Search

Fully non-inductive second (2nd) harmonic electron cyclotron (EC) plasma current ramp-up was demonstrated with a newlly developed 28 GHz system in the QUEST spherical tokamak. A high plasma current of 54 kA was non-inductively ramped up and sustained stably for 0.9 s with a 270 kW 28 GHz wave. A higher plasma current of 66 kA was also non-inductively achieved with a slow ramp-up of the vertical field. We have achieved a significantly higher plasma current than those achieved previously with the 2nd harmonic EC waves. This fully non-inductive 2nd harmonic EC plasma ramp-up method might be useful for future burning plasma devices and fusion reactors, in particular for operations at half magnetic field with the same EC heating equipment.

We report results of benchmarking of core particle transport simulations by a collection of codes widely used in transport modelling of tokamak plasmas. Our analysis includes formulation of transport equations, difference between electron and ion solvers, comparison of modules of the pellet and edge gas fuelling on the ITER baseline scenario. During the first phase of benchmarking we address the particle transport effects in the stationary phase. Firstly, simulations are performed with identical sources, sinks, transport coefficients, and boundary conditions prescribed in the flattop H-mode phase. The transformation of ion particle transport equations is introduced so to directly compare their results to electron transport solvers. Secondly, the pellet fuelling models are benchmarked in various conditions to evaluate the dependency of the pellet deposition on the pellet volume, injection side, pedestal, and separatrix parameters. Thirdly, edge gas fuelling is benchmarked to assess sensitivities of source profile predictions to uncertainties in plasma conditions and detailed model assumptions. At the second phase, we address particle transport effects in the time- evolving plasma including the current ramp-up to the ramp-down phase. The ion and the electron solvers are benchmarked together. Differences between the simulation results of the solvers are investigated in terms of equilibrium, grid resolution, radial coordinate, radial grid distribution, and plasma volume evolution term. We found that the selection of the radial coordinate can yield prominent differences between the solvers mainly due to differences in the edge grid distribution. The simulations reveal that electron and ion solvers predict noticeably different density peaking for the same diffusion and pinch velocity while with the peaked profile of helium, expected in fusion reactors. The fuelling benchmarking shows that gas puffing is not efficient for core fuelling in H-modes and density control should be done by the high field side pellet injection in contrast to present machines.

A 28~GHz system with a high-power gyrotron tube has been used for the QUEST spherical tokamak to form an over-dense plasma for electron Bernstein wave heating (EBWH) and current drive with an 8.2~GHz-wave. Non-inductive high-density plasma ramp-up experiments with dual-frequency (dual$-f$) electron cyclotron (EC) [ 8.2~GHz and 28~GHz ] waves were conducted. A spontaneous density jump (SDJ) to an over-dense state was observed as a bifurcation phenomenon in the dual$-f$ wave experiment. The over-dense plasma on the 8.2~GHz-wave was non-inductively ramped up to 25~kA, and was maintained for 0.4~s under stable plasma equilibrium after two such jumps in one shot. Heating to mildly energetic electrons and bulk electrons was observed even in the over-dense region. The electrostatic EBWH effect on the mildly energetic electrons in the over-dense region is assessed following a dispersion analysis of the 8.2 GHz-wave. The bulk electron heating effect observed is explained as heat exchange from mildly energetic electrons heated by the electrostatic EBWH wave. Remarkably, a high hard-X-ray-radiation temperature ~ 500~keV was also observed in tangential viewing for current-carrying electrons in the over-dense core region. Synergetic heating from the overlap of different 28~GHz EC harmonic resonances as well as higher harmonic heating is discussed for maintaining the highly energetic electrons in the over-dense core region. In addition, the SDJ process and mechanism are considered based on the discussion of the electron heating effects with the 8.2 GHz-wave.

The role of zonal flows in the formation of transport barrier in helical plasmas is analysed using the transport code. A set of one-dimensional transport equations is analysed, including the effect of zonal flows. The turbulent transport coefficient is shown to be suppressed when the plasma state takes the strong positive radial electric field. This bifurcation of the turbulent transport is newly caused by the change of the damping rate of zonal flows. It is theoretically demonstrated that the damping rate of zonal flows plays an important role in global confinement in toroidal plasmas.

Theory-based turbulent transport models have been proposed and used in transport simulations to predict the performance of the International Thermonuclear Experimental Reactor (ITER). We have selected the current diffusive ballooning mode (CDBM), GLF23 and Weiland models as typical transport models. Taking experimental data from the ITPA profile database, simulations have been carried out to compare the results with each other using our one-dimensional diffusive transport code. It is found that each model has unique dependence on devices and operation modes, and most reasonable results among the models can be obtained by the CDBM model for L-mode discharges and by the GLF23 model for H-modes. From an analysis of Te/Ti dependence, predictions of the CDBM and Weiland models could be better in the hot electron regime. The effect of the elliptic cross section of the plasma has been included in the CDBM model, and it is confirmed that an accuracy of the prediction is improved for H-mode discharges. Finally, heat transport simulations for a single particle species have indicated that the CDBM model reproduces Ti profiles more accurately than Te profiles.

A new diagnostic method is proposed for direct measurements of electromagnetic field patterns of fast waves in toroidal plasmas. The fluctuations of the ponderomotive potential at the beat wave frequency between two fast waves with different frequencies produces the actual potential fluctuations via electron and ion motions. A heavy ion beam probe detected the potential fluctuation patterns at the beat wave frequency during the fast wave pulse. The amplitude of the potential fluctuations decreases with increasing electron temperature in fast wave current drive experiments in JFT-2M, owing to the improvement of wave absorption via electron Landau damping. The measured potential fluctuations do not contradict the prediction using full wave code calculations.

Fully non-inductive plasma maintenance was achieved by a microwave of 8.2 GHz and 40 kW for more than 1 h 55 min with a well-controlled plasma-facing wall (PFW) temperature of 393 K, using a hot wall in the middle-sized spherical tokamak QUEST, until the discharge was finally terminated by the uncontrollability of the density. The PFW was composed of atmospheric plasma-sprayed tungsten and stainless steel. The hot wall plays an essential role in reducing the amount of wall-stored hydrogen and facilitates hydrogen recycling. The behaviour of fuel hydrogen in the PFW was investigated by monitoring the injection and evacuation of hydrogen into and from the plasma-producing vessel. A fuel particle balance equation based on the presence of a hydrogen transport barrier between the deposited layer and the substrate was applied to the long-duration discharges. It was found that the model could readily predict the observed behaviour in which a higher wall temperature likely gives rise to faster wall saturation.

We have developed an ion cyclotron resonance frequency (ICRF) heating system for the Ring Trap 1 (RT-1) magnetospheric device. We excite slow waves from the polar region of the dipole magnetic field. The target helium plasma is produced by electron cyclotron heating. The electrons comprise high-temperature (>10 keV) and low-temperature (

Nationally coordinated research on spherical tokamak is being conducted in Japan. Recent achievements include: (i) plasma current start-up and ramp-up without the use of the central solenoid by RF waves (in electron cyclotron and lower hybrid frequency ranges), (ii) plasma current start-up by AC Ohmic operation and by coaxial helicity injection, (iii) development of an advanced fuelling technique by compact toroid injection, (iv) ultra-long-pulse operation and particle control using a high temperature metal wall, (v) access to the ultra-high-β regime by high-power reconnection heating, and (vi) improvement of spherical tokamak plasma stability by externally applied helical field.

The hot-tail (H-T) effect in disruption of impurity injections is considered. The contribution of the H-T effect to runaway electron (RE) current, which arises from fast thermal quenching, is studied using a two-dimensional Fokker–Planck simulation. It is found that in a high-density plasma the total RE current is reduced owing to the high collisionality. We also found that if the thermal quench is fast enough to invoke the H-T effect, the effect produces more seed REs than when the H-T effect is excluded even in high-density plasmas. In the high-density region (${{n}_{\text{e}}}\sim {{10}^{21}}~{{\text{m}}^{-3}}$ ) with fast thermal quenching, nevertheless the increment of the seed REs due to the H-T effect is generally small (tens of milliamperes) while the increment of the total RE current reached 2 MA owing to the avalanche effect.

The ICRF heating experiments conducted in 1999 in the third experimental campaign on LHD are reported, with an emphasis on the optimization of the heating regime. Specifically, an exhaustive study of seven different heating regimes was carried out by changing the radiofrequency relative to the magnetic field intensity, and the dependence of the heating efficiency on H minority concentration was investigated. It was found in the experiment that both ion and electron heating are attainable with the same experimental set-up by properly choosing the frequency relative to the magnetic field intensity. In the cases of both electron heating and ion heating, the power absorption efficiency depends on the minority ion concentration. An optimum minority concentration exists in the ion heating case while, in the electron heating case, the efficiency increases with concentration monotonically. A simple model calculation is introduced to provide a heuristic understanding of these experimental results. Among the heating regimes examined in this experiment, one of the ion heating regimes was finally chosen as the optimized heating regime and various high performance discharges were realized with it.

Instabilities with frequency chirping in the frequency range of Alfven eigenmodes have been found in the domain 0.1% < βh < 1% and vb||/vA ~1 with high energy neutral beam injection in JT-60U. One instability with a frequency inside the Alfven continuum spectrum appears and its frequency increases slowly to the toroidicity induced Alfven eigenmode (TAE) gap on the timescale of an equilibrium change ( ≈ 200 ms). Other instabilities appear with a frequency inside the TAE gap and their frequencies change very quickly by 10-20 kHz in 1-5 ms. During the period when these fast frequency sweeping (fast FS) modes occur, abrupt large amplitude events (ALEs) often appear with a drop of neutron emission rate and an increase in fast neutral particle fluxes. The loss of energetic ions increases with a peak fluctuation amplitude of θ/Bθ. An energy dependence of the loss ions is observed and suggests a resonant interaction between energetic ions and the mode.

An ion cyclotron range of frequency (ICRF) heating experiment was conducted in the third campaign of LHD in 1999. 1.35 MW of ICRF power were injected into the plasma and 200 kJ of stored energy were obtained, which was maintained for 5 s by ICRF power only after the termination of ECH. The impurity problem was so completely overcome that the pulse length was easily extended to 68 s at a power level of 0.7 MW. The utility of a liquid stub tuner in steady state plasma heating was demonstrated in this discharge. The energy confinement time of the ICRF heated plasma has the same dependences on plasma parameters as those of the ISS95 stellarator scaling with a multiplication factor of 1.5, which is a high efficiency comparable to that of NBI. Such an improvement in performance was obtained by various means, including: (a) scanning of the magnetic field intensity and minority concentration, (b) improvement of particle orbits due to a shift of magnetic axis and (c) reduction of the number of impurity ions by means of titanium gettering and the use of carbon divertor plates. In the optimized heating regime, ion heating turned out to be the dominant heating mechanism, unlike in CHS and W7-AS. Owing to the high quality of the heating and the parameter range being extended far beyond that of previous experiments, the experiment can be regarded as the first complete demonstration of ICRF heating in stellarators.

A theoretical model of an internal transport barrier (ITB) is developed. The transport model based on the self-sustained turbulence theory of the current diffusive ballooning mode is extended to include the effects of E × B rotation shear. Delayed formation of the ITB is observed in transport simulations. The influence of finite gyroradius is also discussed. Simulation of the current ramp-up experiment successfully described the radial profile of density, temperature and safety factor. A model of ITB collapse due to magnetic braiding is proposed. Sudden enhancement of transport triggered by overlapping of magnetic islands terminates the ITB. The possibility of destabilizing global low n modes is also discussed.

Physics knowledge (theory and experiment) in energetic particles relevant to design of a reactor scale tokamak is reviewed, and projections for ITER are provided in this Chapter of the ITER Physics Basis. The review includes single particle effects such as classical alpha particle heating and toroidal field ripple loss, as well as collective instabilities that might be generated in ITER plasmas by energetic alpha particles. The overall conclusion is that fusion alpha particles are expected to provide an efficient plasma heating for ignition and sustained burn in the next step device. The major concern is localized heat loads on the plasma facing components produced by alpha particle loss, which might affect their lifetime in a tokamak reactor.

A consistent numerical simulation is performed to study the dynamics in a steady state plasma with improved core confinement which is sustained by a bootstrap current and external drive. A new non-linear link between the profiles of the pressure, current and thermal conductivity is investigated. A self-organized oscillation (i.e. Spatiotemporal limit cycle oscillation) of the plasma pressure and current, coupled by the variation of the confinement enhancement factor, is predicted to occur. In the presence of alpha particle heating, the time variation of the plasma parameters causes a change in the alpha heating power. This provides a new picture of the thermal instability in burning plasmas

A model of edge localized modes (ELMs) in tokamaks is presented. The model of the L-H transition, which is based on electric field bifurcation, is extended to include the temporal evolution and the spatial structure. The existence of an electric field bifurcation implies that there is a hysteresis curve between the plasma gradient (thermodynamic force) and the associated flow of particles and heat. A time dependent Ginzburg-Landau equation is formulated for the electric field development, which leads to a limit cycle solution due to the hysteresis. A self-generated oscillation of the edge density appears, associated with periodic bursts of loss, under the condition of constant particle flux from the core. This is attributed to the small and frequent ELMy activity in H modes. Periodic decay and re-establishment of a transport barrier occur. This oscillation appears near the L-H transition boundary. It is found that in H and ELMy H states the edge region has a diffusion coefficient whose radial structure is intermediate (a mesophase) between the H phase and the L phase. This is attributed to the transport barrier. Its radial structure is governed by ion shear viscosity. The diffusion Prandtl number, the ratio of the viscosity of the diffusion coefficient, is found to determine the thickness of the barrier. The phase diagram of the L, ELMy H, H and L-H bistable states is obtained in plasma parameter space

A mechanism for the onset of the major disruption in tokamaks is proposed which considers the effect of magnetic stochasticity on the growth of the m=2 tearing mode. Toroidicity can cause stochasticity near the separatrix of the m=2 magnetic island, which enhances the current viscosity, resulting in explosive growth. The threshold condition and the time-scale of the rapid growth are studied. The role of the toroidal coupling to the m=1 component is also discussed

A low frequency fast wave current drive scenario for ITER (f ~ 17 MHz < fcT, where fcT is the cyclotron frequency of tritium ions) has been analysed using a 1-D full wave code (TASK/W1). The current drive efficiency varies significantly with changes in the electron density owing to effects of the cavity resonance, even for the standard value of the peak of the parallel wave number N|| chosen for ITER (peak of a main lobe, N||(p)=2.3). The peak value of the current drive efficiency, according to the cavity resonance, agrees with that for the single wave mode for a large number of antennas in the toroidal direction. The antenna loading resistance as well as the current drive efficiency reach a maximum value nearly at the cavity resonance corresponding to that of the eigenmode. Therefore, it may be possible to optimize the current drive efficiency by optimizing the antenna coupling resistance to its maximum value. Frequency feedback control with a combination of instantaneous bandwidths and several preset frequencies is considered to achieve and to maintain good current drive efficiency against a possible change of the electron density. It is shown that this scheme allows good current drive efficiency (γ ~ 0.5 × 1020 A.W-1.m-2 with N||(p)=1.5), similar to that for neutral beam current drive

A series of experiments has been conducted on the JIPP TII-U tokamak since 1989, using the newly constructed 130 MHz radiofrequency system. It has been predicted theoretically that the fast wave in this frequency range interacts weakly with particles. Two mechanisms of wave absorption have been identified in the experiment: electron Landau damping/transit time damping and 3rd harmonic ion cyclotron heating. The former mechanism is intimately connected with fast wave current drive and the latter can provide a new regime of plasma heating or a possible method of controlling the transport of alpha particles. It is found that the efficiency of the 3rd harmonic ion cyclotron heating is improved by using it in combination with neutral beam injection and ion cyclotron range of frequency heating. The heating efficiency obtained is as high as that of conventional heating. The experimental results are also analysed on the basis of a global wave theory which takes into account wave-particle interactions. These mechanisms of interaction are competing with each other; this will also be the case under more realistic reactor conditions.

Recent progress on ITER steady-state (SS) scenario modelling by the ITPA-IOS group is reviewed. Code-to-code benchmarks as the IOS group's common activities for the two SS scenarios (weak shear scenario and internal transport barrier scenario) are discussed in terms of transport, kinetic profiles, and heating and current drive (CD) sources using various transport codes. Weak magnetic shear scenarios integrate the plasma core and edge by combining a theory-based transport model (GLF23) with scaled experimental boundary profiles. The edge profiles (at normalized radius ρ = 0.8–1.0) are adopted from an edge-localized mode-averaged analysis of a DIII-D ITER demonstration discharge. A fully noninductive SS scenario is achieved with fusion gain Q = 4.3, noninductive fraction f NI = 100%, bootstrap current fraction f BS = 63% and normalized beta βN = 2.7 at plasma current I p = 8 MA and toroidal field B T = 5.3 T using ITER day-1 heating and CD capability. Substantial uncertainties come from outside the radius of setting the boundary conditions (ρ = 0.8). The present simulation assumed that βN (ρ) at the top of the pedestal (ρ = 0.91) is about 25% above the peeling–ballooning threshold. ITER will have a challenge to achieve the boundary, considering different operating conditions (T e/T i ≈ 1 and density peaking). Overall, the experimentally scaled edge is an optimistic side of the prediction. A number of SS scenarios with different heating and CD mixes in a wide range of conditions were explored by exploiting the weak-shear steady-state solution procedure with the GLF23 transport model and the scaled experimental edge. The results are also presented in the operation space for DT neutron power versus stationary burn pulse duration with assumed poloidal flux availability at the beginning of stationary burn, indicating that the long pulse operation goal (3000 s) at I p = 9 MA is possible. Source calculations in these simulations have been revised for electron cyclotron current drive including parallel momentum conservation effects and for neutral beam current drive with finite orbit and magnetic pitch effects.

A force model leading to the usual quasilinear particle flux is developed for the equations of motion used in the transport equations of the multi-fluid transport code TASK/TX. The model precisely corresponds to a quasilinear flux consisting of diagonal, thermodiffusive and pure convective contributions, where the turbulent coefficients of the force model are externally provided by a model of the turbulent process. Our approach is consistent in that particle transport can be described through a change in radial particle flux by solving the continuity equation and the equations of motion self-consistently. Time-dependent simulations that vary the ratio of particle diffusivity to thermal diffusivity show that thermal neutrals as a particle source in the core region affect the formation of density profile in the limit of the smallness of the ratio, while an increase in the ratio rapidly decreases the effectiveness of the source effect.

The generation of toroidal rotation due to the radial current torque induced by the charge separation is studied by using the one-dimensional multi-fluid transport code TASK/TX. Owing to the effect of the drift motion, the charge separation occurs as long as fast neutrals, typically from near-perpendicular NBI, are ionized. Coupling the TASK/TX code with the orbit-following Monte Carlo code (OFMC), we have shown that the toroidal rotation is driven due to the generation of the radial current j bulk flowing in the bulk plasma with the near-perpendicular NBI. The simulations have clarified that the NB on the equatorial plane drives the toroidal rotation most efficiently from the aspects of the collisional and j bulk × B torques. The j bulk × B torque becomes a major driver of the rotation in a high density plasma, replacing the collisional torque. In a steady state, the toroidal rotation driven by the j bulk × B torque is determined by the balance among the torque, the viscosity, the convection, the friction with neutrals and the loss of momentum due to charge exchange.

The effect of fast-ion losses due to the toroidal field ripple on the toroidal rotation is studied through numerical simulations. The simulations are carried out by utilizing a multi-fluid one-dimensional transport code, TASK/TX, with a ripple transport model suitable for implementing one-dimensional transport codes. Simulation results are qualitatively consistent with the experiments in JT-60U. It is shown that the return current associated with the outward radial fast-ion current due to the ripple loss flows inwards in the bulk plasma and the resultant torque drives the plasma toroidally in the counter direction of the plasma current. The equilibrium value of the toroidal rotation velocity is determined by the balance between the perpendicular viscosity and the total torque.

In a study of the structure of propagation and absorption of waves in the ion cyclotron range of frequencies (ICRF) in stellarator/heliotron devices, the full Maxwell equation, formulated as a stationary boundary-value problem, is solved numerically in a straight helical configuration. A cold plasma approximation is employed to obtain the conductivity tensor. The shapes of plasma boundary, vessel wall and antenna can be chosen arbitrarily by using a finite-element method. Two-ion hybrid resonance heating by the fast wave is studied. The wave field solution shows tunnelling across the evanescent layer, formation of the cavity resonance and absorption near the hybrid resonance surface. The dependence of the loading resistance on the axial wave number shows a shift due to the helical pitch. The dependence of the loading resistance and the deposition profile on the plasma parameters is also studied. In Heliotron-E-grade plasmas, the fast wave can propagate into the central region of the plasma and the antenna loading resistance is as large as it is in tokamaks. A model of the modular torsatron ATF is studied and good coupling of the fast wave to the plasma is also predicted in this device.

The coupling of ICRF power from a slow-wave antenna to a plasma with finite temperature is examined. A heuristic model, allowing explicit representations of ion Bernstein waves, fast waves and slow waves, is used to clarify how the antenna power is partitioned into the various wave energy fluxes. This model is complemented quantitatively by a more elaborate and realistic computer model. It is shown that such antennas can be highly efficient in transferring most of the antenna power directly to ion Bernstein waves, with only a very small fraction going into fast waves. The potentiality of this coupling scheme for plasma heating in ICRF is briefly discussed.

A global analysis of current drive in tokamaks by using waves in the ion cyclotron range of frequencies (ICRF), considering the entire antenna-plasma system, is presented. A phase shifted antenna array is used to inject toroidal momentum into the electrons. Within the context of quasi-linear theory, a Fokker-Planck calculation is combined with an ICRF wave propagation-absorption analysis which includes kinetic effects and realistic boundary conditions. The radial profile of the current induced by the mode converted ion Bernstein wave and by the magnetosonic fast wave is obtained, together with the global current drive efficiency (total induced current/total emitted power from the antennas) in the high density and temperature plasma regime. The phase dependence of the global efficiency is investigated by changing the launching conditions such as the total antenna number and the antenna spacing. – In medium size tokamaks, the electron power absorption and the associated driven current are found to be affected considerably by the plasma cavity resonance. It is also found that the global efficiency is sensitive to the antenna spacing. When the antenna spacing is increased, the global efficiency is reduced by counter current generation.

The propagation and absorption of second harmonic ion cyclotron range of frequency (ICRF) waves in NBI heated plasmas are investigated for the regime of plasma parameters in JT-60. The quasi-linear diffusion in the velocity space of ions is taken into account. The Fokker-Planck equation and the kinetic wave equation are numerically solved to obtain the spatial profile of the velocity distribution function and the power deposition profile in a self-consistent manner. The calculation of the power partition rate includes two processes: the direct absorption of the wave through wave-particle interactions and the power transfer due to Coulomb collisions. The power partition between electrons and ions is strongly affected by the plasma density and the RF power. The plasma temperature and the NBI power have some influence on power partition and tail formation in the experimental conditions of interest. The acceleration of the injected particles by ICRF heating is studied. The tail temperature, which is defined by the gradient of the velocity distribution function of tail ions, and the total stored energy of the plasma are calculated and the dependence on the plasma parameters is analysed.

A theoretical analysis of ICRF wave heating in a plasma with neutral-beam injection (NBI) is performed. Wave propagation and absorption are examined kinetically in the presence of a high-energy ion beam component. The following findings are reported: 1) the wave coupling efficiency does not deteriorate by the beam; 2) co-operative heating is to be expected, and 3) selective heating of high-energy ions is possible.

The three-dimensional structure of ICRF (Ion Cyclotron Range of Frequency) waves in a tokamak plasma is investigated. In a two-ion-species plasma (majority deuterium and minority hydrogen) with radial density inhomogeneity, the wave equation is solved numerically by employing a cold-plasma approximation. The plasma is immersed in a toroidal magnetic field with a gradient and is surrounded by the vacuum region and the conducting wall. Waves are launched by a Faraday-shielded poloidal-current antenna of finite extent in toroidal and poloidal directions. The wave field and the energy deposition profile are obtained by introducing a simple model for the collision. The wave accessibility condition is examined for plasma parameters and density profiles. In a cold-fluid approximation, two mechanisms of power absorption, i.e. two-ion hybrid resonance and cavity resonance, are found, and the differences between them are studied. The antenna loading impedance is also calculated for each case. High-and low-field-side excitations are compared. Non-plasma losses at the wall are considered in obtaining the coupling efficiency. Good coupling conditions and desirable antenna designs are also discussed. It is found that efficient coupling is expected in a wide range of plasma parameters.

The paper present an analysis of the loss cone boundary in phase space for toroidal helical devices. The effects of the radial electric field and the modulation of the helical field ripple are taken into account. The minimum energy of particles entering the loss cone is calculated. Modulation of the helical ripple is not always effective in reducing the loss when a radial electric field is present. The particle loss due to the loss cone is estimated in the collisionless limit. The impact of the radial electric field on the loss cone is discussed. It is more difficult to find a solution in the case of a positive radial electric field, which is required for the high ion temperature mode. This difficulty is great for systems with a small helical field ripple.

The power deposition profile in the two-ion hybrid resonance heating regime in tokamaks is studied by including the modification of the minority ion velocity distribution. The Fokker-Planck equation and the kinetic wave equation are solved numerically in order to describe the time evolution of the velocity distribution and the deposition profile. The power that is transferred coUisionally to the electrons and majority ions from the minority ions is also calculated. Application to the JET plasma demonstrates strong electron heating near the plasma centre. Control of the deposition profile by varying the minority ion concentration and the magnitude of the magnetic field is also discussed.

The effect of spatial loss on ICRF (ion cyclotron range of frequency) wave heating is studied. A simple model for the energy-dependent loss term is adopted in the Fokker-Planck equation. The case of the minority ion heating by fundamental cyclotron resonance is analysed. It is found that the high energy particle loss imposes a limit on the heating power density, above which an increase in the heating power does not raise the energy transfer to the bulk particles, i.e. the heating efficiency deteriorates. This power limit is serious for losses with strong energy dependence such as ripple diffusion. Small spatial loss can annihilate the increment of the fusion reaction by tail generation.

Propagation and absorption of waves in the ion cyclotron range of frequencies (ICRF) are investigated using the kinetic theory in a high-temperature plasma. The wave equation which includes kinetic effects (such as finite-gyroradius effect and wave/particle interactions) is solved as a boundary-value problem for a two-ion-component plasma (majority deuterium and minority hydrogen) with one-dimensional inhomogeneities. The global structure of the wave field and the absorption mechanism are explained. The power deposition profile for each plasma species and the coupling to the antenna are obtained. The mode conversion of the fast wave to the ion Bernstein wave is associated with the two-ion hybrid resonance, and the latter is absorbed by electrons and deuterons via Landau damping and collisional damping, respectively. Protons absorb the wave which tunnels through the cut-off layer (for strong-field-side excitations) by cyclotron damping. The existence of cavity resonances is also confirmed; these considerably influence the energy absorption.

The connection length L between the magnetic field line and the wall in the scrape-off layer (SOL) region in toroidal helical systems is analysed. It is found that this connection length has a logarithmic dependence on the distance from the outermost magnetic surface to the field line under consideration. Using this dependence in a fluid model, the spatial distribution of the plasma in the SOL region is studied analytically. The edge temperature scales approximately as P0.36 (P being the power flow to the SOL region), as for tokamaks. For a given value of P, the edge temperature in toroidal helical systems is lower than in tokamaks with a similar minor radius.