Impact of interaction between RF waves and fast NBI ions on the fusion performance in JET DTE2 campaign

This work presents a study of the interaction between radio frequency (RF) waves used for ion cyclotron resonance heating and the fast deuterium (D) and tritium (T) neutral Beam injected (NBI) ions in DT plasma. The focus is on the effects of this interaction, also referred to as synergistic effects, on the fusion performance in the recent JET DTE2 campaign. Experimental data from dedicated pulses at 3.43 T/2.3 MA heated at (i) 51.4 MHz, giving the central minority H and n = 2 D, and at (ii) 32.2 MHz for the central minority 3He and n = 2 T. Resonances are analysed and conclusions are drawn and supported by modelling of the synergistic effects. Modelling with transport code TRANSP runs with and without the RF kick operator predict a moderate increase, of about 10%, in DT rates for the case of the RF wave—fast D NBI ion interactions at the n = 2 harmonic of ion cyclotron resonance, and a negligible impact due to synergistic interaction between fast T NBI ions and RF waves. JETTO modelling gives a 29% enhancement in fusion rates due to the interction between RF waves and fast D NBI ions, and an 18% enhancement in fast T NBI ions. Analysis of experimental neutron rates compared to TRANSP predictions without synergistic effects and magnetic proton recoil neutron spectrometer indicate an enhancement of approximately 25%–28% in fusion rates due to RF interaction with fast D ions, and an enhancement of approximately 5%–8% when RF waves and fast T NBI ions are interacting. The contributions of various heating and fast ion sources are assessed and discussed.

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Introduction
Plasma heating by means of radio frequency (RF) waves in the ion cyclotron resonance heating (ICRH) range of frequencies is widely used in the current tokamaks [1].It is also one of the main heating sources that will be used in devices planned for the near future, including the ones which have been foreseen to operate in a deuterium tritium (DT) mixture [2,3].The presence of the DT mixture in burning fusion plasma largely determines the heating scenario to be used with RF waves.
Several ICRH schemes in DT plasma are proposed [2,[4][5][6] for the ITER reactor [7,8].The well established H minority heating scenario at fundamental frequency in D plasmas is not considered for ITER due to the available frequency ranges and partially due to the anticipated parasitic interaction of the RF waves with energetic alphas.The most viable scheme considered for ITER during the active DT phase is by means of ICRH heating of minority 3 He at the fundamental frequency.Under the conditions of a central toroidal magnetic field of 5.2 T, RF waves at 52.5 MHz and toroidal mode number of N ϕ ≈ 27, i.e.ITER's 3 He minority heating scenario [2,4], alphas and fast D ions will interact with RF waves at n = 1 resonance at a major radius shifted from the plasma centre by R − R 0 ≈ −1.6 m [9].Fast ions with a Doppler shift corresponding to parallel velocities of about v || ≈ 1 × 10 7 m s −1 will have a more central resonance.In particular, 0.8-1 MeV negative neutral beam injection (NBI) D ions can also have the required Doppler shift of v || ≈ 1 × 10 7 m s −1 .
It is widely acknowledged that under the conditions of burning DT plasmas, energetic alphas as well as both reactants, D and T ions, can also absorb RF power at fundamental n = 1 [4,9,10] or harmonic n = 2 frequency [11].This phenomenon is also called the synergistic effect and it has been reported in numerous studies [11][12][13][14][15][16][17][18][19][20][21].In the case of H or 3 He minority heating schemes, reactants D and T ions are required to have a certain energy in order to satisfy the Doppler shifted resonance condition necessary for good absorption [12].Understanding the interaction between RF waves and fast ions is essential in order to (a) understand if there is a benefit to the fusion performance from heating directly fusion reactants, fast D and T ions, via RF waves; (b) study the impact of the interaction of RF waves with fast ions on heating, i.e. do the accelerated fast ions or alphas have a different heating efficiency, and (c) to assess the impact of ICRH heating on energetic particles with regard to orbit losses.This paper discusses the synergy between RF waves at frequencies close to n = 2 D and n = 2 T resonances, and energetic D and T ions generated by NBI in JET.Data from the recent JET DT experimental campaign (DTE2) are analysed.NBI, which is the source of fast D and T populations, and ICRH, are the only auxiliary heating sources in the experiments discussed here.
When plasma is predominantly heated by NBI, there are in general two contributions to the fusion rates: thermal and beam-target (BT) reactions.In typical JET conditions, i.e. ion temperature T i ≈ 10 keV and NBI power P NBI ≈ 25-30 MW, thermal and BT rates are of similar magnitude for the DT mixture with nearly equal D and T densities.There are also beambeam (BB) reactions, but they are at least two orders of magnitude lower than BT rates.
The thermal DT reactivity <σ.v> peaks for ion temperatures of DT mixture at about T i ≈ 65 keV, while BT reactions have different maxima for fast D/T collisions on thermal T/D ions.Under the conditions of JET DT plasma, the latter are for energies of E D ≈ 127 keV and E T ≈ 192 keV (figure 1).In general, the JET NBI system can inject fast D and T ions with a maximum energy of the order of E full ≈ 110-120 keV.A substantial number of fast ions are, however, born with energies between half, E full /2, and a third, E full /3, of this energy and as they slow down via collisions a smooth fast ion distribution over the range from T i to E full will be formed, as shown by a shaded rectangle at the bottom left of figure 1.At these energy levels, BT reactions are not fully optimized for fusion performance and further energizing of fast NBI D and T ions would have a beneficial impact on BT rates.Although the full energy of NBI D ions is of the order of E full ≈ 120 keV, i.e. close to the maximum of BTDT, the bulk of the fast ions produced by NBI is for lower energies: approximately 46% of NBI fast ions are born at E full /2, and about 21% at E full /3.Therefore, accelerating lower-energy fast D ions in the range between E full /2 and E full /3 will obviously be beneficial regarding BT rates.As for the fast T NBI ions, the gap between JET's NBI capabilities and BT maximum is larger, and accelerating them up to 200 keV can be regarded as greatly beneficial (figure 1).
It is well known from the literature [22] that for fast ions, the critical energy and the electron-ion slowing down time determine their dynamics in hot plasma.An estimate of these parameters is provided here for DT = 0.5/0.5 mixture at T e = 10 keV, n e = 7 × 10 19 m −3 , table 1. Estimates are based [23,24] on the following well-known expressions: (1) where A is fast ion atomic mass, A j and Z j are plasma composition atomic mass and charge, n j is plasma ion density, lnΛ is the Coulomb logarithm, W crit is the ion critical energy, τ s is the electron-ion slowing down time and τ th is the thermalization time for typical energies of fast ions.One should note that the estimates in table 1 cover only particular cases where plasma parameters, n e , T e , A j and Z j , are close to the specified ones, the ion Larmour radius is small, and orbits do not deviate significantly from flux surfaces.In real experiments where plasma parameters, n e , T e and plasma composition vary significantly from the plasma core to the edge, the parameters in table 1 and equations ( 1)-(3) can change significantly.In general, critical energy is linear with electron temperature, T e , while slowing down time is proportional to T e 3/2 and inversely proportional to electron density, n e .It is essential to also note that, in general, the fast ion species summarized in table 1 do not obey Maxwellian distribution.Except for the thermal fusion born alphas, fast ions are also not isotropic.
The study presented here focuses on n = 2 ICRH heating of fast NBI D and T ions and its impact on the fusion performance.The latter is measured by means of fusion rates which are analogous to neutron rates, both used in total or per unit volume units.The initial assessment of RF wavefast NBI ion interaction in JET DTE2 experiments was reported in [25].This report further extends the findings in [25] by means of adding new data and methods of analysis.Section 2 provides details of the numerical tools used in the study.Section 3 presents the experimental conditions and provides details about plasma parameters in the selected JET DT pulses.Section 4 focuses on the analysis of calculated and measured neutron rates.Discussions on the impact of the RF wavefast ion interaction physics insight of the processes involved is presented in section 5.A summary and conclusions are highlighted at the end.

Numerical tools used in the study
TRANSP [26] code is essentially used for interpretive analysis of the pulses investigated here.In addition, fast ion distribution functions (FI DF) are calculated using NUBEAM code [27] which is a computationally comprehensive Monte Carlo code for NBI heating in tokamaks.ICRH heating is usually split into two separate modules: an RF wave solver, which calculates the wave electric field for the target plasma mixture with selected minorities and the Fokker-Planck (FP) solver, which provides collisional exchange between heated species and the background plasma.Ideally, the two modules, the RF wave solver and the FP code, should be running self-consistently in an iterative loop since changes in the heated specie distribution function result in changes in RF wave dispersion and vice versa.In many applications, this is, however, a challenging task and achieving convergence between the two solvers might not be possible.The RF wave solver for TRANSP is TORIC code [28].It is coupled to a bounce averaging Fokker-Planck solver, FPP code [29], which uses up/down asymmetric equilibria and computes the minority ion phase-space distribution.The energetic minority ion distribution function from FPP is used to compute the collisional transfer of energy to bulk ions and electrons.Energy absorption by electrons, bulk and fast ions can also generally be assessed directly from the wave solver by means of calculating single pass abruption coefficients by each specie from the anti-Hermitian part of the dielectric tensor.
To study the RF wave absorption by fast ions treated by the NUBEAM code, i.e.NBI ions and alphas, a quasi-liner RF kick operator [9] is implemented in NUBEAM [30,31] and used in this study.TORIC provides information about RF electric field components, specifically the E + component and perpendicular wave vector, k ⊥ , for the main toroidal mode with toroidal mode number N ϕ .The RF resonance condition for a given harmonic is then used to calculate the magnetic moment and energy of the particles satisfying the resonant condition [31].Every time a fast ion passes through a resonance layer it receives a kick in magnetic moment space [32].The magnitude of the kick is derived from the quasi-linear theory [33], while the stochastic nature of the wave-particle Table 1.Typical parameters for various fast ions in fusion plasma at D/T = 0.5/0.5 plasma mixture and Te = 10 keV, ne = 7 × 10 19 m −3 .Critical energy and electron-ion slowing down time are estimated according to equations ( 1) and (2), while thermalization time, equation (3), is calculated for ions' typical energy <W>.In these estimates, lnΛ = 17 is assumed.Additional modelling is performed by means of JETTO code [34] coupled to the PION/PENCIL package for computing NBI and RF power absorption, taking into account the synergistic effects.PION code [35] is used in JETTO for ICRH minority and harmonic heating, utilizing its main advantage of being computationally fast, thus compatible with integrated modelling.The code interfaces [36] with the existing PENCIL NBI deposition code [37,38] and accounts for NB and RF synergy effects [13,36], thus providing a flux-surface averaged fast ion distribution function and RF power deposition self-consistently.The orbit effects on fast ion dynamics are neglected in the standalone PENCIL code as the fast ions are constrained to remain on the flux surface of birth throughout the slowing down process.In the PION/PENCIL coupling however, PENCIL only provides fast ion sources to PION, which uses its own slowing down model where orbit effects are included in a simplified way.The effects of toroidal rotation of the plasma on the BT rate are neglected in PENCIL and this is expected to have a small impact on the calculated neutron rates with rotation velocity in the core estimated to be at approximately 10 times lower than injected beam parallel velocity at maximum energy.In the PION/PENCIL package, however, PION subtracts plasma rotation from beam particle velocity, resulting in up to 5% loss of beam power in strongly rotating plasmas.Recent tests between PION/PENCIL and TRANSP, which take full account of toroidal rotation effects, are shown to agree within 5% for beamtarget DD neutron rates in JET high performance hybrid conditions.

Fast ion specie
The workflow for the analysis used in this study includes supplying TRANSP and JETTO codes with experimental profiles for electron density, n e , electron temperature, T e , ion temperature, T i , rotation, impurities and effective charge, Z eff .The two codes are then run in interpretative mode which provides deposition profiles by NBI and ICRH heating, fast ion densities and distribution functions and expected neutron rates.The effects of MHD modes on fast ion transport and losses are neglected in this study.In the pulses studied here, the q-profile and the start of the heating power are optimized, with q > 1 for a long enough period after the start of the heating, so that early MHD activities are avoided [39].Low amplitude and transient n = 2, 3 and 4 modes are observed but are thought to be benign with regard to fast ion losses.A more central n = 1 mode is followed by fishbone activities, which indicate more intense MHD-fast ion interaction appears much later, t > 10 s [39], compared to the time slices of interest in our studies.
For the purpose of this study, fusion reactions are calculated self-consistently with supplied profiles and calculated fast ion distributions.As discussed in the introduction, the two main sources of fusion neutrons, thermal and BT reactions, are approximately of similar order.While thermal neutron rates can be straightforwardly calculated since they are tabulated vs. T i [40], the calculations of BT rates require a detailed knowledge of fast NBI ion DF.The latter is provided by NUBEAM code and the synergistic effects are calculated with the help of the RF kick operator.Under the conditions of the JET DTE2 experiments, the DT fusion reaction has at least two orders of magnitude higher cross-sections than the accompanying DD and TT reactions, and features distinctive 14.1 MeV neutron production.Neutrons created from thermal reactions are nearly monoenergetic and isotropic, while BT neutron spectra can be quite broad and anisotropic [41].The broadening of spectra of the measured neutrons is directly related to energetic reactants as, for instance, for BT reactions the higher the energy of fast NBI ions, the broader the neutron spectrum.High energy neutron diagnostics, therefore, can be used to constrain the interpretative analysis by TRANSP and JETTO.For this purpose, the output of the simulations is used to calculate signals from 'synthetic diagnostics' which can then be directly compared with the measurements from the physical diagnostics.Achieving a high level of consistency between measurements and calculations for neutron rates and neutron spectra is an indication of good fidelity of the analysis.The set of available synthetic diagnostics used here includes neutron yield detectors, a neutron camera, and neutron spectrometers.

Diagnostics
Experimental data from standard JET diagnostics are used as input to the simulations discussed in this study.Electron density and temperature profiles are taken from the high resolution Thomson scattering diagnostics, referred to as HRTS here.The latter does not cover the very core of the plasma, therefore central values of electron density and temperature are taken from light detection and ranging, LIDAR, measurements [42].Electron temperature from the ECE radiometer [43] is also used in the analysis.Radiated power is measured by the bolometric diagnostics [44], while Z eff is assessed by means of bremsstrahlung measurements from visible spectroscopy.Ion temperature T i for the investigated pulses is obtained from the charge eXchange recombination spectroscopy diagnostic [45].
A wide range of neutron emission detectors is utilized.Neutron production counts are taken from the available neutron yield monitors [46].Details of JET's neutron emission neutron profile monitor are provided in [47].The instrument comprises two cameras; the horizontal camera consists of 10 collimators for 10 viewing chords and contains detector channels 1-10, viewing the vertical profile, while the vertical camera, comprising nine collimators and contains detector channels 11-19, views the horizontal (or radial) profile (figure 2(a)).
Data from the upgraded magnetic proton recoil (MPRu) spectrometer (figures 2(b) and (c)) are used in the analysis.The upgraded MPRu neutron spectrometer [48,49] has a horizontal/tangential view of the plasma (figure 2(b)) and probes the neutron energy spectrum by letting a collimated beam of neutrons from the plasma impinge on a thin plastic foil, in which some of the neutrons scatter elastically on protons in the foil, thus producing a secondary beam of protons, with energies that are closely related to the energies of the incoming neutrons.The energy spectrum of the protons is deduced by letting the protons pass through a magnetic field, where they are deflected with different curvature radii depending on their energy.The amount of deflection is determined by recording the strike position, X pos , on an array of scintillator detectors located after the magnetic system, as shown in figure 2(c).Larger values of X pos means a larger radius of curvature and hence a higher energy of the incoming neutron.An example of a measured MPRu spectrum is shown in figure 2(d), together with rough indications of the neutron energies that give rise to the signal in different parts of the spectrum.Precise conversion between X pos and neutron energy is challenging, due to the finite resolution of the spectrometer; however, the resolution function is well known and for a given neutron energy spectrum it is straightforward to determine the expected MPRu spectrum.
Data from JET's neutral particle analyzer (NPA) [50] is used to provide an assessment of the fast ion energies.Neutral particles are detected by means of low energy NPA with horizontal LOS at Z = +0.28m (LOS in figure 2(a) orange line) and high energy NPA (LOS in figure 2(a) red line) which has a vertical LOS at R = 3.07 m.The former diagnostic is an instrument which is designed to obtain energy distributions and the absolute intensity of hydrogen, deuterium and tritium atoms emitted by fusion plasmas in the total energy range 5-740 keV for H neutrals, 5-370 keV for D neutrals, 5-250 keV for T neutrals.The high energy NPA is capable of time resolved measurements of H, D, T, 3 He and 4 He atomic flux emitted by the plasma, in the energy range 0.3-3.5 MeV.

JET DT hybrid pulses
Similar JET 3.43 T/2.3 MA pulses based on the hybrid scenario [39,51,52] during the DTE2 campaign were selected for analysis in this study.ICRH was set up as an H or 3 He minority heating scenario.The minimum concentration of the minorities was used in some cases to ensure maximum RF power for the majority of ions, D and T [53,54], as minority heating scales with their density.Applied RF power in some cases is modulated with a square waveform with 80%-90% modulation depth, P ICRH,max ≈ 4-5 MW, P ICRH,min ≈ 0.4 MW, a and low frequency of about 1 Hz, parameters which provide a sufficient length of time interval, of about 0.5 s to be approximated, as being with full power ICRH or without ICRH power.In our studies, these periods will also be referred to as ICRH power on/off periods.This provides an experimental means to directly assess the synergistic effects.All experiments are in dipole phasing of the RF antenna featuring symmetric spectra with dominant peaks in the co-and counter directions at about toroidal mode number N ϕ ≈ ±27.
Most of the pulses used in the hybrid scenario feature H minority with X[H] = n H /n e ≈ 2%-3%, while a number of experiments are also performed with 3 He minority with X[ 3 He] = n 3He /n e ≈ 3%-4% [53].JET pulse #99596 is at 3.43 T/51.4 MHz with H minority, X[H] ≈ 2%, which gives the central fundamental H resonance at R res,H ≈ 3.00 m and no other resonances in the confined plasma, i.e. inside 2.00 m < R < 3.86 m.The pulse with 3 He minorities investigated here is #99639 at 3.43 T/32.2 MHz with X[ 3 He] ≈ 3.6% which gives fundamental 3 He resonance at R res,He3 ≈ 3.20 m.There are also pulses without injection of minorities [53,54]: #99643 is designed to have n = 2 D ICRH heating with a frequency of 51.4 MHz, while pulse #99886 is with n = 2 T ICRH heating at a frequency of 32.2 MHz.These cases will be referred to as n = 2 D (#99643) and n = 2 T (#99886) ICRH scenarios, while H/He3 minority scenarios will be used to refer to #99596/#99639 correspondingly.The difference between n = 2 and the corresponding ICRH minority scenario is that there is no minority injection in the former.Further details of the ICRH scenarios used for the investigated pulses can also be found in table 2. For JET geometry and a range of magnetic fields, n = 2 D and n = 2 T resonances are never both present simultaneously in the plasma core, i.e. inside the normalized toroidal radius of ρ < 0. Although no minorities are injected in n = 2 D and n = 2 T ICRH heating pulses, one can assume that there is a very small amount of residual H or 3 He in the vessel.The supplies of D at JET are usually of high purity, 99.999%, however, the data from visible spectroscopy indicate X[H] ≈ 0.2%-0.5%,i.e. 2-5 times higher H concentrations, even in the cases where no H is injected.The presence of 3 He in the vessel is also difficult to imagine, particularly when there are long periods during which 3 He is not used.However, bearing in mind that T naturally decays to 3 He with a half-life of about 12.32 years, even the purest T supplies can be easily contaminated with a small amount of 3   pulses are analysed after the transient high-performance phase at the beginning of the heating, i.e. in the period 8.5-9.5 s.Analysis during the early phase before 8 s is avoided as it does not represent steady state plasma with beams penetrating deeply in the core in conditions with lower plasma density.An evenly balanced DT mixture, D/T ≈ 0.5/0.5, is sustained in these experiments, while comparable sources of fast D and T ions are provided by the two NBI sources at JET. NBI power of between 24 and 30 MW is injected by two NBI beamlines, one with D and one with T neutrals.The injected NBI neutrals are at three energy levels, full/half/third energy component with typical values of the power fractions in them 0.5/0.3/0.2 for 100 kV of D beam and 0.6/0.2/0.2 for 100 kV of T beam.The full energy of the injected D and T neutrals in the reported experiments is between 83 and 112 kV.
The other pulses included in the analysis and presented here have, in general, very similar parameters to the ones presented in figure 3. Small variations in plasma parameters and fusion rates are due to slightly inconsistent input power levels and gas injections rates, which diverge within about 10% in the investigated pulse.The only differences with regard to the ICRH heating scenario are in the type of minorities, their concentrations and RF frequencies used in all these pulses.While it is an essential parameter in this study, which determines the amount of RF power available to fast ions, it is worth noting that in many cases, e.g. 3 He minority, the minority concentration could not be precisely controlled and kept constant during JET DT pulses.

Analysis of the synergistic effects in RF wave-fast NBI ion interactions
Determining the impact of the interactions between RF waves and fast NBI ions on fusion performance is quite a challenging task.As discussed in the introduction, the main issues are related to a number of indirect effects of RF waves on the plasma performance, e.g.providing direct and indirect ion heating, which impacts directly on the fusion performance.Due to the complexity of the problem, for the analysis presented here, an approach based on simulations and validation versus available synthetic diagnostics is adopted.
Initially, an assessment of the impact of the RF wavesfast NBI ion interaction on the fusion performance is made by performing a pair of TRANSP and JETTO interpretative runs, one with and the other without the effect of RF waves on fast particles.Due to the specifics of both codes, this is possible for JETTO modelling by running cases with realistic and negligible RF power, while in TRANSP this is done by switching on and off the RF kick operator.Switching off the RF kick operator in TRANSP will result in discarding the synergistic effects only while all other contributions related to the background plasma parameters will be preserved.As discussed in the experimental section, applied RF power in few cases is modulated with a square waveform, thus providing sufficiently lengthy time intervals of about 0.5 s, which can be approximated as being with full power ICRH or without ICRH power.This conclusion is backed up by assessments of the thermalization times shown in table 1, which for both D and T NBI ions with energies of 100 keV, are much shorter than 0.5 s.The thermalization times increase with the energy of the fast ions, equation (3), becoming comparable to 0.5 s for fast D and T ions with energies of about 400 keV.Based on this estimate, the end of the RF power switch off period can be used as a reference to conditions with negligible or no synergistic effects, and the RF power switch on period can be used to assess RF waves-fast NBI ion interaction.
In the next section, the impact of the synergy effects on FI DF is studied.

Fast ion distribution function
Fast ion density in (R, Z) spatial grid and the central distribution function mapped on 2D velocity mesh, derived by TRANSP are discussed here.Detailed analysis of both n = 2 D/T pulses #99643/#99886 is presented in [25], therefore here the emphasis is on showing the change in FI DF due to synergy effects.The latter is illustrated for n = 2 D pulse #99643 in figure 4 for the cases with a RF kick operator and high RF power (figures 4(a) and (b)) with a RF kick operator and low RF power (figures 4(c) and (d)) and without a RF kick operator (figures 4(e) and (f )).High and low RF power phases are referred to here as the periods at the end of modulation phases, considered to approximate steady state with and without synergistic interactions.The high RF power phase during modulation is taken at 8.94 s when P RF ≈ 4 MW is applied, while the lower power phase is selected at 9.44 s with P RF ≈ 0.4 MW (figure 3(a)).Fast D NBI ion density is always peaked in the core, while the cold plasma resonance is also in the vicinity of the mid-radius (figure 4(a)).Although negligible minority concentration X[H] = 0.5% is assumed in this run, the RF wave features very good first pass absorption, as shown by the plots of the |E − /E + | ratio and |E + | field (figure 5).The graph of the RF E + field (figure 5 Central fast D densities are in the order of 5.2 × 10 18 m −3 for the case with a RF kick operator and high RF power (figure 4(a)) and 3.8 × 10 18 m −3 for the case with a RF kick operator and low RF power (figure 4(c)) and 3.9 × 10 18 m −3 , for the case without a RF kick operator and low RF power ).As the injected NBI neutrals have energies lower than 112 kV, the enhancement of fast ions DF for energies higher than 112 keV is purely due to interactions between the RF wave and the fast ions.These changes to FI DF have direct and indirect impacts on the fusion rates.Direct enhancement of BT rates is a result of the increased energy of the fast D ions, i.e. accelerating D ions towards energies of about 130 keV has a direct impact on the BT fusion rates of fast D ions on target T ions (figure 1).The indirect effect of synergistic effects on fusion performance is due to the fact that further energizing the fast D ions leads to enhanced bulk ion heating.The latter is clearly observed from the central T i modulations with ICRH power in figure 3(b), taking into account negligible minority concentration in this case and assuming bulk D interaction with the n = 2 RF wave is small.The thermal velocity of bulk D ions, v th,D = (T i /m i ) 1/2 , is indicated in figure 4(b) by a red circle, while the parallel velocity v || ≈ 1 × 10 6 m s −1 needed for Doppler shifted resonance is provided by a dashed cyan line.Only a small amount of bulk D ions with small perpendicular velocity v ⊥ can interact with RF waves.The intensity of this interaction, however, is very small as for n = 2 it is proportional to a combination of Bessel functions, (J 2 , which is negligible for v ⊥ ≪ 1 × 10 6 m s −1 [25]. A fast ion DF with low RF power and with a RF kick operator is shown in figure 4(d), while for the case at low RF power and no RF kick it is shown in figure 4  The JET NPA diagnostic can provide experimental verification of fast NBI ion interaction with RF waves.The analysis of the data from the NPA diagnostic requires additional data processing and modelling of neutrals' transport in plasma.Assessing the birthplace of fast energetic neutrals from JET's NPA data is also challenging due to the high densities of these pulses.In some cases, there are also nonvalidated NPA channels which make the reconstruction of neutral distribution problematic.Despite all these  In JET conditions, central densities n e ≈ 2n D ≈ 2n T ≈ 7 × 10 19 m −3 and temperatures, T e ≈ T i ≈ 10 keV, the main collision processes acting as a source of energetic neutrals are ionizing collisions of fast ions with bulk neutrals and impurities and CX recombination between these species [50,55].These processes depend on background plasma parameters while escaping neutrals bear the signature, i.e. energy and pitch angle, of the fast ions they originate from.Figure 7 shows that NPA losses are correlated with RF power.Energetic D neutrals are higher during the RF power-on period than during the RF power-off period (figure 7(a)).There is a small number of H neutrals which also follow this trend, while for T neutrals it seems RF power does not have an impact.The latter is clearly seen in figure 7(b) where D and T neutrals trends for a selected three energies are plotted together with RF power.For energies E ≈ 150 keV to E ≈ 200 keV, D neutrals are clearly correlated with RF power while T neutrals are not.This picture is qualitatively consistent with observations in figures 4 and 6.Indeed, during the high RF power phase, the energetic tails of D ions are created for energies exceeding 125 keV (figure 4 influence the source of energetic D neutrals, as seen in figure 7.During the low RF power phase, the energetic D ion tail disappears (figure 4(d)), and so does the detected neutral D flux.Tritium is nonresonant with the RF wave in #99643, so the T fast ion DF is unaffected and therefore detected T neutrals are not correlated with RF power.Figure 7(c) shows the correlation between RF power and D and T neutrals for the highest available energy, E = 500 keV, for pulses #99643 with n = 2 D in red and #99639 with n = 2 T in blue.This is a qualitative indication that RF waves interact with fast D and T ions in plasma and accelerate ions to energies up to 500 keV.

Assessment based on neutron rates and neutron
camera data.Qualitatively, the impact of synergistic effects on fusion performance can be assessed by analysing the response of the DT neutron rates.The latter can be modelled or measured and achieving a good match between both provides additional confidence in the analysis.The effect of synergistic effects can be studied by modelling cases with and without RF wave-fast NBI ion interactions.Initially, this assessment was performed by means of interpretative analysis by TRANSP.
Two runs of TRANSP were carried out: one with the RF kick operator included in the calculations and one without it.Direct comparison between the results from these two runs gives an estimate of the impact of RF wave-fast NBI ion interaction.JETTO interpretative runs were also performed with the same input data and in a similar matter RF impact was investigated by comparing cases with realistic and negligible RF power.
Measured and calculated neutron rates, together with the computed BT and thermal rates, are shown in figure 8 for TRANSP simulations and figure 9 for JETTO runs.Relatively good agreement is observed between the measured and calculated neutron rates, with TRANSP overpredicting total neutrons at 9.0 s by about 13% in #99639 and by about 8% in #99643, and underpredicting the total neutrons by about 12% in #99886.These discrepancies are fully consistent with the expected accuracy of the TRANSP prediction of DT fusion performance, as indicated in recent studies [56].TRANSP results for plasma energy are found to be fully consistent, within 1%, with the diamagnetic measurements.
While measured and calculated neutrons of #99886 are higher than the ones in #99643, a closer look at the contributions to them reveal that this is due to mainly higher thermal rates.The latter is due to higher ion temperature in #99886 as it features higher NBI power.Beam-target rates of the two pulses are approximately similar despite a higher NBI power of #99886.
Comparing TRANSP runs with and without synergistic effects, solid blue lines vs. dashed cyan lines in figures 8(a) and (c) and the solid red line vs. the dashed magenta line in figure 8(b), gives the TRANSP estimate of the impact of the synergistic effects on the fusion performance.The assessments provided here are all at about 9.0 s.Interestingly, TRANSP predicts negligible impacts of the synergistic effects on fusion performance for RF wave interaction with fast T NBI ion cases (figures 8(a) and (c)), where blue lines and cyan dashed lines are almost overlapping.There seems to be no dependence on 3 He minority either, since case #99639 in figure 8(a) is for X[ 3 He] ≈ 3.6%, while case #99886 in figure 8(c) is with negligible X[ 3 He] ≈ 0.35% i.e. the pure n = 2 T case.As for the RF wave interaction with fast D NBI ions, TRANSP predicts a relatively reasonable improvement in fusion rates: approximately 8% for #99596 with H minority of X[H] ≈ 2% (not shown in figure 8) raising to about 10% for the #99643 pure n = 2 D case with no H minorities, solid red vs. dashed magenta lines in figure 8(b).
A similar type of assessment of the fusion performance enhancement due to synergistic effects is repeated with JETTO.Results of JETTO runs in which the same profiles are used as with TRANSP simulations are shown in figure 9. Due to the peculiarity of the PION/PENCIL treatment of fast ions, synergistic effects cannot be simply switched off in JETTO.Instead, runs with full ICRH power are compared versus similar runs, but with negligible RF power.This approach ensures that the thermal neutron rates are still properly accounted for in the interpretive run following the T i profile and DT mixture evolution.On the other side, RF wave-fast ion interactions have a direct impact on the synergistic acceleration of fast NBI ions, hence BT rates, so that having negligible ICRH power in this case can be considered as removing the synergistic effect similar to switching off the kick operator in the TRANSP runs.
In all the cases studied here, JETTO overpredicts the total fusion performance by about 25%-30% for the 3 He minority and n = 2 T cases #99639 and #99886, and by about 40% for the n = 2 D case #99643 (figure 9).Although in dedicated predictive studies on the hybrid scenario with H minority [57], JETTO has been shown to be in good agreement with measured DT neutrons, no systematic studies on the interpretative DT fusion rates in cases with lower minority schemes have been conducted so far.The discrepancies observed here could be partially attributed to the changes in NBI power, figure 3, and injected beam energy which directly impacts the BT reactions.Indeed, PION/PENCIL has a limited capability to account for varying injected energy and fractions caused by individual beam sources being tripped or reenergized during the pulse.The scenarios studied here are also either with 3 He minority, which is difficult to control, or with very low minority concentrations which contribute further to the observed discrepancies in calculated neutron rates.It is worth noting that despite being fed with the same kinetic profiles, i.e. n e , T e , T i , rotation, Z eff , etc., the two codes, TRANSP and JETTO, treat impurities and plasma composition in a completely different way which impacts D and T densities, resulting in different neutron rates.Further investigation of this matter is outside the scope of this study as the emphasis here is on the impact of RF waves on fast NBI ions and, for the expected strength of the synergistic interactions, the PION/PENCIL model is capable of providing a reasonable estimate of how much the fusion performance has been affected.In contrast to TRANSP calculations, JETTO predicts a reasonable impact of the synergistic effects on fusion performance for RF interaction with fast T ion cases, figures 9(a) and (c) blue lines and cyan dashed lines.At 9 s JETTO predicts fusion enhancement due to synergistic effects of about 9% for #99639 with 3 He minority and about 18% for n = 2 T case #99886.RF interaction with fast D ions improves the fusion rates by approximately 12% for the #99596 H minority case (not shown in figure 9) and by about 29% for the #99643 pure n = 2 D case, solid red vs. dashed magenta lines in figure 9(b).The latter numbers are about three times higher than the relevant TRANSP predictions.
Due to the observed discrepancies in TRANSP and JETTO predictions, an alternative method of determining the impact of synergistic effects is discussed here.This method is not sensitive to RF kick operator implementation and is based on the assumption that TRANSP is able to predict fusion performance with good accuracy.For JET this has been shown in recent DD [58,59] and DT experiments [56,57].Recent reports [60] also highlight that in older JET pulses, during the JET C wall period, neutron rates are largely overpredicted by TRANSP.Since the introduction of JET ILW and improved T i measurements, the statistics show relatively good consistency between measured and calculated neutrons.In this assessment, the measured neutron data in pulses with modulated ICRH power is compared to TRANSP predictions without RF synergy effects.For this purpose, a number of JET pulses which feature ICRH power modulation with a square waveform and low frequency of 1 Hz, are analysed.Because of the relatively longer periods with RF power being on or off, i.e. periods of 0.5 s, for which time duration is longer than the fast ion thermalization times (table 1) for fast D and T ions, one can assume that at the end of each ICRH power on/off period, FI DF is settled and steady state, i.e. it is nontransient and does not evolve.In addition, the ICRH power on/off periods are selected such that the background plasma parameters are not evolving and are relatively steady, as shown by the time traces in figures 3(a) and (b).Consequently, by comparing fusion performance at the end of each ICRH power on/off period, one can further constrain the analysis and assess the impact of the synergistic effects.Simulations without the RF kick operator in this case are expected to match reasonably well the neutron rates at the end of the ICRH power-off time intervals.The simulations are then compared to the experimentally measured fusion performances at the end of the ICRH switch-on period and the difference between modelled and measured data can be used as a more realistic assessment of the RF wave-fast NBI ion interactions.Neutron rates from TRANSP runs without the RF kick operator (dashed cyan line in figure 8(a) and dashed magenta line in figure 8(b)), are compared to the experimental data and scaled to match the measurements at the end of ICRH power-off time, 9.5 s in figures 8(a) and (b).This small adjustment, usually in the order of 5%-10%, of the modelled data is needed because sometimes TRANSP predictions deviate slightly from the measurements [56][57][58][59].The scaled predictions for the computed neutron rates (dash-dotted cyan line in figure 8(a) and dash-dotted magenta line in figure 8(b)), are then evaluated versus the measured ones at the end of the RF switch-on period, i.e. 9.0 s in figures 8(a) and (b).This procedure provides a more realistic estimate of the synergistic effects and gives about an 8% enhancement of the fusion performance for #99639 with n = 2 T with a small 3 He minority and about 28% for the #99643 pure n = 2 D case.These numbers are closer to the JETTO predictions than the TRANSP runs with and without the RF kick operator.
The methodology described above is further applied to the measurements by the neutron camera.Channels 15 and 16 are vertical, passing in the vicinity of the plasma centre, and in principle should provide the most accurate assessment of the line averaged rates (blue lines in figure 2(a)).Time traces of neutron camera data and scaled predictions by the TRANSP code are shown in figure 10.In this case, TRANSP is run without the RF kick and predicted neutron rates are scaled to match measurements at the end of the ICRH power-off phase at 9.5 s.Comparing the scaled rates from TRANSP with measurements at the end of the ICRH power-on phase, 9 s, gives a neutron rate enhancement of 7% for #99639 with n = 2 T with small 3 He minority and about 25% for #99643 pure n = 2 D case.These figures are consistent with the estimates described above, which are made with total neutron rate measurements and using the same procedure.

Analysis of neutron spectrum from MPRu measurements.
Data from MPRu is available for #99886 at about 8 s, i.e. the pure n = 2 T ICRH heating case, and relevant analysis is performed for this pulse [53].The initial estimates are done by means of the TRANSP fast ions distribution function in a workflow using an algorithm [41] which calculates expected neutron spectra, which is then converted into the expected MPRu spectrum.The latter is then compared to the MPRu measurements, i.e. data for the number of counts in scintillator detectors (figure 2(c)) versus the strike  The predicted MPRu spectra are in decent agreement with the data from the diagnostic when TRANSP FI DFs are used (figures 11(a) and (d)), for the scattered proton position up to X pos ≈ 35 cm, and in poor agreement for energetic neutrons corresponding to MPRu strike positions of X pos ≈ 39 cm and 41 cm.Very little difference between the calculated spectra by TRANSP, with and without the RF kick operator, is predicted following the dashed blue lines in figure 11(d).Based on these two TRANSP runs with and without the RF kick operator, a negligible impact on the fusion performance is expected to be due to RF wave-fast NBI ion interaction.
Predicted spectra with FI DF from the JETTO run with full RF power are shown by the dotted navy line in figure 11(c).The FI DF used in this case is presented in the same style line in figure 11(f ).Although this JETTO run predicts significant impact on the synergistic effects on the fusion performance, ≈18% increase, the FI DF from this JETTO run results in a spectrum which does not match MPRu measurements for X pos > 30 cm, as shown in figure 11(c).The same comparison with a trial fast T ion DF with a more pronounced RF tail (violet dash dotted line in figure 11(e)) has been attempted and shows very good consistency with experimental data, figure 11(b).
The analysis based on the trial fast T ion DF, with FI DF for energies up to ≈120 keV derived from TRANSP, and a more pronounced RF tail for E > 120 keV (figure 11 The results from MPRu analysis need further clarification.While FI DF with a RF tail (shown in blue in figure 11(e), dash-dotted violet line) matches very well the measured MPRu data, it is clear that this is not the only FI DF that will produce good agreement with experimental MPRu data.Undoubtedly, there are other FI DFs which will fit MPRu measurements and in general the analysis based on synthetic MPRu diagnostics should not be performed by guessing the FI DF.The FI DFs from TRANSP and JETTO, however, do not match the experimental data, as figures 11(a) and (c) show.Therefore, one naturally looks for a possible solution which is close to the predictions by the codes.In our case, this is FI DF based on predicted FI DF by TRANSP for energies up to NBI injection, E < 120 keV, and assuming a RF tail with a temperature of 80 keV for energies E > 120 keV, an assumption which is not completely unfounded.Fast ion DFs from TRANSP are compared to Maxwellian DF with a temperature of 80 keV in   6, one can conclude that the latter is a very good approximation for the FI energetic tail for energies E > 120 keV.

Discussion
Results from the various methods used in the study to assess the impact of RF wave-fast NBI ion interaction are summarized in table 2. Column 3 gives the changes in total neutron rates, ∆R NT /R NT , during ICRH power modulation pulses.These changes include indirect effects due to ICRH heating and therefore real enhancement of the fusion performance due to synergistic effects is expected to be lower.
The estimates of the synergistic effects provided in columns 4 and 5 are presently the most accurate ones as they use combinations of experimental measurements and modelling which is not dependent on the way the RF wave-fast ion interaction is implemented.The method, which uses TRANSP modelling with and without the RF kick operator for pure n = 2 D pulse #99643, evaluates that synergistic interaction between fast NBI D ions and RF waves and leads to a modest improvement in the fusion performance, approximately 10% higher (table 2).In addition, synergistic interaction between fast T NBI ions and RF waves is found to have little or no impact on the fusion performance as no increase in fusion rates has been observed in TRANSP simulations of #99639 and #99886.JETTO modelling with full and low ICRH power, on the other hand, predicts a 29% enhancement of fusion rates due to RF wave-fast D NBI ion interaction, and an 18% enhancement in fast T NBI ions (table 2).
Table 2 shows that TRANSP simulations with and without the RF kick operator (column 6) tend to underpredict the impact of RF wave-fast NBI ion interaction on the fusion performance when compared with experimental observations by neutron diagnostics (columns 4 and 5).The RF kick operator in TRANSP attempts to capture the physics of RF wave-fast NBI ion interaction (figures 4(b) and 6), however, as the MPRu analysis shows (figures 11(a) and (d)), acceleration to high energy is underpredicted.The change of FI DF in TRANSP with the RF kick operator seems to be insufficient to match measured neutron spectra by MPRu.
JETTO runs with lower and realistic power (table 2 column 7) and seems to overpredict the enhancement of fusion performance for the case of #99886 with n = 2 T without minorities.Fast ion DF by PION/PENCIL in this case (figure 11(f )) seems to overestimate the extent of the RF tail, particularly at the high-energy end, as it results in a poor fit to MPRu data (figure 11(c)).JETTO predictions are, however, in relatively good agreement with the assessments from neuron measurements and TRANSP modelling without the RF kick operator (columns 4 and 5) for the cases with modulated RF power, i.e. #99643 with n = 2 D without minorities and #99639 with X[ 3 He] ≈ 3.6%.
Neither of the two methods based on numerical analysis with and without RF wave-fast ion interaction appear to be capable of predicting very accurately the enhancement of the fusion performance.The reason for the significant differences in these predictions could be in the way the RF wave-fast ion interaction is implemented in TRANSP and JETTO.Both codes use various simplifications and approximations to the RF kick operator and RF-induced quasi-linear Table 2.Estimated enhancement of DT fusion rates due to RF wave-fast NBI ion interaction.Column 3 shows the increase in total neutron rates taken at time slices at the end of the RF power switch on/off in 1 Hz modulation cases.Assessment (a) is done using TRANSP run w/o RF kick in 1 Hz modulation pulses and comparing measured neutron rates versus predicted during the high RF power phase.Estimates in (b) are based on similar analysis to that in (a) but neutron camera data from central channel 15 is used instead of total neutron rates.The enhancement noted by (c) is based on MPRu analysis, as discussed in the previous section.The last two columns give an assessment by TRANSP run with and without RF kick operator and JETTO run with very low and real RF power.According to the results from TRANSP and JETTO, the impact of RF wave-fast NBI ion interaction decreases when adding minorities, even at low concentrations, X[H, 3 He ] ≈ 2%-4%.The methods of analysis based on MPRu and ∆R of neutron data (columns 4 and 5 in table 2) show a little or even positive effect on fusion performance by adding a small amount of X[ 3 He] ≈ 3%-4% in the n = 2 fast T NBI interaction, #99886 vs. #99639.In general, adding a negligible number of minorities should help with regard to generating more favourable E + electric field near ion cyclotron resonance.Adding too high a minority concentration, e.g.X[ 3 He] ⩾ 1%, however, would result in most of the RF wave power being absorbed by the minorities and a lower amount of it being available for interaction with fast ions.The two methods of analysis, however, MPRu and ∆R of neutron data, have different sources of errors, and for more complete conclusions on the impact of the minorities, one would ideally want to analyse the #99886 n = 2 T case with modulated RF power, or #99639 with 3 He minority by means of MPRu.Unfortunately, this kind of analysis and comparisons were not possible during the JET DTE2 campaign.

JET
Both modelling approaches, as well as the data based on experimental observations, indicate that accelerating fast D NBI ions by means of interaction with RF waves is more beneficial with regard to the fusion rates than accelerating fast T NBI ions.This conclusion seems to be counter intuitive, given the cross sections for the two cases presented in figure 1.Indeed, one would expect that accelerating fast T NBI ions from the NBI energy range E T ≈ 40-120 keV to energies exceeding 200 keV would significantly benefit BT fusion rates.Nevertheless, it seems better enhancement is observed when RF waves interact with fast D NBI ions.Understanding this phenomenon requires detailed investigation into the complex nature of RF wave-fast ion interactions.Ideally, one would need to map |E + | electric field from the RF wave and fast ion densities in the vicinity of the IRCH resonance.In addition, Doppler shift, trapped ion effects, as well as finite Larmor radius effects should be considered.This is a challenging task, so in the following we briefly discuss possible causes of this observation.
One possible reason for poorer enhancement of the fusion performance with RF waves-T NBI interaction is that T beam penetration is not as central as that of D beams.Indeed, for D and T beams at the same energy, the latter will have a lower velocity by a factor of about (2/3) 0.5 ≈ 0.81 due their higher mass.This means that when both are used in the same target plasma, neutral T beams will travel a shorter distance before being ionized.For plasma optimized for central D NBI deposition, it would mean that T deposition would be further away off axis.The latter is illustrated in figure 12, where fast D in (a) and T in (b) ion densities are plotted for #99886 at 9.4 s.Clearly, fast D density is higher in the centre, while fast T ion density is symmetrical, azimuthally shifted towards outboard.The |E + | field in the plasma centre, i.e. 3.00 < R < 3.10 m, was predicted [25] to be similar for both cases with n = 2 D #99643 and n = 2 T #99886.The number of resonant fast ions will then become an important parameter in quantifying the strength of synergistic effects in the plasma centre and clearly deeper penetration of D beams is beneficial in this case.It is clear from figures 12(a) and (b) that the number of fast D NBI ions will always be greater than the number of fast T NBI ions along the resonance line for any position of the latter in the plasma core.Another reason for the observed lower fusion enhancement in the T NBI case is due to unfavourable resonance location in this case, which is shifted to the LFS, ≈0.15 m, away from the plasma centre, cf figure 4 Another contribution which can, in principle, explain more pronounced synergistic effects with D NBI relies on the fact that RF wave absorption at n = 2 resonance is a finite Larmor radius effect.For equal perpendicular wave vector, k ⊥ , then the particles with larger perpendicular velocity, D ions in our case, will interact more strongly with RF waves.This effect has been assessed in [25] for 100 keV D and T ions and for equal |E + | field, k ⊥ and fast ion densities, and it is found that it would result in about a 40% stronger absorption of RF power by fast D ions compared with T ions.It is also worth noting that BT reactivity for fast D NBI ions has a slightly higher maximum and is greater than fast T NBI BT reactivity for energies up to 165 keV (figure 1).RF waves can accelerate fast NBI ions up to energies of a few hundreds of keV, but there are also changes in FI DF for lower energies, i.e. in the domain where D NBI BT reactivity is greater, E D ≈ 21-165 keV (figures 1 and 6) and it seems that ions in this energy range have a greater contribution to BT reactions.

Conclusions
TRANSP and JETTO simulations are used to study the impact of the synergistic effects between fast D and T NBI ions and RF waves on DT fusion performance.The modelling results are validated versus synthetic diagnostics.
The figures based on the analysis of the experimental data from dedicated pulses at 3.43 T/2.3 MA, heated with an approximately equal amount of D and T NBI and with ICRH power at (i) 51.4 MHz, giving central minority H and n = 2 D and at (ii) 32.2 MHz for central minority 3He and n = 2 T, indicate an approximately 25% enhancement of fusion rates due to RF interaction with fast D NBI ions, and approximately 5%-8% when RF wave-fast T NBI ion interaction is taking place.TRANSP underpredicts the improvement in fusion rates, which is also observed in D-only studies at ASDEX-U [61,62], while JETTO overpredicts them.Based on conclusions from this study, much more detailed and in-depth analysis would be needed to understand how the algorithms on RF wave-fast ion interaction work in each case.The results here suggest that such a further study is necessary in order to understand and highlight possible improvements to the models in the future.
All methods of assessment indicate that, regarding fusion performance, it is more beneficial to consider RF wave-fast D NBI ion interaction for the JET NBI energy ranges and plasma conditions.A plausible explanation for this phenomenon could be in the shallower penetration of T beams when compared to more central D beams.As a result of this study, we conclude that the scenario with fast T NBI ions can be further optimized with respect to achieving higher fusion performance.
A planned JET DTE3 campaign would not have a T NBI source, so studying the RF wave-fast T NBI ion interaction and, in particular, by means of application of modulated RF power, would not be possible.This, on the other hand, would be a great opportunity to study RF wave-bulk T ions.The application of modulated power is again strongly advisable in order to have a better assessment of the synergistic effects.

Figure 1 .
Figure 1.Beam-target reactivities ⟨σ.ν⟩ for DT reaction of a mono energetic beam with energy E on target ions with temperature of T i = 10 keV.D beams on T target ions' reactivity (red) is noted by BTDT, while T beam on D target ions' reactivity (blue) is noted by BTTD.The maximum of the two reactivities is noted by vertical dashed lines, ⟨σ.ν⟩ = 1.40 × 10 −15 cm 3 s −1 at E D = 127 keV for BTDT and ⟨σ.ν⟩ = 1.32 × 10 −15 cm 3 s −1 at E T = 192 keV for BTTD.The energy range of the JET NBI source is approximately noted by a horizontal shaded area colour coded by fast ion density at the bottom left corner.

Figure 2 .
Figure 2. Synthetic diagnostics in typical JET configuration for #99643 at 8.5 s in (a) with line of sight (LOS) of low energy NPA (orange horizontal line), high energy NPA (red vertical line) and central lines of neutron camera (blue lines for channels 15 and 16).Magnetic proton recoil (MPRu) spectrometer schematic is shown in (b), while schematic of detector cross section is in (c).The mapping of MPRu scattered proton positions and approximate location of the expected peak at 14 MeV are shown in (d).
2. Indeed, at 3.43 T and 51.2 MHz, giving n = 2 central D resonance, the position of n = 2 T resonance is at R ∼ 2 m.On the other side, at 32.2 MHz with central n = 2 T resonance, the n = 2 D resonance is outside the plasma at R ∼ 4.8 m.
He if they are stored for a longer period.Plasma parameters and kinetic profiles of #99643 with n = 2 D ICRH heating at 51.4 MHz and #99639 with 3 He minority, X[ 3 He] ≈ 3.6%, ICRH heating at 32.2 MHz are shown in figure 3.These two pulses are at similar electron density, line averaged values of about 5 × 10 19 m −3 , central electron density of about 7 × 10 19 m −3 , central electron temperature of about 7 keV and ion temperature of about 8 keV (figures 3(b) and (c)).Plasma core toroidal rotation in the order of 1 × 10 5 rad s −1 , i.e. about 3 × 10 5 m s −1 in the plasma centre, is measured during these experiments.Both

Figure 3 .
Figure 3. (a) Time traces of (top to bottom) NBI and radiation power, ICRH power, D concentrations, T concentrations, line integrated density, effective charge Z eff , neutron yield R NT and minority concentrations for JET 3.43 T/2.3 MA hybrid type pulses #99643 (red) and #99639 (blue).Time traces from the same two pulses showing (left to right) central density, electron and ion temperature evolution (b).Profiles of electron density, electron and ion temperatures of #99643 (red) and #99639 (blue) at 9 s.Measured values are indicted by symbols and error bars for a few radial positions, while smoother profiles used in TRANSP and JETTO interpretative analysis are given by lines.

Figure 4 .
Figure 4. Fast D NBI ion density and FI DF from TRANSP code for cases with (a) and (b) and without (c) RF kick operator for JET 3.43 T/2.3 MA hybrid type pulse #99643 with D/T mixture of ≈0.5/0.5.(a) Fast D NBI ion density at 8.94 s with P NBI ≈ 24 MW, P RF ≈ 4 MW is shown together with IC n = 2 D resonance (cyan line).(b) FI DF log(f fi (v ∥ ,v ⊥ )) at 8.94 s and R = 3.08 m, Z = 0.30 m (point noted with red diamond in (a) with FI density of n fi ≈ 5.2 × 10 18 m −3 ) together with Doppler shifted IC resonance (cyan dashed line).(c) Same as (a) but at 9.44 s with P NBI ≈ 22 MW, P RF ≈ 0.4 MW.(d) Fast D NBI ion DF at 9.44 s and R = 3.07 m, Z = 0.30 m (point noted with red diamond in (c) with FI density of n fi ≈ 3.8 × 10 18 m −3 ).(e) Same as (b) but for the case without RF kick operator.Unperturbed fast ions DF for the case without RF kick operator at R = 3.07 m, Z = 0.30 m (with FI density of n fi ≈ 3.9 × 10 18 m −3 ) is provided in (f ).

Figure 5 .
Figure 5. Ratio of amplitudes |E−/E+| of E− and E+ fields (a) and |E+| field in (b) for 3.43 T/2.3 MA hybrid type pulse #99643 at 8.94 s with P RF ∼ 4 MW by TORIC in conditions with negligible minority H concentrations, X[H] = 0.5%.n = 2 D cold plasma resonances are indicated by magenta line.ICRH power deposition profiles and the total absorbed ICRH power by species in the labels (c) for minorities (dashed line), fast ions (solid line), bulk ions (dash-dotted line) and electrons (dotted line).
(f ).The fast ion DF from figure4integrated over pitch angle is also shown in figure6as a function of energy.Comparing figures 4(b), (d) and (f ), one clearly sees the impact of the RF waves on FI DF due to synergistic interactions.Indeed, the modified FI DF during the high RF power phase of the modulation (figures 4(b) and 6 in red) features a significant energetic tail, while FI DF during the low RF power phase of the modulation (figures 4(d) and 6 in cyan) is essentially relaxed DF and almost does not feature an energetic tail.The latter is in fact very similar to the FI DF for the case without RF interaction (figures 4(f ) and 6 in blue).This observation is used further in this study to support the assumption that fast D ions would slow down to the original unperturbed DF determined by the NBI source at the end of the low RF power phase, i.e. within ∼0.4-0.5 s after RF power has become negligible.The simulations shown in figures 4 (b), (d), (f ) and 6 show that in terms of RF wave-fast ion interaction, the time at the end of modulation switch-off phase is sufficient to allow FI DF to relax to nonperturbed DF.

Figure 6 .
Figure 6.Fast D ions DF f fi (E) for #99643 at R = 3.08 m, Z = 0.30 m in linear (a) and log10 (b) scale and in an energy range of up to 400 keV.Fast D ions DF at 8.94 s with P RF ≈ 4 MW and n fi ≈ 5.2 × 10 18 m −3 is shown in red (case with RF kick), while at 9.44 s with P RF ≈ 0.4 MW and n fi ≈ 3.8 × 10 18 m −3 is shown in cyan (case with RF kick).The expected fast ions DF at 8.94 s with P RF ≈ 4 MW and n fi ≈ 3.9 × 10 18 m −3 without taking into account RF interaction is in blue (case without RF kick).For comparison, shown are Maxwellian DF, f Max , in magenta for n D ≈ 3 × 10 19 m −3 , T i = 8.55 keV corresponding to the bulk D ion density and temperature at R = 3.08 m, Z = 0.30 m and energetic ion Maxwellian DF with n fi ≈ 5.2 × 10 18 m −3 and T i = 80 keV in dotted magenta.

Figure 7 .
Figure 7. Analysis of NPA data.Low energy NPA data (a) for D (top), H (middle) and T (bottom) neutral fluxes from low energy NPA for pulse #99643 during RF modulation-on period 8.5-9 s in red, black and blue and RF modulation-off period 9-9.5 s in magenta, grey and cyan.Time traces of low energy NPA (b) for pulse #99643 for D (red) and T (blue) neutrals for three selected energies, ≈125 keV (top), ≈153 keV (second graph) and 200 keV (third graph) and modulated RF power (bottom).High energy NPA data (c) for escaping fast D and T particles from high energy NPA for #99643 with = 2 D in red and #99639 for n = 2 T in blue for energies of E N = 500 keV showing that NPA losses are correlated with ICRH power (middle graph) and neutron rates (bottom graph).

Figure 8 .
Figure 8.Comparison of measured and TRANSP neutron rates.Measured neutron rates for the selected three pulses are noted by R NT exp. in black solid lines and shadowed area for estimated experimental errors in all three graphs.Calculated neutrons are noted by R NT and TRANSP with and without RF kick, with estimated error bars in four time-slices for He3 minority pulse #99639 R NT with blue solid line in (a), for n = 2 D pulse #99643 R NT with red solid line in (b) and for n = 2 T pulse #99886 R NT with blue solid line in (c).Total neutron predictions without synergistic effects are provided by dashed cyan lines R NT in (a) and in (c), and dashed magenta line R NT in (b).TRANSP predictions scaled down to match measurements at the end of modulated ICRH power-off period at 9.5 s are provided in dash-dotted cyan line fac * R NT in (a) and dash-dotted magenta line fac * R NT in (b).Beam-target reactions, R BT , and thermal rates, R TH , are indicated by dash-dotted blue and by dashed blue lines in (c).RF power time traces are provided at the bottom of each graph for illustrative purposes.

Figure 9 .
Figure 9.Comparison of measured and JETTO neutron rates.Measured neutron rates for the selected three pulses are noted by R NT exp. in black solid lines and shadowed area for estimated experimental errors in all three graphs.Calculated neutrons are noted as R NT JETTO with RF and by blue solid line for He3 minority pulse #99639 in (a) and for n = 2 T pulse #99886 in (c) and by red solid line for n = 2 D pulse #99643 in (b).Total neutron predictions by JETTO with negligible ICRH power, i.e. under conditions with negligible synergistic effects, are noted as R NT JETTO low RF and are provided by dashed cyan line in (a) and (c) and by a dashed magenta line in (b).RF power time traces are provided at the bottom of each graph for illustrative purposes.

Figure 10 .
Figure 10.Time traces of channels 15 (blue/red solid lines) and 16 (black solid lines) from neutron camera compared to TRANSP simulations without RF kick for channels 15 (dashed orange/cyan line) and 16 (dashed gray line) for #99639 in (a) and #99643 in (b).NBI and RF power time traces are provided at the bottom of the graph.
Figure 11(a) also shows the calculated MPRu spectrum with FI DF from the TRANSP runs with RF kick operator (dashed cyan line), while the MPRu spectrum in figure 11(c) is derived with FI DF from the JETTO run (dotted navy line).The spectrum noted by the violet dash-dotted line in figure 11(b) is derived assuming FI DF from TRANSP for E < 120 keV and an enhanced tail modelled by a Maxwellian with T = 80 keV.The FI DFs from the TRANSP used in this analysis are shown in figures 11(d) and (f ), correspondingly.
(e)), have demonstrated that an increased RF tail in the fast T ion DF leads indeed to a better match of MPRu spectra (figure 11(b)).This RF tail (figure 11(e)) is made of Maxwellian with temperature of 80 keV and exceeds the TRANSP predictions shown by the dashed blue line in figure 11(e).Measured neutron spectra by MPRu seem to be very sensitive to the tail of FI DF driven by RF waves.A too low RF tail (figure 11(d), dashed blue line) leads to an underestimation of high neutron energy channels, X pos > 39 cm, while a too high RF tail produces more energetic spectra than the measurements, as shown in figure 11(c) for FI DF in figure 11(f ) (dotted navy line).It has been assessed that the enhancement of the DT fusion rate from the best fitting FI DF featuring the trial RF tail with a temperature of 80 keV (figures 11(b) and (e), dash-dotted violet line) is about 5%.

Figure 11 .
Figure 11.MPRu analysis for #99886.Graphs (a)-(c) show the predicted spectra using FI DF for fast T ions from the TRANSP run without the RF kick operator (blue dashed line) and the measured ones (black symbols).These are compared to predicted spectra using FI DF from the TRANSP run with the RF kick operator (cyan dashed line) in (a), predicted spectra using FI DF from TRANSP for E < 120 keV and enhanced tail modelled with Maxwellian with T = 80 keV (violet dash-dotted line) in (b) and predicted spectra from the JETTO run with full RF power (navy dotted line) in (c).FI DF for fast T ions used for calculating the spectra in (a)-(c) are shown in (d)-(f ) correspondingly.

figure 6 .
figure 6.Clearly, from figure6, one can conclude that the latter is a very good approximation for the FI energetic tail for energies E > 120 keV.

Figure 12 .
Figure 12.Fast D in (a) and T in (b) NBI ion density from TRANSP code for JET pulse #99886 at 9.4 s.Cold plasma n = 2 T resonance is indicated in (b) by a cyan line.
(a) with figure 12(b).At the position of n = 2 T resonance, R res,T ≈ 3.20 m on the LFS in #99886, one should also take account of the changes in the |E + | field which will have an impact on the interaction of fast T ions with RF waves.TRANSP-TORIC predicts a lower averaged |E + | field at R res,T ≈ 3.20 m than the equivalent field for central resonance, which is due to JET ICRH antennas geometry being focused at the centre of the vessel.The combination of all these factors would result in (i) having a lower number of T fast ions compared to D fast ions in similar conditions interacting with RF waves in the vicinity of the resonance, and (ii) a lower |E + | field due to unfavourable resonance location.Both of these factors will lower the strength of the synergistic effects.