Resistive MHO tearing modes can develop magnetic islands near the
rational magnetic surfaces, where q=m/ n

Kluber, O.

Manso, M.E.

Matias, José

Mendonça, J.

Serra, F.

Silva, A.

Soldner, F. X.

Zohm, H.

Soldner, F.X.

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836 Here, rp =kiln pldrl-1 is the pressure seale length and s = (rlq) ()q I iJr is the dimensionless shear. For the Ohmic case, a factor close to(Pcq2)-~ was deduced from a model based on drift-tearing instabilities and magnetic reconnection 1101. These modes are driven by the current density gradient. It is likely that the a increase with heating power and beta in the intermediate region reflects the growing contribution of pressure-driven modes. e.g. resistive ballooning modes. to magnetic turbulence induced r:ranspon. lt is concluded that the empirical Xe sealings in the OH, Land H regimes are incompatible with purely electrostatic drift wave turbulence. Inclusion of electromagnetic effects yields the P~1 scaling but fails to explain the factor <Peq2)<X which is indicative of resistive ballooning or interchange instabilities. The different sealings in the OB and L, H regimes result from changes in this finite pressure contribution and thus in magnetic turbulence induced transpon. References I 11 Seeker, G., Nucl. Fusion~ (1984) 1364. 121 Seeker, G., Nucl. Fusion 2.8. (1988) 1458. 131 Wagner, F., Gruber, 0., Bnrtiromo, R., Bcckcr, G., Dosch, H.S., et al., iu Controlled Fusion and Plasma Physics 1985 (Proc. 12th Europ. Conf. Budapest, 1985) Part l, European Physical Society (1985) 335. 141 Goldston, R.J., Plasma Phys. Control!. Fusion~ (1984) 87. I 51 Waltz, R.E .• Phys. Fluids 2.8. (1985) 577. 161 Mo1vig, K., Hirshman, S.P., Whitson, J.C .• Phys. Rev. Len.11 (1979) 582. /71 Parail, V. V., Pogutse, O.P., in Plasma Physics and Controlled Nuclear Fusion Research 1980 (Proc. 8th lnt. Conf. Brussels, 1980), Vol. 1, 1AEA, Vienna 1981,67. 18! Ohkawa, T., Pbys. Leu. fiLA (1978) 35. 19/ Drake. J.F., Gladd, N.T., Liu, C.S., Chang, C.L., Phys. Rev. Lett. 44 (1980) 944. 1101 Coppi, B., Mazzucato, E .• Phys. Len. 21A (1979) 337. 1111 Carreras, B.A., Diamond, P.ll. , Murakami, M., Dunlap, J.L., Bell, J.D., et al .. Phys. Rev. Len. ~ (1983) 503. Fr 101 837 CHANGES IN THE DENSITY PROFILE DUE TO THE m=2 TEARING MODE IN ASDEX M. £. Manso, A. S1l va, F. Serra, J. Mat1as, J. Mendon~a rnstituto Super1or TecDico, Llsboa, Portugal H. ZOhm, o. KlUber, F. x. - So ldner Max-Planck-Instltut fur Plasmaphys1k, Garch1nq, F.R.G. 1 - Introduction Res1st1ve MHO tearing modes can develop magnetlc iSlands near the rat1onal magnetic surfaces, where q=m/ n. In some Situations, depending on the shape of the current profile and on the radial position of the q=2 surface, the <m=2,n=l) rotating structure of growing iSlands can come to rest C "mode locking" l ; ln ASDEX, the so-called locked modes can be found for several plasma scenar 10s , and generally they are precursor to dlSruptions / 1/ .The magnetic structure of rotating tearing modes in a tokamak plasma iS quite well known from the measurements of the modulations of the polo1dal magnet1c field. We have studied the effects on plasma density of large ampl1tude m=2, n=l modes 1n ASDEX, using broadband m1crowave reflectometry. 2 - Dens1ty profile deformations Reflectometrlc measurements were performed w1th the ASDEX 0-mode reflectometrlc system, descrlbed 10 an acompany1ng paper / 2/ . Signals were obtalned Wlth two reflectometers coverlng respectlvely the ranges 18-26. 5 and 26.5-40 GHz ) , during Lower Hybr1d Current Dr1ve ( LHCO ) diScharges. Results are shown concerning the shot 29285 where a l ocked mode occured between 1577 and 1585 ms, referlng to: ' a t magnetic 1sland rotat10n at t • l 56S ms, sweep tlme t=2 ms ) , and ( b) mode locktng at t • l580 ms. Before locking, the signals show both amplitude and phase modulations / 2/ Wlth the per1odtc1ty r of the tear1ng mode measured wtth the Mirnov co1ls, T-1 = fr~l.4 KRz. The spectrum exht bitS several high amplitude peaks, related to the observed modulations ( rlg. la ) , showing the strong effect of the magnetic islands on the plasma prOfile. The phase shtft, .la¥ .l F, ot the plasma reflected m1crowaves C 18- 40 GHz l is presented in Flg.2a. It exhibitS two disturbed reg1ons: the beat frequency f ( t oe .ll!l/ .l F) decreases followed by an 1ncrease, corresponding respectively to outward and inward movements of the plasma layers, occur1ng dur1ng the 2ms (0 . 5 KHz) measurtng ttme. The corresponding deformations can be seen on the evaluated profile (Fiq .3a ) . During mode locking, the signal at 26.5-40 GHz presents an abrupt increase in the beat frequency for microwaves with F>F'~31.2 GHz. The spectra exhibit t wo s1ngle peaks respectively at f 1 ~ 22 KHz and r1. ' 40 KHz ( Fig.lb); the peak at f1. can clearly be seen by performing a partial spectral analysis from F' to 40 GHz. The non existence of secondary peaks, 838 (as observed in the frequency spectra before the lockUlq l, confums that these ace due to densLty perturbatLOns Lnduced by the rotat1n9 maqnet1.c J.sland m=2. The phase shLft .lll>/ J.F (18-40 GHz) presents two abrupt JUmps, I see FJ.g. 2b), revealing the dJ.splacement inwards of the reflectJ.ng layers Wlth those denSJ.tLes. The density profile (Fig . 3bJ, presents two densLty plateaus, (coccespondLng to the phase shift )umpsJ respectively foe: ( 11 r = 29-32.5 cm, and !21 r=39-IO . S cm . A (* f1.<L._l f 1• 22kHz ftkHtl 3 - Numer1.cal modelling (0) lbi f'•' >at ~Hr The denslty outSLde ( LnSLde) the plateaus increases (decreases ) and the denslty grad.Lent decreases l J.ncrease) as compared to the pcofLle measured before the magnetic 1.slands develop. So .lt seems that the profJ.le undergo a perLod.Lc deformatLon tr·t 1 that 1s not lJ.mited to the regions where the plateaus occur . The reflectometric antennae are located in the mJ.d-plane, such that for the magnetic 1sland w1.th m=2 the toro1dal angular dtstance to "0" po1.nt J.S -1so: so the first measured plateau should roughly correspond to only 30\ of the J.Sland WLdth; thl.S yields an island wJ.dth of about 10 cm, centered at r - 30-31 cm, wh.l.ch J.S 1n agreement Wlth the results der1ved from the maqnet1c data for the m=2 mode. The second plateau must l1kely be located near another rat1onal surface and lt w1.1l be the subJect of further i.nvest1.gat1.on. In order to have some 1ns1.ght about the characterLStJ.cS of the perturbation origl.natlng the deformations of the profile during the island rotation a numerical study was performedi by considering a profile of parabolic shape with neo=2.5"10 13 cm' The dP.nSJ.ty effects due to the tear1ng mode wJ.th m=2 Cn=l> were SJ.mulated by assum1ng a dens1.ty plateau in ~ ... .. ... ... 4 •· • 839 VP·)F (ll IIH1:Ht) JO-l '" ~ r J '11 { >O -l I Jll~~~ I 10 ... , .. ""'··~ (. r:.t\ \ 0 ,.\1t*l't\f '"' tradlf'tHt) J0 ~1 ~ · r~w~l { ... ~ 0 .rw ' .. , .\ ~\ 02 •• ' .. •• .. oA 0 , 40 .. ,. EJ..q..___l "et•o•3.,.,-J1 r(cm) Fl•t:J.. the profile (q=2, near r- 30 cm> whose width can vary as the width of a rotatlng maqnet1.c l.Sland observed in a fixed posltion ( 0 •0, in the mJ.d-plane), J..e. w• (( l + cos<mo +-"'rotl + (,1 ))/2) When the mode is locked, !,01 ~o, "=lso: and w(l580ms)=l0 cm as concluded before; for frot•l.4 kHz, we cons1.der w{l565msl=8 cm, that takes into account the grow1ng of the 1sland before locking as evaluated from magnettc measurements. Flg.4 shows the numer1.cally estl.mated m1crowave shlfts for: (a) frot •1.4 KHz, (bl f,01 =0 KHz, and the corresponding profiles, F1.g.5 (a) and (b), evaluated us1ng the s1.mulated phase shlfts. Good agreement with the reflectometric measurements 1.s obtained, namely in the observed perturbation when the island is rotating. From the observed deformat1.on of the profile at t=l565 ms, it can therefore be concluded that a density plateau w1th1n the 1sland structure (observed after mode 1ock1ng, at 1580 ms) should already exist before mode lock1.ng occurs, rotating with the magnetic perturbation. .. .. -· ~· Ftq_. __ • o7 ot .. ~~·•''··l 840 ~ .. & 0 I ~ ~ --....... _ ...... ',, ----.. FLq. 5 •, .. ''""'' 1•1 11>1 .. 4 - Concludinq remarks The use of microwave reflectometry provided local i zed denstty measurements with good spatlal and temporal r esolution enabling the study of dens1ty perturbatlons due to m=2 tear1ng mode; the exper1mental resul t s also Lndicates the extstence of other denstt y perturbattons. Further wor k w1ll a1m at the study of the effect on dens1ty of the iSlands d ev eloped tn other maqnetlc surfaces (namely q=J/2 , q=S/2 and q=3l , in order to hav e ins1ght about the modiftcat1ons caused by LHCD on the q-prof1le as compared with the ohmtc reg1me . Expertments that will enable the obtention of a sequence of prof1les during mode lock 1ng are foreseen ; the study of the proftle evolutlon m1ght provide a tool to estlmate the ( nonllnear l growth of t he magnetic islands , and ther efor e con t rtbute to have inSight about t he behaviour ot the plasma befor e disrupt ion . References /1/ H. Zohm, A. Kallenbach, H. Bruhns , G. Fussmann, o. Kl uber , to be published in Europhys. Lett <1990). /2/ H. E. Hanso , F. Serra et al. Thls Conference. E'r 102 8 41 DETERMINATION OF OFF-DIAGONAL TRANSPORT COEFFICIENTS FROM PARTICLE AND POWER BALANCE ANALYSIS ~. w. Schneider, K. l..ackner Max-Pianck-lnstitut fOr Plasmaphysik, EURATOM Assoclatlon, D-8046 Garchlng, FRG 1 . Introduction In ASDEX pellel Injection and IOC discharges give rise to density peaking which cannot be ex-plained by changes in the charged particle deposition profile. Besides a particular plasma boundary behaviour distinct changes In lhe bulk particle transport are necessary and can be described by an Increase of -vp /0 (the rallo of the Inward drill velocity and the diffusion coefficient used to describe formally the particle transport) /1/ . Common to all cases with peaked density proliles - having '1 • (VT/T)/(Vn/n) • '-ni LT < 1 • ls lhat they show an Im-provement in energy and Impurity particle confinement compared with tlat density profile discharges (TJ > 1 ). These related changes of the bulk energy and particle transport properties point towards a common change of tl'le transport coefficients and may be interpreted in terms or a generalized non-diagonal model or particle and energy transport connecting the nuxes with the driving thermodynamic forces. namely the gradients of pressure (p) and temperature(T). Using such a model we look for a consistent set of transport coefficients In the different confinement regimes on ASDEX taking the fluxes from radial particle and power balance analysis using the TRANSP code. The numerical procedure to calculate the coefficients and results for L· and H· mode discharges are presented In lhls paper. 2. Transport eq uatio ns and numerical procedure Using non-equilibrium thermodynamics linear relations between the fluxes of particles (rp) and energy (a ) and lhe true lhermodynamic forces, I.e. the gradients of 1fT and ji}T for both electrons and Ions (with the cl'lemical potential 1!). can be derived satisfying the Onsagef sym-metry for the off-diagonal coefficients. Subtracting the convective energy flux from the total energy flux a to get the conductive heat flux q = a -2.5 kT r p and normalizing the energy flux equation by kT one obtains relations between r p• r q,e and r q,l ( r q =QA<T) and the recalcu· fated forces ( VT e I T e• (1+ TJ I Te) Vp/p and (Tr/ T el VPj/PJ ) still satisfying the Onsager symmetry for off-diagonal coefficients. Assuming n1 • ne. T1 • T e and a plausible relation bet· wean off-diagonal elements the following radial electron transport model results r p = n 0(1+TJ)( - Vnln) • n a(- VTIT) rq =- n a(1+T])(-Vn/n) + n X{- VT/T), +- ·Vplp • ( l+Tf)( - Vn/n) (1) 

Changes in the density profile due to the m=2 tearing mode in asdex

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Changes in the density profile due to the m=2 tearing mode in asdex

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