uctuations and may be unreliable during the 100 us surrounding a MRE The IDS temperature is apparently trustworthy typically showing a rapid increase followed by an almost equally rapid decrease but the emis sion location may move radially Since previous work2 has identi ed from passive charge exchange measurements the existence of a large nonclassical heat input into the ions in MST at a MRE the true ion temperature during a MRE is unknown and may undergo large changes In this article data taken within i 100 us of a MRE from all three diagnos tics have been excluded from the analysis Iquot DATA CHERS and RS pro les taken simultaneously during an ensemble of 400 kA PPCD discharges are shown in Fig 3 Discharges were selected for the ensemble based on the sup pression of uctuations the burstfree PPCD phase during and also for at least 1 ms before the time the beams were ring Each data point represents an average of 15 dis charges pa values for the data points are based on MST equilibria computed by MSTFIT12 The pro les are in excel lent agreement CHERS and RS pro les taken simulta neously during an ensemble of 400 kA standard MST dis charges are shown in Fig 4 Ensemble selection parameters were reversal parameter f 023 and plasma density 09gtlt1013 m 3ltn0lt12gtlt1013 111 Each data point represents 15 discharges The CHERS and RS beams were red during current at top Standard discharges produce higher background signals for both RS and CHERS than do PPCD discharges so they present a greater challenge for the diagnostics Again the two pro les are similar IDS and RS pro les taken during an ensemble of stan dard lowcurrent 190 kA MST discharges are shown in Fig 5 Ensemble parameters were f 7015 and 09 gtlt1013 mT3ltne0lt 12x 1013 m 3 Each data point repre sents the average over ten or more discharges The IDS data points were computed by averaging the IDS measurements during the duration of the RS beam and as before tempera ture measurements made by both diagnostics within 100 us of a MRE were ignored The pa value assigned to each IDS Downloaded 04 Feb 2005 to 12810422390 Redistribution subject to AIP license or copyright see httprsiaiporgrsicopyrightjsp 1894 Rev Sci Instrum Vol 74 No 3 March 2003 CHERSRS comporison Stondord 400 39 3001 I E I gt 3 200 I I 00 39ACHERS ORS O 00 02 04 06 08 10 90 FIG 4 Data from CHERS and RS taken during standard highcurrent MST discharge pa values calculated by MSTFIT data point is the impact parameter of the IDS viewing chord The IDS pro le is consistently 20 30 lower than the RS pro le This apparent discrepancy can be explained by pro le effects as described below IV THEORETICAL EXPECTATIONS The classical ion ion equilibration time between species j and k is13 k 3107328 gmjmk 2 eq nkaZJZe4 lIlAjk 32 T T J quot 1 mj mk where T is temperature m is mass Z is charge and n is density the subscript denotes species and using Ad i 127783211 ij Jami2 Jk 790 ZJanlZe3 mJelemk 477 3 9 7119M if either jke 2 for the Coulomb logarithm This is the time scale for the change of temperature of species j due to collisions with IDSRS comparison 100 I 80 T eV 2039IIDS Doto 39 ORS Doto oo 02 04 06 08 10 p0 FIG 5 Data from IDS and RS taken during standard lowcurrent MST discharge and curves modeling pro le effects on IDS measurements Solid curve assumed true T1 pro le consistent with RS measurement dot dash curve assumed CiV emission pro le arbitrary units consistent with measurements shown in Ref 11 dashed curve derived IDS pro le pa values calculated by MSTFIT for IDS data the pa shown is the viewing chord impact parameter Reardon et al species k Time scales involving energy transfer between electrons and ions are generally much slower than those in volving energy transfer between different species of ions The most poorly known quantities in the above formulas are the impurity densities However these are not needed to cal culate Timp D On the basis of the data we may assume C and C temperatures equal to the D temperature for the purpose of calculating equilibration times An upper bound on Timp D may then be calculated if a lower bound on n D can be given This lower bound may be calculated from Z eff It is plausible that for standard lowcurrent MST discharges Z eff 2 for all radii and that for 400 kA PPCD Z e 5 in the core with the dominant impurity being All 12 In the former case the lowestZ candidate impurity is C and the lower bound on n D which comes by assuming the impuri ties are entirely C is n D ne23 while in the latter case n Dne35 For the IDSRS comparison plasma n 1019m3 Te200 eV and TD 100 eV which leads to gtD50 us 3 For the CHERSRS comparison in PPCD ne1019m3 Te 850 eV TD300 eV and ip 100 us 4 for the CHERSRS comparison in standard discharges n Dne cannot be estimated from Z eff which has not been measured we will have to assume it is not less than in the other two types of discharge Then in the absence of other heat sources and sinks we should expect that for the dis charges studied herein both the C and C temperatures should approach the D temperature in much less than 1 ms V DISCUSSION The CHERS and RS temperature pro les shown above are quite similar as they should be if C equilibrates to the D as fast as Eq 4 predicts On the other hand the IDS temperatures appear to be substantially lower than the RS temperatures even though Eq 3 predicts that C should equilibrate even faster in these colder lowcurrent discharges than C does in the hotter discharges The passive charge exchange measurements presented in Ref 2 which were made in standard 360 kA hydrogen discharges were also generally higher than simultaneous IDS measurements even at early times when T e0lt200 eV The simplest explana tion is that the IDS is not a core diagnostic and that all chords are affected by emission from outside pa 05 even for cold lowcurrent plasmas Assuming that the tempera tures of D and C are equal and that the RS measurement of the D temperature is correct we may deduce the apparent temperature measured by the IDS if the CV emission pro le is known The CV emission pro le in lowcurrent MST dis charges away from MREs has been obtained from Abel inversion of lineintegrated CV measurements along ve dif ferent chords11 In Fig 5 this CV emission pro le is shown as a dot dash line using arbitrary units Assuming a true temperature pro le solid line for D and C that is consis tent with the RS measurements we deduce that the tempera ture measurement of the IDS should fall along the dashed Downloaded 04 Feb 2005 to 12810422390 Redistribution subject to AIP license or copyright see httprsiaiporgrsicopyrightjsp Rev Sci Instrum Vol 74 No 3 March 2003 line39 and indeed the IDS data points do fall close to this line Therefore we conclude that even in lowtemperature plas mas the IDS measurement is not core localized It is of interest to determine whether the true temperature can be accurately backed out from the IDS measurements by the inverse of the above procedure using the CV emission pro le VI CONCLUSION AND FUTURE WORK D C and C temperatures have been measured on MST using the RS IDS and CHERS diagnostics respec tively RS measurements consistently agreed wi RS measurements during highcurrent discharges D and C temperatures were found to be similar RS measurements were consistently higher than IDS measurements during lowcurrent discharges D temperatures were measured to be 20730 higher than C4 temperatures across the pro le The equilibration times calculated from classical charged particle collisions lead to the expectation that all species should have the same temperature on time scales long com pared to 100 Ms Based on this calculation we ascribe the difference between IDS and RS temperatures to pro le ef fects On short time scales such as within 100 us of a MRE Plasma diagnostics 1895 the different ion species are not in thermal equilibrium with each other and measurements of their temperatures should not be expected to agree The ultimate goal of the current research is to quantify the ion power balance that is to nd out whether the measured ion temperatures can be sustained by classical collisional heat transfer from the electrons and if not how much additional input power is needed 1R N Dexter D W Kerst T W Lovell S C Prager and J C Sprott Fusion Technol 19 131 1991 ZE Scime M Cekic D J Den Hartog S Hokin D J Holly and C Watts Phys Fluids B 4 4062 1992 3 G Abrarnov V V Afrosimov I P Gladkovskii A I Kislyakov and V I Perel Sov Phys Tech Phys 16 1520 1972 4E V Aleksandrov et 21 JETP Lett 29 1 1979 5K Tobita et 11 Nucl Fusion 28 1719 1988 6A A E van Blokland 2121 Rev Sci Instrum 63 3359 1992 7A V Anikeev et 211 Phys Plasmas 4 347 1997 8J C Reardon 2121 Rev Sci Instrum 3972 598 2001 9D Craig D J Den Hartog G Fiksel V I Davydenko and A A Ivanov Rev Sci Instrum 3972 1008 2001 1 D J Den Hartog and R J Fonck Rev Sci Instrum 65 3238 1994 H J Chapman PhD thesis University of Wisconsin Madison 1998 12J Anderson PhD thesis University of Wisconsin Madison 2001 13A Anders A Formulary for Plasma Phyn39cx Akadernie Berlin 1990 p 54 Downloaded 04 Feb 2005 to 12810422390 Redistribution subject to AIP license or copyright see httprsiaip0rgrsicopyrightjsp
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