Bilato, R.

Bonoli, P.

Brambilla, M.

Wright, J.

English

MPG.PuRe

Investigation of ICRF heating scenarios in ASDEX-Upgrade with thefull-wave TORIC packageR. Bilato1, M. Brambilla1, J.C. Wright2, P.T. Bonoli21 IPP (MPI) – Euratom Association – Garching, Germany2 PSFC (MIT) – Cambridge (Massachusetts), U.S.AIntroductionRadio frequency (rf) heating with waves in the Ion Cyclotron (ICRF) range of frequenciesplays an important role in the operation of the present fusion devices, and will be one of themost relevant heating systems for ITER. The capability to simulate propagation and absorp-tion of ICRF waves is central for the analysis of experiments, and in designing scenarios withoptimal ICRF performances. Here some possible ICRF scenarios in ASDEX-Upgrade (AUG)are analyzed with the full-wave TORIC code [1], whose capability to simulate large devicesand challenging scenarios (such as mode conversion) has recently been greatly improved by theparallelization of the solver [2]. TORIC solves the wave equation in general toroidal axisym-metric configurations and describes the propagation and absorption of the externally excited fastwave (FW). It models ion absorption at the fundamental ω = Ωci and first harmonics ω = 2Ωcicyclotron resonances, and electron absorption via Landau and transit time damping. In addi-tion, TORIC can simulate the excitation of ion Bernstein waves (IBW) and ion cyclotron waves(ICW) at the ion-ion resonance layer (IIRL). TORIC has been recently provided [3] with newmodules, and in particular with a Fokker-Planck code for ions (SSFPQL) [4], which solvesthe steady state surface-averaged quasilinear Fokker-Planck (FP) equation for ions heated atω = Ωci and at ω = 2Ωci. SSFPQL gives an approximate 2–dimensional distribution functionand the collisional redistribution of the heating power absorbed by the ions at the fundamen-tal cyclotron resonance. The implemented algorithm is very fast, but the suprathermal tails canbe described only up to moderate energies v/vth i <∼ 7, and some toroidal effects important atlarge energies are omitted. The consistency loop between the two codes can be closed, since,in calculating the wave-equation coefficients, TORIC can use the distribution function of theminority ions evaluated by SSFPQL [3].The richness of ICRF physics is mainly due to the strong dependence of the wave propagationand absorption on the plasma composition, i.e. the presence of more ion species with differentcharge to mass ratios. Limiting our analysis to the main plasma compositions used in AUG,we study the transition from the minority (MH) to mode-conversion (MC) heating regimes asfunction of the minority concentration. To guarantee numerical convergence in the MC regime33rd EPS Conference on Plasma Phys. Rome, 19 - 23 June 2006 ECA Vol.30I, P-2.134  (2006)these simulations are performed with up 500 radial elements and 255–511 poloidal modes.Hydrogen in DeuteriumThe AUG ICRF system works mainly at 30 MHz of frequency, and the most common ICRFscenario in AUG is minority heating in D(H) plasmas. The ICRF antennas consist of two strapssuch that the mean peak of the excited spectrum is centered around nφ = 6 and nφ = 12,0 0.1 0.2 0.3 0.4010203040506070#17297 @ 5.1 secP[%]ν HH (ΩcH)D (2ΩcD)electronsututututututututututututututututututututututututututututututututututututututututuuuuursrsrsrsrsrsrsrsrsrsrs rs rs rs rsrsrsrsrsrs rs rs rs rs rs rs rs rs rsrsrsrsrsrsrsrsrsrsrsrsrrrrrrr r r r rrrrututututututututututututututututututututututututututututututututututututututututuuuuuuFigure 1: rf power distribution in a D(H)plasma as function of the H concentrationfor nϕ = 12: solid lines with Maxwelliandistribution functions (df) for the minority,open symbols with df calculated by SSF-PQL with 4 MW of coupled power, and fullsymbols are the second iteration of TORIC-SSFPQL. The dashed lines are the first iter.with 10 MW of rf power.respectively for pi/2 and pi phasings (k‖ ≈3.5m−1 and k‖ ≈ 7.m−1). In this scenario thewaves launched from the low field side (LFS) en-counter first the H cyclotron resonance ΩcH =2ΩcD and then the ion-ion evanescence layer(IIEL), bounded by ion-ion S = n2‖ resonancetowards the high field side (HFS) and by theL = n2‖ cutoff towards the LFS. The rf powernot absorbed neither by ions at ω = ΩcH nor bythe electrons is partially reflected and transmit-ted at the IIEL, and mode-converted to IBWs.As an example, we have considered the dis-charge #17297 at t = 5.1 sec, characterizedby central confining magnetic field B0 = 2 T,density ne(0) ≈ 6.8× 1019 m−3, electron tem-perature Te(0) ≈ 4.6keV, and ion temperatureTi(0) ≈ 4.9keV. As function of the H concen-tration νH ≡ nH/ne, Fig. (1) shows (solid lines)how the rf coupled power is distributed amongthe two ion species and the electrons. The valuesreported for electrons are comprehensive of thecontributions due to damping of FWs and IBWs.The transition to mode-conversion regime startswhen the S = n2‖ resonance emerges from theDoppler-broadened cyclotron resonance layer, which happens when νH is larger than a criti-cal value [5]:νc =2αn‖vthmc{ α21−α2+(n2‖−1)v2AMc2}(1)with α = ΩcM/Ωcm, and vAM the Alfvén speed of the majority ion species. According toEq. (1), MC starts to play a role for νH >∼ νc ≈ 18%, in agreement with TORIC results. In33rd EPS 2006; R.Bilato et al. : Investigation of IC Heating Scenarios in ASDEX-Upgrade with the Full-Wa... 2 of 4Fig. (1), around νH ≈ 20% the decrease of the power absorbed by H with νH is due to theincrease of the IIEL optical thickness with νH in combination with the fact that the reflectedFWs crosses again the ω = ΩcH resonance, with further absorption by the minority. WhenνH is further augmented, the increase of screening of the wave field component E+ by H issuch that the ion absorption at ω = ΩcH is overwhelmed by electron Landau damping. Theopen symbols of Fig. (1) refer to TORIC results after an iteration with SSFPQL, with a re-alistic value of coupled rf power of 4 MW. At low concentrations (νH <∼ 7%) the finite Lar-mor radius effects of the fast minority-ion tail reduces the power absorbed by the minority.0 0.1 0.2 0.3 0.4 0.501020304050607080#13799 @ 3.0 secP[%]ν 3He3He (Ωc3He)D (ΩcD)electronsututututututututututututututututututututututututututututututututututututututututututututututututututrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsutututututututututututututututututututututututututututututututututututututututututututututututututFigure 2: rf power distribution in a D( 3He)plasma as function of 3He concentration.However, as soon the νH increases, the effec-tive perpendicular temperature of the tail de-creases, and a slight increase of the parallel ef-fective temperature causes an increase of thepower absorbed and a shift of the MC transi-tion to a slightly larger concentration. In the caseof 10 MW of coupled power, reported in dashedlines in Fig. (1), there is a further shift of the MCto higher concentrations and an increase of theminority heating for medium values of νH .The results of the 2nd iteration TORIC-SSFPQLfor 4 MW are reported in full symbols in Fig. (1).At moderate values of coupled rf power one iter-ation is enough to reach convergence.Helium 3 in Deuterium and in HydrogenThe main difference of D(3He) respect toD(H) is that the cyclotron resonance of the mi-nority does not correspond to the first harmon-ics resonance of the majority. This implies that the thermal correction σ of the S element ofthe dielectric tensor is not resonant, and the IBWs have much shorter perpendicular wave-lengths (n2⊥ IBW ≈ −S/σ ) [6]. In addition, part of the reflected FWs are converted to ICWs,which are efficiently damped via electron Landau damping. Using the same temperatureand density profiles of #17297, Fig. (2) shows the power distribution for the equilibrium of#13799 at 3 sec (B0 = 3.15 T). In D(3He) scenario there is a clear transition to MC domi-nant regimes around the concentration νc ≈ 9%, as predicted by Eq. (1). When ν3He >∼ 20%,E+–screening by D ions around ω = ΩcD decreases, and they start to play the role of the33rd EPS 2006; R.Bilato et al. : Investigation of IC Heating Scenarios in ASDEX-Upgrade with the Full-Wa... 3 of 4minority. Consequently, to an increase of the fraction of power absorbed by D it corre-sponds a decrease of the power converted in IBWs and ICWs, absorbed by the electrons.0 0.1 0.2 0.3 0.4 0.501020304050607080#20619 @ 3.3 secP[%]ν 3He3He (Ωc3He)H (ΩcH)electronsutututututututututututututututututututututututututututututututututututututututututututututututrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsrsututututututututututututututututututututututututututututut ututututututututututututututututututFigure 3: rf power distribution in a H( 3He)plasma as function of 3He concentration.The modulation of the peak absorption aroundν3He ≈ 9% is due to radially standing waves be-tween the plasma boundary and the L = n2‖ cut-off [7]. The “virtual cavity” length, dependent onν3He, determines the magnitude of |E+|2 at theL = n2‖ cutoff, and thus influences the amount ofrf power transmitted to IBWs, which are mainlyabsorbed by electrons.Finally, in H(3He) mixture the transition to MCregime is at lower concentrations (≈ 3.80%,value predicted by Eq. (1)) and much sharper,as shown in Fig. (3) for B0 = 2.29 T. In thisscenario, the waves have to tunnel across IIELto reach the minority cyclotron layer. Thus, asν3He increases, the fraction of rf power whichcan reach ω = Ωc3He decreases rapidly. This sce-nario is similar to 3He(D) represented in Fig. (1)at high ν3He. However, the transition to MC inH(3He) is sharper and at lower values of the concentration than in 3He(D) , since at the sameion temperature the Doppler broadening is less for 3He than for D ion species.AcknowledgmentsWe are indebted to D. Coster and C. Angioni for the helpful discussions on the ICRF scenariosof interest for AUG.References[1] BRAMBILLA, M., Plasma Phys. and Contr. Fus. 41 (1999) 1.[2] WRIGHT, J. C., BONOLI, P. T., BRAMBILLA, M., et al., Phys. Plasmas 11 (2004) 2473.[3] BRAMBILLA, M. and BILATO, R., to appear in Nucl. Fus. (2006).[4] BRAMBILLA, M., Nuclear Fusion 34 (1994) 1121.[5] WESSON, J., Tokamaks, Clarendon Press, 2003.[6] BRAMBILLA, M., Kinetic Theory of Plasma Waves, Oxford University Press, USA, 1998.[7] COTSAFTIS, M. and SY, W. N.-C., Physics Letters A 93 (1983) 193.33rd EPS 2006; R.Bilato et al. : Investigation of IC Heating Scenarios in ASDEX-Upgrade with the Full-Wa... 4 of 4