The planned upgrade of the RFX-mod device is a good opportunity to widen the operational space of the machine, in both RFP and tokamak configurations. Installation of a power neutral beam injector is also envisaged and a NB system compatible with RFX-mod, formerly installed in TPE-RX, is already available on site. In this work, the METIS simulator is used to study the feasibility of TPE-RX injector integration in RFX-mod circular tokamak plasmas. METIS code allows the simulation of a full tokamak discharge, with the addition of the neutral beam injection (NBI) which, in METIS, is described by a decay equation applied in a simplified geometry and an analytical solution of the Fokker\u2013Planck equation. In this work, RFX-mod scenarios with NBI have been studied, with careful attention to the beam absorption and plasma response to the additional heating

Artaud, Jean Francois

Bolzonella, Tommaso

Sakakita, Hajime

Valisa, Marco

Vallar, Matteo

Vincenzi, Pietro

English

The planned upgrade of the RFX-mod device is a good opportunity to widen the operational space of the machine, in both RFP and tokamak configurations. Installation of a power neutral beam injector is also envisaged and a NB system compatible with RFX-mod, formerly installed in TPE-RX, is already available on site. In this work, the METIS simulator is used to study the feasibility of TPE-RX injector integration in RFX-mod circular tokamak plasmas. METIS code allows the simulation of a full tokamak discharge, with the addition of the neutral beam injection (NBI) which, in METIS, is described by a decay equation applied in a simplified geometry and an analytical solution of the Fokker–Planck equation. In this work, RFX-mod scenarios with NBI have been studied, with careful attention to the beam absorption and plasma response to the additional heating

VALLAR, MATTEO

BOLZONELLA, TOMMASO

VINCENZI, PIETRO

Archivio istituzionale della ricerca - Università di Padova

Original Citation:Requirements and modelling of fast particle injection in RFX-mod tokamak plasmasPublisher:Published version:DOI:Terms of use:Open Access(Article begins on next page)This article is made available under terms and conditions applicable to Open Access Guidelines, as described athttp://www.unipd.it/download/file/fid/55401 (Italian only)Availability:This version is available at: 11577/3221281 since: 2018-02-23T07:48:18Z10.1016/j.fusengdes.2017.04.070Università degli Studi di PadovaPadua Research Archive - Institutional RepositoryRequirements and modelling of fast particle injection in RFX-mod tokamakplasmasM. Vallara,b, J. F. Artaudc, T. Bolzonellaa, H. Sakakitad, M. Valisaa, P. VincenziaaConsorzio RFX (CNR, ENEA, INFN, Universita` degli Studi di Padova, Acciaierie Venete SpA) Corso Stati Uniti 4 -35127 Padova, ItalybUniversity of Padova -Via VIII Febbraio, 35122 Padova, ItalycCEA, IRFM, 13108 Saint-Paul-lez-Durance, FrancedNational Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 2, 1-1-1 Umezono, Tsukuba305-8568, JapanAbstractThe planned upgrade of the RFX-mod device is a good opportunity to widen the operational space of themachine, in both Reversed Field Pinch (RFP) and tokamak configurations. Installation of a power neutralbeam injector is envisaged and a NB system compatible with RFX-mod, formerly installed in TPE-RX, isalready available on site. In this work, the METIS simulator is used to study the feasibility of the injectorintegration in RFX-mod circular tokamak plasmas. METIS code allows the simulation of a full tokamakdischarge, with the addition of the neutral beam injection (NBI) which, in METIS, is described by a decayequation applied in a simplified geometry and an analytical solution of the Fokker-Planck equation. In thiswork, RFX-mod scenarios with NBI have been studied, with focus on the beam absorption and plasmaresponse to the additional heating.Keywords: RFX-mod, NBI, fast particles, METIS, TPE-RX1. IntroductionRFX-mod is a medium size (R = 2 m, a =0.459 m) device capable to work in both tokamakand reversed field pinch (RFP) magnetic configu-ration. As the biggest operational RFP, it reachedthe record plasma current of 2 MA. Its advancedfeedback system for MHD control has been funda-mental in reaching this result. Furthermore the de-vice can reach uncommon tokamak regimes, such asplasmas with q(a) < 2 [1]. Nowadays RFX-mod isunder upgrade: one of the most challenging changesis the integration of the vacuum vessel in the sup-port structure, which will make the feedback sys-tem closer to the plasma edge and thus improvethe plasma control [2].Another important planned upgrade is the integra-tion of a neutral beam injector. Thanks to the col-laboration between Consorzio RFX, Padua, Italy,and the AIST Institute, Tsukuba, Japan, the NBinjector formerly operating on TPE-RX is currentlyavailable. It was designed to operate with a powerof 1.25 MW, accelerating a current up to 60 A of25 keV hydrogen positive ions for 30 ms (nominalconditions), but it can work also with deuterium(with a reduced power of ∼ 0.9 MW). If necessary,the beam could operate also at 15 keV for 60 ms.The injector has a multiaperture three-grid electro-static accelerator with the typical design adoptedfor the positive ion accelerator. The designed fo-cal length is 1860 mm and the effective diameter ofthe extraction region is 345 mm. Close to the focalpoint the spot diameter of the beam trace has beenmeasured to be φ ∼ 36 mm. From the beam profiledata, the divergence has been estimated as θ ∼ 0.8◦[3].The design of the NBI implementation has beenalready studied in [4],[5], assuring that the integra-tion of such system is feasible, with an efficiency(defined as the ratio between the power injectedin RFX-mod and the electrical power to the in-jector) η > 25%. Due to mechanical constraintsmainly linked to toroidal field coils configuration,the only possible injection is along a radial chordon the equatorial plane. In figure 1 the design ofPreprint submitted to Fusion Engineering and Design September 24, 2016the NB system integration can be seen.Figure 1: CAD design of the RFX-mod NB system. [4]The NBI on RFP plasmas has already been stud-ied in [6]. In this work, a set of requirements foran NB system to be applied to RFX-mod tokamakplasmas is analysed, carefully considering the beamshine-through for a wide range of scenarios. Fi-nally some indications of the physical effects to beexpected from NBI-plasma coupling will be high-lighted, with special attention to the beam energyabsorption (both in terms of time dependent quan-tities and of spatial profiles) and to the possibilityof inducing a transition from L to H confinementmodes.2. METIS simulation of RFX-mod tokamakdischargesMETIS [7] is the tool used in this work to simu-late a full RFX-mod tokamak plasma. The METIScode allows simulation of a full tokamak dischargein the time-scale of few minutes on a commercialPC, using relations coming from scaling laws cou-pled with simplified source models. It can evaluateboth the time-dependence and the radial profilesof the physical quantities. For each simulated dis-charge, METIS needs as an input the time depen-dence of plasma current and density, the geometryof the plasma (last closed flux surface shape, ma-jor and minor radius), the plasma composition andthe additional heating (NBI or waves). The otherparameters, such as the plasma composition, theimpurities, the transport coefficients, the MHD in-stability parameters, the profiles shape, neoclassicaleffects, L-H transition coefficients, etc. have beenevaluated and validated with experimental data.Although METIS has been widely used to simu-late different tokamaks, a RFX-mod discharge hasnever been simulated with METIS so far. We there-fore performed as validation a METIS simulation of0 0.5 1050100Time (s)I p (kA)0 0.5 100.20.40.60.8Time (s)ne (1019 m−3 )0 0.5 122.53Time (s)q(a)0 0.5 1123Time (s)V loop (V)0 0.5 1300400500600Time (s)T e (0) (eV)  METIS simulationExperimental dataFigure 2: Comparison between experimental data andMETIS simulation for shot #38688.some reference RFX shots. Results were comparedwith experimental data showing a good agreement(in figure 2 an example is shown). In these simula-tions careful attention has been given to the flattopphase, including the sawtooth instability.In order to include a NB system in METIS simula-tions, it is necessary to define the injection geom-etry, the beam size (considered as a pencil beam),its energy, the beam power wavefunction, the beamcomposition and the scaling law related to the cur-rent drive electron-shielding. Because of the fore-seen normal injection of the RFX-mod NB system,the current drive effect is not considered in thiswork. As output, METIS can provide e.g. thepower deposition to the plasma, the fast particlelosses and the slowing-down time.A set of RFX-mod circular tokamak plasmas dis-charges has been simulated with typical plasma cur-rent and density, as shown in figure 3. In table 1the labels, the density and the normalised densityare indicated for each shot. This database of sim-ulations has been used in this work to study theeffect of the implementation of a NB system. As itcan be noted, the plasma current (thus the Green-wald density) is kept fixed all over the shots (duringthe flattop, Ip = 120 kA, qa = 2.3). The plasmacomposition is unvaried (main gas deuterium, withcarbon and lithium as impurities) while the densityprofile peaking factor (n0/〈n〉) has been estimated.It varies between 1.1 for the UH shot and 1.3 forthe UL shot.20 0.5 104080120Time (s)I p (kA)0 0.5 1 1.500.51Time (s)<n>/nG  ULLMHUH(b)(a)Figure 3: Plasma current (a) and normalised density (b) forthe shots simulated with METIS.Label Name 〈n〉(1018m−3) 〈ne〉/nG(%)UL Ultra-Low 2.5 13L Low 6 32M Medium 10 53H High 14 75UH Ultra-High 18.7 100Table 1: Density parameters for the reference shots. 〈n〉indicates the line-averaged electron density.3. Results for Ebeam = 25 keV0 5 10 15 20Density (1018 m-3)0.250.50.751<Shine through + O.L.>25 keV15 keVFigure 4: Shine-through as function of density. Two symbolsare used for the two beam energies.In the first part of the work the injection of a25 keV deuterium beam at the power of 1.25 MWfor 30 ms during the flattop is studied. In figure 4the average losses of the beam energy (accountingshine-through and orbit losses) are shown: for den-sities below 1019m−3 (M) the losses are high (above70 %) and thus not considered in the following anal-ysis. Figure 5 (a) shows that the central electrontemperature increases during the NBI by aboutFigure 5: Case Ebeam = 25 keV: Te(0) (a), τS(b), Ti/Te(c)and PABS(ρ)(d) for M (blue), H (black) and UH (red) shots.The shaded area is the injection time window.50% and (b) the slowing-down time reaches at max-imum ∼ 0.1 s, thus the fast ions can exchange alltheir energy before the discharge end. In panel (c)it is shown that the average Ti/Te ratio rises upto ∼ 0.9, allowing the exploration of new plasmaconditions in RFX-mod tokamak. The power de-position profile is shown in panel (d), showing thatthe maximum of the absorption is at the center ofthe plasma column. The beam energy is distributedbetween ions and electrons depending on the ratiobetween the beam energy and the so called criticalenergy of the beam [8]: if it’s greater than 1 the en-ergy is given to the electrons, otherwise to the ions.In this case, the critical energy, and thus the en-ergy transfer, depends mainly on the temperature,in fact for a D beam impinging on a D plasma thecritical energy is EC [keV] = 18.6Te[keV]. In fig-ure 6 the ranges of energy distribution are shown,and it can be clearly seen that most of the power isabsorbed by plasma electrons.4. Results for Ebeam = 15 keVSince with a beam energy of 25 keV the shine-through is quite high, a study has been done alsowith the beam energy of 15 keV, with a durationof 60 ms. As shown in figure 4, with the mediumdensity shot at Ebeam = 15 keV the losses are be-low 50 %, indicating that the scenario at reducedenergy is promising in terms of shine-through. Inthis work, the plasma current extracted from thebeam source has been assumed constant, thus thepower injected in the plasma (P = Iext ·∆Vacc) hasbeen scaled linearly.30.25 0.35 0.45MHUH0.550.650.75Fraction to electrons0.40.50.60.7Fraction to electrons0.3 0.4 0.5 0.6Fraction to ionsMHUHFraction to ions25 keV 15 keVFigure 6: Range of power distribution delivered to ions (bot-tom) and electrons (top) during NB injection in analyseddischarges.The results of the simulations with 15 keV NBIare shown in figure 7, which can be directly com-pared to figure 5. It can be seen from panel (a)that the electron temperature (and consequentlythe slowing-down time in panel (b)) tends to sat-urate to a fixed value while the ion temperature(panel (c)) increases until the beam is turned-off.A really interesting feature is that the ratio Ti/Teexceeds 1 for almost all the shots studied. This canbe justified by the fact that at lower energies the en-ergy is exchanged mainly with the plasma thermalions. The absorption profile (d) is similar to thecase of 25 keV, though the values are lower. TheFigure 7: Case Ebeam = 15 keV: Te(0) (a), τS(b), Ti/Te(c)and PABS(ρ)(d) for M (blue), H (black) and UH (red) shots.The shaded area is the injection time window.lowest ratio of the energy with respect to the crit-ical energy results in a higher power deposition tothe ions, shown in figure 6. Notice that the rangeis broader in this case with respect to the 25 keVNBI case.5. ConclusionsIn this work, the METIS program has been usedto simulate the integration of a NB system in RFX-mod. The simulations have been carried on withNB energy of 25 keV and 15 keV, which are theavailable energies for the beam to be installed inRFX-mod and with a fixed geometry due to me-chanical constraints. The results show that the NBIwith E = 25 keV will have a high shine-throughvalue but the power deposited to the plasma allowsthe exploration of different scenarios with higher Teand Ti/Te ∼ 0.9. Similar results are achieved withE = 15 keV, leading to Ti/Te > 1 with a lowershine-through.The addition of NB power can favor the L-Htransition: in usual RFX-mod tokamak ohmic dis-charges, the power flowing through the separatrixis close to the threshold to reach the H mode [9].In figure 8 it is shown that during the beam injec-tion at 25 keV the power becomes higher than thethreshold power needed and thus the L-H transitionoccurs. At 15 keV the power of the beam alone isinstead too low to induce the L-H transition. Thescaling law for the threshold power used is takenfrom [10].Figure 8: PLCFS/PLH . The shaded area represents thebeam injection time window.Further studies involve a better analysis of theL-H transition, different plasma shapes (like an X-point plasma), a deeper study on the particles orbitand particles birth profile inside a RFX-mod toka-mak plasma.4AcknowledgmentsThe project has received funding from the Euro-pean Union’s Horizon 2020 research and innovationprogramme under grant agreement number 633053.The views and opinions expressed herein do not nec-essarily reflect those of the European Commission.References[1] M.E. Puiatti et al., Overview of the RFX-mod contri-bution to the international fusion science program, Nu-clear Fusion 55 (10) (2015) 104012.[2] Peruzzo S. et al., Design of machine upgrades for theRFX-mod experiment, in: 29th SOFT Symposium onFusion Technlogy, 2016.[3] Sakakita H. et al., Characteristics of high-power-densityand focused neutral beam system, in: 32nd Conf.Plasma Physics Control. Fus., 2005.[4] Dal Bello S. et al., Integration design of TPE-RX neu-tral beam injector on RFX-mod, Fusion Engineeringand Design 86 (6–8) (2011) 772–775.[5] Pilan N. et al., The monte carlo simulation of a 1-mwneutral beam injector on RFX-Mod, IEEE Transactionson Plasma Science 40 (4) (2012) 1042–1052.[6] Anderson J.K. et al., Simulation of a power neutralbeam injection in RFX-Mod, in: 38th EPS conferenceon Plasma Physics, 2011.[7] J. F. Artaud, METIS user’s guide (2008).[8] Stix Thomas H., Heating of toroidal plasmas by neutralinjection, Plasma Physics 14 (4) (1972) 367.[9] L. Marrelli et al., Tokamak experiments in RFX-modwith polarized insertable electrode, in: 43rd EPS Con-ference on Plasma Physics, Leuven, 2016.[10] Martin YR et al., Power requirement for accessing theh-mode in iter, Journal of Physics: Conference Series123 (1) (2008) 012033.5

Requirements and modelling of fast particle injection in RFX-mod tokamak plasmas

Requirements and modelling of fast particle injection in RFX-mod tokamak plasmas

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