Modelling the synergy between NBI and ICRF waves in JET fusion product studies experiments

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1 14 th IAEA TM on Energetic Particles, Vienna, 1-4 Sept Modelling the synergy between NBI and ICRF waves in JET fusion product studies experiments M. Schneider, T. Johnson, R. Dumont, J. Eriksson, L.-G. Eriksson, J.B. Girardo, T. Hellsten, V. Kiptily, T. Koskela, M. Mantsinen, M. Nocente, S. Sharapov and JET contributors* * See the Appendix of F. Romanelli et al., Proceedings of the 25th IAEA Fusion Energy Conference 2014, Saint Petersburg, Russia.

2 Outline Fusion product studies experiments at JET NBI+ICRF third harmonic deuterium heating scheme JET fast ion diagnostics for code validation Integrated modelling tools for NBI and ICRH Experimental and modelling results Sawtooth stabilization by fast ions Summary and prospects Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 2

3 Fusion product studies at JET Fusion products are crucial for future fusion devices: To sustain fusion reactions and reach ignition For diagnostic purposes Essential to study fusion products in present day tokamaks. Purpose of JET 2014 fusion product studies (FPS) experiments: To heat NBI D beams up to the MeV range To enhance DD and DHe 3 fusion reactions To measure fusion products with available fast ion diagnostics. To provide data for stringent validation of fast particle codes. Here we review modelling activities addressing this issue within the EUROfusion Code Development project for integrated modelling (WPCD). Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 3

4 Example of JET 2014 FPS shot DD neutron rate #86459 A quite spectacular result! DD neutron rate up by a factor of 6 because of only 3 MW of ICRF power added to 4.5 MW NBI power. Clearly a nice case for ICRF physics study. So how does it work? Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 4

Experimental conditions (1) 3 rd harmonic D heating (ω = 51 MHz ) Because of the possibility to heat H minority ions at the HFS, the ICRH power was progressively increased and magnetic field

5 Experimental conditions (1) 3 rd harmonic D heating (ω = 51 MHz ) Because of the possibility to heat H minority ions at the HFS, the ICRH power was progressively increased and magnetic field decreased (safety reasons): 2.9 < P ICRH < 4.2 MW 2.24 < B T < 2.33 T ω = 3ω cd ICRH resonance layer located in the centre Fund. H 2nd D 3rd D 2 nd H Main competition is between ω = 3ω cd absorption and direct electron damping (TTMP, ELD) ; additional parasitic damping is assumed to take place at the edge. Creation of MeV range D ions. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 5

6 Experimental conditions (2) Enhanced fusion reactions: D D plasmas: D + D He 3 + n D + D T + p This presentation is based of D plasmas only. D He 3 plasmas: D + He 3 α + p D + He 3 Li 5 + γ He 3 ions have been injected in order to induce DHe 3 fusion reactions producing 3.7 MeV α particles, similar to those from DT reactions. [S. Sharapov,Thursday, P38] Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 6

7 Physics considerations (1) ω = 3ω cd ICRH is a Finite Larmor Radius (FLR) effect leading to acceleration & deceleration during a Larmor orbit Net effect, v, because E-field varies over Larmor orbit: Absorption strength 2 k ~ D RF ~ E + J v k 2 ω + E c J v 4 ω c For thermal particles: weak interaction and absorption (k v /ω cd <<1) Strong interaction with energetic particles Create a "seed absorptivity" using NBI [M. Mantsinen et al, PRL 2002] Note: strong coupling between wave deposition and fast particle distribution [L-G Eriksson et al, NF 1998] n = 3 E + B E + v k = k x x Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 7

8 Cross section (barns) log(f) (a.u.) Physics considerations (2) ICRH is a diffusive process: 2 k D RF ~ E + J v k 2 ω + E c J v 4 ω c Diffusion efficient at strong gradients Almost barrier NBI only NBI+ICRH cutoff DD fusion reactivity enhanced at high energy: E JET NBI energy range 3-4 MeV Perfect scheme for accelerating D ions to near the peak of the DD cross section and thereby drastically increase the neutron rate! Projectile energy (kev) Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 8

9 Diagnostics and code validation As already said, fusion product studies are important for mainly two reasons: Fast particle physics Validation of simulation codes In fact these two are inextricably linked: only by comparing simulations with experiment one can make detailed assessments of the fast particle physics. Consequently, having high quality fast particles diagnostics available is crucial. For the 2014 JET FPS experiments three key diagnostics were utilised [M. Nocente,Thursday, P35]: Neutron spectrometers: TOFOR and compact detectors (diamond/liquid scintillator) Gamma ray spectrometers Neutron camera Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 9

Synthetic diagnostic: Monte Carlo for neutron emission spectrum [C Hellesen et al, PPCF 2010] FLR effects [J.

10 TOFOR neutron spectrometer Time of flight detector: measures relative time between 2 sets of scintillators. Deduces the neutron energy and thereby the energy of fusion reactants: D + D He 3 + n Vertical line of sight. Synthetic diagnostic: Monte Carlo for neutron emission spectrum [C Hellesen et al, PPCF 2010] FLR effects [J. Eriksson et al, PPCF 2013] 2 MeV D orbit in JET Detailed comparison between TOFOR and simulations require finite orbit width and FLR effects. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 10

Diamond neutron spectrometer Single Crystal Diamond Detector (SDD) : compactness would enable spectroscopic information along multiple collimated lines of sight. Oblique 47 line of sight.

11 Diamond neutron spectrometer Single Crystal Diamond Detector (SDD) : compactness would enable spectroscopic information along multiple collimated lines of sight. Oblique 47 line of sight. SDD detector Response function computed by MCNP code [ Expected neutron spectrum computed by GENESIS code [Tardocchi et al, PRL 2011] Reference: [M. Nocente et al, sub. to Rev. of Scientific Instrum. 2015] Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 11

12 HpGe gamma spectrometer High Purity Germanium measures the Doppler broadening of gamma-ray emission profiles from multiple excited states: Be 9 + D B 10 + nγ Be 9 + D B 10 + pγ Vertical line of sight. Gamma-ray peak Doppler broadening gives information on reactant energy. Gamma-ray emission profiles predicted by the GENESIS code. Reference: [V.G. Kiptily et al NF (2002)] Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 12

13 Neutron camera Set of scintillators assembled in: one vertical collimator array one horizontal collimator array Reconstruction of the 2D spatial distribution of the emitted neutrons. Reference: [M. Riva et al, FED 2011] Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 13

14 ICRH simulation: a model problem In order to simulate third harmonic ICRF heating with a reasonable degree of physics fidelity one must self consistently solve: E = ω2 c 2 ε f i df i dt Source of particles (NBI) Dielectric tensor (operator) collisions E iωμ 0 j ext wave-particle interaction Thus integrated modelling involving a wave field solver and a solver of the resonating ion distribution function is needed. Wave equation = S 0 + C f i + Q(f i, E) Fokker-Planck equation Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 14

15 ICRF modelling for JET Code Solves Limitations Self-consistency PION Power dep D distrib. Simplified models YES SELFO LION Full wave + FP MC Circular geometry YES SELFO-light LION Full wave + 1.5D distrib. Simplified FP model YES ASCOT/RFOF Monte Carlo (FP) Only FP NOT YET SPOT/RFOF Monte Carlo (FP) Only FP NOT YET ASCOT and SPOT are integrated in the European platform for Integrated Modelling (EU-IM) [G. Falchetto et al, NF 2014]. Augmented with wave-particle interaction module RFOF [T. Johnson et al, AIP Proc. 2011]. They can be used with any EU-IM integrated wave code (CYRANO, EVE, LION, TORIC). Self-consistency can be achieved by solving the wave and Fokker-Planck equations iteratively. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 15

16 Wave codes Beam codes Modelling the NBI+ICRH synergy Synergy scheme in EU-IM platform: BBNBI NEMO CYRANO LION EVE Simplified wave ASCOT RFOF SPOT RFOF Fokker-Planck codes PION is being implemented in EU-IM. ASCOT/RFOF: BBNBI beam code [O. Asunta et al, CPC 2014] Wave from PION [L.-G. Eriksson et al, NF 1993] ASCOT Fokker-Planck [E. Hirvijoki et al. CPC 2014] SPOT/RFOF: NEMO beam code [M. Schneider et al, NF 2011] Wave from PION SPOT Fokker-Planck [M. Schneider et al, NF 2005] Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 16

17 SPOT, ASCOT / RFOF modelling Detailed modelling requires finite orbit width effects: achieved with Monte Carlo codes, SPOT and ASCOT, augmented with the RFOF module. Wave deposition data from PION [M. Mantsinen,Wed., P21]. An algorithm has been developed to make the RFOF absorption profiles roughly consistent with PION: E + = E norm g R, Z E = E E + E norm g R, Z Why E norm? E norm normalisation factor g R, Z shape factor, kept fixed. The wave absorption deforms the ion distribution This modifies the absorption strength The wave E-field must be adjusted to get the required power. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 17

18 On the need for self-consistency SPOT and ASCOT simulations are time dependent (fixed bkg) The evolution of E norm (t), to maintain the power, indicates that the absorption strength evolves as the D tail develops. The global D absorption strength is roughly ~ E norm (0)/E norm (t) 2 SPOT simulation PION simulation: single pass D absorption coefficient goes from ~20% at the beginning of the ICRF phase to ~ 80% towards the end. This clearly shows the need for self-consistent calculations of the wave power deposition and ion distribution function. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 18

19 The RFOF Monte Carlo operator (1) RFOF applies a "kick" in velocity of the markers of OFMC codes every time a resonance is encountered, i.e. when dφ dt = ω nω c k v D = 0 wave ion cyclotron frequency frequency Doppler shift Resonance condition An elaborate algorithm is used to deduce the exact position. The applied kick is obtained from the QL operator of the Fokker- Planck equation adapted to OFMC codes using accelerated collisions [Eriksson PoP 2004]. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 19

20 The RFOF Monte Carlo operator (2) A kick is applied to: I = ωb μ keeping nω c I = E I I φ = P φ N ω E 2-step modified Euler-Maruyama scheme: constant. δi = ξ 2D RF I N ACC ΔI = ξ 2D RF I + δi N ACC ξ = random number, ξ = 0, ξ 2 = 1 E ± = wave polarized E-field J n = first kind Bessel functions φ(t) = phase D RF = Ze 2 τ res+ τ res v E + J n 1 k v ω c + E J n+1 k v ω c e iφ t dt New local velocities and position of the particle (Δv, Δv, ΔR, ΔZ) are deduced from ΔI, keeping ΔI = 0 and ΔI φ = 0. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 20 2

Z(m) Z(m) Results: absorbed / transferred power Input wave from PION

Kick positions n = 3 n = 2 banana tips in the vicinity of the resonance

Collisional power to electrons γ camera E cri 80 kev R(m) R(m) ICRH trapped

region of the resonance layer Ions heated all along the orbit (by thermal

21 Z(m) Z(m) Results: absorbed / transferred power Input wave from PION simulation: P abs,d = 2MW; P abs,e = 0.9MW; k 50 m 1 and E /E Kick positions n = 3 n = 2 banana tips in the vicinity of the resonance layer x10 5 x10 5 #86459 #86459 #86453 Collisional power to ions Collisional power to electrons γ camera E cri 80 kev R(m) R(m) ICRH trapped ions above E cri transfer mainly to electrons: Electrons heated in the region of the resonance layer Ions heated all along the orbit (by thermal and low energy ions) Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 21

Orbits in the potato regime The density of markers with E D > 200 kev have been put in an orbit classification diagram, cf. [Eriksson & Porcelli, PPCF 2001].

22 Orbits in the potato regime The density of markers with E D > 200 kev have been put in an orbit classification diagram, cf. [Eriksson & Porcelli, PPCF 2001] λ = R δ p E μb 0 1 λ ψ φ ψ φ = 2q 0 Bδ p 2 c P φ Ze ψ φ < 1 potato regime ψ φ > 1 standard regime As can be seen most particles with energies above 200 kev are in the potato regime (ψ φ 1). This emphasises the need for full drift orbit treatment. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 22

23 Comparison with experiment Comparison with deconvoluted data: Allows to compare physical quantities Loss of quantitative information from diagnostics 2 diagnostics have been used for this comparison: TOFOR neutron spectrometer BGO gamma spectrometer deconvoluted with DeGaSum [A.E. Shevelev et al, NF 2013] Synthetic diagnostics are the most appropriate method for comparing modelling with experiment. 4 diagnostics were available for this comparison: TOFOR neutron spectrometer Diamond neutron spectrometer HpGe gamma spectrometer Neutron camera Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 23

24 Comparison with deconvoluted data Modelling: SPOT, ASCOT, PION Experiment: TOFOR (neutrons), BGO (gammas) High energy cutoff around MeV SPOT, ASCOT and PION close to TOFOR BGO predicts lower energy cutoff (under investigation). Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 24

25 TOFOR synthetic diagnostic Comparison of reconstructed number of counts & time of flights High time of flights correspond to low energies: - ASCOT - SPOT former version Good agreement for energy cutoff. ASCOT agrees with TOFOR measurements very well SPOT former version displayed discrepancies: this exercise has allowed to identify and fix the issue! TOFOR well suited to aid the validation of NBI & ICRH models. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 25

26 Diamond synthetic diagnostic Comparison of reconstructed number of counts and neutron deposited energy: Overall good agreement between synthetic reconstruction of ASCOT, SPOT and measurements. Less sensitivity to the fast ion tail than the TOFOR spectrometer: could be due to oblique line of sight. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 26

27 HpGe synthetic diagnostic Comparison of gamma-ray intensity measurements for three different time slices: 718 kev 9 Be(d,ng) 10 B 414 kev 1021 kev 4055 kev 2868 kev Good agreement even before the fast ion tail is completely established, due to high energy cutoff early established. Not as sensitive as TOFOR regarding intermediate energies. L5 L4 L3 L2 L1 GS Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 27

28 Neutron camera Reconstruction of the spatial distribution of emitted neutrons: ASCOT/RFOF SPOT/RFOF horizontal vertical horizontal vertical Overall good agreement. Slight discrepancy for ASCOT with vertical camera and SPOT with horizontal camera. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 28

29 Soft X-ray signal Monster sawteeth in FPS experiments Sawtooth can be stabilized by a large population of fast ions in the centre Essential to control this stabilization. 4 discharges display monster sawteeth in fusion product studies experiments [JB Girardo et al, sub. to PoP (2015)]: What mechanism leads to the crash? Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 29

30 Porcelli model for sawteeth Reference: [F. Porcelli, PPCF (1991)] A sawtooth remain stable as long as the potential energy functional is positive: δw = δw MHD + δw NBI +δw ICRH usually negative (destabilizing) usually positive (stabilizing) MHD potential energy functional: computed by MISHKA [A.B. Mikhailovskii et al, PP Reports 1997] Kinetic energy functional: δw NBI computed analytically [C. Angioni et al, PPCF 2002] (using ion distribution from NEMO beam model + SPOT) δw ICRH computed by HAGIS [S. Pinches et al, CPC 1998] (using ion distribution from SPOT/RFOF) Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 30

Broadening of the fast ion distribution. No stabilization anymore: δw decreases until the crash.

31 FIR interferometry Results for sawtooth stabilization δw is found to be increasing: not consistent with crashes. However: For 2 of the discharges: Tornado modes are observed Fast particles expelled from the core. Broadening of the fast ion distribution. No stabilization anymore: δw decreases until the crash For the 2 other discharges: ELM bursts are observed. Trigger inward cold front reaching q = 1 surface. Destabilization D α signal Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 31

32 Summary Recent JET experiments were aimed at studying fusion products from DD and DHe 3 reactions. 3 rd harmonic ICRF heating with NBI synergy modelled using SPOT and ASCOT codes extended with RFOF module using PION wave deposition data. SPOT and ASCOT are implemented in the EU-IM framework, while PION is being implemented. Comparison with n and γ synthetic diagnostics has shown the value of synthetic diagnostics for validating heating codes. Sawtooth analysis shows a stabilization by fast ion distribution, yet crashes occur, possibly due to tornado modes or ELM bursts. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 32

33 Prospects The validation of ICRH codes has only been started: Application domain to be mapped Self-consistent simulations are mandatory This activity is being carried out within the EU-IM framework (EUROfusion WPCD project): Full wave codes are being adapted to treat non-maxwellians FP Monte Carlo codes are modified to handle variation of kinetic profiles in transport solvers for ICRH simulations The EU-IM Heating and Current Drive workflow is ready for self-consistent ICRH modelling. Synthetic diagnostics need to be implemented in EU-IM Next step: integration of sawtooth description in EU-IM and ITER Integrated Modelling Analysis Suite [F. Imbeaux et al, IAEA 2014] for full self-consistency. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 33

34 Thank you! Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 34

35 References (1/9) S. Sharapov et al, IAEA-EP 2015 "Fast Ion D-D and D- 3 He Fusion on JET" => Overview of JET 2014 Fusion Product Studies experiments M. Mantsinen et al, PRL, 88 (2002) 10 "Alpha-Tail Production with Ion-Cyclotron-Resonance Heating of 4 He-Beam Ions in JET Plasmas" => ICRH 3 rd harmonic He 4 heating (NBI+ICRH synergy) L.-G. Eriksson et al., Nucl. Fusion, v.38, p.265 (1998) "ICRF heating of JET plasmas with the 3 rd harmonic deuterium resonance" => ICRH D heating in D plasmas Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 35

36 References (2/9) M. Nocente et al, IAEA-EP 2015 "Dual sightline measurements of MeV range deuterons with neutron and gamma-ray spectroscopy at JET" => JET neutron and gamma diagnostics for JET Fusion Product Studies experiments C. Hellesen et al, PPCF 52 (2010) "Neutron spectroscopy measurements and modeling of neutral beam heating fast ion dynamics" => TOFOR synthetic diagnostic J. Eriksson et al., PPCF 55 (2013) "Finite Larmor radii effects in fast ion measurements with neutron emission spectrometry" => FLR effects in TOFOR synthetic diagnostic Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 36

37 References (3/9) "A General Monte Carlo N-Particle (MCNP) Transport Code" => MCNP code M. Tardocchi et al, PRL 107, (2011) "Spectral Broadening of Characteristic γ-ray Emission Peaks from 12 C 3He, pγ 14N Reactions in Fusion Plasmas" => GENESIS code V.G. Kiptily V.G. et al, Nuclear Fusion (2002) "γ-ray diagnostics of energetic ions in JET" => JET gamma-ray diagnostics. G. Falchetto et al, Nucl. Fusion (2014) "The European Integrated Tokamak Modelling (ITM) effort: achievements and first physics results" => WPCD project Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 37

38 References (4/9) T. Johnson et al, AIP Proc. 1406, 373 (2011) "Library for RF Interactions in Orbit Following Codes" => RFOF code M. Mantsinen et al, IAEA-EP 2015 "Analysis of ICRF heating and ICRF-driven fast ions in recent JET experiments" => PION for JET Fusion Product Studies experiments O. Asunta et al, Comp. Phys.Comm., 188 (2015) Modelling Neutral Beams in Fusion Devices: Beamlet-Based Model for Fast Particle Simulations. => BBNBI code Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 38

39 References (5/9) L.-G. Eriksson et al, Nuclear Fusion 33 (1993) 1037 "Comparison of time dependent simulations with experiments in ion cyclotron heated plasmas" => PION code E. Hirvijoki et al, Comp. Phys. Comm., 185 (2014) "ASCOT: Solving the kinetic equation of minority particle species in tokamak plasmas" => ASCOT code M. Schneider et al, Nucl. Fusion 51 (2011) "Simulation of the neutral beam deposition within integrated tokamak modelling frameworks" => NEMO code Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 39

40 References (6/9) M. Schneider et al, PPCF 47 (2005) "On alpha particle effects in tokamaks with a current hole" => SPOT code L.-G. Eriksson, M. Schneider, Phys. Plasmas, 12, (2005) "Monte Carlo operators for ions interacting with RF waves" => QL operator with acceleration scheme for MC codes. L.- G. Eriksson, F. Porcelli, PPCF 43 (2001) "Dynamics of energetic ion orbits in magnetically confined plasmas" => Orbit classification. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 40

41 References (7/9) T. Hellsten et al, 21 st Topical Conference on RF Power in Plasmas, Lake Arrowhead, California (2015) "RF Heating for Fusion Product Studies". => SELFO-light simulations for JET FPS experiments. A. Shevelev et al, Nucl. Fusion 53 (2013) "Reconstruction of distribution functions of fast ions and runaway electrons in fusion plasmas using gamma-ray spectrometry with applications to ITER" => DeGaSum deconvolution code (γ-spectrum fast ion distrib) M. Riva et al, Fus. Eng. and Design 86 (2011) ''The new digital electronics for the JET Neutron Profile Monitor: Performances and first experimental results" => JET neutron camera. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 41

42 References (8/9) J.B Girardo et al, submitted to Phys. Plasmas (2015) "Stabilization of Sawteeth with 3 rd Harmonic Deuterium ICRF-Accelerated Beam in JET Plasmas" => Sawtooth analysis of JET Fusion Product Studies experiments. F. Porcelli, PPCF (1991) "Fast particle stabilisation" => Porcelli model for sawteeth A.B. Mikhailovskii et al, Plasma Physics Reports (1997) "Optimization of computational LHD normal-mode analysis for tokamaks" => MISHKA code Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 42

43 References (9/9) C. Angioni et al, PPCF (2002) "Neutral beam stabilization of sawtooth oscillations in JET" => Analytical expression of δw NBI for JET S.D. Pinches et al, Comp. Phys. Comm. 111, 133 (1998) "The HAGIS self-consistent nonlinear wave-particle interaction model" => HAGIS code F. Imbeaux et al, Proc. 25 th IAEA Fus. Energy Conf, TH/P St-Petersburg (2014) "Design and First Applications of the ITER Integrated Modelling & Analysis Suite" => IMAS platform. Mireille Schneider IAEA Technical Meeting on Energetic Particles 1-4 Sept Page 43

Analysis of ICRF heating and ICRF-driven fast ions in recent JET experiments

Analysis of ICRF heating and ICRF-driven fast ions in recent JET experiments M.J. Mantsinen,,a, C. Challis 3, J. Eriksson, L.-G. Eriksson 5, D. Frigione 6, D. Gallart, J. Garcia 7, C. Giroud 3, T. Hellsten