Crombé, Kristel

Lyssoivan, A

Noterdaeme, Jean-Marie

Tripsky, M

Van Schoor, M

Vervier, M

Wauters, T

English

Ghent University Academic Bibliography

Monte Carlo simulation of ICRF discharge initiation at ωLHR < ωM. Tripský1,2, T. Wauters1, A. Lyssoivan1, M. Vervier1, K. Crombé1,J.-M. Noterdaeme2, M. Van Schoor1, TEXTOR team31 Laboratory for Plasma Physics, ERM/KMS, 1000 Brussels, Belgium, TEC partner2 Ghent University, Department of Applied Physics, 9000 Ghent, Belgium3 Forschungszentrum Jülich, IEK-Plasmaphysik, 52425 Jülich, GermanyIntroductionThe radio-frequency (RF) plasma production technique in the ion cyclotron range of fre-quency (ICRF) is applied for wall conditioning (ICWC) in superconducting fusion machines(Te = 3 − 5eV, ne < 1012 cm−3), for RF-assisted start-up in tokamaks and for target plasmaproduction (ne = 1013 cm−3) in stellarators [1].To investigate plasma initiation by ICRF antennas the Monte Carlo code RFdinity1D wasdeveloped and presented in [2]. The code was improved recently on several of its aspects con-cerning 3D binary collision physics, implementation of Coulomb collisions and electron lossesdue to drifts and recombinations. A description with focus on its improvement compared to theprevious version will be given in next section, simulation results and comparison with experi-ments on TEXTOR are presented in the third and fourth section.Model DescriptionThe 1D code describes the motion of electrons around the torus along one toroidal magneticline by two velocity components: a component perpendicular(vθ =√v2x + v2y)and parallel(vz) to the magnetic field line. This report presents simulations for one-strap and two-strapantenna electric field (monopole phasing). The electric field profile Ez for each strap is appro-ximated by the sum of two Gaussians with opposite sign centered around the two gaps betweenthe strap and the antenna box. The shape of the profile is based on vacuum field simulations forthe ITER antenna by Lyssoivan [1]. The electrons are accelerated by the parallel component ofthe RF electric field Ez (with respect to BT ) in front of the antenna and are initially uniformlydistributed along the length of the magnetic field line with initial velocities sampled from a lowenergy Maxwell distribution (Te,0 = 0.5eV).The collisions of electrons with hydrogen molecules are treated according to a Monte CarloCollision schema (MCCS) [3]. The electron specific free path length is calculated byλMC =− 1nH2σT (εi)+neσrec(εi)log(1−ξ ) , (1)where nH2 and ne are the hydrogen and electron densities, σT (εi) is the sum of the electron im-pact collision cross sections of ionization, excitation and dissociation reactions for the electronenergy εi, σrec(εi) is the electron ion recombination cross section, and ξ is a random number41st EPS Conference on Plasma Physics P1.133(0 ≤ ξ < 1). Upon the collision, the collision type is determined according to MCCS and thescattering angle is calculated with respect to the type of the collision [3]. In case of an ioniza-tion collision, the energy of the ejected electron strongly depends on the energy of the incomingelectron, implemented in the model according to [3].The electron-ion Coulomb collisions are calculated according to Takizuke-Abe [4], and areincluded in the simulation once the electron density reaches ne = 1014 m−3. The ion population,uniformly distributed over the torus, is considered to be Maxwellian, with temperature correctedafter each coulomb collision.Simulating breakdownPlasma initiation is governed by electron impact ionization. At low densities, when recom-bination and drift losses are insignificant the electron density (ne) time evolution follows theequationdned t= nenH2〈σ(ε)v〉ione,H2 = neνion , (2)where nH2〈σ(ε)v〉ione,H2 is the ionization rate νion.Figure 1(a) gives three simulated electron density evolutions in time for the electric field withone strap in a TEXTOR torus size. The simulations with E0 = 12kV/m and E0 = 20kV/m atf = 29MHz reach a stable density level of ne ≈ 6 ·1018 m−3 within 1ms. The density saturationoccurs due to two effects: i) the recombination reactions become frequent and balance out theionization reactions, ii) the drop of the hydrogen density nH2 in the considered closed systemwith constant number of particles reduces the e−H2 collision frequency. The threshold densitywhen the Coulomb collisions (ne = 1014 m−3) are taken into account is highlighted in Fig. 1(a)(black dashed line). It is clear that at this stage the electron-ion Coulomb collisions do not havea significant effect on the evolution of ne (see Fig. 1(a)). However at higher electron densitythe electron energy distribution converges into a Maxwell distribution with an energetic tail.The critical density for both slow waves (SW) excitation (ω = ωp,e) nSW(cut-off)e,crit and the lowhybrid resonance (ω = ωLHR) nSW(LHR)e,crit are as well indicated. A first principle validity limitof the present code version is considered to be nSW(cut-off)e,crit . It is expected that upon slow waveexcitation the E‖ field will diverge from the vacuum field. On approaching the LHR, where E‖becomes very strong the vacuum field cannot be used further and simulation results beyond thisdensity with the present code version are not valid. The numerical definition of the breakdownmoment in simulations was nevertheless put at the upper validity limit nSW(LHR)e,crit , based on [5].Simulated dependencies on Electric field strength and frequencyE-scan and f -scan simulations at pH2 = 0.05Pa with TEXTOR torus dimensions and a hypo-thetical one strap antenna with dimensions corresponding to one strap of the TEXTOR doublestrap antenna are shown in Figure 1(b). The points represent a surface of νion (See eq. (2)) in theE-f plane. The f-scan suggests a decreasing νion with increasing frequency in the ICRF range of41st EPS Conference on Plasma Physics P1.1330 0.5 1 1.5101010151020Time [ms]ne[ m−3]neSW(LHR) ≈ 2.9e+16 [m−3]neCC = 1.0e+14 [m−3]ne(SW cut−off) ≈ 1.0e+13 [m−3](a)  E0 = 8kV/m f = 29MHzE0 = 12kV/m f = 29MHzE0 = 20kV/m f = 29MHz 20 25 30 35 40 45 50 0 10 2030 40 5060 700246x 104   f=38MHz(b)   f=35MHz   f=32MHz   f=29MHzE0 [kV/m]   f=20MHzf [MHz]νion[ Hz ]0 0.2 0.4 0.6 0.8 1 1.2 1.400.20.40.60.81E/f [kV/m/MHz]νNORMi on[ -](c)  SimulationνionRFνionPMDFigure 1: Parametric discharge initiation scans for TEXTOR torus size dimensions for electric field of one strap:(a) ne as a function of time with exponential fits (Eq. (2)) at pH2 = 0.05Pa , (b) Surface of νion in E-f plane atpH2 = 0.05Pa, (c) Normalized ionization rate νNORMion as function of E0/ f for theoretical formulas νRFion and νPMDiontogether with simulated values at pH2 = 0.01Pa.interest. Furthermore, it is clear that for fixed frequency the values of νion remain close to un-changed above 25kV/m, suggesting the existence of an optimal minimal electric field strengthabove which the ionization rate νion and also the breakdown time remain constant. For the lowerelectric fields a rapid increase of νion is observed from a threshold E0 where the plasma initiationbecomes possible until the described optimal E0.E0 f E0/ f νion40 20 2,0 5,283 ·10470 35 2,0 1,905 ·104Table 1: The values of E0, f and νionfor same ratio of E0/ f .The shape for the simulated E-dependency can be partiallyexplained based on the theory presented in [6], separating theionization rate near the antenna νRFion where electrons gain en-ergy from the oscillating RF field, from the ionization ratefar from the antenna region νPMDion where electrons are con-sidered to gain energy from the Ponderomotive force as il-lustrated in figure 1(c). The approximative theory predicts for both rates a dependency on theratio of electric field strength and frequency E0/ f . The dependencies are plotted in Figure 1(c)together with simulations at pH2 = 0.01Pa, fixed frequency of 29MHz and varying E0. All threecurves were normalized for better legibility. The theoretical E0/ f dependency is however notsufficient to fully describe the νion dependency on E0 and f . The ionisation rates for the twogreen highlighted points shown in Fig. 1(b) with equal E0/ f ratio, given in Table 1, differ by afactor∼ 2,8. The latter evidences the need to explore the νion dependency on E0 and f by usingmore sophisticated models (for example RFdinity1D presented here).RF power scan and pressure scan and comparison with experimentsSimulations with the idealized monopole electric field for TEXTOR torus and antenna di-mensions were performed to compare them with the experimental breakdown time (tbkdn) de-pendencies on RF power and pressure obtained on TEXTOR.The Figure 2(a) represents tbkdn as a function of the electric field strength in the simula-41st EPS Conference on Plasma Physics P1.133tions and the experiments. The experimental tbkdn tendency is clearly reproduced by the sim-ulations. The values for the experimental plot were estimated at best effort from the voltageat the feeding point of the strap via transmission line voltage measurements taking into ac-count the radial exponential decay of the E‖ field in the torus. The saturation in the experimentsoccurs around E0 ' 20kV/m (PANT = 100kW) while the saturation in the simulations startsaround E0 ' 10kV/m.Experimental breakdown times tbkdn as a function of pressure with constant antenna powerPANT = 100kW at f = 29MHz are shown in Figure 2(b) (red curve) together with the simula-tions for f = 29MHz and two electric field amplitudes: E0 = 5kV/m and E0 = 20kV/m. Athigher E0, the tbkdn is not expected to vary much (See Fig. 2(a)). Again the simulated trendmatches the experimental one.5 10 15 20 25 30 35 400510152025303540E0 [kV/m]tbkdn[ ms ](a)  TEXTOR, p=0.018Pa, f=29MHzSimulation, p=0.018Pa, f=29MHz0 0.01 0.02 0.03 0.04 0.05 0.060123456pH2 [Pa]t bkdn[ ms ]  (b)TEXTOR, P=100kW, f=29MHzSimulation, E=20kV/m, f=29MHzSimulation, E=5kV/m, f=29MHzFigure 2: (a) Breakdown time as a function of electric field strength for simulation at pH2 = 0.018Pa andf = 29MHz (blue line) and for experiment on TEXTOR at pH2 = 0.018Pa and f = 29MHz (red line), (b)Breakdown time as a function of neutral pressure pH2 at f = 29MHz and for two electric field amplitudesE0 = 5kV/m and E0 = 20kV/m (blue and green lines), the red lines represent experimental tbkdn on TEXTOR.AcknowledgementsThis work was carried out using the HELIOS supercomputer system at Computational Sim-ulation Centre of International Fusion Energy Research Centre (IFERC-CSC), Aomori, Japan,under the Broader Approach collaboration between Euratom and Japan, implemented by Fusionfor Energy and JAEA. This project has received funding from the European Union’s Horizon2020 research and innovation programme under grant agreement number 633053. The viewsand opinions expressed herein do not necessarily reflect those of the European Commission.References[1] A. Lyssoivan and et al., Plasma Phys. Control. Fusion 54, 074014, (2012)[2] M. Tripsky, T. Wauters, AIP Conference Proceedings 1580, 334 (2014).[3] V. Vahedi, M. Surendra, Computer Physics Communications 87, 179-198 (1995)[4] T. Takizuka and H. Abe, J. Comput. Phys. 25, 205, (1977)[5] A. Lyssoivan and et al., Proc. 41EPS P2.030, this conference (2014).[6] F.C. Schüller, Report on Applications of ICWC on ITER, (2009)41st EPS Conference on Plasma Physics P1.133

Monte Carlo simulation of ICRF discharge initiation at omega_LHR < omega

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Monte Carlo simulation of ICRF discharge initiation at omega_LHR < omega

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