Third harmonic ICRF heating in LHD hydrogen experiments

The ion cyclotron range of frequencies (ICRF) heating power injection in the hydrogen experiment in LHD was demonstrated after the upgrade of ICRF antennas. The ICRF wave couples and accelerates the energetic particles injected by perpendicular-NBIs with 40 keV. The simulation by the MORH code shows the existence of energetic particles around the ICRF third harmonic resonance layers. As the result of ICRF heating power deposition, the beta value increased by 0.2% in absolute beta mainly due to the increased energetic particle content. The increase of energetic ions particularly around 60 keV, which should be accelerated by the ICRF heating, is observed. The ICRF heating efficiency was approximately 30%–50%, estimated from the break-in-slope analysis at the turn off timing of ICRF power from the stored energy measured by diamagnetic loops. This increase of the stored energy is mostly the contribution of the increased energetic particles. The heating efficiency increases as the density increases.


Introduction
In order to investigate the physics of the high beta plasma confinement, the low magnetic field experiments have been performed in the Large Helical Device (LHD). To realize a commercial fusion reactor, high beta confinement is required for reducing the construction cost of the reactor. The ion cyclotron range of frequencies (ICRF) heating is studied in this low magnetic field condition using ICRF higher harmonic wave heating. From the viewpoint of the fusion reactor, the research on the ICRF higher harmonic wave is important in considering the type of antenna that can be used, such as the option of a wave guide antenna. In previous LHD studies, ion heating by a second harmonic wave and electron heating by high harmonic fast waves are investigated [1][2][3]. In this study, the ICRF third harmonic experiments with 100% hydrogen plasma demonstrate the validity of the ICRF wave coupling with fast ions and increased energetic particles. In tokamaks, JET and ASDEX-Upgrade demonstrated ICRF third harmonic heating in deuterium plasmas in the presence of neutral beam injection (NBI) [4,5]. In their experiments, the count rate of the neutron generated by the D-D fusion was increased with ICRF heating. The third harmonic ICRF wave accelerated the energetic particles injected by NBI. In this operation, the neutron generation efficiency increased by the synergistic effect of ICRF and NBI heating. These research results are also important for the investigation for the confinement of energetic particles.
For ICRF heating in the LHD experiment, three kinds of antennas were used for the injection of ICRF waves. Two poloidally located antennas, poloidal array (PA) antenna and field aligned impedance transforming (FAIT) antenna, and one toroidally located antenna, and hand shake type (HAS) antenna are used to inject ICRF power. The FAIT antenna was installed [6] in the LHD experimental campaign in 2013, the Faraday shield on the PA antenna which had an arcing problem was removed and the PA antenna continued to perform soundly [7]; further, the ICRF control system was upgraded [8]. After these upgrades, ICRF power that radiated to the plasma increased up to 4.5 MW [9]. This is the same power level with the JET and ASDEX-Upgrade third harmonic experiments. With this ICRF heating system on LHD, several experiments have been performed for the investigation of ICRF third harmonic characteristics and achieving a higher beta value. These experiments can demonstrate the synergistic effects of the energetic particles injected by NBI and accelerated by the third harmonic ICRF wave. Figure 1 shows the schematic equatorial plane cross section of the LHD and heating system configuration. The dotted arrows show the injection directions from #1 to #5 NBIs. The LHD has five NBIs; three negative NBI systems #1 to #3 for the tangential direction with 180 keV with a total maximum power of 16 MW, and two positive NBI systems #4 and #5 for the perpendicular direction with 40 keV with the maximum power of 12 MW each. Three pairs of ICRF antennas, HAS, FAIT, and PA antennas, are shown with green rectangles. Each antenna has two straps inserted from the upper port and the lower port of the vacuum chamber. HAS is a toroidal array antenna, whereas FAIT and PA are poloidal array antennas. By the installation of the impedance transformer, which are optimized at the frequency of 38.5 MHz, the loading resistance became approximately two times larger, and the total ICRF heating power was increased [10]. The blue dashed line shows the line of sight of the compact neutral particle analyzer (CNPA) [19]. CNPA can measure the time evolution of the perpendicular energy distribution function of the energetic neutrals within less than 160 keV. Figure 2 shows the poloidal cross section of LHD with the lines of calculated flux surface and magnetic field contours, right hand cut-off, and the hydrogen resonance layers of the ICRF heating for the typical parallel wave number k = 5.0 m −1 at 38.5 MHz.

Experimental setup
In order to evaluate the pressure of the fast ions in the LHD, the MORH code [11] is used. This code is a drift kinetic orbitfollowing the Monte Carlo code. The finite beta equilibrium is calculated by HINT2 [12,13]. The birth profiles of fast ions injected by NBI, which are used as the fast ion source of the MORH code, are calculated by FIT3D code [14]. The result shows that the fast ion density n f injected by the perpendicular-NBIs (p-NBIs) is accumulated close to the third harmonic resonance layer as shown in figure 2, by the blue color contour. The higher n f can be seen at the upper and the lower regions. In LHD, the low magnetic field regions are located in the upper side and in the lower side in the cross-section shown in figure 2, and fast ions are trapped in the ripple. The upper and lower asymmetry is derived from the deposition profile of the NBI injected from the outer side of the vacuum chamber. In order to inject the ICRF power to achieve a high beta plasma, we utilize the third harmonic ICRF heating. In this condition, the ICRF heating power is considered to be absorbed by the energetic ions from the p-NBIs at the third harmonic resonance layers.

Experimental results
For the investigation of the LHD high beta experiment with ICRF heating, the gas of the NBI and target plasma are 100% hydrogen, the toroidal magnetic field is 1.0 T at the vacuum magnetic axis, R = 3.56 m, and the NBI injection powers are 2 MW by the tangential-NBIs (t-NBIs) and 12 MW by the p-NBIs. The initial plasma was generated by using only NBIs [15]. The increasing beta value by ICRF heating can be evaluated by comparison with and without ICRF injection shown in figure 3. The 4 MW ICRF heating clearly contributed to the increase of the beta value from 2.4% to 2.6%. In this ICRF third harmonic experiments with NBI, the ICRF wave was absorbed and the stored energy was increased. The increase of radiation loss power is 0.7 MW during the 3.7 MW ICRF heating. This ratio is less than 20% of the net injected power. The stored energy is slightly increased approximately by 20 kJ during the ICRF heating on timing. The electron density and the temperatures of the ions and electrons are almost constant with and without ICRF injection. Figure 4(a) shows the energy distribution functions of neutral flux measured by CNPA. The vertical axis indicates the measured count rate of the neutral particles at the energy range of more than 80 keV. At the energy range of less than 80 keV, the data is measured using the count rate together with the calibration factor of the detector size. The solid lines indicate the case with p-NBI, and the dotted lines indicate the case without p-NBI. In both cases, the ICRF injection increases the count of neutral flux from the blue lines to the red lines. The neutral flux ratio, which is the energy distribution function with ICRF injection divided by the distribution function without ICRF injection, is strongly increased at the energy of 40-80 keV shown by the solid line in figure 4(b) when p-NBI injection is present. In the case of p-NBI, the neutral flux count is increased up to more than five times at around 60 keV. These results indicate that the ICRF wave accelerates the 40 keV particles injected by p-NBIs. However, the distributions of the electron density and the electron temperature measured by Thomson scattering are almost the same as shown in figure 5. In this low magnetic field experiment, the relatively large Larmor radius causes the orbital loss of energetic particles [3,16]. This energy loss is attributed to one of the reasons for the small contribution to the electron temperature. Almost all of the increase of the stored energy of the diamagnetic signal should be considered to be the accelerated particles. When the electron density and temperature are almost constant, using the changing of the stored energy at the ICRF power turning off timing as shown in figure 6, the heating efficiency η can be evaluated by the following equation [17]. The waveforms of the NBI and ICRF heating power, beta value was measured by diamagnetic loops, the radiation loss power measured by a bolometer, the electron density was measured by interferometer, and the ion and electron temperatures were measured in the high beta experiments. The energy of t-NBIs is 180 keV, and p-NBIs is 40 keV. The beams and the target plasma are hydrogen, and the toroidal magnetic field is 1 T at the magnetic axis.
where ∆P is the step in ICRF power. In the case of figure 6, the differential value dW/dt of this discharge is approximately −1.6 MJ s −1 , and the heating efficiency η is 44%. The dependence of the heating efficiency on the electron density is shown in figure 7 in the range n e at ρ = 0.7-0.9. Here, the energetic particles injected by p-NBIs and the ICRF third harmonic resonance are located. All of the results in figure 7 are discharges with p-NBIs, because in the case without p-NBIs, dW/dt and the heating efficiency are small. The ICRF heating efficiency is approximately 30%-50% estimated by the breakin-slope at the ICRF turn off timing. This value of the efficiency and increasing tendency when the density is increased are similar results of previous research in second harmonic ICRF heating experiments [20]. One reason for this increasing tendency is that the ICRF perpendicular wave number k ⊥ increases with the density increasing [21]. As a result of the ICRF injection, the maximum beta value is increased up to 4.1% [18]. As the experimental condition of the highest beta discharge, the magnetic field is 0.5-1.0 T, vacuum magnetic axis is around 3.60 m, and the heating power is 15 MW by the t-NBIs and 10 MW by the p-NBIs.

Conclusion
The ICRF injection in the high beta experiment in LHD was performed. ICRF wave couples and accelerates the energetic particles provided by p-NBIs with 40 keV to approximatlyapproximately 60 keV when 3.7 MW of ICRF is applied. The simulation by the MORH code shows the presence of the energetic particles around the ICRF third harmonic resonance layer. As the results of ICRF heating power deposition, the plasma stored energy increased during the ICRF injection, and the beta value clearly increased. The increase of the ion and electron temperatures were not observed. However, the increase of the high energy ion tail was observed. The increase of the beta value is mostly due to the contribution of the increased energetic particles. The ICRF heating efficiency is estimated to be approximately 30%-50%, and the radiation loss is less than 20%. The heating efficiency increases with the electron density increase. These results indicate the effectiveness of the ICRF third harmonic hydrogen heating under higher density and good confinement.   The electron density dependence of the heating efficiency using similar discharges #128803-844. Even in the similar discharges, the heating efficiency has variation of 5%-10%.