De Pena Hempel, S.

Kallenbach, A.

Meister, H.

Peeters, A.

English

MPG.PuRe

MEASUREMENTS OF THE RADIAL ELECTRIC FIELDAT ASDEX UPGRADES. de Peña Hempel, H. Meister, A. Kallenbach, A. Peeters and ASDEX Upgrade TeamMPI für Plasmaphysik, EURATOM AssociationD-85748 Garching, Germany1. IntroductionIn a fusion plasma the radial electric field Er, which is associated with a reduction in turbulencethrough sheared E × B flow stabilization and a subsequent improvement in confinement, isrelated to a mutual interaction between the cross field heat and particle transport (∇pi), thecross field angular momentum transport (vφ) and the poloidal velocity vθ. There are severalfeedback loops whereby Er and its shear can change and affect the confinement propertiesof plasma. For example, an increased shear in the E × B drift can lead to a suppressionof fluctuations and hence to a reduction in the radial transport, a subsequent steepening ofthe pressure gradient and thereby to a modification of the electric field itself. To provideinsight into the interplay between the different processes, the radial electric field can be inferredindirectly from spectroscopical measurements using the radial component of the momentumbalance equation Er = 1Zieni∇pi + vφBθ − vθBφ. Since this Er evaluation indeed neglects thecontribution of the inertial terms to the balance equation, it has to be applied with some care andthe approximation made has to be verified for each single case.To measure the poloidal rotation a new spectroscopic diagnostic has been installed at theASDEX Upgrade tokamak and a deconvolution procedure has been developed and applied inorder to recover the radial spatial resolution that is lost due to the integration of the spectralemissivity along the lines of sight. This paper presents first measurements of helium vθ profilesand Er in the centre of ASDEX Upgrade plasmas and their connection to the formation of coretransport barriers in enhanced reversed shear (ERS) plasmas.2. DiagnosticsThe time evolution and the spatially resolved profiles of the impurity ion density ni, ion temper-ature Ti and toroidal rotation velocity vφ in the core plasma of the ASDEX Upgrade tokamakare routinely monitored in neutral beam heated discharges using the toroidal charge exchangerecombination spectroscopy (CXRS). In addition, in order to determine the last term in the bal-ance equation a measurement of the poloidal velocity is necessary. For this purpose a second,high throughput CXRS-system with viewing chords that look (both down and up) across thepath of a heating neutral beam has been designed and installed to measure the helium and carbonpoloidal rotation.The sightline geometry is chosen to minimize the effects that emerge from the energydependence of the excitation rate coefficient for the observed spectral line and simultaneouslyto maximize the radial resolution within the experimental constraints due to the restricteddiagnostic access. Even so, the CX-cross-section effects can significantly distort the apparentpoloidal rotation profile when not properly treated.3. Atomic physics effects on the measured line shapeThe measured charge exchange emission spectra are strongly affected by the dependence of theCX-cross-section on the relative energy of the beam neutrals and the observed impurity ions, aswell as by the Zeeman splitting and the fine-structure components. The clearest manifestationof these effects is an additional shift in the line position and a modified Doppler width, whichdepend sensibly on the observation angle, magnetic field, beam energy, plasma rotation and iontemperature. This leads to apparent velocities and temperatures that can greatly differ from thereal values.Since the plasma geometry in ASDEX Upgrade is not up-down symmetric it is not possibleto separate the Doppler shift and broadening from these atomar effects by the substraction ofopposing views as is done in other experiments. Therefore they need special consideration andmust be taken into account in the analysis during the inversion procedure.The Zeeman splitting of the energy levels and the apparent non-thermal line broadeningcaused by this effect are included using the corrective derating factors ηZeeman described in[1], additionally scaled for arbitrary transition levels n, ion charges Z and magnetic fieldsBmag, and modified to take into account the increasing contribution of the σ-component fornon-perpendicular viewing geometries. For convenience of computation the ηZeeman have beenparametrized independently of the measured temperature.Due to collisional l-mixing not only a single emission line will occur after charge exchangetransfer but the whole set of allowed transitions between the l-levels of the upper and thelower shell will be observed simultaneously. The superposition of each of these fine structurecomponents to form the measured sum profile is calculated by using their correct centralwavelengths and relative intensities as available from computations of the ADAS (Atomic Dataand Analysis Structure [2]) code for a given parameter set (EBeam, ne, ni, Te, Ti, Zeff andBmag). However, since the single wavelengths differ only very slightly the resulting line shapecan be essentially approximated by a single Gaussian, whose width and peak position define anapparent temperature and an apparent velocity. These are obtained by applying a least squaresfit to the ADAS result for each parameter set and are summarized in a structured output forfurther calculations.The cross section effects are solved analytically using the algebraic expressions presentedin [3], with readily available input parameters, such as observation angle, beam energy, plasmarotation and ion temperature.4. Inversion ConceptThe line-integrated vθ-measurements described in the previous section sample an extended radialrange due to the relative height of the neutral beams compared to the poloidal curvature radiusof the flux surfaces. In order to recover this lost radial spatial resolution a flexible deconvolutiontechnique has been developed.The standard matrix inversion method of the Abel integral equation, which assumes ro-tational symmetry and isotropic emission, is adapted to handle the variation of the emissionarising from the neutral beam (necessary to measure the fully stripped impurity ions in theplasma core) and an anisotropic spectral emissivity by introducing a weighted length matrixWijk which relates an emissivity vector,Ej , to the measured brightness vector,Bi, by the matrixmultiplication Bi =∑jk WijkEj . According to [4] the index i refers to a sightline, the index jdesignates the zones of equal poloidal flux and the index k additionaly partitions the plasma intozones of different neutral beam density. The emissivity profile is readily calculated by invertingthe length matrix. Expanding the basic idea of the inversion concept developed by R.E.Bell [4]by making a proper redefinition of Wijk, Ej and Bi various quantities as the impurity densityvector nimpj , the toroidal rotation vφj , the poloidal flow velocity vθj and the ion temperature Timpjcan successively be determined from the charge exchange measurements taking into accountspecific geometry factors and the contribution of several neutral beams.First, a length matrix, Wijk = Lijknbeamijk 〈σCXv〉effijk can be defined, which contains thevertical and the radial variations of the neutral beam density nbeamijk determined from an indepen-dent beam attenuation calculation, the effective charge exchange rate 〈σCXv〉effijk and the lengthof the viewing chord in a given zone Lijk. By inverting this matrix the impurity density vectorcan be obtained from the measured brightness vector, BCXi .Next the flow velocity is deconvolved by solving (BCXi uCXi ) =∑jk ECXijk (vjΘzij +∆λCXijk ),where ui is the apparent rotation velocity, ECXijk = Wijknimpj is the integrated local emissivityfor the particular viewing geometry being considered and Θzij contains directional informationof the velocity vector. A calculation of a matrix of cross section and fine structure shifts ∆λCXijkis also assumed, which requires measurements of T impj and the velocity vector itself. However,as next to no effect can be found from the cross section effect on the deduced ion temperatures,a first approximation of T impj is obtained by mapping the measured values onto a mean poloidalflux label defined as 〈ρ〉i =∑jk ρijkEijk. Further, since the magnitude of the expected poloidalvelocity is typically more than an order of magnitude smaller than the toroidal velocity, itscontribution to the correcture term for vφ has not to be considered in practise. So, assuming noflow in radial direction, the velocity vector can accuratly be determined without the need of anyiteration by following a two step procedure: first the toroidal rotation is inverted neglecting theeffect of vθ and then the poloidal velocity is deconvolved from the measurements of the verticalCX-system after recalculating ∆λCXijk with the inferred vφ.Finally, the impurity ion temperature profile can be obtained from the evaluation ofBCXi[kTCXimc2+λ20c2uCXi2]=∑jk ECXijk(kTimpjmc2+λ20c2[vjΘzij + ∆λCXijk]2).As the presented matrix inversion procedure is very sensitive to the gradient of the bright-ness, to handle real data with errors it is combined with a curvature and error minimizationprocedure based on the regularization method of Tikhonov [5].5. ResultsHere the phenomenology of core barrier dynamic in an Enhanced Reverse Shear (ERS) plasma atASDEX Upgrade is examined by means of first measurements supplied by the new spectroscopicdiagnostic and the implemented deconvolution procedure.Er t −E r t 0θθv−vneoin104msion temperaturein keVt = 0.689 st = 0.725 st = 0.761 st = 0.797 s1Zieni∇ pi in 105 V m vφBθ in 105 V mtotal in 105 V mErρpolvθBφ in 105 V mθ θv −vneo in 104 m sρpolsafety factor qin 104 m sθvion diamag. directiona) b) c)d) e)g)f)h) i)Figure 1. The eight first pic-tures show the temporal evolu-tion of the ion temperature pro-file a), the poloidal rotation ve-locity b), the safety factor c), thedifferent contributions d), e), f) tothe total radial electric field Er g)and deviation of the measured vθfrom neoclassical predictions h)during the ERS transition of dis-charge #10701. Finally, in picturei) vθ − vneoθ is plotted versus themeasured change inEr for all thetimes and radii.The presented discharge (#10701) is seen to undergo an enhancement in its confinementcharacteristics shortly after the start of the neutral beam heating phase, as indicated by thesteepening of the helium temperature profile in Fig. 1 a) . The onset of the core transport barrieris accompanied by a localized spontaneous excursion of the poloidal velocity from the heliumions originally rotating in the ion diamagnetic drift (negative) direction (Fig. 1 b)). As the extentof this velocity shear region is small compared to the radial separation of the vertical sightlines,the width of the reversal region and the full magnitude of the positive velocity obtained fromthe deconvolved data can be strongly disturbed by the resolution of the system. Though, theradially deconvolved vθ profiles indicate that this flow reversal is clearly localized outside theregion that ultimately becomes the transport barrier region but very close to the minimum in thesafety factor profile, q (Fig. 1 c)), as derived self-consistently from ASTRA code calculations.The dynamic of the enhanced core confinement is characterized by a propagation of thetransport barrier, as defined by the change in the slope of the ion temperature, and the locationof qmin outward with time. This expansion is maintained during the period of vθ reversal andstops as the poloidal rotation returns to its initial value after the confinement transition.Since the vθ excursion precedes measurable deviations in other background plasma profiles,its contribution (Fig. 1 e)) dominates the spontaneous decrease of the plasmaEr (Fig. 1 g)) earlyin time. As described in [6] this indicates the change in Er shear to be a causal element of theconfinement bifurcation and points to its threshold character. As the flow reversal subsequentlyrelaxes and the transport barrier moves outward, the diamagnetic contribution to the radialelectric field (Fig. 1 d)) cannot compensate the term vφBθ (Fig. 1 f)) in the plasma core anylonger, leading to an enhancement of Er in this region. Contrary to the fast vθ-activity outsidethe steep gradient region, the increased central electric field strength is sustained during theentire period of enhanced confinement.Poloidal flow evaluations from steady state neoclassical considerations [7] that describethe measured profiles quite accurately during the period of lower confinement, however cannotpredict the dynamics of the large poloidal velocity and the velocity shear observed. Thereforethe behaviour of vθ in the core deviates from these calculations especially at the bifurcationtime (Fig. 1 h)). The difference between the measured and neoclassically predicted vθ exhibitsa strong temporal and spatial correlation to the measured change in Er (Fig. 1 i)). In the regionwhere this change is dominated by the vθBφ contribution this correlation is trivial. Not so,however, in the central plasma region where the enhancement of the measured radial electricfield arises from the displacement of the transport barrier and may be related to an increase of theion heat diffusion χi towards the plasma centre [8]. A possible interaction mechanism betweenEr and χi may be induced through the dependence of χi on the trapped orbit squeezing factorS = 1 − mc2eB2θ∂Er∂r, χi ∝ S−3/2. First estimates show that at the time where the ion temperatureflattens in the centre, the squeezing factor S is significantly smaller than 1, leading to an increasein χi. Detailed calculation will be addressed in future work.References[1] R.P. Schorn, E. Wolfrum et al.: Nuclear Fusion 32, 351–359 (1992)[2] H.P. Summers: JET Joint Undertaking Report JET-IR(94)-06, 1994[3] M. von Hellermann et al.: Plasma Phys. Control. Fusion 37, 71 (1995)[4] R.E. Bell: Rev. Sci. Instrum. 68(2), 1273–1280 (1997)[5] R. Wunderlich et al.: Max-Planck-Institut für Plasmaphysik Report IPP 5/37, 1992[6] E.J. Synakowski et al.: “Formation and structure of internal and edge transport barriers”.Accepted for publication in Plasma Phys. Control. Fusion (1998)[7] Y.B. Kim et al.: Phys. Fluids B 3(8), 2050–2060 (1991)[8] G. Pereversev et al.: This conference, 1998

Measurements of the Radial Electric Field at ASDEX Upgrade

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Measurements of the Radial Electric Field at ASDEX Upgrade

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