Bilato, R.

Brambilla, M.

Feng, Y.

Tardini, G.

English

MPG.PuRe

A neutral beam injection source for the TORIC/SSFPQL packageR. Bilato, M. Brambilla, Y. Feng, G. TardiniMax-Planck Institut für Plasmaphysik - Germany, EURATOM Ass.Introduction0.0 0.2 0.4 0.6 0.8 1.0r/a0.00.10.20.30.40.50.60.70.8[1020 /(s m3)ASDEX-Upgrade: #17870 Beam 1 1.0 0.5 0.0 0.5 1.0LegendreSINBAD (prompt)SINBAD (orbit-averaged)TRANSP0.0 0.2 0.4 0.6 0.8 1.0r/a0.000.050.100.150.200.25[1020 /(s m3)ASDEX-Upgrade: #17870 Beam 61.0 0.5 0.0 0.5 1.0LegendreSINBAD (prompt)SINBAD (orbit-averaged)TRANSPFigure 1: Deposition profiles calculated withSINBAD for a radial (A) and a tangential (B)sources. The inset shows the Legendre polynomialreconstruction used in SSFPQL.The iteration loop between the ion-cyclotron (IC)full–wave TORIC code and the surface-averagedkinetic Fokker-Planck (FP) SSFPQL solver hasbeen implemented to simulate the close interplaybetween IC generated fast-ion tails and IC wavepropagation and absorption [1]. In many fusion de-vices an important high-energy ion population canbe generated and sustained by neutral beam injec-tion (NBI). Synergetic effects can be expected whensimultaneously applying NBI and IC heating. Toaddress these effects, a NBI source and a fast par-ticle loss term have been recently added to SSF-PQL [4].In a first step the NBI source for SSFPQL hasbeen obtained from the Monte Carlo code (MC)FAFNER [2]. The MC approach is very detailed indescribing the particle trajectories but very noisy:SSFPQL needs a smooth source with more angularinformation. The NBI deposition profiles can be ac-curately calculated also with a beam model, whichis faster and is not affected by the statistical noise typical of MC codes. To exploit this advan-tage, the beam-model routine SINBAD [3] has now been interfac d with SSFPQL.Interface with SINBADSINBAD is a fast beam deposition routine based on a simplifiedbut nevertheless rather ac-curate “narrow” beam model. The main simplification consists in assuming “pointsize”sources,as justified by the distance between sources and plasma boundary, much longer than the sourcewidth. Nevertheless, SINBAD takes into account important beam geometry features, such asbeam divergence and focusing, relevant in the plasma core where t e plasma section is com-37th EPS Conference on Plasma Physics P5.144parable with the beam width. SINBAD determines the NBI deposition profiles as functions ofthe pitch angleµv = v‖/v (here parallel and perpendicular refer to the direction of the localconfining magnetic field), and performs the expansion of the deposition profiles in Legendrepolynomials ofµv. The coefficients of this expansion are transferred to SSFPQL and used tobuild the NBI source in the Fokker-Planck equation [4]. Optionally, SINBAD averages the ini-tial deposition profile along the first guiding-center driftorbit of each newborn ion. In thisway orbit broadening effects and prompt losses are taken into account. When used as sourcein the FP equation, the beam deposition profiles should not ber it-averaged. In the case ofa surface-averaged FP solver like SSFPQL, however, averaging over the first orbit can be re-garded as a rough approximation for finite banana-width effects in the beam source. In con-verting SINBAD to a Fortran 90 module for TORIC-SSFPQL package, we have extended it totake into account standard numerical tokamak equilibria astho e used in TORIC. In addition,the orbit-average routine has been rewritten from scratch to integrate the Morozov-Solov’ev0.0 0.2 0.4 0.6 0.8 1.0r/a0.000.020.040.060.080.100.120.14Pe [MW/m3AUG Beam 1: Electron heating0 20 40 60 80 100E [keV]10-810-710-610-510-410-310-210-1100at r/a=0.26 = 0.0 = 0.25 = 0.75 = 1.0Figure 2:Power collisionally transferred fromNBI fast ions to electrons calculated by SSFPQL.The inset shows the Deuterium distribution func-tion at the maximum of the NBI deposition andfor different values ofµv. Dashed and dotted linesrefer to positive and negative values ofµv.equation for the same numerical equilibrium [5].Figure (1) shows the deposition profiles for the ra-dial source 1 (60 keV, frame A) and the tangentialsource 6 (93 keV, frame B) calculated with SIN-BAD for an ASDEX-Upgrade like plasma (refer-ence discharge is # 17870 with only Deuterium,central Te ≈ 4 keV, ne ≈ 8× 1019m−3, B ≈ 2 Tand 2.5 MW of NBI at only full energy). For com-parison Fig. (1) also shows the deposition profilecalculated with the TRANSP code. The agreementis good in the outer part of the plasma, but some-what less in the plasma core. Moreover, in compar-ison with TRANSP results, the shining through ra-diation predicted by SSFPQL is lower for beam 1and higher for beam 6. This can be explained interms of the different stopping rate coefficients used in thetwo codes (as shown in fig-ure (2.5) of [6]), and will be investigated further in the future. When weighted with the spe-cific volume, however, the agreement in the outer plasma region matters much more thanin the plasma core. In both cases of Fig. (1) the neutral beam ws injected in the direc-tion of the toroidal magnetic field: the newborn ions drift towards the plasma inner sideand the drift is larger for trapped ions. As a consequence, the orbit-averaged profiles show37th EPS Conference on Plasma Physics P5.144a depletion in the peripherical region in favour of a centralpeaking, more visible in thecase of source 1, which is oriented more radially. In the caseof counter-injection the orbit-averaged profiles are lower along the whole radial profile because of higher prompt losses.When used as source in SSFPQL, SINBAD predicts about one fourth f the total NBI poweris absorbed by electrons, with the deposition profiles shownin figure (2). In this caseEcrit ≈18Te[keV]; this favours electron heating in the cooler plasma periphey.0.0 0.2 0.4 0.6 0.8 1.0r/a0.000.050.100.150.200.250.300.350.40dP/dV [MW/m3 ] ASDEX-Upgrade 25856 @ 3.8 secSINBADSINBAD: orbit-averagedFAFNER0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.000.050.100.150.20[a.u.]AUG #25856 at r/a=0.1(solid),0.5(dashed)60 keV30 keV20 keVFigure 3:(A) Power deposition density profilesof NBI source 3 calculated with SINBAD andFAFNER codes. (B) Corresponding distribution inpitch angle for two radial points calculated withSINBAD.The inset of figure (2) shows the distributionfunction calculated with SSFPQL at the maximumof the ionization profile. The effects of NBI are visi-ble around the injection energy 60 keV, particularlyfor low µv since the orientation of beam 1 is almostradial. When fast ions are reactant of nuclear re-action with neutron yield, such as Deuterium, theextent of fast-ion tail can be estimated from theneutron rate. The neutron rate predicted with SSF-PQL for this case is about 1.5×1015 neutrons/secin good agreement with 1.55×1015 calculated withTRANSP code.ICRF-NBI synergySimultaneous application of NBI and IC heatingcan produce high-energy ion tails. In particular, ionheating at IC harmonics is a finite Larmor radius(FLR) effect, and, therefore, preferentially acceler-ates ions with large perpendicular energy,k⊥ρi >∼ 1with k⊥ the perpendicular wave number andρi =v⊥/Ωci the particle Larmor radius. The recent ex-tension of SSFPQL to include a NBI source [4] al-lows us to take into account the effects NBI fast-ion tails inthe wave propagation and absorp-tion calculated with TORIC [1]. We apply this tool to ASDEX-Upgrade discharge 25856, forwhich the experimental neutron rate is available. We have analyzed the time around 3.8 secwhere the plasma is characterized by a central electron temperatureTe0 = 2.7keV, densityne0 = 6.8×1013cm−3, confining magnetic fieldB0 = 2.6T and 5% of Hydrogen in Deuteriumplasma. The source 3 of NBI system was delivering 2.5 MW at 60 keV, with contributions at1/2 and 1/3 of the full energy, carrying respectively 36% and 16.7 % of the total power. The37th EPS Conference on Plasma Physics P5.144ICRF system was delivering a nominal 4.2 MW power at 36.5 GHz frequency, correspondingto on-axis Hydrogen fundamental heating. Figure (3.A) shows the deposition density profilescalculated with FAFNER and with SINBAD. Although they differ considerably close to theplasma axis, the difference is negligible in the global balance. Much more noticeable is thedifference between orbit and not orbit averaged profiles, asalready discussed. Figure (3.B)shows theµv–dependence of the ionization rate atr/a = 0.1, 0.5, calculated by SINBAD.NBI N rate Pe PD PHsource [1014] [%] [%] [%]FAFNER 1.35 53 43 4SINBAD 1.34 53 43 4SINBAD (OA) 1.58 47 48 5Table 1:Global results of SSFPQL with onlyNBI source.Because of the noise of MC codes, when usingFAFNER the coefficients of the expansion of NBIsources in Legendre polynomials are obtained oneach magnetic surface by performing a minimumsquare error fitting assuming a Gaussian distributionin µv [4]. This excludes the possibility of describ-ing asymmetries in the pitch-angle profiles, which arepresent in theµv-distributions calculated with SIN-BAD (e.g. dashed lines in fig. (3.B)). Table 1 summarizes the global results of SSFPQL withonly NBI power, calculated with FAFNER, and with SINBAD withand without orbit-average.Only the results obtained with the bounce-averaged input from SINBAD differ slightly from theothers. The experimental neutron rate is 3.5×1014 /sec, higher than that calculated with onlyNBI source 1.3× 1014 /sec. When 4 MW of ICRF is considered, the predicted neutron rate,1.7×1015 /sec , exceeds by far the experimental value. The reduction of synergetic effects islikely to be due to diffusive losses of fast ions during thermalization. To reproduce the experi-mental neutron rate the power lost by fast Deuterium ions is etimated by SSFPQL to be about0.55 MW.References[1] M. Brambilla, R. Bilato Nuclear Fusion49 (2009) 085004.[2] G.G. Lister A fully 3d neutral beam injection code using monte carlo methods, TechnicalReport 4/222, Max–Planck Institut für Plasmaphysik, Garching, 1985.[3] Y. Feng, B. Woll, K. Hüber Computer Physics Communications88 (1995) 161.[4] R. Bilato, M. Brambilla, L.D. Horton, C.F. Maggi, J. Stober, submitted to Nuclear Fusion.[5] V. Belmondo, R. Bilato, M. Brambilla, O. Maj, Varenna conference 2010.[6] M. Kraus, Diplomarbeit, TUM, 2010.37th EPS Conference on Plasma Physics P5.144

A neutral beam injection source for the TORIC/SSFPQL package

http://hdl.handle.net/21.11116/0000-0008-AFFB-9

A neutral beam injection source for the TORIC/SSFPQL package

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MPG.PuRe