Analysis of Bulk Ion Heating with ICRH in JET High-performance Plasmas

JET P(98)81 M J Mantsinen et al Analysis of Bulk Ion Heating with ICRH in JET High-performance Plasmas

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JET P(98)81 Analysis of Bulk Ion Heating with ICRH in JET High-performance Plasmas M J Mantsinen 1, L-G Eriksson, V P Bhatnagar, G A Cottrell, A Gondhalekar, C Gormezano, R König 3, P Lomas, E Righi 4, F G Rimini, A C C Sips, D F H Start*, F X Söldner, D Testa 5, B Tubbing, K-D Zastrow. JET Joint Undertaking, Abingdon, Oxfordshire, OX14 3EA,UK. 1 Also at Helsinki University of Technology, Association Euratom-Tekes, Espoo, Finland. Present address: CEA Cadarache, St Paul Lez Durance, France. 3 Present address: Max-Planck-Institut für Plasmaphysik, Euratom Association, Garching, Germany. 4 Present address: NET Team, Garching, Germany. 5 Also at Imperial College of Science, Technology and Medicine, London, UK. Present address: MIT, Plasma Science and Fusion Centre, Cambridge, USA. * We pay tribute to Dr D F H Start who died suddenly in August 1998 during the completion of this article Preprint of a Paper submitted for publication in Plasma Physics and Controlled Fusion February 1999

ABSTRACT In the JET experimental campaign with the Mark IIA divertor, high-performance discharges have been achieved with combined neutral beam injection and ion cyclotron resonance heating (ICRH). In the experiments ICRH was normally tuned to the fundamental hydrogen resonance, coinciding with the second harmonic deuterium resonance, near the plasma centre. With the addition of ICRH, increased plasma energy content, electron temperature and bulk ion heating have been obtained. Due to acceleration of deuterium beam ions, the deuterium-deuterium fusion reactivity has also been enhanced. In the present paper ICRH in JET high-performance deuterium discharges is analysed using numerical simulations, with the aim to investigate under which conditions good bulk ion heating can be obtained with ICRH. 1. INTRODUCTION Heating with waves in the Ion Cyclotron Range of Frequencies (ICRF) is a well-established method for auxiliary heating of present-day tokamak plasmas, and its potential for heating of reactor plasmas has been demonstrated using deuterium-tritium (D-T) plasmas on JET [1, ] and TFTR [3, 4]. Together with neutral beam injection (NBI) and electron cyclotron heating, ion cyclotron resonance heating (ICRH) is one of the main auxiliary heating methods envisaged for ITER and future reactor plasmas. In order to predict the performance of ICRH in ITER, it is important to benchmark present theoretical modelling with experimental results. For predictions of bulk ion heating, it is especially valuable to investigate scenarios with a considerable fraction of bulk ion heating on present tokamaks. In the JET experimental campaign with the Mark IIA divertor, significant bulk ion heating with ICRH has been obtained in ICRH-only D-T plasmas [1, ], and in high-performance (hotion H-mode and optimised shear) plasmas by adding ICRH to NBI [5]. In the present paper ICRH in the JET high-performance deuterium discharges with deuterium NBI is analysed, with emphasis on analysing the bulk ion heating. In these discharges ICRH has normally been tuned to the fundamental hydrogen resonance, which coincides with the second harmonic deuteron resonance near the plasma centre (ω ω ch = ω cd ). In addition to bulk ion heating, an increased plasma energy content, electron temperature and deuterium-deuterium (D-D) fusion reactivity have been obtained with ICRH [5]. Due to the interaction with the ICRF waves, deuterons have been accelerated above the maximum deuteron NBI energy, which has been observed with a high-energy neutral particle analyser (NPA) [6]. The present experiments are not the first experiments to demonstrate an enhanced ion tail by tuning ICRF waves to resonance with injected beam particles as proposed by Stix [7]. Observations of interaction between beam ions and ICRF waves have been reported earlier on JET [8-11], as well as on many other tokamaks [3, 1-18]. Results from these experiments have been analysed with numerous models, see for example Refs [18-]. On JET the enhancement of the 1

D-D fusion reactivity due to absorption of ICRF power on deuterium beam ions has been studied [11], the power absorbed on deuterium beam ions has been estimated [1], and the effects of damping on the residual hydrogen ions during second harmonic heating of deuterium beam ions have also been investigated [9]. Detailed numerical and analytical studies also exist on the enhancement of the beam-driven current [3, 4], and of the fusion reactivity [5-9], but systematic investigation of the effects of ICRF-accelerated beam ions on heating of the bulk plasma is lacking. In the present paper our aim is to investigate under which conditions ICRH provides significant bulk ion heating in JET high-performance discharges. Good bulk ion heating is important for the JET high-performance discharges as well as for a reactor in order to reach a high ion temperature at high plasma density and thus a high thermal fusion reactivity. In order to provide bulk ion heating with ICRH at ω ω ch = ω cd as used in the present experiments, one has to ensure that a significant fraction of the ICRF power is deposited on the hydrogen ions and deuterons, and that the ions absorbing the wave power deposit power on bulk ions through collisions. It is relatively easy to obtain the former in the JET high-performance plasmas, since the single-pass damping on ions is relatively strong as compared with the direct electron damping. In order to obtain the latter, it is important that that the average energy of the resonating ions is comparable to or lower than the critical energy at which an ion transfers energy equally to background electrons and ions [3]. This, together with the fact that the D-T fusion reaction rate peaks around a deuteron energy of 1 kev, are the two main reasons why tail formation due to ICRH on the deuteron beam distribution function above the maximum deuteron injection energy (8 kev in JET D-T plasmas and 14 kev in deuterium plasmas) should not be strong. Since the power partition between the hydrogen ions and deuterons depends on plasma parameters which can be controlled, it should be possible, at least to some extent, to optimise the distribution functions of the two resonating species so that the bulk ion heating is maximised. In the analysis presented in this paper, we use the PION code [31, 3] to calculate the ICRF power deposition and the velocity distributions of resonating ions. In order to take the deuterium beam ion distribution function into account, NBI source terms have been included in the code. Previously, the PION code has been used to analyse various heating scenarios in JET [3-34] and has generally been found to provide an adequate description of the ICRF physics on JET. The paper is organised as follows. In Section we discuss theoretical considerations governing the power partition between deuterons and hydrogen ions, and the extent to which bulk ion heating can be obtained with ICRH. In Section 3 the model implemented in the PION code to account for NBI is discussed, and in Section 4 an analysis of JET experiments is presented. Finally, in Section 5 the results are summarised and discussed.

. THEORETICAL CONSIDERATIONS.1. Power partition For ICRH tuned to ω ω ch = ω cd the competing absorption mechanisms are fundamental hydrogen damping, second harmonic deuterium damping, and direct electron damping via electron Landau damping (ELD) and transit time magnetic pumping (TTMP). (According to the calculations presented in this paper, mode conversion, estimated with the Budden model [35], is negligible as compared with the competing absorption mechanisms in this scenario.) The absorption strength of the second harmonic deuterium damping, and hence the ICRF power partition among the different absorbing species, depend strongly on the deuteron velocity distribution function. To lowest order the local power partition between hydrogen and deuterium damping scales as [9, 31] p p D H k = c wd 1 nhmd cd ω, (1) where p H and p D are the power density absorbed by hydrogen and deuterons, respectively, c 1 is a constant, k is the perpendicular wave number, w D is the deuterium energy density, n H is the hydrogen density, and m D and ω cd are the deuteron mass and cyclotron frequency, respectively. This expression has been obtained by ignoring the finite Larmor radius (FLR) effects for the hydrogen absorption and including FLR effects to the second order for the deuteron absorption. In reality c 1 depends on various parameters such as the average squared parallel velocities of hydrogen ions and deuterons. However, analysis of JET high-performance discharges with PION shows that in practice c 1.3.4. From Eq. (1) we see that deuterium absorption can be increased as compared with hydrogen absorption by decreasing the hydrogen density, or by operating at high plasma densities, since k increases with the plasma density. By writing the deuterium energy density w D in Eq. (1) as a sum of thermal and non-thermal contributions, we see that both contributions play a role in the power partition. In JET high-performance deuterium discharges the non-thermal contribution due to deuterium beams is typically about -3% of the total deuteron energy density, and therefore can play a significant role in the power partition. Furthermore, we also see that an increase in the non-thermal contribution due to absorption of ICRF power by deuterons enhances the deuteron absorption as compared with hydrogen absorption. By moving the resonance layer to regions where the deuterium energy density is low, the deuteron absorption decreases as compared with hydrogen absorption according to Eq. (1). This plays a role for the multiple frequency operation of the JET ICRF antennas when the ICRF power is divided between up to four frequencies, spreading the resonance over a 3 4 cm wide region covering the plasma centre and the low field side (for comparison, the minor radius of a 3

JET plasma is typically about 1 m). However, since the deuteron energy density profiles are relatively broad in JET in the absence of ICRF waves, the main effect of the multiple frequency operation on the deuteron absorption is to decrease the deuteron absorption power density (for a given input power the power density decreases when the plasma volume that absorbs the power increases). Due to the lower deuteron absorption power densities, we expect a smaller enhancement by ICRH in the deuteron energy content and hence, according to Eq. (1), a smaller enhancement in deuteron absorption for multiple frequency operation... Maximising ion heating The extent to which ICRH tuned to ω ω ch = ω cd provides bulk ion heating depends on the details of the driven ion energy distribution functions. In order to provide bulk ion heating, it is important that the tail formation on the ion energy distribution functions is not strong. This is because the fraction of the energy a high-energy ion transfers to bulk ions decreases rapidly as the ion energy E increases beyond the critical energy E crit [3], i.e. we have W W i e =(E crit /E) 3/ where Ẇi and Ẇ e denote the rate of energy transfer to ions and electrons, respectively. From this expression we see that for an ion with E/E crit = 1, 1.5 and we have W W i e = 1,.54 and.35, respectively. Consequently, the average fraction of bulk ion heating when an ion undergoes a complete thermalization decreases rapidly as E/E crit increases [3]. For an ion with an initial energy E/E crit =1, 1.5, and for example, the average fraction of bulk ion heating during the slowing down is about 75, 65, and 55%, respectively [3]. In JET high-performance plasmas, which have electron temperatures in the range of 1 15 kev, the deuteron beam injection energy (up to 14 kev in JET deuterium plasmas and 8 kev in D-T plasmas) is not much lower than the critical energy for deuterons, E D,crit 15 5 kev. This, together with the fact that D-T fusion reaction rate peaks around a deuteron energy of 1 kev, means that the deuteron acceleration above the maximum injection energy should be avoided. However for D-D, the fusion cross section has a maximum in the MeV energy range, and the D-D fusion reactivity can be significantly enhanced when deuterons are accelerated by ICRF waves. The analysis of the JET high performance discharges indicates that in order to avoid strong deuteron acceleration, the local deuteron absorption should stay below a critical power density given by p D,crit k Tw = c t E B e D s,d D,inj [1+(E D,crit /E D,inj ) 3/ ]. () Here, T e is the electron temperature, t s,d is the slowing down time of deuterons, and the constant c -3. The parametric dependence of this criterion is obtained by requiring that the energy diffusion of deuterons due to ICRF waves is larger than their energy diffusion due to collisions at the typical deuteron beam injection energy E D,inj. For JET high-performance discharges, we find that p D,crit is typically about.-.3 MW/m 3. 4

Because the critical energy for hydrogen ions is a factor of two lower than that for deuterons, and because the average energy of the minority hydrogen ions is typically larger than that of the majority deuterium ions, fundamental hydrogen absorption mostly gives rise to electron heating. 3. NUMERICAL METHODS In order to simulate ICRH in JET high-performance discharges with ω ω ch = ω cd, it is important that the deuterium beam ion distribution function is taken into account. To accomplish this, NBI source terms have been included in the PION code. Here, the method employed follows closely that in Ref. [36] where comparisons against full two-dimensional numerical calculations are presented. In Ref. [36] the steady-state solution was obtained; this method is extended to solve a time-dependent case here. The PION code calculates the ICRF power deposition and velocity distribution of the resonating ions; see Refs [31, 3]. In order to simulate polychromatic ICRH, PION has been upgraded to perform power deposition calculations for all frequencies. The NBI source rates, as well as all other input data to the PION code, are taken directly from the JET experimental data base. For each beam species and injection energy, the NBI source rates are required as a function of time and flux surface co-ordinate, and are provided in our case by the CHEAP code [37]. For a given flux surface and injection energy, the NBI source is assumed to be a Gaussian in velocity for numerical reasons, with the peak centred at the injection energy corrected for bulk plasma rotation effects, and with a half width typically corresponding to 1 % of the thermal velocity. The correction for the bulk plasma rotation takes into account that a beam particle deposited in a passing orbit moving in a co-rotational direction in the laboratory frame suffers a reduction in energy in the rotating plasma, and a passing particle moving in a counter-rotational direction has its energy increased. Finally, to maintain the injected number of particles at each injection energy, the beam source terms are normalised appropriately. In NBI-heated discharges the plasma density, and especially the density of the beam species, can increase rapidly during the discharge. In the simulations it is important to make sure that the density of the resonating ions is consistent with the measured one. In PION, where radial particle transport (other than that due to finite orbit widths [31, 3]) is not included, the following procedure has been adopted. If the increase in the total number of ions due to NBI on a flux surface during one time step is less than the difference between the densities at the end and in the beginning of that time step, we add a portion of a Maxwellian to the distribution function at the end of the time step. If, on the other hand, the beam source terms add more particles on a flux surface within one time step than is consistent with the measured particle density on that flux surface, we have to introduce particle losses in order to maintain the measured deuterium density. For numerical reasons it was necessary to introduce two types of loss terms. In normal circumstances the number of particles lost during the time step is less than 5% of the total 5

number of particles at the beginning of the time step, in which case we introduce a loss term that removes the required number of particles from the thermal (Maxwellian) background. If, on the other hand, the losses are more than 5% of the total number of particles at the beginning of the time step, we introduce an additional loss term, that removes the particles in excess of 5% from the whole distribution function. 4. ANALYSIS OF ICRH HEATING IN HIGH-PERFORMANCE DISCHARGES 4.1. Overview of the main effects due to ICRH To illustrate the main effects of ICRH in highperformance JET discharges, we start with a 3MA/3.45T optimised shear discharge with 16 MW of NBI and 6 MW of ICRF power applied at a single frequency of 51 MHz. The main plasma parameters of the discharge are shown in Fig. 1. In this discharge, as in all discharges analysed in this paper, the dipole phasing of the JET ICRF antennas was used, corresponding to a parallel wave vector of about k II 9m 1 Pulse No: 38437 15 P NBI 1 5 P ICRF 3 1 1 at the maximum of the antenna spectrum. One 6.5 7. 7.5 8. Time (s) should note that in this discharge the plasma Fig.1: Time evolution of plasma parameters for density is relatively low and the ICRF power optimised shear discharge 38437 (B tor = 3.45 T, I p = relatively high which maximises the effect of 3 MA, f = ω/π = 51 MHz). Here, R NT is the D-D neutron rate, n ICRH on the D-D fusion reactivity as compared e the line-averaged electron density, T e the electron temperature, T i the ion temperature, P ICRF and with optimised shear discharges later in the P NBI the ICRF and NBI power, respectively, and W DIA experimental campaign or with hot-ion the plasma diamagnetic energy content. H-mode plasmas analysed below in Sections 4. 4.3. A comparison between the simulated and experimental D-D neutron yield and total plasma diamagnetic energy content is shown in Fig.. Simulations with PION, using measured plasma parameters as input, have been done both with and without taking ICRH into account. Without ICRH, the simulated D-D neutron yield is about 5%, and the total plasma diamagnetic energy content about 3% lower than the measured ones. With ICRH, reasonably good agreement is obtained assuming a fixed hydrogen concentration of η H = nh ( nd + nh) = %, with both the simulated neutron rate and the total plasma diamagnetic energy content being within the 1% P (MW) R NT (1 16 n/s) W DIA (MJ) T (kev) n e (1 19 m 3 ) 5 3 1.5 1.5.5 5.5 6. error bars of the measurements. For this discharge no reliable measurement of η H exists, but η H % is in agreement with typical experimental estimates at the plasma edge for a large number of JET high-performance discharges. It is also worth pointing out that for this discharge, the since the time behaviour of the discharge can be reproduced relatively well. This can be partly related to the fact that in this discharge the internal transport barrier forms relatively late in the T i () T e () JG97.17/9c 6

Pulse No: 38437 5 η H = 1% 1 Pulse No: 38437 4 Simulated, NBI+RF % 8 R NT (1 16 s 1 ) 3 Measured 4% W DIA (MJ) 6 4 Simulated, NBI+RF Measured Simulated, NBI 1 Simulated, NBI 5.5 6. 6.5 7. 7.5 8. 5.5 6. 6.5 7. 7.5 Time (s) Time (s) JG98.449/1c Fig.: Measured and simulated D-D neutron rate (a) and plasma diamagnetic energy content (b). The simulation results are shown both with and without ICRF power. In (a) the sensitivity of the simulated D-D neutron rate to the hydrogen concentration η H is also shown. In (b) η H =% has been assumed. assumption of a fixed hydrogen concentration in time appears to be a good enough assumption high-power phase, at t 6.9 s, and consequently the period of the reduced particle transport after the formation of the internal transport barrier, when the deuteron density is often strongly increasing due to NBI fuelling and low particle diffusivity, is not long enough to affect η H significantly. Investigation of the importance of this effect for ICRF power partition in JET optimised shear discharges is beyond the scope of this paper, and is left for future work. The calculated power partition for η H = % is shown in Fig. 3. As can be seen, hydrogen absorption dominates in the beginning of the discharge, taking about 8% of the total ICRF power. Gradually, as the plasma density and the ion temperature increase, deuteron absorption Pulse No: 38437 P ICRF, TOT increases. Towards the end of the high per- 6 formance phase the hydrogen damping is about 4%, deuterons absorb up to 5%, and direct electron damping is about 1% of the total ICRF power. Both the deuterium and hydrogen absorption profiles are peaked, with most of the power absorbed within half of the plasma minor radius. Typically, the profile of the hydrogen absorption is somewhat broader than 4 P H P D P ELD/TTMP that of deuteron absorption due to larger Doppler 5.5 6. 6.5 7. Time (s) 7.5 8. broadening. Fig.3: ICRF power partition between hydrogen, deute- rium and direct electron damping assuming η H = %. P(MW) JG98.449/c 8. JG98.449/3c 7

The sensitivity of the simulated D-D neutron yield to η H is shown in Fig.. As can be seen, the simulated D-D neutron yield depends rather strongly on η H which according to Eq. (1) plays an important role for the ICRF power partition between deuterons and hydrogen. When η H decreases, the fraction of the ICRF power absorbed by deuterons increases; at t = 7 s, for example, the total deuteron absorption is 3.8,.7 and 1.55 MW for η H = 1,, 4 %, respectively. Note that the variation in the D-D fusion reaction rate due to the change in the deuterium dilution is of the order of 5 % when η H is varied between 1 and 4 %; the main difference in the simulations is therefore due to the difference in the deuteron absorption. The sensitivity of the power partition to the hydrogen concentration has been confirmed in JET hot-ion H-mode plasmas where the hydrogen concentration has been varied using hydrogen gas puffs. These experiments will be discussed below in Section 4.. In the simulations the power density absorbed in the plasma centre by deuterons reaches 1.1 and.65 MW/m 3 for η H = and 4%, respectively. This is significantly more than p D,crit.5 MW/m 3 estimated from Eq. () without ICRH, and is therefore consistent with the notable enhancement due to ICRH in the D-D reactivity in Fig. as well as in the calculated average energy of fast deuterons. In the simulation with ICRH the simulated average energy E D of deuterons above 1.5 times the thermal velocity in the plasma centre, at t 7 s, reaches 148 and 18 kev for η H = and 4%, respectively, while without ICRH we have E D 9 kev. The profiles of collisional power transfer from deuterons and hydrogen ions to bulk ions and electrons at t = 7 s are displayed in Fig. 4. Here, results from two simulations, with and without ICRF power, are displayed. In addition to enhancing the collisional electron heating, ICRH leads to a considerable increase in the Pulse No: 38437 t = 7s 1. bulk ion heating within the half minor radius. p ci At t = 7 s, the increase due to ICRH in the.8 collisional electron heating is about 3.75 MW p of which 3% comes from deuterons, and the ci.6 increase in the collisional bulk ion heating due NBI+RF to ICRH is about 1.3 MW of which the deuterons contribute 9%. The contribution from the.4 p ce NBI hydrogen ions to the collisional bulk ion heating is small, about.1 MW, due to the large. average energy of the high-energy hydrogen p ce ions (up to 1.3 MeV in the plasma centre). Because the electron temperature is typically..4.6.8 1. s Fig.4: Power density transferred in collisions to bulk higher in an RF-heated discharge than in one ions (p ci ) and electrons (p ce ) for simulation with NBIonly and with combined NBI and ICRF heating. Here, with NBI alone, there is also some gain in the bulk ion heating because of the higher η H = % is assumed. Furthermore, s = ψψ a r/ a and ψ critical velocity (E crit T e ). Thus, when we do a is the poloidal magnetic flux at the plasma edge and r/ a is the normalised minor radius. p (MW/m 3 ) JG98.449/4c 8

simulations with NBI alone, but using the parameters of a discharge with combined heating, we overestimate the bulk ion heating somewhat. Consequently, when calculating the gain in bulk ion heating due to ICRH by taking a difference between the bulk ion heating simulated with ICRF power and that simulated without ICRF power for a discharge with combined heating, we underestimate the gain to some extent. 4.. Sensitivity to the hydrogen concentration Experiments have been carried out in JET hot-ion H-mode plasmas with hydrogen gas puffs to vary the hydrogen concentration. In addition to confirming the sensitivity of power partition between hydrogen ions and deuterons, the experiments provide valuable information on whether it is better to damp the ICRF power on hydrogen ions or deuterons in order to optimise the bulk ion heating. An overview of two 3.1 MA/3.45 T deuterium discharges, one with and one without hydrogen gas puff, is shown in Fig. 5. In both discharges about 6 MW of ICRF power was applied at a single frequency of 51 MHz. In the high performance phase the hydrogen concentration, as determined from H α and D α signals at the plasma edge, is % for one and 6% for the other discharge. The discharge with low η H reaches a higher fusion reactivity than the discharge with high η H, while the total plasma energy contents and electron densities are nearly identical. Furthermore, as shown in Fig. 6, there are clear differences in the high-energy deuteron counts measured by the NPA [6]. In particular, the deuteron counts are significantly smaller for the discharge with high η H throughout the whole heating phase. P (MW) R NT (1 16 s 1 ) W DIA (MJ) (kev) (1 19 m 3 ) η H (%) Pulse No: 38179 ( ), 3818 ( ) P NBI 1 P ICRF 1 5 1 7 5 3 1 15 1 5 n e T i () T e () 1. 1.5 13. 13.5 Time (s) Fig.5: Plasma parameters for two ELM-free hot-ion H-mode plasmas (discharges 38179 and 3818) with different hydrogen concentrations η H (B tor = 3.45 T, I p = 3.1 MA, f = ω/π = 51 MHz). JG98.449/5c Counts Counts P ICRF (MW) Counts 6 4 4 1 1 Pulse No: 38179 Pulse No: 3818 E = 87keV E = 36keV E = 561keV 1. 1.5 13. 13.5 Time (s) Fig.6: Counts of deuterium atoms measured by a highenergy NPA for discharges 38179 and 3818 with low and high η H, respectively. Note that the signals have been smoothed over a.1 s time window. JG98.593/c 9

Figure 7 shows a comparison of the simulated Pulse No: 38179, 3818 4 and experimental D-D neutron rates for the two discharges. As can be seen, the agreement Pulse No: 38179 is reasonable for both discharges. The ex- 3 perimental and simulated plasma diamagnetic energy contents are also in reasonably good Simulated Pulse No: agreement for both discharges. According to the simulations the contribution from ICRH to the total plasma diamagnetic energy content is very similar, reaching about 3 MJ, in both discharges. However, there are significant differences 1 3818 Measured in the simulated ICRF contributions to 1. 1.5 the D-D neutron rate and the total deuteron Time (s) 13. 13.5 energy content between the two discharges. In the discharge with high η H, the effect of ICRH on the D-D fusion reactivity and deuteron energy Fig.7: Comparisons of the simulated and experimental D-D neutron rate for discharges 38179 and 3818 with low and high η H, respectively. The fall-off of the simulated neutron rates is not shown because the available content is negligible, while in the dis- time-resolution of the key diagnostics is not high enough to accurately simulate the exact time of the beginning of charge with low η H, the D-D fusion reactivity the fall-off in hot-ion H-modes where the high-performance and the deuteron energy content are enhanced by about 3% and about 1 %, respectively, phase is typically terminated by a single MHD event. due to stronger deuteron absorption. According to the simulations, the fusion reactions in the discharge with high η H originate from deuteron energies below kev. In the discharge with low η H most of the fusion reactions take place at deuteron energies below kev, the contribution from energies above kev being about % to the total fusion reactivity in the plasma centre. According to the simulations, deuteron absorption is about.5 MW in the discharge with high η H, while in the discharge with low η H it reaches about 1.8 MW as shown in Fig. 8. For the discharge with low η H, the deuteron power density (reaching.95 MW/m 3 in the plasma centre) as given by PION at t = 13 s is larger than the critical power density (about.4 MW/m 3 in the plasma centre) as given by Eq. () within s = ψ / ψa ~ < H this is the case only for s ~ <.1 (at t = 13 s we now have p D.7 MW/m 3 and p D,crit. MW/ m 3 in the plasma centre). In the case of low and high η H E D is about 115 and 85 kev, respectively, while in the simulation with NBI-only we have E D 7 kev in the plasma centre. In both discharges the bulk ion heating due to ICRH is about 1.9 MW and the collisional electron heating due to ICRH is about 3. MW at t = 13 s. The similar heating of the bulk plasma is consistent with the similar ion and electron temperatures in the discharges. In the discharge with high η H the deuterons contribute 5% and 3% to the collisional ion and electron heating, respectively, while in the discharge with low η H the deuteron contribution to the collisional ion R NT (1 16 s 1 ) JG98.449/13c 1

Pulse No: 38179 Pulse No: 3818 6 P ICRF, TOT 6 P ICRF, TOT P H 4 P H 4 P (MW) P (MW) P D 1. P ELD/TTMP 1.5 13. 13.5 14. Time (s) JG98.449/6c 1. P ELD/TTMP P D 1.5 13. Time (s) JG98.449/7c 13.5 14. Fig.8: ICRF power partition between hydrogen, deuteron and direct electron damping for (a) discharge 38179 with low η H and (b) for discharge 3818 with high η H. and electron heating is 6% and 16%, respectively. In the discharge with high η H, the collisional bulk ion heating from hydrogen is increased as the average energy of the hydrogen tail ions is reduced from 65 kev in the plasma centre in the case of low η H to below 3 kev in the case of high η H. Note the reduction both in the average energy of deuterons and hydrogen ions as well as the improvement in the collisional ion heating due to ICRH in the discharge with low η H as compared with the discharge analysed in Section 4.1 with the same ICRH power level and a similar η H but with a significantly lower electron density. Figure 9 shows the profiles of the different ICRH contributions to the collisional bulk ion and electron heating. As we can see, the profile of the collisional power transfer from hydrogen ions to electrons is broader in the case of low η H. This is due to finite orbit width effects. Pulse No: 38179 t = 13s.5 Pulse No: 3818 t = 13s.6.4.5 p c RF (MW/m 3 ).3. H e D i p c RF (MW/m 3 ).4.3. H e.1 D H e i..4 s JG98.449/8c.6.8 1..1 D i H D e..4 i s JG98.449/9c.6.8 1. Fig.9: Profiles of the collisional power transfer from hydrogen ions and from deuterons to the bulk electrons and ions due to ICRH (a) for discharge 38179 with low η H and (b) for discharge 3818 with high η H. 11

Furthermore, the profile of power transfer from hydrogen ions to the bulk ions is significantly broader than the profile of power transfer from the deuterons to the bulk ions. This is because a large fraction of the bulk ion heating from the hydrogen ions originates from the outer plasma regions where the hydrogen absorption power density is low enough to keep the average energy of the hydrogen ions comparable to the critical energy. Our conclusion therefore is that deuteron absorption provides a more peaked bulk ion heating profile. The calculated deuteron energy distribution functions for the two discharges are shown Pulse No: 38179 and 3818, t = 1.7s 5 in Fig. 1, together with the deuteron distribution function for the NBI-only simulation. To 3 be able to compare with the NPA measurements, the calculated distribution functions are 35 Pulse No: 38179 line-integrals from s = to s =.6. As can be 4 NBI+RF seen in Fig. 1, the calculated distribution function extends above the maximum deuterium 45 NBI Pulse No: 3818 beam injection energy in both discharges. Furthermore, there are significantly fewer highenergy deuterons in the case of high η H, which E (MeV) 5.5 1. 1.5. is in agreement with the high-energy NPA Fig.1: Calculated line-integrated deuterium ion energy measurements shown in Fig. 6. One should note distribution functions for discharges 38179 and 3818 with low and high η H, respectively. that more detailed comparisons between the NPA measurements and the distribution functions given by PION are not meaningful. This is because PION solves the pitch-angle-averaged velocity distribution function [31, 3] which is not detailed enough to compare with the distribution functions given by the NPA, which is a line-integrated measurement that covers a narrow region of phase space [6]. To summarise, the analysis of the JET hot-ion H-mode discharges with different hydrogen concentrations shows good agreement between simulations and experimental results. The results indicate that the power partition between hydrogen ions and deuterons sensitively depends on the hydrogen concentration η H, as predicted by theory. By increasing the hydrogen concentration, the deuteron absorption and the tail formation on the deuteron distribution function are reduced. Even though there is little difference in the total bulk ion heating with ICRH between the discharges with low and high η H, the profile of the bulk ion heating due to ICRH is significantly more peaked in the plasma centre in the case of low η H. Hence, in order to provide bulk ion heating concentrated in the plasma centre using ICRH at ω ω ch = ω cd, the most promising scenario is the one in which a significant fraction of ICRF power is damped on deuterons with the deuteron tail not reaching too high energies. Furthermore, operating at high plasma densities appears to be effective in minimising the tail formation and maximising the bulk ion heating. In (f D ) (a.u.) JG98.449/1c 1

4.3 The effects of spreading the ICRF resonance One technique to maximise the bulk ion heating with ICRH is to use multiple frequencies (polychromatic operation) in order to minimise the tail formation on the distribution functions of the resonating ions. The differences between operation with single and multiple frequencies are illustrated with three 3.8 MA/3.45 T discharges with approximately the same NBI power but with different ICRH schemes as shown in Table 1. The discharges have a similar electron density and hydrogen concentration throughout the high-power phases, and as can be seen in Fig. 11, the total energy content as well as the ion and electron temperatures are similar up to t 1.9 s. At t 1.9 s the discharge with a single ICRF frequency (discharge S) suffers a sawtooth crash, after which its performance deteriorates as compared with the discharges with multiple frequencies (discharges M1 and M). Table 1 The total NBI and ICRF power, ICRF power applied at each frequency, and the major radii of the cyclotron resonance layers (ω ω ch = ω cd ) for the analysed discharges. Discharge P N BI PICRF ( MW) (MW) S 4474 17. 8. M1 435 19.. M 438 17. 9. 5 ICRF frequencies R r es (m) 5 51MHz 3.15 3 1MW at 48, 51 and 53 MHz 3.4, 3.15, 3. 1 4 1.5MW at 49.5, 51 and 53 MHz 3.3, 3.15, 3. 1 Data from the high-energy NPA indicate the presence of high-energy deuterons above the maximum deuteron beam injection energy for all discharges in Table 1. The line-integrated deuteron energy distribution functions in the energy range.8 1.1 MeV have been constructed at t 1.8s (before the sawtooth crash in discharge S) from the NPA measurements using the method outlined in Ref. [6]. As shown in Fig. 1, the high-energy deuteron tail is considerably stronger in discharge S than in discharges M1 and M. This indicates that polychromatic operation produces fewer fast deuterons. Furthermore, the high-energy deuteron tail clearly decreases when going from 4.5 MW to 3 MW of ICRF power applied with multiple frequencies. P (MW) R NT (1 16 s 1 ) W DIA (MJ) T i ()(kev) T e ()(kev) n e (1 19 m 3 ) Pulse No: 435 ( ), 438 ( ), 4474 ( ) P NBI 1 P ICRF 4 1 5 1 15 1 5 5 3 1 1. 1.5 13. Time (s) 13.5 14. Fig.11: Main plasma parameters for three discharges with approximately the same NBI power, but with different ICRH schemes as shown in Table 1. JG98.449/11c 13

Pulse No: 435, 438, 4474; 1 14 t = 1.8s Good agreement between the simulated and experimental fusion reactivity and plasma energy content has been obtained for all discharges 1 13 in Table 1. According to the simulations, deuterons absorb up to about 45, 1 1 Pulse No: 4474 4 and 35% of the total ICRF power in discharges S, M1 and M, respectively. The difference Pulse No: 438 between discharges M1 and M is ac- 1 11 counted for by the higher NBI power and therefore Pulse No: 435 the higher deuteron energy content in dis- 1 charge M1. The difference in the calculated 1..4.6.8 1. 1. E (MeV) deuteron absorption in discharges S and M Fig.1: Deuterium ion energy distribution functions deduced with similar NBI and ICRF powers, is due to from NPA measurements for discharges in Table 1. differences in the ICRH schemes. By spread- ing the ICRF resonance in discharge M using multiple frequencies, the deuteron absorption is decreased, which is in agreement with Eq. (1) discussed in Section.1. According to the simulations, the fraction of the total ICRF power going to bulk ion heating at t = 13. s is 38%, 51% and 41% in discharges S, M1 and M, respectively. In discharges S and M 7%, and in discharge M1 66% of the bulk ion heating due to ICRH comes from deuterons. Furthermore, the D-D fusion reactivity is enhanced by ICRH by about 3%, 9% and 17% in discharges S, M1 and M, respectively. These results indicate that the deuteron tail formation is significantly smaller and the bulk ion heating is somewhat better for multiple ICRF frequencies. As is shown in Fig. 13, the high-energy tails in the simulated line-averaged deuteron energy distribution functions are less pronounced with polychromatic operation, in agreement with the NPA measurements. The simulated high-energy hydrogen tails 5 are also reduced for polychromatic operation. However, the differences between discharges 3 S and M are not very large, while for discharge M1 the hydrogen energy distribution function 35 is significantly smaller (e.g. about 15 times at Pulse No: 4474 5 MeV) than the distribution functions for the 4 other two discharges. These results are in qualitative agreement with observations of toroidal 45 Pulse No: 438 Alfvén eigenmode (TAE) activity driven by 5 Pulse No: 435 high-energy particles. In discharges S and M.5 1. high-frequency TAE activity is clearly present, E (MeV) Fig.13: Simulated deuterium ion energy distribution while in the discharge M1 high-frequency TAE functions for the discharges in Table 1. ƒ D (m kev 1 st 1 ) JG98.579/1c In (f D ) (a.u.) JG98.449/1c 1.5. 14

modes are not observed. Typically, a substantial population of particles with energies above 5 kev are required to excite these modes [38]. 5. SUMMARY AND DISCUSSION ICRH heating at ω ω ch = ω cd in the JET high-performance discharges with NBI has been studied, with emphasis on bulk ion heating with ICRH. In particular, the sensitivity to hydrogen concentration and the effects of spreading the cyclotron resonance using multiple frequencies have been analysed. In general, good agreement between the simulations and experimental results has been obtained. When the effect of second harmonic damping of the ICRF power on the deuteron beam distribution function is not taken into account, the D-D fusion reaction rate can be underestimated by up to a factor of two. The collisional power transfer from high-energy ions to the thermal bulk ions is found to be significantly greater in the plasma centre for combined NBI and ICRH than for NBI alone. The main advantage of the damping of ICRF power on deuterons is found to be the fact that the deuteron absorption gives rise to bulk ion heating which is concentrated in the plasma centre, while hydrogen absorption gives rise to a significantly broader bulk ion heating profile. Of the studied cases, an application of 3 MW of ICRF power using multiple frequencies gives the highest bulk ion heating fraction of about 5 % of the total ICRF power. Operation with multiple frequencies and/or high plasma densities has also been found to minimise the tail formation on the deuteron distribution function above the injection energy. For the low hydrogen concentrations (about 5% of the deuterium concentration) which characterise the discharges without hydrogen gas puffs, the power absorbed by the secondharmonic deuterium resonance is typically about 3 5% of the total ICRF power. The competing absorption mechanisms are the absorption at the fundamental hydrogen resonance and direct electron heating (ELD/TTMP), which typically take about 4 6% and less than 1% of the total ICRF power, respectively. A simple criterion () has been presented for the deuteron power density below which significant acceleration of deuterons above the injection energy is avoided. Together with Eq. (1) for the power partition between hydrogen ions and deuterons, this criterion may be useful in the design of future experiments. From these results one can obtain an estimate for the maximum ICRF power that could be applied at a single ICRF frequency without causing significant tail formation above the deuteron injection energy. In the case of strong damping, which characterises the JET high-performance discharges, we typically have P D /P ICRF ξ/(1+ξ), where P D is the power absorbed by deuterons, P ICRF is the total ICRF power and ξ is an average of the ratio p D /p H given by Eq. (1) in the plasma centre. Furthermore, in the case of strong damping with a single ICRF frequency and a central resonance, the total ICRF power density typically scales s s. For a typical width of s. for JET high-performance discharges, [ / ] [39] as exp ( ) this translates to a maximum central power density of the order of ηp ICRF /V where V is the total 15

plasma volume and η 3 4. Hence, the requirement of negligible deuteron tail formation gives an upper limit to the total applied ICRF power P ICRF < (1+ξ)Vp crit,d /(ξη). Above this limit specific measures, such as multiple ICRF frequencies, should be used in order to avoid tail formation above the deuteron injection energy. In D-T plasmas the physics of the interaction at ω ω ch =ω cd remains the same as in deuterium plasmas. Results from the analysis of ICRH in JET D-T plasmas are presented elsewhere, see e.g. Refs [4, 41]. One source of complication in the analysis of ICRF heating in D- T plasmas arises from the fact that the third harmonic tritium resonance and the second harmonic resonance of fusion-born alpha particles coincide with the fundamental hydrogen resonance and the second harmonic deuteron resonance. Simulation results show, however, that third harmonic tritium damping and second harmonic damping on alpha particles are negligible as compared with the competing absorption mechanisms in JET high-performance D-T plasmas. One should also note that, for a similar total plasma energy content in deuterium and D-T plasmas, the deuteron energy density is reduced in D-T plasmas as compared with deuterium plasmas [w D (D-T).5w D (D-D)]. Hence, according to Eq. (1), we expect smaller deuteron absorption as compared with hydrogen absorption in D-T plasmas than in deuterium plasmas. ACKNOWLEDGEMENTS The authors gratefully acknowledge the support of the JET experimental team. The work carried out by one of the authors (MM) was done under a task agreement between JET Joint Undertaking and Association Euratom-TEKES. REFERENCES [1] Start, D.F.H., et al. (1998) Phys. Rev. Lett. 8 4681. [] Start, D.F.H., et al. Bulk Ion Heating with ICRH in JET D-T plasmas (1998) submitted for publication in Nuclear Fusion. [3] Phillips, C.K., et al. (1995) Phys. Plasmas 47. [4] Wilson, J.R., et al. (1995) Phys. Rev. Lett. 75 84. [5] Gormezano, C., et al. (1997) in Proceedings of 1th Topical Conference on RF Power in Plasmas, 1 3 April 1997, Savannah, USA, pp. 3-1, AIP Conference Proceeding 43, American Institute of Physics, Woodbury, New York, Eds P.M. Ryan and T. Intrator. [6] Korotkov, A.A., Gondhalekar, A., and Stuart, A.J. (1997) Nucl. Fusion 37 35. [7] Stix, T.H. (1975) Nucl. Fusion 15 737. [8] Bures, M., et al. (199) Europhysics Conference Abstracts (Proc. 199 International Conference on Plasma Physics, Innsbruck, 9 June 3 July, 199) Vol. 16C Part II pp.881-884, Eds. Freysinger, W., Lackner, K., Scrittwieser, R., Lindinger. W. [9] Adams, J.M., et al. (1991) Nucl. Fusion 31 891. [1] JET Team (presented by Jacquinot, J.) (1987) in Plasma Physics and Controlled Nuclear 16

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