The role of combined NNBI and ICRH heating for burning plasma physics studies in FAST H-mode scenarios Alessandro Cardinali a With the collaboration of: G. Calabrò a, M. Marinucci a, A. Bierwage c, G. Breyiannis a, S. Briguglio a, C. Di Troia a, G. Fogaccia a, P. Mantica d, G. Vlad a, X. Wang e, F. Zonca a, B. Baiocchi d, M. Baruzzo b, V. Basiuk f, R. Bilato g, M. Brambilla g, F. Imbeaux f, S. Podda a, M. Schneider f a) ENEA C.P. 65 - I-00044 - Frascati, Rome, Italy b) ENEA-Consorzio RFX, Padova, Italy c) Japan Atomic Energy Agency, Naka, Japan d) Istituto di Fisica del Plasma, Euratom-ENEA-CNR Association, Milan, Italy e) Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou, PRC f) CEA, IRFM, F-13108 Saint Paul Lez Durance, France g) Max-Planck-Institut für Plasmaphysik-Euratom Association, Garching, Germany 1
Summary Goal of the experiment High energy particle physics Description of the FAST tokamak Scenarii Description of the external power system NNBI ICRH The Physics of particle-particle & wave-particle interaction Quasi-linear Fokker-Planck equation Vlasov-Maxwell wave equation system The numerical tools Integrated scenarii Conclusions
Goal of the FAST experiment: High energy particle physics Preamble: The main difference between present days experiments and ITER will be the presence of alpha particles produced in DT reactions as the main heating source. Fusion alphas, with small characteristic orbit size (compared with the machine size), will mainly heat electrons and excite meso-scale fluctuations[f. Zonca]. In present day experiments relatively low energy fast ions, such as those generated by neutral beam injection and/or by ICRH minority heating, are characterized by medium or large orbit size and transfer their energy to thermal plasma ions while exciting macro-scale collective modes. The key control physical quantity for accessing burning plasma relevant dynamic regimes are plasma current, density and temperature, Plasma current is directly connected with particle orbit widths normalized to the machine size: Higher current means smaller fast particle dimensionless orbits. Relatively high density and low temperature, means lower critical energies above which fast particle predominantly heat electrons via collisional slowing down [Zonca F 008 Int. J. Mod. Phys. A 3 1165]. 3
Some quantities definitions & parameter requirements I Plasma radius normalized particle orbit width of fast particles: ˆρ fast Z fast 1/ M fast E fast m p a fast B T fast To be relevant for ITER, FAST experiment must have, as first requirement: ˆρ fast Z fast 1/ M fast E fast = ˆρ ITER m p a fast B T fast Z α 1/ M α E α ITER m p a ITER B T ITER In ITER the normalized orbit are ˆρ ITER = a ITER m α m proton 10 3 1.60 E ITER(eV ) 0.01 ( cm) 9.58 10 7 B T ITER ( Tesla)Z α ( gramms) m α 4
Some quantities definitions & parameter requirements II Plasma current scaling: a fast B T fast a ITER B T ITER = ξ I p fast I p ITER The requirement E fast E ITER = M α M fast Z fast Z α ξ I p fast I p ITER Recall us that in order to have a well confined orbit width and a relevant energy (above the critical energy) the plasma current must be I p fast = 1 ξ Z α Z fast M fast E fast M α E ITER I p ITER 5
Scaling of the plasma current for fast particles of different species 1 10 hydrogen deuterium helium3 Plasma current in MA 8 6 4 0 0 00 400 600 800 1000 Energy of fast particles in kev 6
The critical energy I To make clearer the concept of critical energy, and to quantify this concept, we write down some equations [D.V. Sivukhin, Reviews of Plasma Physics, Ed. Leontovich, Consultants Bureau New York, 4 93 (1966)]. From the theory of binary Coulomb collisions we can write the energy decrease of a test particle due to background species s with Maxwellian distribution function as: Ion dynamics dw b dt = 4πZ b e v b ( ) ( ) erf w ln Λ b,i n i Z i e i w i m i + m b m i m i m b π e w i + ( ) 4πZ b e erf w ln Λ b,e n e e e w e m e + m b v b m e m e m b π e w e b is the test particle; i (background ions); e(background electrons) ln Λ b,s is the Coulomb logarithm test particle-ions(electrons) collisions v b is the test particle-velocity-thermal-velocity-ratio w s = v ths ( ) Electron dynamics 7
The critical energy II The Sivukhin s equation simplifies considerably when: v thi << v b << v the For energies of test particles(deuterium) of about 1MeV, and plasma (deuterium) temperature of 10keV we have: v thd 6.9 10 7 cm/sec v beam D 1.38 10 9 cm/sec v the 4. 10 9 cm/sec dw b dt W b 4πZ b e 4 n e ln Λ b,e 3 π m e m b v the 1+ π Z 3 i m e n i v the m i n e W b 3/ m b 3/ ln Λ b,i ln Λ b,e Electron dynamics Ion dynamics 8
The critical energy III Defyining the critical energy W c ( kev ) = m b m p m e m p /3 ( π ) 1/3 ln Λ b,i ln Λ b,e /3 =14.8 M b i n i Z i i n e m p m i n i Z i n e 1 M i /3 /3 m p v the T e = ( kev ) the slowing down time τ sd = π Z b e 4 n e m b m e v the 1 ln Λ b,e 3 = 0.01 M 3/ bt e kev ( ) Z b n e10 14 ln Λ b,e = 9
We obtain the following equation The critical energy IV dw b dt = W b τ sd 1+ W c W b 3/ Which can be analytically integrated W b W c = 3/ W b0 3/ W +1 c e 3t τ sd 1 /3 W c If << 1 the test particle will be slowed-down by the electron species with the characteristic time t= sd / W b0 W c W b W c = W b0 W c e t τ sd If >> 1 the test particle will be slowed-down by ion species W b0 W b = 1 e W c 3t τ sd /3 10
The critical energy IV The fraction of energy transferred to the electrons and ions vs the ratio W is plotted showing the role c of the critical energy W b 11
On this basis a set of plasma and tokamak parameters have been chosen which are relevant for accessing burning plasma relevant dynamic regimes A device operating with deuterium plasmas in a dimensionless parameter range as close as possible to that of ITER and equipped with ICRH and NNBI as a main heating scheme would be able to address a number of important burning plasma physics issue. Information about the fundamental dynamic behaviour of fast ions in burning plasmas can be obtained by experimental studies of the fast ion tail produced by Ion Cyclotron Resonant Heating (ICRH) & NNBI injection. 1
FAST plasma parameters and scenarii Table 1: Operating scenarios H-mode & Extreme H-Mode scenarii of FAST are relevant for burning plasma physics studies The H-mode & Ext-H-Mode scenario of FAST have been obtained from the equilibrium calculated by MAXFEA code, and using iteratively the predictive 1.5-D transport code JETTO. To this end ICRH minority heating and NNBI heating are essential tools in FAST The FAST load assembling has been conceived to accommodate 30 MW of ICRH in 3 He minority heating scheme and 10MW of NBI (NNBI - Energy=0.7MeV (H) 1MeV (D)). FAST H-mode referente HMR H-mode extreme HME AT Full NICD I p (MA) 6.5 8.0 3.5 q 95 3.6 5 5 B T (T) 7.5 8.5 6 3.5 H 98 1 1 1. 1. <n 0 > (m -3 ) 5 1.4 1 β N 1.3 1.7. 3.4 τ E (s) 0.4 0.65 0.0 0.10 τ Res (s) 5.5 5 3 5 T 0 (kev) 13.0 9.0 1 7.5 Q 0.65 1.5 0.3 0.06 t discharge (s) 0 13 55 170 t flat-top (s) 13 45 160 I NI /I p (%) 15 15 60 >100 P ADD (MW) 30 40 40 40 13
THE TOKAMAK In the Fusion Advanced Studies Torus (FAST) [A. Cardinali, et al.; Minority ions acceleration by ICRH: a tool for investigating burning plasma physics, Nucl. Fusion 49 (009) 09500], the reference and extreme H-mode scenarios require 30-40 MW of external heating, mainly supplied by NNBI (10MW) and ICRH (30MW). These H-mode scenarios, both reference and extreme, are characterized by high magnetic field B=7.5-8,5T and high plasma current I p =6.5-8MA for a discharge time duration of about 13-0sec, with peak density.4-5x10^0m^-3 and temperature of the order of 10keV at the plasma centre. 14
Cryostat External Poloidal Coil Central Solenoid Toroidal Field Coil FAST load assembly view 15
Layout of the heating system: ICRH antenna Reference geometry (before optimization) with some relevant dimensions [m]. The antenna structure (figure) consists of a single cavity containing eight straps, two toroidal by four poloidal, protected by a Faraday Shield (FS) made of 30 conducting bars with squared crosssection. The analysis of the structure has been made with TOPICA (a computer code developed by the Plasma Facing Antenna Group of Politecnico di Torino), and 4MW per antenna has been calculated to be coupled to the plasma. 16
Power Spectra analysis Power spectra for the H-mode (left) and steady state(right) plasma profiles, provided a SOL length of 3 cm Power spectra for the H-mode (left) and steady state(right) plasma profiles, provided a SOL length of 3,4,5 cm 17
Layout of the heating system: NBI system M. Baruzzo, et al.first NBI Configuration Study for FAST Proposal, Proceedings of the 36th European Physical Society, Conference on Plasma Physics, Dublin, Ireland, June 9-July 3, 010, P4.194 (010). M. Baruzzo et al., Requirement specification for the neutral beam injector on FAST, 6th Symposium on Fusion Technology, Porto, Portugal, Sept. 010. FAST equatorial port and Neutral Beam (vertical section). FAST Neutral Beam Injector 18 Critical points between FAST equatorial port and Neutral Beam (horizontal section).
THE PHYSICS I The tokamak FAST, as said before, is essentially devoted to study the physics of fast particle: i) instabilities connected to this energetic ion population, ii) the radial transport of energetic ions due to collective mode excitations, iii) the coupling of meso-scalefluctuations with micro-turbulence,etc The key parameter for these studies is ß hot (thermal/magnetic energy density ratio) of the supra-thermal population, which can reach values up to 3%, well in line with the needs for exciting meso-scale fluctuations with the same characteristics of those expected in various regimes of reactor relevant conditions. ß hot, or its parallel and perpendicular component is defined as β hot = µ 0 p B β hot = µ 0 p B 1 = 4πµ 0m α B dµ dvv 4 µ f α ( v, µ )dvdµ 1 1 = πµ 0m α B dµ dvv 4 1 µ 1 0 0 ( ) f α v,µ ( )dvdµ 19
THE PHYSICS II In order to reconstruct the ß hot profile it is necessary to calculate the hot-particle distribution function, which results from NNBI and/or ICRH interaction with the plasma. Therefore before doing the physics of high energy particles, me must deal with NNBI and ICRH plasma interaction physics. To this end a SIMULATION of NNBI+ICRH heating, in FAST H-mode and extreme-h-mode scenarii, is obtained by a D full wave electromagnetic code TORIC [M. BRAMBILLA, Plasma Phys. Control. Fusion 41 1 (1999)] combined with SSFPQL [M. BRAMBILLA, Nuclear Fusion 34 111 (1994)], which solves the quasi-linear Fokker-Planck equation in -D velocity space in presence of ICRH and NBI. This heating code is iteratively coupled to the transport code for four time step in the profiles evolution, in order to have the self consistent evaluation of the plasma & power deposition profiles. 0
Interaction between Neutral beam and plasma particles: Fokker-Planck equation and distribution function I Concerning the NBI-plasma interaction, the starting point is the Fokker-Planck equation (D.V. Sivukhin; C.C.F. Karney) In spherical geometry we have: C( f b, f e ) + C( f b, f i ) = = Γb,e v v Φ ( u 1 f ew)v b v v + 1 v the + Γb,e 4v Ψ ( u ew) 3 + Γb,i v µ 1 µ ( ) f b µ + v Φ ( u 1 f iw)v b v v + 1 v thib + Γb,i 4v Ψ ( u w 3 i ) µ 1 µ µ ( ) f b f b t m α f b m e m b m i f b + + ( ) + C f b, f s s=i,e Φ u e w = Cδ ( v v birth ) where ( ) = erf ( u w) u w i i Φ u i w Ψ u i w ( ) = erf ( u i w) erf u w i Γ b,i = 4πn q i bq i ln Λ b,i m b ( ) = erf ( u w) u w e e Ψ u e w ( ) = erf ( u e w) erf u w e Γ b,e = 4πn q e bq e ln Λ b,e m b ( )er f ( u w) i u ib w ( ) ( u w)er f ( u w) i i u i w ( )erf '( u w) e u e w ( ) ( u w)erf '( u w) e e u e w u e = ( E beam m beam ) v the u ib = ( E beam m beam ) v thi w = v ( E beam m beam ) 1
Interaction between Neutral beam and plasma particles: Fokker-Planck equation and distribution function II To obtain the previous collisional operator we have used the following approximations: the background electrons are isotropic and Maxwellian. the background ions are isotropic and Maxwellian. The equation finally can be written at the steady state as Γ b,e w + Γb,i w w Φ( u w 1 f b e )w w w + v b w Φ u 1 f ( iw)w b w w + v b v thi m b f b v the m e m b f b m i + Γb,e 4w Ψ u w 3 e ( ) + Γb,i 4w Ψ u iw 3 ( ) µ 1 µ ( ) f b µ 1 µ µ + ( ) f b ( ) µ = δ N δt δ v v ( birth )δ µ µ birth 4πv birth ( )
Interaction between Neutral beam and plasma particles: Fokker-Planck equation and distribution function III To have some insight about the solution we make further assumptions: Isotropy µ = 0 v thi << v b << v the The equation assumes the relevant form: 1 τ sd v v v 3 3 ( + v c ) f b = δn birth δt ( t) roi ( ) 1 H v v birth 4πv v The solution is the classical slowing down distribution function f b = τ sd 4π 1 v 3 3 ( + v c ) δn birth ( t) δt roi H ( v v birth ) 3
Interaction between Neutral beam and plasma particles: Fokker-Planck equation and distribution function IV The distribution function is very different from a Maxwellian At large velocities it decays like 1/v 3 It becomes flat below the critical velocity It is not a good approximation of NBI It is a good approximation for the alpha-particle slowing down Anyhow, once known the distribution function we are able to calculate the Power Deposition Profiles of NBI and the hot parameter as defined before. These are the ingredients to perform the subsequent high energy particle physics. 4
Interaction between Ion cyclotron wave (ICRH) and plasma particles: Wave + Fokker-Planck equations and distribution function Maxwell-Vlasov non-linear integro-differential equation system Funzione di distribuzione E = 1 E c t 4πq α c t E = 1 B c t t f α + v f α + q α v B E + + E ext + m α c + vf α ( r, v,t)dv v B ext c v f α = 0 Campo elettrico & magnetico Campi esterni When considering collisions and mutual interaction between wave and particles we have (quasilinear-fokker-planck equation) d t f α = s C( f b, f s ) + C( f b, f b ) + S wave E ( ) + q s E dc m s f s 5
The previous equation system must be simplified on the basis of physics considerations If the field amplitudes are small such that W wave E << W thermal κt Fourier analysis for the time-dependence of the field (harmonic field) Linearization of the kinetic equation around a Maxwellian In the quasi-linear approximation (collisions) Drift approximation for orbits F α f α r, v,t e iωt r, v (,t) = F α r, v,t ( ) = Fα QL distorted ( ) + ( v,µ ) f α r, v,t ( ) B( r ) = B ( r 0 ) + Δr B ( r ) + 1 ( Δ r ) T B Δr +... For ICRH the cold plasma approximation (CPA) does not apply: Warm Plasma Limit. The presence of warm modes of propagation (like Bernstein modes) does not allow this limit. The integro-differential character of the equation cannot be removed. 6
Interaction between ICRH and plasma particles: Fokker-Planck equation and distribution function for minority species Concerning the ICRH-plasma interaction, the starting point is the Fokker-Planck equation (T.H. Stix, C.C.F. Karney, M. Brambilla) f min t s=species C( f min, f s ) + Q( f min ) + P( f min ) = 0 C( f min, f species ) = S collisions Q( f min ) = S wave P( f min ) = S Edc 7
The collision operator ( ) C f min, f s = species=electrons,ions = ν min,e w + ν min,i w w Φ u 1 f ( ew)w min w w + v th min v the w Φ u w 1 f ( i )w min w w + v th min v thi m min m e m min m i f min f min + ν min,e 4w Ψ u ew 3 + ν min,i 4w Ψ u w 3 i ( ) ( ) µ 1 µ µ 1 µ ( ) f min µ ( ) f min µ + Isotropic Maxwellian background of ions and electrons w = v v th min Φ( u i w) = erf ( u iw) u i w Φ( u e w) = erf u ew ( ) u e w ( )erf '( u i w) u i w ( )erf ' u e w u e w ( ) Ψ( u i w) = erf ( u i w) erf ( u iw) u i w Ψ( u e w) = erf ( u e w) erf ( u ew) u e w ( )erf ' u i w u i w ( ) ( )erf ' u e w u e w ( ) 8
Simplified quasi-linear diffusion operator due to ICRH In cylindrical geometry ( ) = S w = 1 ( v S w ) v Q f i = 1 v v v v D f i v where D = D ql ( v ) = D ql ( v, µ ) ( = D 0 E ) J p k v 1 µ Ω ci ( ) 1/ 9
Finally the equation to be solved at the steady state is: 1 w w Φ u 1 f ( ew)w min w w + v th min v the + Z w w Φ u 1 f ( iw)w min w w + v th min v thi 1 µ w ( ) m i m e m i m i f min f min w w D ql w, µ ν min,e v w fmin th min w µ f min µ + 1 4w Ψ u ew 3 + + 1 w ( ) Z 4w Ψ ( u iw) 3 µ µ 1 µ µ 1 µ ( ) f min µ 1 µ µ ( ) f min ( ) ( ) D ql w,µ µ + = ν min,e v w fmin th min w µ f min µ 30
Interaction between ICRH and plasma particles: Fokker-Planck equation and distribution function for minority species II To have some insight about the solution we make further assumptions: Isotropy µ = 0 v thi << v b << v the The equation assumes the relevant form: 1 w w 1 A w ( ) + w D( v, µ ) ql ν min,e v th min w F w w The solution is the classical Maxwellian distribution function for high energy particles found by Stix ln F w ( ) lnc = dw w 0 ( ) + w F( w) B( w) ( ) wb w ( ) ql w D w, µ + A w ν min,e v th min ( ) = 0 ( ) = Φ( u e w) + ZΦ( u i w) A w B w ( ) ( ) = Φ( u e w) T min T e + ZΦ( u i w) T min T i 31
It is possible to define a temperature of the minority tail T mintail = T e ( 1+ D ε) D = 3 A i A min D 0 1/ 4 3 π = 3 A i A min 1 P abs 1/ 4 3 π 4ν min/i n min T min ε = n e Z i n i m e m i T i T e 1/ 3
The numerical procedure in order to determine the distribution function of the heated (ICRH+NNBI) species and all the relevant quantities for the burning plasma physics analysis -The transport code JETTO (formation of the plasma scenario) -The wave code TORIC (which solves the D wave equation in general equilibrium geometry) -The D Fokker-Planck solver (which solves the D Fokker Planck equation for both ICRH and NBI heating system) -The HMGC and XHMGC codes which analyze the physics of energetic particles instabilities 33
The iteration process JETTO code t=7sec TORIC+SSQLFP codes Quasilinear Power Deposition Profiles JETTO code t=8sec TORIC+SSQLFP codes Quasilinear Power Deposition Profiles JETTO code t=9sec TORIC+SSQLFP codes Quasilinear Power Deposition Profiles JETTO code t=10sec TORIC+SSQLFP codes Quasilinear Power Deposition Profiles Steady State Reached EXIT HGCM code 34
Example of integrated calculation: Summary plots Summary plots show the evolution of the parallel(a) and perpendicular(b) effective temperatures, and of the tail minority fraction(c) for all the iteration procedure, corresponding to three different times of the discharge (7s,8s,9s ) and a total 30MW ICRH power coupled to the plasma. 35
The calculation of the ß hot for the sequence shown before 36
-hot is the relevant parameter in establishing the relevance of the FAST H-mode scenarii in order to study the energetic particles-induced Alfvenic instabilities. 3.5 d e n s i t y = 5 X 1 0 19 cm -3 FAST P ICRH =10MW/m -3 ; n min =0.01; 3 He; B=7T d e n s i t y =. 3 X 1 0 0 cm -3 3.5 FAST Hmode extreeme n =.5X10 0 m -3 ; n e min =0.0; 3 He; B=8.5T 7. 5 power density=50m W / m -3 3 3 36.5 18.5 14 beta_hot in % 1.5 beta_hot in % 1.5 9.5 1 1 0.5 d e n s i t y = 5 X 1 0 0 m -3 0.5 power density=5m W / m -3 (a) 0 4 6 8 10 1 electron temperature in kev 0 4 6 8 10 1 14 16 electron temperature in kev Figures a)-b) - a) plot of -hot vs the electron temperature for several values of the plasma density at fixed ICRH power density and toroidal magnetic field for H-mode Scenario 1% of 3 He. b) as before but several values of power density and fixed density and magnetic field for the Extreme H-mode scenario % of 3 He. 37 (b)
hot as calculated by the ICRH full-wave code (TORIC-SSFPQL) and using the JETTO code (part of the JAMS JET suite of integrated codes with GLF3 transport model. For ICRH heating profiles we have used the TORIC code which is run outside JETTO and requires a few iterations. 300 50 FAST H-mode extreme scenario evolution of T_eff n=.94x10^0 m^-3; f=78mhz; B=8.5T; I_p=8MA; 3 H e = % 0.01 0.008 FAST H-mode extreme scenario evolution of β_hot n=.94x10^0 m^-3; f=78mhz; B=8.5T; I_p=8MA; 3 H e = % temperature in kev 00 150 100 T_perp t=9s T_para t=9s T_perp t=10s T_para t=10s T_perp t=11s T_para t=11s β_hot ICRH 0.006 0.004 β_hot perp t=9s β_hot para t=9s β_hot perp t=10s β_hot para t=10s β_hot perp t=11s β_hot para t=11s 50 0.00 0 0 0. 0.4 0.6 0.8 1 x 0 0 0. 0.4 0.6 0.8 1 x Effective temperature of the energetic ion minority ß hot profile 38
When including NNBI (Deuterium beam of energy=1mev and P NNBI =10MW) on the same plasma target we have a PDP as calculated by ASCOT included in the JETTO code (part of the JAMS JET suite of integrated codes with GLF3 transport model, and consequently a calculated ß hot (parallel). 1 0.05 NNBI Power Deposition Profiles [MW/m^3] 10 8 6 4 electrons ions FAST H-mode extreme scenario 3rd iteration + NNBI n=.94x10^14 cm^-3; f=78mhz; T_e=10.578;T_i=9.87 kev; B=8.5T; I_p=8MA; 3He=% beta_hot-nnbi parallel 0.0 0.015 0.01 0.005 FAST H-mode extreme scenario β_hot profile P_NNBI=10MW deuterium beam E=1MeV on ICRH heated plasma at P_ICRH=30MW n=.94x10^0 m^-3; f=78mhz; B=8.5T; I_p=8MA; 3 H e = % 0 0 0. 0.4 0.6 0.8 1 ro_pol Power deposition profiles of the beam 0 0 0. 0.4 0.6 0.8 1 ro_pol parallel ß hot profile 39
A comparison in the determination of the hot profiles is made by using two transport models for both ICRH and NNBI 0.01 0.01 β hot perpendicular BgB+rotation β hot parallel BgB+rotation β hot perpendicular GLF3 β hot parallel GLF3 0.06 0.05 FAST H-mode extreme scenario β_hot profile P_NNBI=10MW deuterium beam E=1MeV on ICRH heated plasma at P_ICRH=30MW n=.94x10^0 m^-3; f=78mhz; B=8.5T; I_p=8MA; 3 H e = % beta_hot 0.008 0.006 0.004 Scenario Hmode extreme third iteration. P ( I C R H ) = 3 0 M W + P ( N N B I = 1 0 M W on ohmic plasma target f=78mhz, n peak=10; fraction He3=1% or % beta comparison vs transport model: BgB+ rotation & GLF3 r e s o n a n c e s : 1) r=0.5(hfs) the fundamental of deuterium ) r=0.77(llfs) the fundamental of helium 3 beta_hot-nnbi parallel 0.04 0.03 0.0 BgB transport model + rotation GLF3 transport model 0.00 0.01 0 0 0. 0.4 0.6 0.8 1 ro_pol 1. 0 0 0. 0.4 0.6 0.8 1 ro_pol The BgB transport model seems to predict a broader perpendicular hot profile with respect to the GLF3 reaching at the peak the value of 1.1%, well in line with ITER expectation. Concerning the parallel hot profile (due to the NNBI power deposition) seems to be broader and much more peaked than the hot obtained with GLF3 transport model. 40
Changing the operation ICRH-frequency (f=8mhz) the deposition profile is on-axis. ß hot is optimized and can reach 3%. 1400 0.035 temperature in kev 100 1000 800 600 400 perpendicular temperature parallel temperature FAST H-mode extreme scenario 3rd iteration n=3.x10^14 cm^-3; f=8mhz; T_e=15.4;T_i=14.6 kev; B=8.5T; I_p=8MA; He3=% β hot 0.03 0.05 0.0 0.015 0.01 beta hot perpendicular beta hot parallel Scenario Hmode extreme 3rd iteration. P(ICRH)=30MW on ohmic plasma target f=8mhz, n peak=5; resonances: 1) r=0.6(hfs) the fundamental of deuterium ) r=0.1(llfs) the fundamental of helium 3 00 0.005 0 0 0. 0.4 0.6 0.8 1 x 0 ρ pol 0. 0.4 0.6 0.8 1 Effective temperature of the energetic ion minority ß hot profile 41
Once the FAST extreme H-mode scenario profiles are determined self-consistently with the iterative procedure described above, these are used as initial condition for numerical studies of resonant excitations of energetic particle driven Alfvénic fluctuations and related transports [3]. The FAST extreme H-mode scenario is characterized by a dense spectrum of Alfvénic fluctuations with the same wavelength and frequency spectra that are expected in ITER (peaked at 15 < n < 5). a) Application of the HMGC&XHMGC codes for the stability study b) c) -In Figs. a)-b)-c). a) Intensity contour plot of the n=8 Alfvénic mode in the space of normalized frequency and radial position. The shear Alfvén continuous spectrum for n=8 is indicated by the black solid line; b) Intensity contour plot of the n=16 Alfvénic mode in the space of normalized frequency and radial position. The shear Alfvén continuous spectrum for n=16 is indicated by the black solid line; c) Effect of n=8 and n=16 saturated EPM on the ß hot radial profile. -Both figures demonstrate the destabilization of EPM fluctuation branches, which track the toroidal precession resonance with the ICRH induced supra-thermal ion tail, as expected in this case and as predicted by theory. -The effect of n=8 and n=16 saturated EPM on the ß hot radial profile, shown in Fig. C), suggests that significant radial redistributions of energetic particle are expected with limited global losses. 4
Conclusions The proposed tokamak FAST in the H-mode scenarii is particularly indicated in order to investigate (experimentally) energetic particle physics: e.g. Alfvénic mode excitation, supra-thermal particle transports etc. Numerical tools like the hybrid MHD gyro-kinetic code HMGC and XHMGC can be used for predicting and interpreting the experimental data. A wide study of the wave-particle interaction is mandatory to establish if the conditions required for this goal are fulfilled by the experiment. For example the generation of a high energy population of ions with relevant value of hot. Numerical codes like TORIC+SSFPQL are devoted to study the interaction between ICRH and NBI with the plasma particles. The use of these numerical tools has been integrated in a global numerical investigation which includes a transport codes (like JETTO) with several transport models. The result of this analysis show that, as for the FAST H-mode reference scenario, the envisaged extreme H-mode scenario not only maximizes the machine performance and neutron yield, but is as well capable of addressing integrated experiments that are relevant in the view of ITER (e.g. preparation of ITER operations). 43
References Modeling Transport, ICRH and NBI. [1] A. Cardinali et al, Nucl. Fusion 49 (009) 09500. [] A. Pizzuto et al, Nucl. Fusion 50 (010) 095005. [3] G. Cenacchi and A. Taroni 1988 JETTO: A free boundary plasma transport code; report JET-IR (88) 03 [4] M. Brambilla, Plasma Physics and Controlled Nuclear Fusion 41 1 (1999) [5] M. Brambilla M 1994 Nucl. Fusion 34 111. [6] Brambilla M 007 Nucl. Fusion 47 75. [7] Brambilla M and Bilato R, submitted to Nucl. Fusion. [8] F Mirizzi et al., Fusion Engineering and Design 84 (009) 1313 1316 [9] M Baruzzo, Proceedings of the 37th EPS Conference on Plasma Physics, Dublin, Ireland, June 010, P5-14 Modeling Instabilities. [1] Briguglio, S, Vlad G, Zonca F, and Kar C, 1995 Phys. Plasmas 3711. [] X. Wang et al., 011, Phys. of Plasmas, 18 05504. [3] L. Chen, F. Zonca, 007, Nucl. Fusion 47 S7. 44