Influence of ICRF-NBI synergy on fast ion distribution and plasma performance in second harmonic heating experiments with deuterium NBI at EAST

Ion Cyclotron Range of Frequencies (ICRF) heating and Neutral Beam Injection (NBI) can have synergy due to the acceleration of NBI beam ions by ICRF wave fields at their harmonics. To understand the influence of ICRF-NBI synergy on fast ion distribution and plasma performance, dedicated experiments and TRANSP simulations have been carried out on EAST. The simulation results are consistent with the experimental results. They show that the ICRF-NBI synergy not only accelerates the NBI beam ions with energy lower than 80 keV to energy larger than 300 keV, but also generates fusion neutrons with energy larger than 3 MeV. Moreover, ICRF-NBI synergy improves the plasma performance by increasing the poloidal beta, plasma stored energy, core ion temperature, total neutron yield and kinetic pressure. In a typical H-mode plasma with 1.0 MW NBI and 1.5 MW ICRF power, it was observed that ICRF-NBI synergy increases the poloidal beta, plasma stored energy, core ion temperature and neutron yield by ∼35%, 33%, 22% and 80%, respectively. Various parameter scans show that the ICRF-NBI synergetic effects can be enhanced by decreasing the minority ion concentration or the distance between the harmonic resonance and magnetic axis, or by increasing the ICRF heating power or NBI beam energy. Consequently, this leads to a generation of fast ions with higher energy. For instance, the maximum energy of the fast ion tail increases from 300 to 600 keV as n(H) decreases from 5% to 0.1%.

Ion Cyclotron Range of Frequencies (ICRF) heating and Neutral Beam Injection (NBI) can have synergy due to the acceleration of NBI beam ions by ICRF wave fields at their harmonics. To understand the influence of ICRF-NBI synergy on fast ion distribution and plasma performance, dedicated experiments and TRANSP simulations have been carried out on EAST. The simulation results are consistent with the experimental results. They show that the ICRF-NBI synergy not only accelerates the NBI beam ions with energy lower than 80 keV to energy larger than 300 keV, but also generates fusion neutrons with energy larger than 3 MeV. Moreover, ICRF-NBI synergy improves the plasma performance by increasing the poloidal beta, plasma stored energy, core ion temperature, total neutron yield and kinetic pressure. In a typical H-mode plasma with 1.0 MW NBI and 1.5 MW ICRF power, it was observed that ICRF-NBI synergy increases the poloidal beta, plasma stored energy, core ion temperature and neutron yield by ∼35%, 33%, 22% and 80%, respectively. Various parameter scans show that the ICRF-NBI synergetic effects can be enhanced by decreasing the minority ion concentration or the distance between the harmonic resonance and magnetic axis, or by increasing the ICRF heating power or NBI beam energy. Consequently, this leads to a generation of fast ions with higher energy. For instance, the maximum energy of the fast ion tail increases from 300 to 600 keV as n(H) decreases from 5% to 0.1%. a See Wan et al 2017 (https://doi.org/10.1088/1741-4326/aa7861) for the EAST Team. * Authors to whom any correspondence should be addressed.
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Introduction
Plasma heating with radio-frequency (RF) waves in the Ion Cyclotron Range of Frequencies (ICRF) and Neutral Beam Injection (NBI) are two main heating methods which have been widely used in magnetic confinement fusion devices. They are robust in ion heating and will be further considered in future machines, such as ITER [1,2]. With these two heating methods, a fusion power of 10 MW and 15 MW had been achieved in TFTR and JET, respectively [3,4]. ICRF and NBI can have synergy owing to the acceleration of NBI beam ions by RF wave fields close to the Ion Cyclotron (IC) harmonics, as a results of the finite Larmor radius (FLR) effects. Understanding the ICRF-NBI synergy are of great importance not only to the improvement of plasma performance, but also to the generation of fast ions and fusion neutrons.
Previously, a lot of efforts have been devoted to studying the ICRF-NBI synergy on multiple fusion devices, such as JET [5][6][7][8][9][10], ASDEX Upgrade [11,12], DIII-D [13], TEXTOR [14], JT-60 [15][16][17] and ITER [18]. It was shown in these devices that ICRF-NBI synergy can lead to an efficient generation of fast ions as well as a prominent increase of neutron yield, ion temperature and plasma stored energy. In particular, the JT-60 experiments showed that the energy confinement time in the presence of ICRF-NBI synergy is three times larger than NBI alone or ICRF alone, due to the acceleration of NBI beam ions by ICRF wave in its 2nd harmonic of Deuterium (D) [15]. The JET experiments indicated that the synergetic D-NBI and 2nd [6,7,9] or 3rd [19][20][21][22][23][24] harmonic ICRF generated fast ions with energy up to 2 MeV. For instance, it was found that 4 He-NBI fast ions are significantly accelerated by ICRF wave in their 3rd harmonics [25][26][27]. Moreover, ICRF could accelerate D-NBI fast ions near the ion-ion hybrid layer both in D-3 He [28,29] and H-D [5,30] plasmas when the ratio of the two main ion species is appropriately chosen, such that the injected NBI ions are resonantly heated as the third ion species. The ASDEX Upgrade experiments indicated that the synergetic 2nd harmonic ICRF and NBI generated fast D ions with energy up to 500 keV [12,31], which is an order of magnitude larger than that with NBI only.
Besides experiments, vast numerical attempts have also been tried to self-consistently calculate the fast ion distributions in the presence of ICRF and NBI.  [44]. In these approaches, TORIC, AORSA, EVE, LEMan and PION are ICRF codes which calculate the full-wave equations and generate the RF wave fields, wave numbers and power absorption. The kinetic Fokker-Planck codes SSFPQL and CQL3D, or the Monte-Carlo particle orbit codes ORBIT-RF, SPOT/RFOF and VENUS, are used to calculate the distribution of fast ions. The ICRF-NBI synergetic effects can then be studied by adding NBI modules/codes in the above listed simulation packages. For instance, the multiple-beam NBI code SINBAD [45] is included as a module in SSFPQL [11]. Besides, the full particle orbit code SPIRAL has also been used to calculate the synergy between ICRF and NBI in NSTX [46]. The ICRF code PION was coupled with the beam deposition code PENCIL and the transport code JETTO to calculate the synergy between ICRF waves and resonant NBI ions in JET [47].
In this paper, the TRANSP code package [48,49] is used to self-consistently simulate the ICRF-NBI synergetic effects. It solves a bunch of transport equations, including the particle, momentum and energy balance equations. The equilibrium and measured plasma parameters, including the ion temperature, electron density and electron temperature profiles, are used as inputs. Plasma profiles which cannot easily be measured, such as the current density, are evaluated by associated numerical models in the package. A lot of heating modules are included in TRANSP, such as the ICRF code TORIC [32] and the NBI code NUBEAM [50]. To calculate the ICRF-NBI synergetic effects self-consistently, TORIC provides the electric field, perpendicular wave vector and toroidal wave number to the RF-kick operator [51] in NUBEAM. In turn, NUBEAM generates the total energy density and beam ion density. The RF-kick operator plays a key role in calculating the acceleration of NBI beam ion by ICRF wave fields.
Apart from wave accessibility and electric field polarization, one of the necessary requirements for efficient acceleration of NBI beam ions by ICRF waves is the wave-particle resonance condition: in which ω is the angular wave frequency, Ω cj = q i B/m i is the ion cyclotron frequency, q i and m i are the ion discharge and ion mass, k ∥ and v ∥ are the wave number and ion velocity parallel to the background magnetic field, respectively. The subscript j means the charged particle of j, n is an integer representing the harmonics of resonance. For thermal ions, the wave-particle resonance condition is determined by ω = nω cj . The resonant ions absorb RF power close to their cyclotron resonance position at R the ≈ (nq i B 0 R 0 ) / (ωm i ), in which B 0 and R 0 are the magnetic field and major radius at the magnetic axis, respectively. In a D plasma with H minority ions, the D 2nd harmonic resonance position overlaps with the H fundamental resonance position.
The RF power absorbed by these two heating schemes depends on the concentration of minority ions. Due to FLR effect, ICRF harmonics (n ⩾ 2) preferentially accelerates NBI fast ions with Larmor radius ρk ⊥ ⩾ 1, in which k ⊥ is the perpendicular wave number and ρ = v ⊥ /ω cj [11]. Moreover, for fast ions with a sufficiently large Doppler shift, the wave-particle resonance condition is dominated by ω = k ∥ v ∥ . Consequently, the fast ions absorb RF power near the ion-ion hybrid layer at R fast ≈ R the + ( n tor v ∥ ) /ω, in which n tor is the toroidal wave number.
To have a better understanding of ICRF power absorption by different heating mechanisms, in particular the minority ion heating at fundamental resonance and majority ion heating at harmonic resonance, a factor is often used to describe the single-pass power absorption: For Hydrogen minority resonance, 2η is determined by [52,53]: in which n H /n D is the Hydrogen minority concentration, R is the Stix parameter and ω PD is the Deuterium ion frequency. When the minority concentration is small (n H / n D < 0.1), an increase of this value will lead to an increase of single pass power absorption by Hydrogen minority at its fundamental resonance and a decrease of power absorption by Deuterium at its 2nd harmonic resonance. However, if the minority concentration is large enough (n H / n D > 0.1), the cyclotron layer, the fast wave (FW) left-hand cut-off layer and the mode conversion layer will be well separated. Consequently, the power absorbed by Hydrogen minority will decrease while more wave will be mode-converted to Ion-Bernstein waves. The latter tend to heat the electrons through Landau Damping. For thermal ion and (NBI) fast ion heating at high harmonic resonances, 2η has the following forms, respectively [52,53]: where β i is the thermal ion beta, β f ⊥ is the fast ion perpendicular beta and n f is the fast ion density. n represents the harmonics of resonance. For 2nd harmonic resonance heating (n = 2), the thermal ions and fast ions both have 2η = π Rω PD β/2c. When the thermal ions or fast ions have larger energy, which can be achieved by increasing the ICRF or NBI heating power, β and thus the RF power absorbed by 2nd harmonics will be larger.
Though abundant experimental or theoretical studies on ICRF-NBI synergy were carried out on many devices, yet the studies on EAST are rare. Due to the need to increase the plasma confinement and plasma temperature on EAST, understanding the effects of ICRF-NBI synergetic heating become rather important. This paper serves to quantitatively/qualitatively characterize the influence of synergy between 2nd harmonic ICRF and NBI on fast ion generation and plasma performance on EAST with both experiments and TRANSP simulations. To achieve the best synergetic effects, various plasma parameters including the minority ion concentration, the magnetic field, the ICRF and NBI heating power are scanned. While the parameter scans can be easily realized in the simulations, it is quite difficult to obtain a complete list of cases in experiments due to limitation of heating capability, impurity generation, plasma control, diagnostics and so on.
The rest of paper is organized as follows. The EAST experimental results on 2nd harmonic heating of deuterium NBI, including the influence of ICRF-NBI synergy on plasma performance and neutron yield, are discussed in section 2. TRANSP simulations in line with experiments are discussed in section 3. Various parameters, including the concentration of minority ion, toroidal magnetic field (thus resonance position), ICRF heating power and NBI beam energy, are scanned. Finally, conclusions are made in section 4.

Experimental results
EAST is a middle-sized tokamak with a major radius of R = 1.85 m and a minor radius of r = 0.45 m. It is equipped with a Molybdenum first wall and Tungsten divertors, and is flexible to run in upper or lower single-null and double-null magnetic configurations. It has four NBI lines (1L/1R/2L/2R), two ICRF antennas, two lower hybrid (LH) antennas and four Electron Cyclotron Resonance Heating (ECRH) beams, with a total auxiliary heating power larger than 10 MW. This allows the machine to run in long-pulse high-confinement mode (Hmode) plasma scenarios. The configurations of NBI, ICRF, LH and ECRH heating and the locations of some neutron diagnostics are shown in figure 1. The four NBI beam lines are 1L and 1R in port A, 2L and 2R in port F. They have injection angles (with respect to the radial direction) of 23.8 • , 15.2 • , 21.3 • , 12.7 • and tangential injection radii of 1.26, 0.73, 1.14, 0.61 m, respectively [54]. While the four positive ion beam lines have different injection angles, their diameters and divergence angles in the poloidal cross-section are the same. Each beam line can inject fast ions with energy up to 80 keV at a source power of ∼2 MW. Both in the experiments and simulations, the full, half, and one-third energy fractions of the beam are E: E/2: E/3 = 80%: 14%: 6% [54].
Since 2021, the synergetic heating between 2nd harmonic ICRF and NBI has been routinely used to improve the plasma performance on EAST. To characterize their synergetic effects, a series of experiments (#101 734-101 745, While the LH and ECRH power are fixed throughout the whole the discharges, ICRF and NBI are powered in a manner such that cases with ICRF only, NBI only and NBI + ICRF are built. NBI blips are used in a few discharges to facilitate the charge exchange recombination spectroscopy (CXRS) and fast-ion D-alpha spectroscopy (FIDA) diagnostics. In the experiments, H-mode plasmas both in upper singlenull (#101 734-101 745) and double-null (#102 108-102 117, #113 624-113 671) magnetic configurations are studied. The distance between the antenna and the separatrix is fixed as R gapout = 8 cm in all discharges. The antenna coupling depends on the FW evanescent distance from the antenna to the position of cut-off density [55]. The new ICRF antennas have a small parallel wave vector of k ∥ = 7.5 m −1 , thus the FW cut-off density is n e_co = 2.8×10 18 m −3 . In our studied H-mode plasmas, despite the distance from the antenna to the separatrix is ∼8 cm, the SOL density is mostly above n e_co . Consequently, the FW evanescent distance is less than 1 cm, leading to a rather good ICRF power coupling in the SOL. The concentration of H minority ion in the edge plasma is n(H) = 4%-5%, as measured by optical spectroscopic multichannel analysis system. Thus, H fundamental heating is the dominant heating scheme. However, the H concentration in the core plasma is unknow due to the lack of related diagnostics. Decreasing n(H) is expected to increase the D 2nd harmonic ICRF heating and thus the ICRF-NBI synergy effects.
In the first series of discharges (#101 734-101 745), the ICRF and NBI heating power are P IC = 1.5 MW and P NBI = 1.0 MW (line 1L), respectively. Comparing to NBI alone, the ICRF-NBI synergy increases the poloidal beta β p , plasma stored energy W MHD , core ion temperature T i and neutron yield Y n by ∼35%, 33%, 22% and 80%, respectively. In the second series of discharges (#102 108-102 117), a larger NBI power (∼3 MW) is used, as shown in figure 2. The ICRF-NBI synergy increases β p , W MHD , T i and Y n by ∼36%, 35%, 20% and 100%, respectively, which are in the same level as the previous case. The higher neutron yield suggests that more fast D ions are generated. Moreover, the increase of plasma parameters is in the same level for single-null and double-null magnetic configurations, suggesting that the magnetic configuration does not play an important role in the ICRF-NBI synergy.
In our studies, the Neutron Emission Spectroscopy (NES) was used to measure the neutron energy distribution. It is a diagnostic based on the spectroscopic measurement of the fusion neutrons (D + D → 3 He (0.82 MeV) + n (2.45 MeV)) along a collimated line of sight. It uses an inorganic scintillator crystal C 7 LYC enriched with 7 Li to measure the spectroscopy of 2.45 MeV neutrons based on the 35 Cl(n,p) 35 S reaction [56]. The energy of protons emitting from the scintillator dependents linearly on the neutron energy plus the Q-value of the reaction (0.615 MeV). The shape of neutron energy is thus determined by the finite energy resolution of the detector and the energy distribution of the incoming neutrons. In the measured neutron energy distribution, values below 2 MeV are due to the energy loss caused by neutron scattering. Moreover, the Time-Of-Flight Enhanced Diagnostics (TOFED) neutron spectrometer [57] was used to measures the time-off-light (t TOF ) of the neutrons scattered from the primary scintillation detectors to the secondary ones. The neutron energy is estimated with E n = 2m n R 2 /t 2 TOF ≈11766/t 2 TOF . For instance, t TOF = 108-41 ns corresponds to E n = 1-7 MeV. ICRF-NBI synergy not only increases the neutron yield, but also influences the fast neutron distribution significantly, as shown in figure 3. Comparing to NBI only, ICRF-NBI synergy not only produces a larger tail of fusion neutrons with E > 3 MeV, but also increases the magnitude of the neutron distribution by a factor of ∼1.5 for cases with NBI beam energy of 50, 55, 60 keV. Moreover, when increasing the NBI beam energy, the tail of fast neutron becomes larger, suggesting that more D ions are accelerated and the ICRF-NBI synergy is stronger. The increase of neutron yield by ICRF-NBI synergy is in the range of 80%-100%, and it does not show obvious difference when varying the beam energy. In line with the NES results, the TOFED measurements show that the number of neutrons with smaller time of flight (corresponding to larger energy) are increased due to the ICRF-NBI synergy.
In addition, a comparison of NBI lines 1L and 2L is made in figure 4(a), in which 1L is injected more tangentially. It is shown that NBI 1L produces a larger NES signal than NBI 2L, suggesting that for the studied range of injection angles, a more tangentially injection seems to generate more fast ions. This is because a more vertical NBI beam injection will cause more charge exchange, shine through and orbit losses of the injected NBI fast ions. More details will be given in section 4. Moreover, injecting two NBI beam lines (1L + 2L) simultaneously lead to a larger NES signal than with one NBI line (1L or 2L), as expected. A further increase of ICRF power from 0.8 MW to 1.5 MW not only increases the total number of fusion neutrons, but also increases the energetic tail of NES.
Furthermore, attempts have been made to characterize the influence of D 2nd harmonic resonance position on ICRF-NBI synergy. Cases with B t = 2.4, 2.5 and 2.6 T are investigated. Figure 4(b) shows that a larger energetic tail of NES is generated when the resonance position is on the magnetic axis (i.e. B t = 2.5 T) or slightly on the low field side (i.e. B t = 2.6 T) than when it is on the high field side (B t = 2.4 T). In addition, the neutron yield for the cases with B t = 2.4, 2.5 and 2.6 T are respectively 8.7 × 10 13 , 1.02 × 10 14 and 1.01 × 10 14 n s −1 , indicating that a better ICRF-NBI synergy is obtained in the latter two cases. The lower amount/ tail observed in neutrons for the high-field case might be due to poorer absorbing conditions, in particular, direct electron damping tends to be stronger when the resonance is at the high field side, as the wave propagates through the center where the plasma is hottest and densest which is beneficial for direct electron damping. This is also indicated by the TRANSP/T-ORIC simulations in the next section ( figure 13).

Comparisons of TRANSP simulations and experiments
TRANSP simulations in line with experiments were carried out. The simulation time for each case is larger than 0.5 s, and the plasma parameters only take about 0.1 s to reach a steady-state with a time step of 0.02 s. In the simulations, the magnetic equilibrium, plasma current, loop voltage, toroidal magnetic field, major radius as well as the ion temperature (T i ), electron temperature (T e ) and electron density (n e ) profiles were used as inputs. The ion density is determined by the ion compositions and charge conservation. The 2D profiles were first fitted with the experimental data, including the reflectometry and interferometry for n e , the Electron Cyclotron Emission and Thomson scattering for T e , and CXRS for T i . These experimental profiles and equilibrium were then used in the ONETWO code [58] to calculate the more selfconsistent fitted profiles (as shown in figure 5), which were finally used in TRANSP. In addition, the heating power of ICRF, LH, ECRH and NBI were set as the same as the experiments. With these inputs, the TRANSP interpretative modeling calculates a lot of time-dependent plasma parameters, including the transport coefficients, 2D plasma profiles and fast ion distributions. In particular, the non-Maxwellian fast ion distributions (f i ) are calculated with the Fokker-Planck equation [59]: in which C (f i ), S (⃗ v) and L (⃗ v) are the particle collision, source and sink terms, respectively. Q (f i ) is the quasi-linear RF diffusion operator describing the strength of RF heating. It depends on the ICRF wave fields, perpendicular wave number, power absorption, cyclotron frequency of resonant ions and harmonic number of heating. The ICRF-NBI synergy effect mainly comes from this term. Several simulated plasma parameters were compared with the measured ones. Firstly, the D-D fusion neutron yields as a function of time are compared, as shown in figure 6. In the studied discharge #102 110, two NBI lines (1L and 2L) are   used. The calculated neutron yield is in good agreement with the measured one for the time intervals with NBI only (2.5-3.0 s). However, it is overestimated by ∼20% for the case with NBI + ICRF heating (3.0-3.5 s). In the experiments, the concentration of high-Z impurities and the radiated power became larger when switching on ICRF. However, these high-Z impurities were not considered in the simulations. It is hypothesized that the change of high-Z impurity concentrations leads to more fast ions losses in experiments than in simulations. Unfortunately, currently there is no way to measure the total fast ion losses on EAST. The D-D fusion generated neutron distributions are then compared, as shown in figure 7. In the simulations, the Deuterium fast ion distribution generated by TRANSP was used as input in the GENESIS code [60] to calculate the neutron distributions. The results are then compared with the NES and TOFED measurements. Both the simulation and experimental results show that the ICRF-NBI synergy enhances the fast neutron tail evidently. However, several differences can be pointed out. For instance, the distribution peak measured by TOFED is at energy of E n = 2.3 MeV, which is lower than the simulated one by 0.15 MeV. This is mainly due to the cocurrent view angle of the TOFED measurement which causes 'doppler shift' of the distribution. In addition, the 'half-width' of the neutron distribution measured by NES is larger than the simulated one. This broadening of distribution is due to the low resolution of the NES measurement. Nevertheless, the shape of the NES neutron distribution is correct.
Moreover, the FIDA diagnostic was used to measure the spectroscopy vertically from the B-port in the discharge #101 735. In the simulations, the Deuterium fast ion distribution calculated by TRANSP was used as input in the FIDASIM code [61] to obtain the corresponding spectroscopy. It is worth to mentioning that the calculated spectroscopy is at the same location as the measured one. The fast ion energy The simulations can correctly predict the variation trend of the neutron yield and neutron distribution when the NBI or ICRF heating parameters change. However, at current stage, it is still hard for the simulations to reach quantitative agreement with the measured neutron distributions owing to multiple factors, such as the measurement errors and the simplifications of simulation models.

Parameter scan
In this section, parameters including the H concentration, toroidal magnetic field, ICRF power, NBI beam ion energy and tangential injection radius are scanned. The plasma composition is H minority in D bulk plasma, and the only impurity considered is carbon with a concentration of 3.3%. The reference case uses n(H) = 1%, B t = 2.4 T, P IC = 1.5 MW, E beam = 60 keV (corresponding to P NBI = 1.0 MW) and R tan = 0.733 m.

Scan of minority ion concentration
H concentration is essential in determining the RF power absorbed by NBI beam ions at their 2nd harmonics. Decreasing n(H) is expected to enhance the ICRF-NBI synergy, as previously indicated in JET simulations [7]. To have a more quantitative understanding of this, TRANSP simulations with a scan of n(H) from 0.1% to 10% is performed. To achieve different n(H) on EAST, decreasing n(H) is obtained by various wall cleaning methods, such as Lithium coating, and increasing n(H) is often obtained by H gas injection. In reality, n(H) = 1%-10% is the most common situation while n(H) = 0.1% is almost impossible. Nevertheless, the case with n(H) = 0.1% is simulated to investigate the possible strongest acceleration of NBI beam ions.
The calculated left-hand RF electric field (E + ) and RF power absorption by each ion species are shown in figure 9. In the case with n(H) = 0.1%, the background thermal D ions, NBI fast ions and H minority ions absorb ∼55%, ∼15% and ∼10% of the total RF power, respectively, making the ICRF-NBI synergy the most significant one among the studied cases. The rest RF power is absorbed by electrons through Landau Damping, Transit Time Magnetic Pumping (TTMP) and Ion Bernstein Wave. When n(H) = 1%, the background thermal D ions and H ions absorb ∼26.5% and ∼55.0% of total RF power, respectively. The NBI beam ions absorb ∼7.3% of the total RF power and they can still be effectively accelerated. When n(H) increases to 5%, the amount of RF power absorbed by H minority ions increases to ∼80.2% while those absorbed by background D thermal ions and NBI beam fast ions decreases to ∼10.3% and ∼3.1%, respectively. When n(H) further increases to 10%, the H minority ions, D thermal ions and NBI beam fast ions absorb ∼84.2%, ∼5.8% and ∼2.9% of the total RF power, respectively. It can thus be concluded that as n(H) increases, the amount of RF power absorbed by H minority ions increases while that absorbed by NBI beam fast ions and background D thermal ions decreases. The RF power absorbed by NBI beam ions decreases by 135% when n(H) increases from 1% to 5%, but it does not change much when it increases from 5% to 10%.
The ICRF-NBI synergy is most significant when n(H) is lowest. Thus, to obtain a most prominent ICRF-NBI synergy, n(H) has to be kept as small as possible. However, it is very hard to decrease n(H) to 0.1% in reality. For D 3rd harmonic ICRF heating, this is not an issue, because it requires a smaller toroidal magnetic field (about two thirds of D 2nd harmonic) to obtain on-axis heating. With this magnetic field, the H fundamental resonance position is moved far away from the magnetic axis and the RF power absorbed by H minority becomes negligible. As a result, the D 3rd harmonic heating is the dominant heating mechanism. However, plasma scenarios are very hard to develop with the low toroidal magnetic field (∼2/3 * 2.5 = 1.67 T) required by 3rd harmonic heating on EAST. Even if these scenarios are developed, they are quite unstable due to impurity accumulation, and only a low 3rd harmonic ICRF power (<1 MW) can be used. Thus, 2nd harmonic ICRF is still the most often used heating scenario for ICRF-NBI synergetic heating on EAST.
Different n(H) leads to different ICRF-NBI synergies and thus different fast ion distributions. A comparison of fast ion distribution for the cases with NBI only and ICRF-NBI synergy is shown in figure 10. In the case with NBI only, the majority of NBI beam ions have energies in the range of [15, 65 keV]. They can be accelerated to energies of an order of magnitude larger by ICRF-NBI synergy. The energetic tail of the fast ions (hereinafter fast ion tail) depends strongly on n(H). For instance, the fast ions have energy up to 600 keV and 300 keV when n(H) is 0.1% and 5%, respectively. The increase of fast ion energy is in consistent with the RF power absorption by NBI beam ions. By integrating the fast ion distribution over the pitch angle, a 1D fast ion distribution is generated, as depicted in figure 11. It clearly shows that when n(H) is lower, more NBI beam fast ions are accelerated. In addition, the fast ion tail becomes larger. The fast ion distribution is a function of energy (E), pitch angle (v ∥ /v), radial position (r/a) and poloidal angle (theta). To obtain a 2D fast ion distribution in the energy-pitch angle map, the distribution is averaged over the whole x and theta ranges. To obtain a 1D distribution as a function of E, the distribution is further averaged over the whole pitch angle ranges.
The calculated plasma profiles are also given in figure 11. Comparing to NBI only, the total neutrons, poloidal beta, total ion heating and kinetic pressure are all increased by ICRF-NBI synergy. These parameters are largest when n(H) = 0.1%, and they gradually decrease as n(H) increases from 0.1% to 5%. When n(H) further increases, for instance to 10%, the fast ion tail, total neutrons and poloidal beta are roughly the same since the RF power absorbed by NBI beam ions remains almost the same. However, the total ion heating and kinetic pressure becomes larger when n(H) increases from 5% to 10%. This is not only due to the RF energy absorbed by H minority ions becomes larger, but also because the fast H ions are less energetic on average at n(H) = 10% which will tend to increase ion heating as seen in figure 11.
The fast ions produced by ICRF-NBI synergy will undergo slowing down by transferring part of their energy to the background plasmas through collisions. Whether more power is transferred to the ions or electrons is determined by the relation between the energy of resonant ions E res_ion and the critical energy E crit = 14.8AT e [∑ n j Z 2 j /n e A j ] 2/3 [62]. Here, A is the atomic mass of the resonant ions, n e and T e are the background electron density and temperature, respectively. n j , A j and Z j are the density, mass and atomic number of the ions, respectively. If E res_ion > E crit , the resonant ions transfer more power to the background electrons than the background ions, and vice versa. For instance, in a plasma with n e = 5 × 10 19 m −3 , T e = 5 keV and n(H) = 1%, E crit = 93.8 keV for D ions and E crit = 46.9 keV for H ions. Thus, the H fast ions could heat the background electrons much easier than the fast D ions.

Scan of toroidal magnetic field
For a fixed ICRF heating frequency, the toroidal magnetic field (B t ) determines the D 2nd harmonic resonance position and influences the amount of RF power absorbed by the thermal and NBI beam fast ions. On EAST, the ICRF heating frequency is 37 MHz, thus the D 2nd harmonic (or the H fundamental) resonance position is on the magnetic axis when B t = 2.5 T. The resonance position will move towards the low field side when increasing B t , and to the high field side when decreasing B t . To quantitatively understand the influence of resonance position on ICRF-NBI synergy, a scan of B t is performed. The RF power absorbed by the D thermal ions and NBI beam ions is depicted in figure 12. The D 2nd harmonic resonance position is on the right side of magnetic axis when B t > 2.5 T, and vice versa. The RF power absorbed by D thermal ions and NBI beam ions are most significant when the resonance position is closest to the magnetic axis, and they decrease as the resonance position moves away from the magnetic axis. Moreover, the RF power absorption is more concentrated in a layer close to the 2nd harmonic resonance position for D thermal ions, but it is in a much wider radial region for NBI beam ions due to a larger Doppler shift and thus larger RF absorption region.
A more quantitative description of RF power absorption profile by different plasma species is shown in figure 13. When the resonance position is on-axis with B t = 2.5 T, not only the RF power absorption profiles near the magnetic axis are most peaked, but also the direct ion heating (i.e. heating of thermal D ions) and heating of beam (i.e. heating of NBI fast ions) are most significant. The RF power absorbed by NBI beam ions only decreases slightly when the resonance position is not far away from the magnetic axis, for instance when it is ∼7 cm away from the magnetic axis with B t = 2.6 T. However, this power absorption decreases dramatically when the resonance position moves further away from the axis. For instance, it decreases by ∼50% when B t changes from 2.5 to 2.7 T. The resonance position in the latter case is ∼15 cm away from the magnetic axis. Thus, to achieve the best ICRF-NBI synergy, it is optimal to use on-axis ICRF heating.
The influence of D 2nd harmonic resonance position on plasma parameters is shown in figure 14. The fast ion tail in the energetic part (E ∼ 500 keV) appears to be a bit larger when the resonance position is on the low field side than on the high field side, since the density of NBI fast ions on the low field side is larger due to the beam penetration effects. But the overall fast ion distribution does not show notable difference. The direct ion heating, however, shows an apparent difference, owing to the change of H fundamental and 2nd harmonic heating schemes when changing B t . The total ion heating, total ion neutrons and kinetic pressure are largest when the resonance position is on the magnetic axis. They gradually decrease as the resonance position moves away from the magnetic axis. This is in line with the experimental findings. Moreover, the peaked RF ion heating location roughly follows the move of the resonance position, an effect also shown in figure 12. Thus, controlling B t is an effective way to manipulate the radial position of ICRF power deposition.

Scan of heating power
The acceleration of NBI beam ions by RF waves is associated with the strength of RF wave electric fields as well as the initial distribution of NBI beam ions. It is expected that the ICRF heating power and NBI beam energy can have remarkable influence on ICRF-NBI synergy. To understand this, parameter scan of ICRF power and NBI beam energy are performed. It is worth mentioning that the NBI heating power depends nonlinearly on the beam energy. For instance, NBI beam energies of 40, 50, 60, 65 and 70 keV on EAST correspond to NBI power of 0.4, 0.8, 1.0, 1.14 and 1.45 MW, respectively. The NBI power stated here represents the power entering the plasma, which is about 50%-60% of the NBI source power. The exact percentage depends on the beam energy. Both the beam source power and the percentage are measured experimentally for each acceleration voltage.
The results of ICRF power scan are shown in figure 15. They indicate that a larger ICRF power generates a larger RF electric field and causes a stronger acceleration of NBI beam ions, consequently leading to a larger fast ion tail. The accelerated fast ions have energy up to 300 and 600 keV when P IC = 0.5 and 3.0 MW, respectively. Moreover, the total neutrons, poloidal beta, total ion heating and kinetic pressure increase as the ICRF heating power increases. These increases are nonlinearly, especially when the ICRF heating power is high.
The results of NBI beam energy scan are shown in figure 16. As the beam energy E beam increases from 40 to 70 keV (namely P NBI increases from 0.4 to 1.45 MW), the ICRF-NBI synergy and the number of fast ions in all energy range are increased significantly. In addition, the increase of total neutrons and poloidal beta is evident while the increase of total ion heating and kinetic pressure is in a much smaller level. To understand this, cases with different P NBI but fixed E beam and cases with different E beam but fixed P NBI were studied. They suggest that the total neutrons and poloidal beta can be influenced by the fast ion distributions and NBI beam energy. However, the total ion heating and kinetic pressure are more sensitive to the total NBI heating power. For instance, for a fixed E beam = 60 keV, the maximum ion heating density increases from 0.88 to 1.25 MW m −3 as P NBI increases from 1.0 to 4.0 MW.

Scan of NBI injection angle
Furthermore, scan of the NBI injection angle was performed. The NBI injection angle is controlled via changing the tangential injection radius R tan , as depicted in figure 1. Cases with R tan varying in the range of [0.066, 1.971 m] are investigated, meaning that the toroidal injection angle (Φ ) varying in the range of [11 • , 23 • ]. Since the NBI source is 9.17 m away from the tokamak center, thus this injection angle scan is indeed in a very large range. In particular, the case with R tan = 0.066 m (Φ = 11 • ) is a vertical injection. It leads to less sufficient ionization of NBI beam neutrals and larger charge exchange, shine through and orbit losses of NBI fast ions than other cases ( figure 17). These fast ion losses become smaller as the NBI toroidal injection angle becomes larger (i.e. more tangential injection). The smallest fast ion losses and largest NBI power absorption are found when R tan = 1.658 m (Φ = 21 • ). As the toroidal injection angle further increases, part of the NBI fast ions can penetrate the low field side of the plasma. This leads to an increase of shine through and orbit losses of fast ions and a decrease of NBI power absorption, for instance the Figure 14. Comparisons of NBI Deuterium fast ion distribution, total neutrons, poloidal beta, total ion heating and kinetic pressure for cases with different toroidal magnetic field. The NBI Deuterium ion distribution is averaged over the entire radial, poloidal and pitch angle ranges. Figure 15. Comparisons of NBI Deuterium fast ion distribution, total neutrons, poloidal beta, total ion heating and kinetic pressure for cases with different ICRF power. The NBI Deuterium ion distribution is averaged over the entire radial, poloidal and pitch angle ranges. Comparisons of NBI Deuterium fast ion distribution, total neutrons, poloidal beta, total ion heating and kinetic pressure for cases with different NBI beam energy. The NBI Deuterium ion distribution is averaged over the entire radial, poloidal and pitch angle ranges. case with R tan = 1.971 m (Φ = 23 • ). Besides, the number of fast ions with energy around 60 keV (i.e. the NBI full energy with a fraction of beam >80%) is smaller in the cases with R tan = 0.066 m and 1.971 m, i.e. the most vertical and most tangential injections, respectively. Consequently, the total neutron yield and poloidal beta in these two cases are small than other cases, as shown in figures 18(b1) and (b2). Different NBI injection angle will lead to different fast ion distribution. The fast ion distributions of two representative cases (R tan = 0.066 m and 1.971 m) are shown in figures 18 (a1) and (a2). One of the most prominent effects is that a more vertical injection leads to more trapped particles while a more tangential injection generates more passing particles. For instance, the majority of NBI fast ions have pitch angle around v ∥ /v = 0 when R tan = 0.066 m, and it becomes v ∥ /v = 1.0 when R tan = 1.971 m. Nevertheless, the fast ion tail with energy larger than 100 keV has similar shape in the 2D energy-pitch angle map, since the 2nd harmonic ICRF mainly accelerate NBI ions with pitch angle around v ∥ /v = 0.3. The total fraction of trapped particle remains almost the same (∼33%) when the NBI beam energy is varied. However, it decreases monotonously from 48% to 10% as the tangential radius R tan increases from 0.066 to 1.971 m.

Conclusions
ICRF and NBI are two heating methods which can efficiently heat plasma ions in magnetic confinement fusion devices. They can have synergy due to the acceleration of NBI beam ions by ICRF wave fields near the harmonic resonance layer. To understand the synergy between 2nd harmonic ICRF and NBI and its influence on fast ion distribution and plasma performance, a series of experiments were carried out on EAST. It is shown that in a typical H-mode plasma, the ICRF-NBI synergy not only increases the poloidal beta, plasma stored energy, core ion temperature and neutron yield in the level of 35%, 33%, 22% and 80%, respectively, but also enhances the energetic tail of fusion neutron distribution with E > 3 MeV.
In line with the experiments, TRANSP simulations were carried out. The calculated neutron yield is in good agreement with the measured ones. Moreover, the fast deuterium ion distribution calculated by TRANSP is used as input in the GENESIS and FIDASIM codes to calculate the DD fusion neutron distribution and FIDA spectroscopy, respectively. The calculated Deuterium fast ion spectroscopy has qualitative/quantitative agreement with the FIDA measurement. However, the calculated normalized neutron distributions have some discrepancies with the TOFED and NES measurements. The TOFED measurement view angle and the NES measurement resolution are believed to the reasons. Nevertheless, they all show that the ICRF-NBI synergy increases the tail of the fast neutron distribution evidently.
To enhance the ICRF-NBI synergy effect, various parameter scans are performed, including the H minority concentration, D 2nd harmonic resonance position, ICRF power, NBI beam energy and NBI injection angle. Both the simulation and experimental results indicate that the ICRF-NBI synergy increases the total number of fast ions as well as the energy of the fast ion tail significantly. For instance, for a fixed P IC = 1.5 MW, the NBI beam ions with initial energy lower than 80 keV can be accelerated to 300, 450 and 600 keV by ICRF when n(H) is 5%, 1% and 0.1%, respectively. The ICRF-NBI synergy, which depends strongly on the total amount of RF power absorbed by NBI beam ions, can be enhanced by decreasing the minority ion concentration, by minimizing the distance between magnetic axis and resonance position, by increasing the ICRF power or the NBI beam energy, and by optimizing the NBI injection angle.
The obtained results indicate that the ICRF-NBI synergy is not only an efficient way to improve the plasma performance by increasing the plasma stored energy, plasma temperature, poloidal beta and so on, but also robust in generating energetic ions and energetic neutrons. The effects of ICRF-NBI synergy can be enhanced by optimizing a series of plasma and heating parameters, allowing this method to have more flexibilities. Thus, the ICRF-NBI synergy can be used as a heating method in current or future fusion devices to improve plasma performance and achieve higher fusion triple products. It can also facilitate the studies of energetic particle physics by generating abundant fast ions. Further efforts will concentrate on understanding the fast ion distribution generated by ICRF-NBI synergy in various plasma scenarios, and their effects on MHD and energetic particle modes.