Analysis of fusion alphas interaction with RF waves in D-T plasma at JET

This work studies the influence of radio frequency (RF) waves in the ion cyclotron resonance heating (ICRH) range of frequencies on fusion alphas during the recent JET D-T campaign. Fusion alphas from D-T reactions are created with energies of about 3.5 MeV and therefore have significant Doppler shifts enabling synergistic interactions between them and RF waves at a broad range of frequencies, including the ones foreseen for future fusion machines in ITER (Schneider et al 2021 Nucl. Fusion 61 126058) and SPARC (Creely et al 2020 J. Plasma Phys. 86 865860502). Resonant interactions between RF waves and alphas, also called synergistic effects, will modify the alpha distribution and ultimately will have an impact on alpha orbit losses and heating. Data from JET 3.43 T/2.3 MA pulses based on the hybrid scenario (Hobirk et al 2023 Nucl. Fusion; Hobirk et al 29th IAEA FEC23 Conf. (16–21 October 2023); Challis et al 48th EPS Conf. on Plasma Physics (27 June–1 July 2022) during the DTE2 campaign (Maggi et al 2023 Nucl. Fusion)) were used for the analysis in this study. The impact of synergistic effects on alpha orbit losses and alpha heating are assessed. The conclusions are based on the analysis of experimental data for fast alpha losses, i.e. measurements from neutral particle analyser (NPA), fast ion losses scintillator detector, Faraday cups (FCs), and TRANSP (Hawryluk et al 1980 Physics of Plasmas Close to Thermonuclear Conditions vol 1 (CEC) pp 19–46) simulations. Experimental data and TRANSP analysis indicates that there are indeed changes in the alpha distribution function (DF) due to interaction with RF waves. Data from the NPA show increased 4He flux in the range from a few hundred keV up to 800 keV for pulses with RF power, while TRANSP clearly shows modifications in the fast alpha DF for these energies. Data from the scintillator detector and the FCs were compared for pulses with and without ICRH power and versus cases with enhanced alpha losses due to MHD activity. The trends from these diagnostics consistently show no additional alpha losses due to interaction with RF waves. TRANSP predictions for the impact of ynergistic effects on alpha heating show up to a 42% increase in alpha electron heating and up to a 25% increase in alpha ion heating. These effects, however, become negligibly small, less than 1%, when alpha heating is compared to the total auxiliary heating power in the investigated JET pulses.

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Introduction
Fusion alphas from D-T reactions are born with energies of about E α = 3.5 MeV.As they slow-down via collisions and exchange energy with background plasma species, an alpha distribution function (DF) covering the energy range from the thermal background up to about 3.5 MeV will be built up and sustained.Under conditions of burning fusion plasma, i.e. fuel mixture of D/T ≈ 0.5/0.5, electron density n e ≈ 1 × 10 20 m −3 and temperature T e ≈ 10 keV, the alpha slowing down time is τ se [s] ≈ 0.37 (T e /10[keV]) 3/2 / (n e /10 20 [m −3 ]) ≈ 0.37 s, while the critical energy of 4 He ions is of the order of E cr,4He [keV] ≈ 33T e [keV] ≈ 330 keV meaning alphas will be predominantly heating thermal electrons.
Alphas born at E α = 3.5 MeV will have an absolute velocity of about 1.3 × 10 7 m s −1 which manifests a significant Doppler shift in the presence of radio frequency (RF) waves in the ion cyclotron resonance frequency range.It has been recognised that for ITER [1] and SPARC [2] RF wave/alpha interaction could be a concern regarding: (i) parasitic absorption of ion cyclotron resonance heating (ICRH) power, (ii) enhanced alpha orbit losses and (iii) impact on alpha heating efficiency.For ITER's main ICRH heating scenario during the active phase of operation, i.e. 3 He minorities with an RF of f = 52.5 MHz, vacuum central toroidal magnetic field of B t0 = 5.2 T and toroidal refractive index N ϕ = ±27, fusion born alphas will satisfy the wave particle resonance condition at R − R 0 ≈ −1.60 m for the n = 1 resonance [3].Therefore, one would expect significant synergistic interaction between alphas and RF waves.
While alpha losses due to toroidal field (TF) ripples and their interaction with MHD modes are well covered in the literature, e.g.[4][5][6][7][8][9] there seems to be insufficient research with regard to losses due to interaction with RF waves.This deficiency is even more surprising given the fact that early assessments at TFTR have indicated that the expected alpha losses due to interaction with RF waves are of similar order as those from locked modes, tearing modes and ELMs and larger than those expected from fishbones, see table 7 in [10].The gap in research in this field could be partially due to the lack of experimental data on fusion alpha confinement and interaction with the background plasma.Indeed, the only D-T experiments prior to the JET 2021 campaign were as follows: TFTR D-T campaign in 1994 [10,11] and previous JET D-T campaign in 1997 [12].In the latter, the main focus of the ICRH related studies was on exploring various ITER relevant ICRH heating scenarios [13] while synergy between alphas and RF waves was somewhat under-researched.TFTR studies [10,11,14,15] have shown that RF waves can induce alpha losses by heating marginally passing alphas and converting them into marginally trapped particles which then impact on the vessel wall [14,16].Calculations of the losses [11] with a one-dimensional kinetic integral wave code [17] have indicated that about 5%-10% of the RF power input to the plasma is absorbed by the fusion-generated alpha particles, while the measured alpha particle losses are found to be consistent with this estimate.
Modelling activities of alpha physics were widely available in the late 80s and early 90s after large scale implementations of parallel Monte-Carlo (MC) codes for fusion calculations, for instance ORBIT [18,19], NUBEAM [20], OFMC [21] and more recently ASCOT [22] and LOCUST [23].This largely enabled modelling and assessing alpha heating and alpha orbit losses due to TF ripple and MHD modes.The modelling of the interaction of the alphas with RF waves, however, required implementing an additional algorithm to account for the synergistic effects between RF waves and resonant alphas.This was only available in recent years for instance, in the framework of the ORBIT-RF code coupled with TORIC [24] and AORSA [25] as well as in the TRANSP/NUBEAM code coupled to TORIC via the so-called RF kick operator [26,27].
Recent D-T experiments at JET in 2021 [28], here referred to as DTE2, have provided a solid basis for studying the interaction of fusion alphas with RF waves.This was possible owing to the significant fusion rates achieved during DTE2, of the order of 2-4 × 10 18 s −1 , as well as significant ICRH heating power, 4-5 MW, applied in these experiments in conditions in which energetic alphas have in-vessel resonances.In addition, diagnostic upgrades prior to the JET 2021 campaign provided several additional fast ion diagnostics, a scintillator probe [29,30] and Faraday cup (FC) array [30,31], which allowed for deep insight into alpha losses.
This work studies the interaction between RF waves in ICRH range of frequencies and fusion alphas from the recent JET DTE2 campaign.The impact of this interaction on alpha DF and subsequent effects on alpha orbit losses and alpha heating has been assessed.The conclusions are based on modelling work and analysis of relevant experimental data.Section 2 provides details of the modelling tools used in the study.This is followed by a summary of the experimental setup, a description of the pulses used in the analysis and essential diagnostics.Results of the predicted changes in alpha DF due to synergistic effects by means of TRANSP modelling are discussed in section 4. Experimental results and observations are discussed in section 5. Summary and conclusions are presented in the final section of this manuscript.

Details on modelling tools
The TRANSP [32,33] code was principally used in the analysis presented here.Alpha DFs were calculated by the NUBEAM [20] which is a computationally comprehensive Monte Carlo code for neutral beam injection (NBI) heating in tokamaks.The RF wave solver for TRANSP is the TORIC [34].Studying the interaction between RF waves and alphas via TRANSP simulations was feasible only after the implementation of the RF kick operator in NUBEAM [26,27].In general, the following workflow was adopted in calculating the alpha interaction with RF waves: TORIC provides information about RF electric field components and the wave vector for each toroidal mode.The RF resonance condition for a given harmonic is then used to calculate the magnetic moment and energy of the resonant particles [26,27].Every time an alpha particle passes through the resonance layer it receives a kick in magnetic moment space [35].The magnitude of the kick is derived from the quasi-linear theory [36], while the stochastic nature of the wave-particle interaction is reproduced by means of a Monte Carlo random number for the phase of the gyroorbit.Studying the impact of RF waves/alpha interaction usually requires a pair of TRANSP simulations: one with and the other without RF kick operator.Comparison between the two runs directly shows the impact of the synergistic effects on alpha DFs and heating.
Alpha losses can in principle be calculated by TRANSP; however, due to relatively good confinement and small number of lost particles at JET, numerous MC markers would be required to achieve reasonable spatial and temporal resolutions.Running TRANSP with a large number of particles, i.e. exceeding 10 6 , has been shown to be computationally inefficient.By choosing to use 32k MC markers for alpha particles in this study, a compromise between timesaving TRANSP runs and reasonable level of digital noise in lost particle output has been achieved.At the same time, the spatial resolution of the lost alphas was compromised, meaning that a direct quantitative comparison to the lost alpha diagnostics cannot be made.However, the total losses from TRANSP can be compared qualitatively to the measured data and this is used in the analysis presented here.An additional limitation in numerical simulations is due to the fact that TRANSP with TORIC cannot provide an accurate estimate of the ICRH power absorbed by the alphas.The wave solver TORIC code works with Fokker-Planck solver FPP code [37] to provide self-consistent power absorption profiles in TRANSP simulations.The FPP code is a bounce-averaged zero-orbit width code which for lighter and/or less energetic ions, e.g.minorities and NBI fast ions, is a reasonable approximation.For energetic alphas with significant orbit drifts and banana widths, however, this approximation is crude.TORIC itself also uses a great simplification, namely a bi-Maxwellian DF, in representing alphas and other fast ion species in the wave dispersion relation.For the wave solver, however, this approximation should be adequate [34,38] and able to provide with reasonably good quality the wave electric field and perpendicular wave number.These quantities are needed for RF kick operator calculations in the MC code NUBEAM.In this way one can still use TRANSP and TORIC to assess alpha losses and heating due to synergistic effects.The absorption of ICRH power by alphas, however, cannot be estimated precisely by means of the TORIC and FPP codes and therefore is not discussed here.

Experimental setup and diagnostics used in the study
Experimental data from standard JET diagnostics were used as input to the simulations discussed in this study.Electron density, n e , and temperature, T e , profiles were taken from the High Resolution Thomson Scattering diagnostics, referred to here as HRTS.The latter does not cover the very core of the plasma, therefore central values on electron density and temperature are taken from Light Detection And Ranging, LIDAR, measurements [39].Electron temperature from the ECE radiometer [40] was also used in the analysis.Radiated power was measured by the bolometric diagnostics [41], while Z eff was assessed by means of Bremsstrahlung measurements from visible spectroscopy.Ion temperature, T i , for the investigated pulses was obtained from the charge exchange recombination spectroscopy (CXRS) diagnostic [42].
Neutron production counts were taken from the available neutron yield monitors [43].Measurements are based on the neutron activation technique, which has been used at JET for a long time mainly to determine local neutron fluence at certain measuring points.These measurements were supported by neutron transport calculations to relate the neutron fluence to the total yield of neutrons from the plasma.
A schematic showing the locations of the diagnostics used in this study is provided in figure 1.A neutral particle analyser (NPA) [44] is used in addition in pulses where it was set to detect 4 He neutrals, and its line of sight is shown in figure 1.
The scintillator probe [29] is located at the outboard midplane, figure 1, and consists of a scintillator plate, a chargecoupled device (CCD) and a photomultiplier tube (PMT) detector, figure 2. The lost fast ions passing through a collimator, figure 2(a), impact on the scintillator plate, figure 2(b), images of which can be recorded via CCD or detected by an array of PMTs.Separation of the fast ion species can be done JET cross-section with equilibria from #99886, 9 s (dashed blue line) and #99950, 9 s (dashed magenta line).Shown are approximate positions and line of sight of used diagnostics: Faraday cups, FC1 to FC5, (red squares for cups #1 to #5 from top to bottom and 3 radial positions of cups #1 and #4); fast ion losses scintillator detector, Sci.Det., (blue square near Faraday cup #3); neutral particle analyser, NPA, line-of-sight (vertical orange line).
by assessing the expected Larmour radius and pitch angle from the image on the scintillator [29].The error-bars due to finite instrument resolution are ∆θ ≈ ±1.5 degrees for the pitch angle, and of the order of ∆E ≈ ±0. 4 MeV for energies of about 2.5 MeV as ∆E increases for higher energies [45].The data discussed here use signals from four PMTs, #10, #11, #14 and #15, which cover the region of the expected lost alphas with Larmour radius between 9 cm and 12 cm and pitch angles between 55 • and 80 • , figure 2(b).
The FCs [30,31,46] are an array of five pylons distributed at different poloidal locations as shown in figures 1 and 3(a).Each pylon, figure 3(b), can contain up to three FCs foil stacks separated radially.The FC foil stack is composed of four conductive Ni foils separated by mica layers.Lost fast ions will penetrate into the stack and deposit to the foils depending on their energy.The corresponding foil in which a particular ion deposits will then measure the penetrating ion as current.The fast ion energy deposition for various ion species as a function of FC foil depth can be found in [46].Fusion alphas in the energy range E α = 2.48-3.55MeV are detected by foil 2, data from which is only used here.Separation by species is impossible by FCs so in presence of ICRH power various fast ion species contributions accelerated by RF waves have to be accounted for, e.g.foil 2 also collects fast H minorities in the range 0.68-0.96MeV, as well as D in 0.79-1.10MeV, T in 0.84-1.20 MeV and 3 He in 2.30-3.35MeV.
JET D-T pulses carried out at 3.43 T/2.3 MA based on the hybrid scenario [47][48][49] with D/T mixture of about 0.5/0.5 were used as references for the analysis in this study.This scenario has demonstrated one of the highest fusion performances in the JET DTE2 campaign, with a relatively large amount, greater than or approximately equal to 60%, of the total neutron rates, R NT , coming from beam-target reactions [47].Time traces of core electron density and temperatures as well as neutron rates and heating powers by ICRH and NBI for two similar pulses, #99886 and #99950, are shown in figure 4(a).Electron density and electron temperature by HRTS diagnostic and ion temperature by CXRS spectroscopy diagnostic for the two pulses at 9 s are shown in figure 4(b).
While the investigated pulses differ in the ICRH heating scenario used, in general, they have very similar time evolution and plasma parameters.In all pulses NBI heating in the range P NBI = 25-30 MW was applied at 7 s, after the plasma current profile featuring low magnetic shear was formed.This is then accompanied by a transient high-performance phase between 7 s and 8 s during which beams penetrate deeply in the core under conditions of lower plasma density.ICRH power was ramped up from the same time and P ICRH = 3-5 MW were sustained during the pulses.Dipole phasing of ICRH antennas which features toroidal refractive index N ϕ = ±27 was used in all experiments reported here.
Different ICRH scenarios were investigated in this study, all summarised in table 1 (see section 4.4), and it was found that in all cases energetic alphas inside the plasma boundary are resonant with RF waves.In the H minority scenario at B t0 = 3.43 T and f = 51 MHz, with a hydrogen concentration of X [H] = n H /n e ≈ 2%, and in pure n = 2 D heating, achieved by not injecting H minority, fundamental resonances are at R res,D ≈ 1.5 m (outside the vessel) and R res,H ≈ 3.00 m, respectively.Under these conditions alphas in the core are resonant for zero Doppler shift, i.e. for v ∥ ≈ 0 m s −1 , with RF waves at 51 MHz at n = 2 harmonic.For the ITER relevant heating scenario, 3 He minority with X [ 3    In analysing prompt orbit losses, the initial phase when heating and fusion rates are ramping up is used to compare the trends from lost alpha diagnostics versus neutron rates.In this approach, the latter is used as a proxy for alpha source rates.Alpha DFs are analysed after approximately 5 slowing down times, i.e. after t = 8.5 s.In the pulses studied here, the qprofile and the start of the heating power were optimised, with broad q > 1 region for a long enough period after the start of the heating, so that early MHD activities were avoided [47].MHDs are well known to have a negative effect on fast ion confinement and induce additional alpha losses [4,10].Low amplitude and transient MHD modes were observed but are thought to be benign with regard to fast ion losses.More central n = 1 mode followed by fishbone activities, which indicate a more intense MHD-fast ions interaction appear in one of the investigated pulses, #99950 in time interval 9 s < t < 10 s, and the signals from the lost fast alpha diagnostics in this case were used as an indication of the expected trends in conditions with enhanced alpha losses.

Analysis based on TRANSP modelling
The physics of RF wave/alpha interaction and its impact on alpha losses is outlined here by investigating alpha orbits and alpha DF.

Insight into alpha orbits and DF for JET DTE2 pulses
Under the conditions of JET DTE2 pulses as described in the previous section, i.e. at 3.43 T/2.3 MA, alphas born in the plasma core, for a toroidal normalised radius of ρ t < 0.3, are well confined with regard to orbit losses.The region in which all alpha orbits are confined in the plasma volume, derived by means of TRANSP runs and an orbit tracing code for 3.43 T/2.3 MA JET pulse #99643 at 8.94 s, is indicated by the shaded area in figures 5(a) and (c).The low field side (LFS) boundary of this area is somewhere between 0.3 < ρ t < 0.4 while on the high field side (HFS) the confined alpha boundary is extended up to ρ t ≈ 0.6.From TRANSP and orbit tracing code simulations one can deduce the innermost region where alpha orbit losses start to appear, which in our case is on the LFS for R > 3.35 m, Z ≈ Z mag ≈ 0.25 m, figure 5(a).For a slightly more peripheral location, e.g. at R = 3.46 m, Z = 0.16 m, figure 5 shows an example of five alpha orbits in (a) and alpha DF in (b).From figure 5(b) and following the orbit of trapped particle #4, it is clear that the losses in the wedge region of alpha DF around v ∥ ≈ −5 × 10 6 m s −1 will end up on the outer board in the proximity of fast ion loss diagnostics, figure 1(c).
The cold plasma n = 2 resonance for 4 He is shown by the vertical dashed line at R ≈ 3 m in figure 5(a).For alphas in the selected position, at R = 3.46 m, Z = 0.16 m, to be able to interact with RF waves, a significant Doppler shift is required as indicated by dashed cyan lines in figure 5(b).The latter is derived from the wave-particle resonance condition for n = 2 and N ϕ = ±27 and taking the local values of the magnetic field in the expression for ion cyclotron resonance frequency Ω ci : (1) In the selected position and at the selected time slice, figures 5(a) and (b), the co-passing (particle #1 in cyan), the counter-passing alpha (particle #5 in magenta) as well as the deeply trapped one (particle #3 in black) are non-resonant because of their either too high or too small v ∥ .Co-trapped (particle #2 in blue) and counter-trapped (particle #4 in red) alphas, however, are resonant as they have the necessary parallel velocity to interact with RF waves despite being away from the IC resonance.In addition, particles #2 and #4 will experience an even greater interaction with RF waves as they approach the IC resonance at a later stage of their orbit transits and having turning points near the resonance will further intensify this interaction.In the selected location co-and counter-trapped alphas will experience interaction with RF waves in the form of a kick in velocity space, which is proportional to RF induced quasi-linear diffusion coefficient, D QL : where |E + |, |E − | and k ⊥ are left-handed, right-handed electric field and perpendicular wave vector of the RF wave.For n = 1 and n = 2 resonance D QL is also proportional to combinations of Bessel functions of order n − 1, n + 1: J n−1 , J n+1 .The E + field of the RF wave is quite strong in the selected position on the LFS as provided by TORIC in figure 5(c).Therefore, the diffusion in alpha velocity space for n = 2 resonance, which is finite Larmour radius effect, depends on the particle perpendicular velocity v ⊥ .Resonant interaction between RF waves and alphas will modify the distribution of the latter and ultimately will have an impact on alpha orbit losses and heating.This has been studied first by means of TRANSP simulations.

Modifications to alpha DF due to interaction with RF waves
TRANSP calculations of alpha DF for the JET 3.43 T/2.3 MA pulse #99643 with P ICRH ≈ 5 MW, f = 51 MHz which in conditions of no H injection gives n = 2 central resonance for D and 4 He ions, R res,He4 ≈ 3.00 m, are shown in figure 6.The position at which the alpha DF is analysed, R = 3.08 m, Z = 0.21 m is selected to be near the magnetic axis where fusion rates and alpha density are the highest.Figure 6(b) and the red line in figure 6(d) show the alpha DFs, f (v ∥, v ⊥ ) and f (E α ), with TRANSP accounting for RF wave/alpha interaction, while figure 6(c) and the blue line in figure 6(d) show the unperturbed alpha DFs, which is achieved by disabling the RF kick operator in TRANSP.Significant changes in the alpha DF due to interaction with RF waves are predicted for energies up to about E α = 3 MeV, while for energies exceeding 3.5 MeV, the impact of RF waves is small as seen from figures 6(b)-(d).
The estimated quasi-linear diffusion coefficient from equation (2) in this case (figure 9 solid line) increases for perpendicular velocities of up to v ⊥ ≈ 1.2 × 10 7 m s −1 and then decreases becoming relatively small for v ⊥ > 1.5 × 10 7 m s −1 .Modifications in alpha DF are consistent with this assessment as a large increase in alpha populations with v ⊥ ≈ 0.4-1.2× 10 7 m s −1 corresponding to energies E α ≈ 0.5-3 MeV is seen in figure 6(b) and (d).
TRANSP calculations of the alpha DF for JET 3.43 T/2.3 MA pulse #99886 with P ICRH ≈ 3.5 MW, f = 33 MHz which gives central n = 2 resonance for T ions with no minority 3 He injection are shown in figure 7.In this case, the fundamental cold plasma 4 He resonance is away on the HFS, at R res,He4 ≈ 2.41 m, requiring a large Doppler shift for central alphas at R ≈ 3.08 m, Z ≈ 0.31 m, assessed to be of the order of v ∥ ≈ 5 × 10 6 m s −1 and noted by the dashed blue line in figure 7(b).Modifications to the alpha DF due to interaction with RF waves in this case are lower than in the case discussed in figure 6 and mainly for lower energies, up to about E α = 2 MeV, figures 7(b) and (d).
The estimated quasi-linear diffusion coefficient is now different as for n = 1 RF wave/alpha interaction one would expect greater contribution from particles with v ⊥ ≈ 0 m s −1 .Indeed, D QL is shown in figure 7(c) and as the dashed blue line shows it is finite for particles with v ⊥ ≈ 0 m s −1 and further increases with v ⊥ for values up to v ⊥ ≈ 1.3 × 10 7 m s −1 .This is not surprising given that the first pass abruption of RF wave in this scenario is not great, cf E + field in figures 7(f ) and 4(c).Under such conditions E − field, i.e. λ term in equation ( 2), is essential and is responsible for the second maximum at v ⊥ ≈ 1.3 × 10 7 m s −1 .The unperturbed alpha DF and its derivative to v ⊥ in the domain v ∥ ≈ 5 × 10 6 m s −1 , v ⊥ > 1.3 × 10 7 m s −1 are however very small, figure 7(c), so no significant impact of the synergistic effects on alpha DF is predicted in this domain, figure 7(b).
Figures 6 and 7 clearly show that the central alphas can interact with RF waves in both scenarios: n = 2 D and n = 2 T heating.Modifications to the alpha DF due to this interaction extend up to E α = 3 MeV.No, or very negligible, acceleration of alphas beyond their birth energy of E α = 3.5 MeV is predicted.

Orbit losses
For JET pulse #99643 at 3.43 T/2.3 MA the shaded region in figures 5(a) and (c) indicates the location where all alphas with E α < 3.5 MeV are confined with regard to orbit losses.It was found that in the non-shaded region in figures 5(a) and (c) alpha losses with E α < 3.5 MeV start to appear.As discussed in the previous section, alphas in the central region are well confined and TRANSP simulations indicate that no significant acceleration exceeding energies of 3.5 MeV is expected to take place due to interaction with RF waves.One would naturally then investigate the impact of synergistic effects on alpha losses outside the confined area, e.g. on the HFS inboard midplane and LFS outboard midplane.
Moving to HFS towards the inner wall, losses appear for R < 2.4 m and Z ≈ Z mag for pulse #99643.It is essential to note, however, that a negligible impact of synergistic effects on alpha losses is expected in this region because (i) alpha density, n α , decreases significantly, by more than a factor of 40 in this particular case, as we move towards the plasma periphery as shown in figure 6(a) and (ii) RF electric field |E + | also decreases by at least 4-5 times as shown in figure 5(c).A rough estimate based on the fact that RF wave/alpha interaction is proportional to n α and |E + | 2 of the wave according to equation (2) gives at least three orders of magnitude lower intensity of such an interaction on the HFS compared to the plasma centre.For the case with central n = 2 T resonance #99886 and figure 7, the picture is very similar when moving to HFS.RF electric field |E + | is again becoming very small, figure 7(f ), while n α decrease is of a similar order, both factors contribute to diminishing synergistic effects on the HFS inboard midplane.Our attention would now turn to the LFS outer midplane, where losses start to appear for R > 3.25 m and RF electric field is significantly higher.
The next step in this investigation is to move outwards towards more peripheral regions on LFS, i.e. for R > 3.35 m for which radius alpha particles' broad banana orbits start to intercept the first wall.The loss cone, which is the region in alpha DF where banana widths are larger than the distance to the wall and consequently particles there experience imminent orbit loss, appears for R > 3.35 m, figure 5.For locations further outside on the LFS, the loss cone becomes larger.The pulse with central n = 2 T resonance #99886, giving R res,He4 ≈ 2.41 m, figure 7(a), then would require enormous Doppler shift for alphas on the LFS to have n = 1 4 He resonance, while n = 2 4 He resonance in this case would be outside the plasma.The pulse with central n = 2 4 He resonance #99643, however, would require a reasonable Doppler shift for alphas at locations on the LFS and so these cases are investigated further numerically with TRANSP.Alpha DF for JET pulse #99643 at R = 3.28 m, Z = 0.17 m (location shown in figure 6(a) by blue plus marker) with and without RF  Figure 8 shows that for outboard locations at R > 3.35 m the modification of the alpha DF due to RF wave/alpha interaction starts to contribute to orbit losses.The two DFs with and without RF kick, figures 8(a) and (b), are at R = 3.28 m which is the furthest location at which there is no loss cone in alpha DF.The appearance of the loss cone is clear at R = 3.46 m, Z = 0.16 m location, shown in figures 8(c) and (d).In Dopplershifted resonance locations, v ∥ ≈ ±5.5 × 10 6 m s −1 for N ϕ = ±27, RF wave interaction with alphas seem to result in pushing a small number of particles towards higher v ⊥ .In particular, for v ∥ ≈ −5.5 × 10 6 m s −1 counter-passing particles are accelerated towards the loss cone which manifests in enhanced orbit losses, an observation consistent with TFTR studies [14].This effect is, however, very benign on JET as only small modifications to the alpha DF can be seen around the loss cone.
Further insight into RF wave/alpha interaction is provided in figure 9 where shown are estimated quasi-linear diffusion coefficients, D QL , quantifying the intensity of synergistic interaction and derived according to equation (2) for the three positions discussed above.These three locations are selected so as to reflect the expected losses due to synergistic processes in conditions where interactions take place away from the centre as we approach the outer wall.3 × 10 7 m s −1 the unperturbed alpha DF is severely depleted of particles.This is due to (i) lower n α as fusion rates decrease when moving to the periphery and (ii) the presence of a loss cone in the region of interest.The latter exists even without RF interaction, as figure 8(d) shows and the role of the synergistic effects is only to push a small amount of alphas in this region.Moving further outward one would expect the Doppler shift to increase, i.e. dashed cyan lines in figure 8(c) will move further away to higher |v ∥ | in a region which is even more depleted from fast alphas.The lost cone will also expand so the number of particles necessary for RF wave/alpha interaction will decrease significantly.Moving inward one would expect to have more favourable conditions for interaction.Indeed, figure 8(a) shows lower Doppler shift, v ∥ ≈ −3.5 × 10 6 m s −1 , and according to the dashed line in figure 9 one would expect an intense interaction for v ⊥ = 0.6-1.2× 10 7 m s −1 .Alpha density is also higher, n α = 3.4 × 10 16 m −3 , and in these conditions alphas with energy E α = 1-3 MeV will interact with RF waves.To induce alpha losses in this case RF interaction with alphas with v ∥ ≈ −3.5 × 10 6 m s −1 , v ⊥ > 1.3 × 10 7 m s −1 would be needed.In this range, however, D QL decreases significantly, while alpha DF derivative to v ⊥ is also small, hence negligible losses will be induced by the RF waves.In the very centre, figure 6(b) and the solid line in figure 9, show a very similar picture, namely D QL decreases significantly for v ⊥ > 1.5 × 10 7 m s −1 and is only able to push a small number of particles to the region with energies E α ≈ 4 MeV.These particles in the core are, however, confined, so no additional losses are expected.
TRANSP provides an output for alpha orbit losses by means of the rate of total number of lost particles over the whole plasma boundary, i.e. the last closed flux surface, noted here as R α, loss .A more detailed output containing a snapshot of the locations and energies of the lost particles is also available.As discussed in the previous section, the detailed spatial analysis would require a greater number of MC markers and expensive TRANSP runs, therefore it is not used here.TRANSP data for orbit losses, R α, loss , with and without RF kick operator are shown in figure 10.
Figure 10(a) shows estimated rates of alpha losses, R α, loss , over the whole plasma boundary by TRANSP for n = 2 D pulse #99643 with and without synergistic interaction.The two TRANSP runs were performed with the same input profiles and heating, the only difference being turning on/off the RF kick operator.One would also expect a difference in fusion performance due to the synergy between fast NBI ion and RF waves [51].Despite the statistical noise due to the lower number of MC markers used in these simulations, it can be noted that alpha losses are slightly higher during RF switch-on periods in the case with RF kick operator.The observed higher losses are, however, found to be correlated with the higher fusion rates, i.e. the alpha source.This is clearly indicated in figure 10(b) where calculated alpha losses, R α, loss , are plotted versus calculated neutron rates, R NT .In both cases, with and without RF kick operator, the trends approximately follow a straight line for the ratio of lost alphas to created ones of R α, loss /R NT = 0.12 indicated by the dashed black line in figure 10(b).Based on these simulations it can be concluded that the interaction of alphas with RF waves does not lead to enhanced alpha losses, rather that the increased losses are due to increased fusion rates.

Impact on alpha heating
Alpha heating of electrons was unambiguously observed during DTE2 [52] and is therefore considered an experimentallyverified phenomenon.The observed changes in the alpha DF due to synergistic interaction with RF waves are expected to have an impact on alpha heating efficiency as well.Figures 6(d) and 7(d) clearly show that the modification of the alpha DF in the region of the 4 He critical energy, i.e. in our conditions E cr,He4 ≈ 330 keV noted by the dashed vertical line, will manifest changes in the electron and ion heating efficiencies of alphas.This is further studied here by means of TRANSP simulations.Similar runs with and without RF interaction are compared with regard to the alpha heating profiles.Power transfer to both species, electrons and ions, in all investigated scenarios has been studied and the results are summarised in table 1.In all cases of interest alpha heating is split between electrons and ions with an average ratio of about 0.89/0.11.Table 1 shows that alpha electron heating was in the range 8%-16% of Table 1.Impact of RF waves/alpha interaction on alpha's heating of electrons and ions.All cases are 3.43 T/2.3 MA D/T ≈ 0.5/0.5 hybrid type of pulses, except for #99965 at the bottom of the table for which pulse details of Bt/Ip and fusion mix are provided.The ICRH scenario is listed in column 2. Alpha heating of ions, column 3, and electrons, column 4, are provided by TRANSP with/without RF kick.Second row in columns 3 and 4 show total heating power to ions and electrons.the total electron heating for the 3.43 T/2.3 MA scenarios and 20% in n = 1 D heating scenario, #99965.At the same time, alpha heating of ions is negligible and only account for 0.5%-1.2% of the total ion heating.An interesting observation is that while alpha electron heating changes due to synergy effects, ion heating is practically unaffected.To a certain extent, this is not surprising given that alpha heating on ions is very modest and the alpha DF is mainly affected for larger energies, E > 500 keV.With a critical energy of 4 He in D/T mixture for JET conditions with T e ≈ 10 keV of about E cr,He4 ≈ 330 keV, the changes in alpha DF due to synergistic effects, figures 6(d) and 7(d), are expected to mainly impact the electron heating.
The analysis of the alpha heating with and without synergistic effects is discussed here on the basis of (i) changes in alpha heating and (ii) impact on the total heating.The changes in alpha heating due to RF wave/alpha interaction are not small: alpha heating of electrons varies and increases by up to 42% due to RF induced changes in alpha DF, while for ions one gets up to 25% increase.Alpha electron heating in all 3.43 T/2.3 MA pulses are highest for n = 2 D case #99643.Alpha ion heating in all 3.43 T/2.3 MA pulses are highest for H minority case #99950.When these figures are translated into contribution to total electron and ion heating, the second lines in table 1, the figures are much smaller: typically, one sees an increase in alpha electron heating within 1% of total electron heating.The changes in alphas contribution to total ion heating due to synergistic effects are even smaller, less than 0.2% of the total ion heating power.

Experimental results
The predictions from TRANSP are backed up by experimental observations.The JET NPA diagnostic can provide  experimental verification of alpha particle interaction with RF waves.The analysis of the data from the NPA diagnostic and obtaining a more quantitative assessment of the origin and the distribution of the neutrals 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.Figure 11 shows measured neutral fluxes of energetic 4 He neutrals by NPA for two pulses, with (cyan) and without (red) RF heating.Enhanced losses of 4 He particles in the pulse with RF power are observed for energies between ≈600 keV and 800 keV.One can conclude that the TRANSP predictions for the impact of the RF waves on alpha DF are in qualitative agreement with this observation.Indeed, changes in the alpha DF for energies between 600 keV and 800 keV due to RF waves can be clearly seen in figures 6(d) and 7(d).
Images from a lost ion scintillator CCD from n = 2 D pulse #99643 are shown in figure 12. Lost ions are shown as colour-coded spots indicating the intensity of the image versus gyro-radius (ρ on the left scale) and pitch angle (θ on the top scale) of the ions striking the scintillator plate.The calculated energy of the lost alphas is provided on the right scale.The footprint of the losses in figure 12 clearly indicates a peak in the region 3.5-4.5MeV and spread of the order or errorbars ∆E ≈ ±0. 4 MeV.The existence of alphas with energy greater than the birth energy of E α = 3.52 MeV and up to 4.5 MeV is consistent with the expected broadening of alpha source by Doppler effects for thermal and BT reactions [53].No alpha losses were measured for E α < 3 MeV and E α > 5 MeV.Comparing figures 12(a) and (b) for the phases with and without ICRH power one clearly sees no significant impact of RF waves apart from higher intensity of the spot during ICRH on phase.This trend is correlated with neutron rates, i.e. reaction rates, which also increase due to higher power input, are next studied by examining signals from photomultipliers and neutron yield diagnostics.The lost alphas with energies of about E α ≈ 3.5 MeV detected by PMTs in the scintillator detector are analysed and shown in figures 13(a) and (b) versus neutron rates which are taken as a proxy for the alpha source rate.The two diagnostics, PMT and neutron yield monitor, are set up with very different sampling rates, i.e. different time vectors.In the investigated time interval neutrons were sampled with a time resolution of ≈6 ms, while PMT data was collected at a much higher rate between 0.16 ms and 0.04 ms.The shortest timescale events discussed here are the MHD related alpha losses which are usually very transient, ≈0.05-0.1 ms, while on the other side neutron rates are expected to evolve on a time scale with energy and particle confinement times as well as with NBI ions slowing down, i.e. at least tens of ms.Based on this assessment, comparing alpha losses on a very short time scale versus neutron rates is done here by interpolating the latter on the PMT time vector, which is with much higher time resolution.The PMT signal can in principle be processed to give an assessment of alpha losses in terms of physical units, e.g.W m −2 , but this requires a complex processing of the data and absolute calibration of the scintillator probe.For the purpose of this study, PMT signals from relevant photomultipliers, PMTs #10, #11, #14, #15 in figure 2(b), are averaged and provided as a single signal in arbitrary units which was shown to be proportional to alpha losses [54].A JET pulse with NBI heating only, #99802, 7-7.99 s, is used as a reference to indicate the expected dependence of alpha losses on fusion rates in conditions with no ICRH power.The straight line (red diamonds in figure 13, #99802, 7-7.99 s) in this case clearly shows a linear trend of the losses with fusion rates.For comparison, the expected level of PMT signal for enhanced alpha losses due to MHD is shown (magenta triangles figure 13, #99950, 9-10 s).They are shown as bursts of activities clearly exceeding the expected linear trends.In addition, in figure 13(b) shown are alpha losses in quiescent periods between fishbones (black stars, #99950, 9.46-9.47s) indicating a slightly lower, but in general similar level of losses to the reference case #99802.The measured trends for pulses with central n = 2 4 He resonance, #99950 H minority and #99643 n = 2 D as well as #99965 with central n = 1 4 He resonance are shown in figure 13(a).Clearly, the former two cases follow closely the linear dependence set by the reference NBI only pulse #99802 and do not deviate from the straight line as the losses in #99950 after 9 s due to bursts of MHD activities, figures 13(a) and 14(a) bottom.This means that the calculated R α.loss vs. R NT trends, figure 10(b), are consistent with the experimental data and no additional alpha losses were seen in the investigated RF pulses with n = 2 central resonance.As for the case with central n = 1 4 He resonance, #99965, trends still follow straight line but with a lower slope.This observation is fully consistent with better confined alphas at higher plasma current.The impact of the RF waves in this case, however, is difficult to assess as there were no reference pulses without ICRH power to compare against.Similar trends were observed for pulses with central T resonance, figure 13(b).In both cases, #99634 with 3 He minority and #99886 with n = 2 T heating indicate no deviation from the expected dependence of the alpha losses on the fusion rates.
Time traces of heating power, neutron rates, signals from FC pylons #2 and #3, foil 2 and averaged signal from PMT from loss ion scintillator detector for #99950 and #99643 are shown in figure 14(a).Signals from FCs are, usually, very noisy so a simple moving average with 8192 samples, 40.96 ms window, is applied to them.The low frequency modulations seen on PMTs and FCs in #99643 are correlated with P ICRH as well as with the neutron rates.The data from the FCs are again plotted versus the neutron rates, R NT .Similarly to figure 13 this is done for the signals from FC pylon #3 foil 2 for the pulses discussed above.Here again, a pulse without ICRH power, #99802, was used as a reference.As for the case in which enhanced alpha losses due to MHD activities were observed by the scintillator detector PMT, #99950, 9-10 s, see figures 13(a) and 14(a), it was noted that the noise in the data from FCs does not allow for the detection of alpha losses due to MHD.Indeed, the time scale for the latter is not sufficiently long for the smoothed FC signals.In addition, a significant contribution to the FCs noise is due to fast minority ions accelerated by ICRH, cf reference without ICRH power #99802 with very smooth dependence of FCs on R NT .This means that no proper reference with excessive alpha losses was available for FCs data analysis and therefore only a comparison versus losses observed in #99802 is discussed here.
FCs data are approximately linear with neutron rates for the reference pulse without ICRH power, #99802.The observed trends for this pulse are consistent with a fast ion loss scintillator probe.The noise in pulses #99886 (cyan) and #99950 (magenta) and relatively clear linear dependence for #99802 (red) can be explained by the fact that the latter pulse, #99802, does not feature ICRH.Indeed, for pulses with ICRH power, i.e. #99886 and #99950, a large number of fast H, D and T ions as well as alpha particles are expected to be generated, which would affect the FC measurements.In pulses with sole NBI power only alphas are expected to impact FC measurements, hence the clear linear dependence on the fusion rate.The trends in figure 13(a) and (b) clearly show that FCs signals follow the linear dependence set by the reference case #99802.The noise in FC data due to all other fast ions generated by ICRH was further processed statistically: averaged and standard deviations calculated and shown in figure 14 by white symbols and lines.Clearly, within the error bars, all data from FC signals are consistent with the trend from the reference case #99802.Based on these observations it can be concluded that data from FC also show no indication of enhanced alpha losses due to interaction with RF waves.

Discussion and conclusions
The analysis reported here provides further insight into the consequences of RF waves/alpha interaction expected to take place in future fusion devices.In conditions such as in JET DTE2 hybrid type pulses with fusion rates of 2-4 × 10 18 s −1 and maximum ICRH power of 4-5 MW, all five ICRH scenarios listed in table 1 have 4 He resonances in the plasma.In all five cases, energetic alphas have sufficient energy, i.e.Doppler shift and perpendicular momentum, to interact effectively with RF waves.The results of this study show that there are moderate changes in the alpha DF due to this interaction, all in the energy range E α ≈ 0.5-3 MeV.Experimental data show increased 4 He flux for energies from a few hundred keV up to 800 keV for pulses with RF power, while TRANSP clearly shows modifications in the fast alpha DF in this energy range.This, however, seems to have a negligible impact on alpha losses.Data from a lost ion scintillator detector and FCs consistently show no excessive alpha losses due to RF wave/alpha synergistic effects.TRANSP estimates of the losses are consistent with the experimental observations: a linear increase of total alpha losses to fusion rates with a slope of R α, loss /R NT = 0.12 was derived for the cases with and without RF kick operator.
Changes in alpha electron and ion heating due to RF waves/alpha interaction were studied by means of TRANSP simulations with and without RF kick.The predicted increase in alpha electron heating due to the synergistic effects is relatively small when compared to the total electron heating, but it can reach up to 42% if alpha electron heating only is considered.For ions alpha heating is negligible with regard to the total ion heating, while alpha ion heating itself is found to increase by about 25% at most.These figures are therefore important for devices which would rely heavily on alpha heating in particular, future reactors designed to operate close to 'burning plasma' conditions, while for JET with dominant auxiliary heating the changes are small.
An interesting observation at JET, which seems to be inconsistent with TFTR observations, is that alpha losses due to interaction with RF waves are lower than the losses caused by fishbones.Indeed, according to table 7 in [10] alpha losses due to interaction with RF waves are expected to be 4 times higher than the ones by fishbones in TFTR.In JET conditions, however, figures 13(a), (b) and 14(a) show that the fishbone losses prevail.A possible explanation of this observation could be due to the different ripple in these two devices.TFTR had fewer number of TF coils than JET and therefore alpha losses in TFTR are more affected by the comparatively larger TF ripple.As a consequence of this alpha interaction with RF waves resulting in radial displacement would result in more ripple losses in TFTR conditions compared to JET.
He] = n He3 /n e ≈ 2%-4%, at B t0 = 3.43 T and f = 32 MHz, and for the corresponding pure n = 2 T heating, the fundamental resonances are at R res,T ≈ 1.6 m (outside the vessel), R res,D ≈ R res,He4 ≈ 2.4 m and R res,He3 ≈ 3.2 m.In this case, central alphas, i.e. at R ≈ 3.0-3.1 m, require Doppler shift of v ∥ ≈ 5 × 10 6 m s −1 , to interact with RF waves at 32 MHz at fundamental n = 1

Figure 2 .
Figure 2. (a) Schematic of lost fast ion scintillator diagnostic in JET with an image of the scintillator plate in (b) The observed alpha losses are shown by the green spot and are for Larmor radii between 9 cm and 12 cm and pitch angle between 55 • and 80 • .Image is mapped on PMTs numbered #1 to #16, the line of sight of which is shown by white rectangles.Alpha losses for the experiments reported here are detected by PMTs #10, #11, #14 and #15.

Figure 3 .
Figure 3. (a) Schematic of FCs array of 5 pylons and schematic of an individual pylon showing the three radial bins.Reprinted from [46], with the permission of AIP Publishing.(b) The structure of each stack.Reprinted from [31], with the permission of AIP Publishing.

Figure 4 .
Figure 4. (a) Time traces of electron density ne and temperature Te, ion temperature T i , neutron rates R NT and applied NBI and ICRH power, P NBI and P ICRH , for JET 3.43 T/2.3 MA hybrid pulses: #99886 with n = 2 T ICRH heating scenario (blue) and #99950 in H minority scheme (magenta).(b) Profiles of electron density and temperature, ion temperature vs. normalised toroidal flux radius ρt from the pulses shown in (a) at 9 s.

Figure 5 .
Figure 5. (a) Example of fast alpha orbits for 3.43 T/2.3 MA JET pulse #99643, 8.94 s and particles born at R = 3.46 m, Z = 0.16 m with Eα = 3.5 MeV and pitch angles of θ = 20 • (co-passing orbit 1 in cyan), θ = 70 • (co-trapped orbit 2 in blue), θ = 88 • (deep trapped orbit 3 in black), θ = 111 • (counter-trapped orbit 4 in red) and θ = 160 • (counter passing orbit 5 in magenta).(b) Alpha DF at R = 3.46 m, Z = 0.16 cm i.e. same location as the starting points of the orbits shown in (a).The position of orbits starting points in (a) are shown by the corresponding number and colour coded points in (b).Also shown in (b) by dashed cyan lines are Doppler shifts for n = 2 4 He interaction with RF waves with N ∥ = ±27.RF wave E+ electric field calculated by TORIC is shown in (c).The quasi-linear diffusion coefficient due to RF waves for n = 1 (solid blue) and n = 2 (dashed cyan) is shown in (d).Position of cold plasma n = 2 IC resonance for 4 He and the region where there are no alpha orbit losses are shown by vertical dashed cyan line and shaded area in (a) and (c).

Figure 5 (
d) shows calculated D QL for n = 1 (solid blue line) and n = 2 (dashed cyan line) at the selected position, R = 3.46 m, Z = 0.16 m, as a function of alpha v ⊥ .Clearly the resonant alphas have the necessary v ⊥ ≈ 0.6-1.0 × 10 7 m s −1 for strong interaction with RF waves at n = 2 resonance.This interaction can be even stronger than the interaction of resonant ions with RF waves at fundamental frequencies.Indeed, in the velocity range v ⊥ = 0.6-1.0 × 10 7 m s −1 the computed quasi-linear diffusion coefficient for n = 2 interaction, dashed cyan line in figure5(d), exceeds the corresponding one for n = 1, solid blue line in figure5(d).

Figure 6 .
Figure 6.(a) TRANSP output for alpha density during the high performance phase of JET D-T pulse #99643 at 8.94 s, n = 2 D scenario.(b) Alpha DF log 10 [f (E,θ)] on (v ∥ , v ⊥ ) mesh near the magnetic axis, R ≈ 3.08 m, Z ≈ 0.21 m (blue diamond in (a)) from TRANSP run with RF kick operator.(c) Same as (b) but for TRANSP run without RF kick.(d) Alpha DF f (E) at same location for the case with (red) and without (blue) RF kick.The position of the cold plasma n = 2 4 He resonance is shown in (a) by vertical cyan line.Necessary Doppler shift for the selected location for ICRH dipole phasing, N ϕ = ±27, and n = 2 4 He resonance is shown in (b) by dashed cyan lines.

Figure 7 .
Figure 7. (a) TRANSP output for alpha density during the high performance phase of JET D-T pulse #99886 at 9.40 s, n = 2 T scenario.(b) Alpha DF log 10 [f (E,θ)] on (v ∥ , v ⊥ ) mesh near the magnetic axis, R ≈ 3.08 m, Z ≈ 0.31 m from TRANSP run with RF kick operator.(c) Same as (b) but for TRANSP run without RF kick.(d) Alpha DF f(E) at same location for the case with (red) and without (blue) RF kick.The position of the cold plasma fundamental 4 He resonance is shown in (a) by vertical dashed blue lines.Necessary Doppler shift for the selected location for ICRH dipole phasing, N ϕ = ±27, and n = 1 4 He resonance is shown in (b) by dashed blue line.RF wave E+ electric field calculated by TORIC is shown in (f ).The quasi-linear diffusion coefficient due to RF waves calculated according to equation (2) for n = 1 (dashed blue) and n = 2 (dotted cyan) is shown in (e).

Figure 8 .
Figure 8. TRANSP output of the alpha DF log 10 [f (E,θ)] on (v ∥ , v ⊥ ) mesh at two locations on the LFS for JET D-T pulse #99643, n = 2 D scenario.Results in (a) are for TRANSP run with RF kick operator at R ≈ 3.28 m, Z ≈ 0.17 m and in (b) for TRANSP run without RF kick operator.Results in (c) are for TRANSP run with RF kick operator at R ≈ 3.46 m, Z ≈ 0.16 m and in (d) for same location but without RF kick operator.Shown in (a) and (c) by vertical dashed cyan lines are parallel velocities required for n = 2 Doppler shifted resonance for ICRH dipole phasing, N ϕ = ±27.
Alpha DF for the three points of interest with and without RF kick are shown in figures 6(b) and (c) for the innermost point, figures 8(a) and (b) for the intermediate point and figures 8(c) and (d) for the outermost point.For the purpose of estimating D QL as in equation (2), TORIC output for k ⊥ , E + and E − fields was taken.Alpha density drops dramatically towards the plasma periphery, cf n α ≈ 6.7 × 10 16 m −3 for the plasma centre, R = 3.08 m, versus n α ≈ 3.4 × 10 16 m −3 for the location at R = 3.28 m and n α ≈ 1.2 × 10 16 m −3 for R = 3.46 m as indicated in figure 9 legends.Figures 6(b), 8(a) and (c) provide the alpha DF with RF kick operator for the three cases and from dashed cyan lines in these figures one can clearly

Figure 9 .
Figure 9.Estimated D QL derived according to equation (2) for three positions in outer midplane for JET pulse #99643, 8.94 s.The locations at which D QL is calculated are provided in the legend together with computed density of the alphas.

Figure 10 .
Figure 10.TRANSP output for time traces of the rate of the total alpha orbit losses, R α,loss (direct output from the code by dots and smoothed lines), and fusion rates, R NT , by dashed lines in (a) and alpha losses, R α,loss , versus fusion rates, R NT , in (b).In (a) the TRANSP run with RF kick operator is shown by red dots and smoothed solid red line, while the run without RF kick operator is noted by blue dots and smoothed solid blue line.In (b) same colour code is used for simulations with and without RF kick operator.

Figure 11 .
Figure 11.Losses of energetic 4 He particles detected by NPA in energy range 200 keV to 800 keV for JET D-T pulse with ICRH #99950 (cyan) and #99802 without ICRH power (red).

Figure 12 .
Figure 12.Images from a lost ion scintillator CCD from n = 2 D pulse #99643 during ICRH power on phase at 9 s in (a) and ICRH power off phase at 9.5 s in (b).

Figure 14 .
Figure 14.(a) Time traces of heating, P NB , P RF , neutron rates, R NT , signals from Faraday cups pylon #2 foil 2 (FC2 foil 2) and FC pylon #3 foil 2 (FC3 foil 2) and averaged signal from photo multiplier, PMT, from loss ion scintillator detector for #99950 (magenta) and #99643 (cyan).(b) and (c) FC3 foil 2 data versus measured neutron rates, R NT .Reference #99802 (red diamonds) without ICRH power and #99950 (magenta triangles) in time interval when enhanced alpha losses due to MHDs were observed.In (b) signals from #99643 (cyan circles) n = 2 D ICRH scheme, #99596 (blue squares) H minority pulse similar to #99950, and #99965 (black stars) n = 1 D ICRH scheme are shown with their averaged values and standard deviations in white.In (c) #99886 (cyan circles) with n = 2 T ICRH scheme and #99634 (blue squares) with 3 He minority ICRH heating are shown with their statistical averages and deviations in white.