Ion cyclotron range of frequency heating experiments on the large helical device and high energy ion behavior *

Ion cyclotron range of frequency heating experiments on the large helical device and high energy ion behavior * R. Kumazawa, T. Mutoh, T. Seki, T. Watari, K. Saito, Y. Torii, F. Shimpo, G. Nomura, M. Yokota, A. Kato, D. A. Hartmann, Y. Zhao, A. Fukuyama, H. Okada, K. Ohkubo, M. Sato, S. Kubo, T. Shimozuma, H. Idei, Y. Yoshimura, T. Notake, Y. Takita, S. Kobayashi, S. Itoh, Y. Mizuno, O. Kaneko, Y. Takeiri, Y. Oka, K. Tsumori, M. Osakabe, K. Ikeda, S. Yamamoto, T. Kawamoto, E. Asano, N. Ohyabu, K. Kawahata, A. Komori, H. Yamada, K. Akaishi, N. Ashikawa, M. Emoto, H. Funaba, M. Goto, K. Ida, S. Inagaki, N. Inoue, M. Isobe, A. Krasilnikov, S. Masuzaki, T. Minami, J. Miyazawa, T. Morisaki, S. Morita, S. Murakami, S. Muto, Y. Nakamura, Y. Nagayama, H. Nakanishi, K. Narihara, Y. Narushima, K. Nishimura, N. Noda, T. Kobuchi, S. Ohdachi, T. Ozaki, B. J. Peterson, A. Sagara, S. Sakakibara, R. Sakamoto, H. Sasao, M. Sasao, K. Sato, M. Shoji, H. Suzuki, K. Tanaka, K. Toi, T. Tokuzawa, I. Yamada, S. Yamaguchi, M. Yokoyama, K-Y. Watanabe, T. Watanabe, K. Matsuoka, K. Itoh, S. Sudo, K. Yamazaki, Y. Hamada, O. Motojima, M. Fujiwara, and the LHD Experimental Group National Institute for Fusion Science, Toki 509-5292, Japan


I. INTRODUCTION
One of the major concerns of the Large Helical Device ͑LHD͒ project is whether the ion cyclotron range of fre-quency ͑ICRF͒ heating in helical systems works well, can sustain the plasma in a steady state and whether high energy ions can be confined well or not.In the third experimental campaign of 1999 the ICRF heating experiment provided an answer to this concern. 1he LHD is the largest super-conducting heliotron-type device with 1/mϭ2/10 continuous helical coils.The main physical research is the investigation of currentless and disruption-free steady-state plasmas.3][4] The major and minor radii are 3.9 m and 0.6 m, respectively, and the designed toroidal magnetic field strength is 3 T.
In the third campaign, the LHD experiments achieved several remarkable improvements: ͑1͒ A maximum plasma stored energy of 0.88 MJ was attained with the heating power ͑4.7 MW͒ of neutral beam injection ͑NBI͒ and ICRF heating.͑2͒ The maximum energy confinement time was 0.3 seconds.͑3͒ The highest electron and ion temperatures were 4.4 keV and 3.3 keV.͑4͒ Long-pulse operations lasting more than 1 minute were obtained using NBI only and using ICRF heating only.͑5͒ The maximum beta value was 2.4%.͑6͒ The maximum electron density was 1.1ϫ10 20 m Ϫ3 with the hydrogen pellet injection. 5,6he final goal of the ICRF heating on the LHD is high power heating of 10 MW and plasma sustainment in steady state at 3 MW.[9][10][11][12] In the second experimental campaign, ICRF heating experiments were carried out in helium plasma with minority hydrogen ions using a pair of loop antennas at the magnetic field strength Bϭ1.5 T of the standard configuration, i.e., R ax ϭ3.75 m.The increase in the plasma stored energy was proportional to the applied ICRF heating power up to 300 kW.The maximum increase was found to be 13 kJ at P ICH ϭ300 kW, which was the same amount as that with electron cyclotron heating ͑ECH͒ only. 13,14However, the plasma could not be sustained by ICRF heating only.
The third experimental campaign was carried out in 1999. 1,15The magnetic field strength was increased to B ϭ2.75 T and the inward-shift of the magnetic axis to R ax ϭ3.6 m was mostly employed.The carbon plates were installed at the helical divertor legs, and this was useful for reducing the impurity penetration in the case of ICRF heated plasma.In this paper, the ICRF heating experimental results and the behavior of high energy protons accelerated by the ICRF wave field are described.In Sec.II, the ICRF heating mode and the ICRF heating experimental setup, including a pair of loop antennas and an impedance matching system, are described.In Sec.III, several ICRF heating experimental results are reported.In Sec.IV, the behavior of high energy protons is introduced and the ICRF heating efficiency is discussed.Then we summarize the ICRF heating experiments on the LHD and mention the future plan in Sec.V.

A. Experimental setup
The antenna is 60 cm in length, 46 cm in width and 17 cm in depth.The antenna strap is 30 cm in width.The surface of the antenna is fitted to a configuration of the last closed magnetic surface.The position of the ion cyclotron heating ͑ICH͒ antenna can be shifted inward by 15 cm by using a swing mechanism.All the components of the antenna, i.e., the Faraday shield, side limiters, antenna strap, back plate, and inner and outer conductors are cooled by purified water. 1 The rf power is transmitted to each antenna from the high power radio frequency ͑rf͒ generator via a liquid impedance matching system.It consists of three liquid stub tuners, which are identical. 9All the rf components of the transmission lines, including the liquid stub tuners and the ceramic feed-through, are cooled by purified water to achieve a high rf power steady-state operation.
An optical measurement method is employed to estimate the ratio of the hydrogen minority ions.Spectroscopic apparatuses are installed at the vacuum port adjacent to the ICH antenna to monitor H␣ ͑656.3 nm͒ and HeI ͑587.6 nm͒ signals.
Hydrogen or helium glow discharge cleaning was carried out everyday for the wall conditioning after the plasma experiment was over.A titanium gettering, which covered about 30% of the LHD vacuum vessel surface, was employed in the middle of this experimental campaign; consequently the oxygen impurity was remarkably reduced.It was routinely carried out for an hour just before the experiment started.The vacuum base pressure was maintained in the order of 10 Ϫ6 Pa.

B. ICRF heating mode
The ICRF heating efficiency depends mainly on the location of the minority ion cyclotron resonance and the ionion hybrid resonance layers.Figure 1 shows the typical heating scenario referred to as Mode-I, in which the ICRF heating experiments were mainly carried out in the third campaign.The minority cyclotron resonance, L ͑left hand͒ cutoff, R ͑right hand͒ cutoff, and ion-ion hybrid resonance ͑in dotted line͒ layers are plotted in Fig. 1.Here the magnetic field strength, the frequency and the wave number are B ϭ2.75 T, f ϭ/2ϭ38.47MHz and k ʈ ϭ5 m Ϫ1 , respectively.The plasma parameters are a central electron density, n e (0)ϭ1.0ϫ10 19m Ϫ3 and a minority hydrogen ratio of 10% in the helium plasma.The ion-ion hybrid resonance is located between the magnetic axis and the minority ion cyclotron resonance, which is the same configuration as in the Compact Helical Stellerator ͑CHS͒ experiment. 16,17As the ratio of hydrogen ions to helium ions becomes higher, the hybrid resonance layer moves toward the magnetic axis.When the frequency is decreased or the magnetic field strength is increased, the ion cyclotron resonance layer moves toward the lower magnetic field ͓see / ci ϭ0.68, 0.75 and 0.81 in Fig. 2͑a͔͒.In accordance with the shift of the cyclotron resonance layer, the ion-ion hybrid resonance layer also moves to the lower magnetic field side and is separated into two layers; that is referred to as Mode-II.

A. Optimization of ICRF heating
The characteristics of ICRF heating in helical devices are thought to be different from those in tokamaks because of the difference of the magnetic field configuration.A series of experiments was carried out in order to optimize the ICRF heating by scanning the magnetic field strength, the applied frequency and the minority ion concentration.The situation in which the fast wave accesses to the resonance layers is drastically changed, when the minority ion cyclotron resonance layer is shifted, as shown in Fig. 2͑a͒.In the cases of / ci ϭ0.68, ϭ0.75, and ϭ0.81, the fast wave directly approaches the ion-ion hybrid resonance layer and the wave energy is efficiently transferred to electrons via the mode converted Ion Bernstein Wave ͑IBW͒.The fraction of power absorbed by electrons to the total absorbed rf power, P ele / P abs , was employed as the most appropriate figure to facilitate the physical understanding.P ele / P abs was observed at 100% at / ci ϭ0.68 and gradually decreased in the cases of / ci ϭ0.75 and ϭ0.81. 18On the contrary, the ion heating becomes dominant in the cases of / ci ϭ0.92 and / ci ϭ1.01.This phenomenon was explained by considering how much a fraction of the fast wave directly accesses to the ion-ion hybrid resonance layer. 18n Fig. 2͑b͒, the energy confinement time normalized by International Stellarator Scaling 95 ͑ISS95͒, 19 E / E ISS95 is plotted with solid circles in seven cases.In the cases of / ci ϭ0.68, ϭ0.75 and ϭ0.81, E / E ISS95 is about 1 and the maximum values of more than 1.5 were obtained in / ci ϭ0.92 and ϭ1.01.It is noted that the optimal confinement was attained when the heating power deposition was located near the magnetic axis.In this figure, the ICRF heating efficiency is also plotted using open circles. A igher heating efficiency is observed at / ci ϭ0.68 ͑electron heating͒ and / ci ϭ0.92 ͑ion heating͒.The fact that a higher heating efficiency is obtained in / ci ϭ0.92 than in / ci ϭ1.01 can be explained by two reasons: One is effective power absorption via cyclotron resonance heating.The ion heating can be optimized when the minority ion cyclotron resonance layer is located at the saddle point, i.e., the gentle gradient of the magnetic field strength, which is characterized by the helical magnetic configuration.18 The other is the better confinement of the high energy ions in / ci ϭ0.92, which will be described in Sec.IV A. The best plasma performance can be obtained in / ci ϭ0.92 because of the higher energy confinement time and the heating efficiency.

B. ICH sustained plasma
The plasma was sustained by injecting ICRF heating power only.An initial plasma was started by fundamental electron cyclotron heating ͑ECH, 82.6 and 84.0 GHz with 0.4-0.5 MW͒.The ICRF heating power was applied to the ECH plasma 0.1-0.2seconds before the turning-off of the ECH.After the ECH was turned off the plasma could be sustained by an ICRF heating larger than 0.2 MW.The ratio of the hydrogen to helium ions, H␣/HeI is also a key to optimizing the ICRF heating.
A typical discharge of the ICH-sustained plasma with P ICH ϭ1.3 MW is shown in Fig. 3.The average line electron density is n e ϭ1.8ϫ10 19 m Ϫ3 with a stored plasma energy of 200 kJ.In this operation, the intensity ratio of H␣ to HeI was maintained between 0.8 and 0.7, which was converted to about 10% of the hydrogen ion minority ratio to the electron density.The electron density was adjusted by using a helium gas puffing.The hydrogen ion density was maintained by the FIG. 2. ͑a͒ Various minority ion cyclotron resonance layer in ICRF heating experiments is denoted by the ratio of an applied frequency to an cyclotron frequency on the magnetic axis / ci .͑b͒ Dependence of E / E ISS95 and heating efficiency on / ci .
recycling from the vacuum wall.The electron temperature was 1.7 keV at the magnetic axis.The radiated power was observed to be P rad ϭ250-300 kW during the ICRF heating.
The parameters of the ICH-sustained plasma were similar to those of the neutral beam injection ͑NBI͒ plasma with the same absorbed power level, which will be introduced in Sec.III D.

C. Additional ICRF heating to NBI heated plasma
The ICRF heating was applied to the negative-based NBI plasma with the hydrogen pellet injection at the electron density of n e ϭ10ϳ8ϫ10 19 m Ϫ3 as shown in Fig. 4. The plasma stored energy reaches 760 kJ at an ICRF heating power of 0.76 MW and an NBI power of 3.5 MW.An increase in the plasma stored energy is observed to be about 50 kJ during the ICRF heating.To clarify the additional ICRF heating effect, a series of the experiments was conducted using three different electron densities, i.e., n e ϭ1.0 ϫ10 19 m Ϫ3 , 2.0ϫ10 19 m Ϫ3 and 3.3ϫ10 19 m Ϫ3 .The counterinjection of NBI was used and the port-through power of NBI was almost constant at P pt ϭ1.45 MW (E inj ϭ130 keV) in the series of experiments.The absorbed power of NBI is calculated by measurement of the temperature increase of the armor tiles with and without plasma. 20On the other hand, the rf power absorbed by the plasma can be estimated by the decay of the plasma stored energy.The heating efficiency was 80-85%.The radial distribution of radiated power in the additional ICRF heated plasma was the same that of the NBI heated plasma, which was measured by a multi-channel bolometer array. 21The radiated power increased with an additional ICRH heating power.The dependence of the plasma stored energy on the total heating power was plotted in Fig. 5, where open and solid circles represent the NBI plasma alone and the NBI-ICRF heated plasma, respectively.These experimental data can be compared with the calculated plasma stored energy by solid lines using a power dependence of ISS95 with enhancement factors, i.e., 1.4-1.6.It is found that the ICRF heating is comparable with the NBI heating.

D. A comparison of ICH-sustained plasma with NBI heated plasma
In the previous section, it was shown that the ICRF heating has the same heating quality as that of the NBI heating in the case of the additional ICRF heating.Here the ICRF heated and sustained plasma is directly compared with the NBI heated plasma, selecting discharges with the same heating power and the same line average electron density.The time evolutions of various plasma parameters of ICRF heated plasma ͑a͒ and NBI heated plasma ͑b͒ are shown in Fig. 6: The absorbed heating power is 1 MW in both cases.The electron density was n e ϭ1.0ϫ10 19 m Ϫ3 as shown in Fig. 6.The measured plasma stored energy of ICRF heated plasma was the same as that of NBI heated plasma, i.e., 170 kJ.Comparing the radiated power of the ICRF heated plasma measured by bolometer array, it was observed to be larger than that of the NBI heated plasma.The time evolutions of the impurity radiation, i.e., OV and FeXVI are also plotted in Fig. 6 and the line radiation intensity is larger than that of the NBI plasma by a factor of 2.
The radial profiles of the electron density, radiation power and the electron temperature are compared with those of the NBI heated plasma.The electron temperature was measured by a YAG laser Thomson scattering system with 120 channel detectors, in which the spatial resolution is several mm 22 and the electron density was measured by 13 channels of a far infrared ͑FIR͒ laser interferometer. 23These radial profiles are shown in Fig. 7͑a͒ for the ICRF heated plasma at 4 seconds and in Fig. 7͑b͒ for the NBI heated plasma at 1.5 seconds.It is readily seen that these profiles are quite similar and that the ICRF heating could have the same heating quality as the NBI heating; as the heat deposition profile in the ICRF heating is not obtained, the detail characteristics of the confinement is not discussed.The radial radiated power profile is a similar distribution to that of NBI heated plasma as shown in Figs.7͑a͒ and 7͑b͒; however the radiation power is larger than in the NBI plasma.
The energy confinement time is compared between three different plasmas, i.e., ICH-sustained, NBI-sustained and the ICRF additional heating referred as to ICHϩNBI.These confinement times are compared with ISS95 and the improvement factor is found to be over 1.5 in the three different plasmas.It is found to be a little larger at the lower energy FIG. 6.A comparison of ICRF heated plasma with NBI heated plasma.͑a͒ Time evolutions of parameters of ICRF heated plasma with ICRF heating power.͑b͒ Time evolutions of parameters of NBI heated plasma with NBI power.FIG. 7. A comparison of radial profiles of ICRF heated plasma with those of NBI heated plasma.͑a͒ Radial profiles of the electron density, radiation and electron temperature for ICRF heated plasma.͑b͒ Radial profiles of the electron density, radiation and electron temperature for NBI heated plasma.confinement, which was obtained at a relatively low electron density.

E. Long pulse of ICH-sustained plasma
A long-pulse operation was tried at the end of the third experimental campaign, using ICRF heating.The pulse length was lengthened shot by shot from 5 to 45 seconds in order to age the tetrode tubes of the final amplifier.The pulse duration time of ICH-sustained plasma was able to be prolonged up to 68 seconds as shown in Fig. 8.The radiated rf power from the antennas, the average plasma stored energy, the line average electron density, the electron temperature on the magnetic axis, the ion temperature and the radiation power are P ICH ϭ0.7 MW, W p ϭ110 kJ, n e ϭ1.0ϫ10 19 m Ϫ3 , T e0 ϭ2.0 keV, T i0 ϭ2.0 keV and P rad ϭ200 kW, respectively.The ion temperature was measured from Doppler broadening of TiXXI ͑0.261 nm͒ using an x-ray crystal spectrometer. 24he minority fraction was kept constant at H␣/HeIϭ0.7 and the impurity accumulation of FeXVI and OV was not observed during the long-pulse operation as shown in the bottom of Fig. 8.The energy confinement time and the operation time are given E ϭ0.19 seconds and 68 seconds, respectively, and the fusion triple product is n e E T i0 ϭ3.8 ϫ10 18 m Ϫ3 keV s.The first goal of the steady-state discharge in the LHD is n e E T i0 ϭ1.5ϫ10 19 m Ϫ3 keV s.It can be achieved at a higher electron density, e.g., n e ϭ4 ϫ10 19 m Ϫ3 at a 1ϳ2 MW level of the ICRF heating power, rather lower than 3 MW, which has been predicted to be required to achieve the objective of the LHD project; this will be discussed in the next section.

F. Parameters of ICRF heated plasma
A scaling of a fusion triple product is derived from ISS95 in the following equation: 18 .͑1͒ To determine the numerical factor experimental data are plotted in Fig. 9 whose abscissa and ordinate are n e (ϫ10 19 m Ϫ3 ) 1.02 P ICH (MW) Ϫ0. 18 and n e E T i0 (ϫ10 20 m Ϫ3 keV s), respectively.The experimental range of the average electron density and the ICRF heating power are 0.75 ϫ10 19 m Ϫ3 Ͻn e Ͻ1.8ϫ10 19 m Ϫ3 and 0.69 MWϽ P ICH Ͻ1.3 MW, respectively.The numerical factor can be determined to be 0.03 from this figure.The fusion triple product of the long-pulse discharge ͑described in E͒ is also plotted using a solid circle.
The density limit is another interest in reactor relevant plasmas, because the fusion triple product is almost proportional to the electron density as described above.The electron density of the ICRF heated plasma discharge so far achieved is n e ϭ1.8ϫ10 19 m Ϫ3 .The density limit obtained in medium size of Heliotron and Stellarator devices 25 predicts n e ϭ4ϫ10 19 m Ϫ3 at P ICH ϭ1.3 MW.The achieved domain of the electron density is far below the density limit; therefore, a trial of the higher electron density discharge of ICRF heated plasma will be an important issue in the coming experimental campaign.

A. Improved orbit of high energy ions
One of the major concerns in heliotron systems is whether high energy ions can be confined or not, due to the nonaxisymmetric magnetic configuration.As described in the previous section, one of the main reasons of the successful ICRF heating may be the improvement of the particle orbit of the trapped high energy ions accelerated by ICRF electric field.The position of the magnetic axis, R ax is a key parameter determining the behavior of the deeply trapped ions and the MHD stability aspect.The inward-shifted configuration reduces the deviation of the particle orbit from the magnetic surface but deteriorates the MHD stability.The standard configuration has been selected to be R ax ϭ3.7 m as a compromise.When the orbits of ions with perpendicular pitch angle are compared between the different magnetic axis configurations, i.e., R ax ϭ3.75 m and ϭ3.6 m, the improvement of the drift surface of a trapped particle is remarkable in the inward-shifted configuration. 26In the coming 4th experimental campaign, it will be interesting to compare the ICRF heated plasma performance and the transfer efficiency ͑see Sec.IV C͒ among R ax ϭ3.6 m,ϭ3.75 m and further outward shifted R ax ϭ3.9 m.As described in Sec.III A, the heating efficiency is lower at / ci ϭ1.01 than at / ci ϭ0.92; however, the enhancement of the energy confinement time is the same, as shown in Fig. 2͑b͒.The lower heating efficiency can be also explained by comparing the orbit of the high energy ions perpendicularly accelerated by the rf field.The trajectory of ions with the pitch angle of 90 degrees at / ci ϭ0.92 is poloidally and toroidally along the minimum magnetic field strength.These ions behave as deeply trapped particles in the helical ripple and are confined well in the case of the inward shifted configuration, i.e., R ax ϭ3.6 m.On the other hand, ions accelerated at / ci ϭ1.01 behave as transition particles referred to as ''trapped-detrapped particles.''The trajectory is stochastic because such a particle is trapped in the helical ripple or in the toroidal ripple and sometimes becomes a passing particle without Coulomb collisions. 27High energy ions with a pitch angle of 90 degrees at two ICRF heating conditions, i.e., / ci ϭ0.92 and / ci ϭ1.01 are categorized in 2 groups; transition particles and trapped particles.High energy ions with a pitch angle of 90 degrees at / ci ϭ0.92 are trapped particles and are well confined.On the other hand, perpendicularly accelerated ions at / ci ϭ1.01 are transition particles, which is the another reason for the lower heating efficiency, which was seen in Fig. 2͑b͒.

B. Energy spectrum of high energy ions
The most successful ICRF heating has been achieved when the resonance layer of minority hydrogen ions was located at the saddle point on the mod-B surface ͑see Fig. 1͒.Most of the ICRF heated power was absorbed by the high energy ions. 18A Natural Diamond Detector ͑NDD͒ 27,28 was installed to measure the high energy on tails and a fast particle neutral analyzer with a capability to separate the species by time of flight 29 was also equipped in the LHD.A spectrum of the high energy ions was measured by the NDD at the ICH-sustained plasma.Time evolutions of the plasma parameters and the ICRF heating power are shown in Fig. 10͑a͒.The ICRF heating power ranges from 1.1 to 1.3 MW.The line average electron density and the electron temperature on the magnetic axis are n e ϭ1.0ϳ1.2ϫ10 19m Ϫ3 and T e0 ϭ2.2ϳ2.1 keV, respectively.The ratio of H␣/HeI gradually decreases from 1.2 to 0.9 with the increase in the electron density.The spectrum of high energy ions at 30-250 keV are shown in Fig. 10͑b͒, where the gating time to count the neutral particle number is 0.2 seconds.In Fig. 10͑b͒, three high energy ion spectra are shown in different periods of the discharge.Open squares show that of the ECH plasma in the first period, i.e., 0.0-0.2s before ICRF power is turned on.Then open circles and open triangles are those of the ICRF heated plasma at 3.0-3.2s and 5.0-5.2s, respectively.The effective temperature of the high energy tail ions is derived from the ion energy spectrum, which is compared with that given by Stix's formula. 30,31The effective ion temperature can be theoretically calculated from the following equation, which is derived from the energy balance between the ICRF absorbed power and the energy dissipation via the electron drag: T eff ϭT e ͩ 1ϩ P abs s 3n H V H T e ͪ .

͑2͒
Here P abs , s , n H and V H are the absorbed ICRF heating power, the Spitzer's slowing down time, the minority ion density and the heating volume respectively.Neglecting 1 in the bracket, T eff is proportional to P abs T e 1.5 /n e n H V H . Figure 11 shows a comparison between the measured T tail and the calculated T eff .The minority ion density is difficult to measure but was deduced from the spectroscopic measurement of H␣ and HeI.In the wide range of factor 2, T tail agrees with the theoretical T eff . 31No saturation was observed up to T tail ϭ75 keV in Fig. 11, indicating that the high energy ions were well confined so that the ion energy can be sufficiently transferred to electrons.

C. Enhancement of confinement time due to high energy ions and energy transfer efficiency
An enhancement of the energy confinement time due to the existence of high energy ions was expected on the basis FIG. 10. High energy ion measurement using NDD: ͑a͒ Time evolutions of parameters of ICRF heated plasma with ICRF heating power and measure tail temperature T tail in the energy range from 30 to 250 keV.͑b͒ Counts number of high energy particle in the energy range from 30 keV to 250 keV during 0.2 seconds in three different periods.
of calculations of high energy ion orbits based on the Monte Carlo simulation. 26The total plasma stored energy W tot consists of two parts: one is the plasma stored energy of the bulk plasma W bulk and the other is that of the high energy ion W tail : W tot ϭW bulk ϩW tail , W tot ϭ P total E glb , ͑3͒ W bulk ϭ P trns E bulk and W tail ϭ P abs E tail .
The ICRF heating power is first absorbed by minority ions and then the high energy ion tail is formed.The bulk plasma is heated by the high energy ions via the electron slowing down process.Here P total , P abs and P trns are the total heating power, the absorbed power by high energy ion and the transferred power to the bulk plasma, respectively.In the case of the experiment, P total is the same as P abs .E total , E bulk and E tail are the global energy confinement time, the energy confinement times of the bulk plasma and the high energy ions, respectively.E tail is given by E tail ϭ s /2, when the power transfer efficiency is employed as ϭP trns / P abs .The global energy confinement time is written in the following equation:

͑4͒
On the other hand, the scaling of the power transfer efficiency was formulated with the Monte Carlo simulation in the following form: The orbit loss crossing the last closed magnetic surface is regarded as the energy loss of the high energy ions.The exponents of ␣, ␤, ␥ and ␦ have been determined as ␣ϭ1, ␤ϭ2, ␥ϭ2 and ␦ϭ1.A numerical factor C depends on the ratio of minority ions, species of minority ions and a dimension of the device, etc.An enhancement of the global confinement time from that of ISS95 is expected in accordance with Eq. ͑4͒.When the transfer efficiency is ϭ1.0, the confinement enhancement may be found to be more than 10 at the longer s , i.e., at the lower electron density.It is plotted against the electron density for the ICRF heating dis-charges, i.e., P abs ϭ0.5 MW in Fig. 12.The increase in the normalized ratio of the global energy confinement time is observed in the lower electron density discharge.The enhancement, however, is smaller than that estimated in the case of ϭ1.0, which causes a lower transfer efficiency in the lower electron density discharge.The transfer efficiency can be deduced from the experimental data.In the analysis the average electron temperature is calculated from the bulk plasma confinement time, which obeys ISS95 with an enhancement factor.In Fig. 12, the estimated enhancement of the confinement time is plotted in three cases of the numerical factor C in Eq. ͑5͒, i.e., Cϭ0.0 (ϭ1.0), Cϭ0.05 and Cϭ0.1.The transfer efficiency can be determined by fitting the experimental enhancement factor in the following form: The electron temperature measured at the half-radius of the plasma agrees well with the calculated electron temperature.
It is also of interest to compare the transfer efficiency with that deduced by the Monte Carlo simulation, in which the bulk plasma is the same as in the experiment.The transfer efficiency agrees well with that of the simulation; however, the experimental one is a little lower than that of the simulation.The difference between them may be derived from the other loss process, which is not included in the Monte Carlo simulation, e.g., the charge exchange loss near the plasma edge.
One of the final goals of ICRF heating is an achievement of the high power heating at 10 MW.The scaling of the transfer efficiency with the Monte Carlo simulation can predict whether the ICRF heating at 10 MW will be successful or not in the future experiment.Figure 13 gives an answer to this question; the transfer efficiency is improved to 95% even at 10 MW of ICRF heating, when the electron density is increased to 4ϫ10 19 m Ϫ3 .

V. SUMMARY
Results of ICRF heating experiments on the LHD were summarized with regard to two topics.

͑1͒
The ICRF heating experiments demonstrated significant results with regard to the additional heating to the NNBI plasma, and the ICH-sustained plasma with high stored energy up to 200 kJ and at a long pulse of 68 seconds at 1 MW level.The ICRF heating power was mostly absorbed by minority protons in the optimized ICRF heating.The confinement characteristics of the ICRF heated plasma are the same as those of the NBI plasma.The energy confinement time is longer by a factor of 1.5 than that of ISS95.
͑2͒ The deeply trapped high energy ions accelerated by the ICRF electric field were observed to be confined well by measuring the energy spectrum up to 250 keV.The tail ion temperature scales with Stix's formula, which may result from employing the configuration of the inward-shifted magnetic axis.The dependence of the transfer efficiency of the high energy tail ion to the bulk plasma on the electron density was experimentally obtained and it was found to agree fairly well with that of the Monte Carlo simulation.This result suggests that the ICRF heating will be successful even at 10 MW at an electron density of more than 4 ϫ10 19 m Ϫ3 .Impurity accumulation was not observed in the whole ICRF heated plasma, and this is thought to result from the installation of carbon divertor plates and a forementioned improvement in the high energy particle confinement due to the inward shifted R ax .
Three more identical antennas will be installed to double or triple the ICRF heating power in the coming experimental campaign.A long-pulse operation more than 5 minutes will be tried at the higher fusion triple product, e.g., n e E T i0 ϭ1.0ϳ1.5ϫ10 19m Ϫ3 keV sec in the coming experimental campaign of 2000.

FIG. 1 .
FIG. 1. ICRF heating mode referred to as Mode I: Locations of ion cyclotron resonance of minority ions, ion-ion hybrid resonance, R cutoff, and L cutoff are plotted in the case of the electron density of n e (0)ϭ1.0ϫ10 19 m Ϫ3 , n H /n e ϭ10%, Bϭ2.75 T, and f ϭ38.47 MHz.

FIG. 3 .
FIG. 3. Time evolutions of parameters of the plasma sustained by ICRF heating only with P ICH ϭ1.3 MW.

FIG. 11 .
FIG. 11.A comparison of measured tail temperature T tail with effective temperature calculated T eff by Stix's formula.