Characteristics of fast ³He ion velocity distribution exciting ion cyclotron emission on JT-60U

On JT-60U, the plasma current flows clockwise in the toroidal direction as seen from above the torus. The toroidal magnetic field is also in the clockwise direction. Positive-ion sourced NBs (P-NBs) were installed in both almost perpendicular and tangential directions to the toroidal magnetic field. The tangential P-NBs consisted of both co-current (CO) P-NBs and counter-current (CTR) ones. The beam lines of the perpendicular P-NBs were also slightly tilted in both CO and CTR directions. In addition, negative-ion sourced NBs (N-NBs) were installed in the almost CO-tangential direction. Here, acceleration voltages of the P-NBs and the N-NBs were about 85 kV and 350 kV, respectively.

ICRF antenna straps were installed on the wall on the low field side and used not only for the ICRF heating, but also for the measurement of the ICEs [7–10]. The measured data was recorded by an oscilloscope with the sampling frequency of 500 MSamples s^–1 during 100 μs. The sampling was repeated at every 50 ms.

The disappearance of the ICE(³He) in spite of the relatively high neutron emission rate was observed in a discharge of E48473. Figure 1 shows the time evolution of (a) the plasma current I_p, (b) the safety factor at the 95% toroidal magnetic flux surface q₉₅ and (c) the major radial position of the midplane edge of the plasma on the low field side R_edge in E48473. I_p was controlled so as to be constant in the time range of figure 1. q₉₅ and R_edge are stationary until t = ∼7.0 s and become almost stationary again from t = ∼9.2 s, indicating that the plasma equilibrium is almost stationary until t = ∼7.0 s and from t = ∼9.2 s.

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Figure 2 shows time evolution of (a) CO-tilted perpendicular (solid line) and CO-tangential (dashed line) P-NB powers, (b) CTR-tilted perpendicular (solid line) and CTR-tangential (dashed line) P-NB powers, (c) a line-averaged density $\overline{{n}_{e}},$ (d) a stored diamagnetic energy of the plasma W_d, and (e) the neutron emission rate S_n in E48473. Plasma parameters such as $\overline{{n}_{e}}$ and W_d, and S_n are also almost stationary until t = ∼7.0 s and from t = ∼9.2 s as well as the plasma equilibrium as shown in figure 1. Figure 2(f) shows time evolution of a frequency spectrum of fluctuations measured with the ICRF antenna strap. Dotted and dashed lines indicate D (f_cD) and ³He ion cyclotron frequencies (f_c3He) at the midplane edge of the plasma on the low field side, respectively. The temporal changes of these cyclotron frequencies can be explained by the change of the plasma edge position shown in figure 1(c). Observed fluctuations in the frequency near lf_cD (l = 2, 3) are interpreted as the ICE(D). The fluctuation observed in the frequencies near 2f_c3He is the 2nd harmonic ICE(³He). Only harmonics of the ICE(³He) were often observed in the relatively high density plasma on JT-60U while the fundamental one was not observed [8], although its mechanism is not understood. The 2nd harmonic ICE(³He) becomes weak and disappears as the plasma equilibrium changes in spite of that S_n from t = ∼9.2 s is much higher than that until t = ∼7.0 s. Here, we focused on the 2nd harmonic ICE(³He) before and during its disappearance, and compared the distribution between the cases with and without the ICE(³He) excitation. Figure 2(g) shows the temporal evolution of its toroidal wavenumber k_φ measured with the ICRF antenna straps arranged in the toroidal direction.

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We evaluated the fast ³He ion distribution until t = ∼7.0 s and from t = ∼9.2 s as the cases with and without the ICE(³He) excitation, respectively. At t = 5.4 and 9.4 s, radial profiles of the electron density and temperature were measured. Figure 3 shows radial profiles of (a) the electron density n_e, (b) the electron temperature T_e and (c) the safety factor q at t = 5.4 s and 9.4 s in E48473. The radial profiles of q indicate that the magnetic shears are positive. Using n_e and T_e in figure 3, we calculated a slowing down time of the fast ³He ions with the energy of 0.82 MeV at the plasma axis τ_s0. τ_s0 at t = 5.4 and 9.4 s is respectively about 0.15–0.2 s and 0.2–0.25 s. In general, the fast ion velocity distribution becomes stationary after the time scale of the slowing down time elapses. Even on timescales longer than τ_s0 after S_n has become almost stationary, the 2nd harmonic ICE(³He) continues to be observed until t = ∼7.0 s and is not detected from t = ∼9.2 s. Thus, we evaluated the fast ³He ion distributions under the stationary conditions (slowing-down distributions). The parameters in figure 3 were used for the orbit calculations to evaluate the distributions.

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As mentioned in section 3.2, we calculate the fast ion orbits by using the parameters at t = 5.4 s and 9.4 s to evaluate the fast ³He ion slowing-down distribution in the cases with and without the ICE(³He) excitation in E48473, respectively. Figure 4(a) and (d) show the birth profiles of the ³He ions on the R–Z plane at t = 5.4 and 9.4 s in E48473, respectively. The beam-thermal fusion component of the birth profiles was evaluated by the orbit calculations of the fast D ions, and the thermal–thermal component was evaluated from the bulk plasma parameters as we mentioned in section 2. The beam–beam fusion component was small even near the plasma axis, where the beam–beam fusion reaction rates are the highest, compared with the beam-thermal fusion reaction rates: The beam–beam fusion component was estimated to be about 9% of the beam-thermal fusion component. Here, we did not include the beam–beam DD fusion produced ³He ions since the influence of the beam–beam fusion reactions on the ³He ion birth distribution was estimated to be small but the calculations of the beam–beam components are very complicated. These birth profiles were used for the initial condition of the fast ³He ion orbit calculations. Figure 4(b) and (e) show the magnetic surfaces on the R–Z plane at t = 5.4 s and 9.4 s, respectively. Figure 4(b) and (e) also show examples of guiding center orbits of the fast ³He ions passing through the plasma edge on the low field side. The fast ³He ions drawing large banana orbits can pass through both the region near the plasma center and the plasma edge on the low field side, and its scales strongly depend on the energies E and pitch angles ϕ_pitch. Figure 4(c) and (f) show the sampling boxes used for the evaluation of the distribution. These sampling boxes are located at the midplane edge of the plasma on the low field side.

First, we evaluated the fast ³He ion slowing-down distributions at the midplane edge of the plasma on the low field side in the cases with and without the ICE(³He) excitation in E48473. Figure 5 shows the evaluated energy E and pitch-angle ϕ_pitch distributions of the fast ³He ions at the sampling boxes (see figure 4) in the case (a) with and (b) without the ICE(³He) excitation. Here, we calculated the critical energy at the plasma axis E_cr0 at which energy transfer rates from the fast ions to bulk electrons and to bulk ions via collisions are equal. E_cr0 is about 90 keV at t = 5.4 s and about 130 keV at t = 9.4 s. In the region of E > E_cr0, the distributions in both cases have strong pitch-angle anisotropy, peaking at ϕ_pitch ∼ 54° for the case (a) and at ϕ_pitch ∼ 58° for the case (b). These pitch-angle distributions become broader when E < E_cr0. This is because pitch-angle scatterings begin to frequently occur due to the ion–ion collisions when E becomes lower than E_cr0. In the case with the excitation, the bump-on tail structure in the energy direction is formed and its highest distribution density is located around E = 500 keV and ϕ_pitch = 54°. Using averaged values of the frequency and k_∣∣ of the observed 2nd harmonic ICE(³He) and f_c3He at the midplane edge of the plasma on the low field side during t = 5–7 s in E48473, we calculated a resonant energy E_res that can satisfy the Doppler-shifted ³He ion cyclotron resonance condition of equation (1). The frequency of the observed 2nd harmonic ICE(³He) and 2f_c3He averaged during t = 5–7 s in figure 2(f) are ∼47.3 MHz and ∼49.4 MHz, respectively. Averaged k_φ of the 2nd harmonic ICE(³He) in figure 2(g) is about −4.75 m⁻¹. The negative value of k_φ indicates that the waves propagate in the CTR direction. Here, we assumed k_∣∣ ∼ k_φ. v_f∣∣ of the fast ³He ions is in the CO direction as shown in figure 5(a). Hence, the Doppler shift of k_∣∣v_f∣∣ is consistent with a downshift in the 2nd harmonic ICE(³He) frequency from 2f_c3He since k_∣∣v_f∣∣ is negative. E_res as a function of ϕ_pitch is shown in figure 5(a). E_res passes near the location of the highest distribution density in the bump-on tail structure, indicating that the evaluated fast ³He ion distribution is almost consistent with the experimental observations of the frequency and k_φ of the 2nd harmonic ICE(³He) in terms of the cyclotron resonance condition of equation (1). On the other hand, in the case without the excitation, the distribution has a broader structure in the energy direction around ϕ_pitch = 58°, where the distribution density of the fast ³He ions having E = 500 keV is the highest. When R_edge becomes smaller, even relatively low energy ³He ions can reach the plasma edge on the low field side. As a result, the number of the relatively low energy ³He ions at the plasma edge can increase and they would make the bump-on tail structure broader in the energy direction.

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Figure 6 shows normalized (a) pitch-angle and (b) energy distributions f_3He on the distributions shown in figure 5 in the cases with (circles) and without (squares) the ICE(³He) excitation. The pitch-angle distributions are averaged from E = 480 to 520 keV. The energy distributions are averaged in ϕ_pitch = 54° ± 3° in the case with the excitation and in ϕ_pitch = 58° ± 3° in the case without the excitation. These distributions are normalized by their maximum distribution densities f_max. The pitch-angle distributions in both cases have an almost same sharply peaked structure. The energy distribution has the bump-on tail structure with a peak at E ∼500 keV in the case with the excitation. On the other hand, the energy distribution has a relatively flat structure from E = ∼E_cr0 to ∼500 keV in the case without the excitation.

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Next, we evaluated the fast ³He ion slowing-down distributions at several R positions on the low field side as well as the evaluation at the plasma edge. Figure 7 shows R position dependences of normalized gradients of the energy distribution (Δf/ΔE)/f₀ in the cases with (circles) and without (squares) the ICE(³He) excitation in E48473. Here, R_axis is R at the plasma axis. Δf/ΔE is a gradient of the energy distribution f(E) from E = 200 to 500 keV and f₀ is the distribution density at E = 500 keV in f(E). f(E) is the energy distribution averaged around the pitch angle where the population in the fast ³He ion distribution is the largest. Large positive (Δf/ΔE)/f₀ indicates that the bump-on tail structure is peaked in the energy direction. (Δf/ΔE)/f₀ near the plasma edge on the low field side in the case with the excitation is much larger than that in the case without the excitation. As we mentioned in section 1, the plasma edge on the low field side is a possible emission region for the ICE(³He) because the observed frequencies of the ICE(³He) were always near the ³He ion cyclotron frequencies there. The large value of (Δf/ΔE)/f₀ is localized at the plasma edge in the case with the excitation. Hence, it is suggested that the formation of the peaked bump-on tail structure is necessary for the excitation of the ICE(³He).

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Finally, we applied this evaluation method to several discharges where at least one of the NBs is injected and S_n is more than 2 × 10¹⁴ n s^–1. Figure 8 shows a relation between the amplitudes of the 2nd harmonic ICE(³He) and (Δf/ΔE)/f₀ at the midplane edge of the plasma on the low field side. Circles and squares indicate data points when the ICE(³He) is observed and not, respectively. When the ICE(³He) is not observed, the amplitudes are set to be on the horizontal axis. The ICE(³He) is observed in the region of the relatively large (Δf/ΔE)/f₀. Hence, the analysis results of the fast ³He ion distribution show that the formation of the relatively peaked bump-on tail structure is necessary to excite the ICE(³He).

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In the previous theoretical studies for the MCI [2, 22] and for the CAE instability [20, 21], the necessity of the sharply peaked fast ion velocity distribution for the excitation of the ICE has been suggested. In both models, the linear growth rate drastically increases as the spread of the distribution becomes smaller. The analysis results of the characteristics of the fast ³He ion distribution with the OFMC code are qualitatively consistent with the dependence of the growth rate on the spread of the velocity distribution in the previous theoretical studies. It is found that the excitation condition of the ICE(³He) strongly depends on the characteristics of the fast ³He ion distribution on JT-60U.

Using Monte-Carlo simulations for evaluation of the alpha-particles distribution and calculating anti-Hermitian parts of susceptibility tensor of its distribution under similar parameter conditions to those of TFTR, Hellsten et al concluded that the thermonuclear alpha particles even in the steady-state condition can destabilize edge localized magnetosonic eigenmodes on the low field side due to the strong inversion of the distribution function along the characteristics of cyclotron interaction by neo-classical effects [36]. Our result is consistent with their result. Quantitative evaluations of the growth rates based on realistic wave and velocity distribution models are future works. The calculation of the anti-Hermitian parts of the susceptibility tensor of the evaluated distribution as in the work by Hellsten et al [36] would be the first step toward the quantitative evaluations of the growth rates based on the realistic models.