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Heavy ion beam probe (HIBP) systems have been designed for the new tokamak, PLATO [A. Fujisawa, AIP Conf. Proc. 1993, 020011 (2018)]. The designs have been completed, and the installations are in progress. Two HIBPs are being installed in toroidal sections 180° apart to investigate long-range correlations in the toroidal direction. Each HIBP consists of an injection beamline and a detection beamline as usual. Yet, one of the HIBPs is equipped with an additional detection beamline; the measurement positions of its two detection beamlines can be placed on almost the same magnetic surface yet at poloidal angles that differ by ∼180°. The use of three detection beamlines allows us to investigate spatial asymmetry and long-range correlations in both the toroidal and poloidal directions, simultaneously. The detected beam intensity is expected to be enough for turbulence measurements in almost the entire plasma region when the electron density is up to 1 × 1019 m−3 by selecting appropriate ion species for the probe beam. Each detector has three channels 10 mm apart, allowing measurement of local structures of micro-scale turbulence. Therefore, using the HIBPs on the PLATO tokamak will enable both local and global properties of plasma turbulence to be investigated, simultaneously.

New polarizer and launcher systems on a 28-GHz electron-cyclotron (EC) heating and current drive (HCD) system have been developed for non-inductive second-harmonic EC-plasma-current ramp-up in the QUEST spherical tokamak. A launcher system with two quasi-optical mirrors providing beam steering capability was designed to focus the incident beam to a small-sized waist of ∼0.05 m at the second-harmonic EC resonance layer. A relatively large focusing mirror was designed based on a Kirchhoff integral code developed to derive wave solutions. The focusing property of the launched beam was first confirmed with a 3-dimensional (3D) electromagnetic-wave simulator. Focusing characteristics were also checked at low-power test facilities, together with the steering capability. The performance of this launcher system was demonstrated to work as designed, and assembled in the QUEST device. The system was applied to the non-inductive second-harmonic EC plasma ramp-up experiments with no optimization required regarding the incident polarization. The results obtained for the non-inductive plasma ramp-up are also presented.

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.

The one-dimensional fluid-type transport code, TASK/TX, is developed compatible with the flux coordinates in a tokamak. Unlike diffusive transport equations usually adopted in conventional transport codes, the governing equations conform to a two-fluid model consisting of Maxwell’s equations and the multiple fluid moment equations for each species.Quasi-neutrality and ambipolar flux conditions are not imposed, which are inherently satisfied as a consequence of the equation system solved. The neoclassical particle flux is not approximated by the flux–gradient relationship, and the total particle flux composed of the neoclassical and turbulent contributions is directly treated as the dependent variable. The quantities related to neoclassical transport are intrinsically calculated without external neoclassical transport modules. In other words, TASK/TX by itself has the function of a neoclassical transport solver based on the moment approach as well. Several numerical tests clearly reveal the unique features of TASK/TX not possessed by conventional transport codes.

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.

After several experimental campaigns in the Kyushu University Experiment with Steady-state Spherical Tokamak (QUEST), the originally stainless steel plasma-facing wall (PFW) becomes completely covered with a deposited film composed of mixture materials, such as iron, chromium, carbon, and tungsten. In this work, an innovative colorimetry-based method was developed to measure the thickness of the deposited film on the actual QUEST wall. Because the optical constants of the deposited film on the PFW were position-dependent and the extinction coefficient k1 was about 1.0–2.0, which made the probing light not penetrate through some thick deposited films, the colorimetry method developed can only provide a rough value range of thickness of the metal-containing film deposited on the actual PFW in QUEST. However, the use of colorimetry is of great benefit to large-area inspections and to radioactive materials in future fusion devices that will be strictly prohibited from being taken out of the limited area.

In the west end of GAMMA 10/PDX, the end-loss ion flux is utilized for divertor simulation experiments. It is important for controlling parameters of the end-loss ion flux to investigate the efficiency of ion cyclotron range of frequency (ICRF) heating in the west plug/barrier cell, which is next to the west end region. The ICRF heating experiments in the west plug/barrier cell have been performed. In this study, three-dimensional simulations of the ICRF wave propagation were carried out in the plug/barrier cell for the first time. Two types of antennas, a Double Half Turn (WB-DHT) and a Nagoya Type-III (WB-Type-III) antennas, are evaluated. As the results, it is clarified that the WB-Type-III antenna is more effective for the ion heating than the WB-DHT antenna when the frequency is near the ion cyclotron resonance frequency at the midplane of the plug/barrier cell. An additional experiment with the WB-Type-III antenna which is located near the midplane of the plug/barrier cell has been performed. The improvement of the power absorption has been observed. The WB-Type-III antenna located near the midplane is more effective for the ion heating. The experimental results are consistent with the simulation of the wave propagation analysis.

We have developed a self-consistent integrated simulation model of core and scrape-off-layer (SOL)/divertor transport. This model enables the user to investigate operational scenarios with compatible high-confinement core plasmas and detached divertor plasmas. A 1.5D core code TOPICS-IB and a 2D divertor code SONIC are successfully coupled using a Multiple Program Multiple Data parallel computing system. This integrated code, which can include Monte-Carlo models for neutrals and impurities, provides efficient plasma/neutral simulations. The dynamic simulation for the L/H transition in JT-60SA is carried out by this integrated code using a current-diffusive ballooning mode (CDBM) transport model that includes the E×B shearing effect. The impact of SOL/divertor transport on the L/H transition is studied (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A new one-dimensional transport code named TASK/TX, which is able to describe dynamic behavior of tokamak plasmas, has been developed. It solves simultaneously a set of flux-surface averaged equations composed of Maxwell's equations, continuity equations, equations of motion, heat transport equations, fast-particle slowing-down equations and two-group neutral diffusion equations. The set of equations describes plasma rotations in both toroidal and poloidal directions through momentum transfer and evaluates the radial electric field self-consistently. The finite element method with a piecewise linear interpolation function is employed with a fine radial mesh near the plasma surface. The Streamline Upwind Petrov-Galerkin method is also used for robust calculation. We have confirmed that the neoclassical properties are well described by the poloidal neoclassical viscous force. The modification of density profile during neutral beam injection is presented. In the presence of ion orbit loss, the generation of the inward radial electric field and torque due to radial current is self-consistently calculated.

Non-disruptive ? collapses with a regular intermittency have been observed after a forced turn-off of neutral beam current drive (NBCD) in JT-60U fully non-inductive, reversed shear (RS) discharges. Self-consistent transport simulations with improved core confinement have first clarified that the redistribution of 'return current' induced after the NBCD turn-off lowers the safety factor of magnetic shear reversal, qmin. Linear MHD stability analysis has also revealed that this lowering of safety factor leads to n = 1 kink-ballooning instability with the modes localized around the internal transport barrier (ITB) of higher qmin (~6) discharges. It was also pointed out that an increase in the bootstrap current under continuous NB heating can lead to ITB reconstruction and thus causes subsequent ? collapses.

Development of an integrated simulation system for helical plasma is described that draws new experimental plans, including those in new devices, and does experimental data analysis from the viewpoint of integrated physics. The integrated simulation system to be developed has a modular structure that consists ofmodules for calculating magnetohydrodynamic (MHD) equilibrium/ stability, transport, and heating. Each module can be selected in accordance with a user's request and can be combined with other modules. When we want to perform the integrated simulation during the entire plasma duration, a transport module is to be a core module. An integrated tokamak transport code will be extended for the helical configuration and used as a transport module. As the first step of the extension, time evolution of the plasma net current, which is consistent with the three-dimensional MHD equilibrium, is planned to be solved for Large Helical Device plasmas by taking into account the bootstrap current and the beam-driven current.

The formation of eigenmodes with the m = 1 fast Alfven waves in the ion-cyclotron range of frequency are investigated in the axisymmetric central cell of the GAMMA 10 tandem mirror. When the fast waves with frequencies near the fundamental ion-cyclotron frequency have been used for the plasma production, the saturation in the density has been observed. The spatial structure of the excited wave field is calculated in the central cell using a two-dimensional full wave code. The results of numerical analysis indicate that the increase in plasma density depends strongly on the eigenmode formations associated with the boundary conditions. The results of numerical analysis are compared with the results of measurements of the waves with magnetic probes. A very good degree of agreement is found between the theoretical results and the experimental results. It is suggested that the simultaneous excitation of several radial eigenmodes with high-harmonic fast waves is effective for higher density plasma production.

Alfven eignemode experiments have been carried out by using the negative-ion-based neutral beam in JT-60U. For bursting instabilities in the frequency range of Alfvn Eigenmodes, two types of mode activity have been observed. In one type called Abrupt Large-amplitude Event (ALE), enhanced transport of the energetic ions was detected. The enhanced transport showed the clear energy dependence based on measurements performed using a natural diamond detector. In another type of bursting event called the fast Frequency Sweeping (fast FS) mode, frequency up-down chirping is observed on the time-scale of a few ms, much faster than equilibrium changes in the background plasma. This frequency chirping was well reproduced by the non-linear simulation code, MEGA, for magnetohydrodynamics (MHD) with energetic particles. The slow up-frequency sweeping of the Reversed-Shear-induced Alfven Eigenmode (RSAEs), due to the slow evolution of qmin was also observed. These experiments were analyzed by using the NOVA-K code. It is shown that the most unstable modes are localized around the minimum in the magnetic safety factor (qmin) in the analysis.

On the GAMMA 10 tandem mirror, Magneto Hydro Dynamic (MHD) stabilization is kept with high pressure plasmas in the minimum-B anchor cell. To enhance ion heating in the anchor cell, direct anchor heating is introduced with an anchor antenna. The enhancement of the anchor heating is clearly observed. However, the antenna loading is very small in the case of strait bar-type antenna. In this paper, a newly designed antenna is introduced for the anchor heating. The antenna shape is improved to be an elliptical shape for matching the plasma shape. Three dimensional numeral simulation is introduced for the evaluation antenna loading with the antenna shape. Remarkable improvement is observed both in the experiment and in the simulation.

Long-pulse operation and high-energy particle confinement properties were studied using ion cyclotron range of frequency (ICRF) heating for the Large Helical Device. For the minority-ion mode, ions with energies up to 500 keV were observed by concentrating the ICRF heating power near the plasma axis. The confinement of high-energy particles was studied using the power-modulation technique. This confirmed that the confinement of high-energy particles was better with the inward-shifted configuration than with the normal configuration. This behavior was the same for bulk plasma confinement. Long-pulse operation for more than 2 min was achieved during the experimental program in 2002. This was mainly due to better confinement of the helically trapped particles and accumulation of fewer impurities in the region of the plasma core, in conjunction with substantial hardware improvements. Currently, the plasma operation time is limited by an unexpected density rise due to outgassing from the chamber materials. The temperature of the local carbon plates of the divertor exceeded 400 deg, C, and a charge-coupled device camera observed the hot spots. The hot spot pattern was well explained by a calculation of the accelerated-particle orbits, and those accelerated particles came from outside the plasma near the ICRF antenna.

Recent progress in the development of electron cyclotron heating⁄current drive systems in regard to power and pulse duration have allowed the extension of two normalized parameters (toroidal electric field Eφ and wave power density p). In the extended regime, the conventional theory requires consideration of a distorted electron distribution function. The first validation of the ECCD theory in the extended regime having large Eφ and p is presented. Linear calculation has a tendency to overestimate the EC driven current, as normalized parameters for Eφ and p increase. While the EC driven current IEC obtained by a linearized Fokker-Planck calculation (1.1 MA) did not agree with the measured EC driven current (0.74 ± 0.06MA), non-linear calculation of the Fokker-Planck equation considering the effect of Eφ (0.76 MA) shows close agreement with the experimental result. Calculations show that the decreasing effect of Eφ on IEC was stronger than the increasing effect of p on IEC in the experiment.

The status of transport simulation in reversed magnetic shear configuration of tokamaks is described. Based on the turbulent transport model of the current diffusive ballooning mode,the formation of internal transport barrier and the sustainment of reversed shear configuration is examined. The issues in developing the steady state sustainment scenarios are also discussed.

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 (

In tokamak operations, breakdown of plasma is the first step of the plasma build-up. In this paper, we present a combinative investigation of radio frequency (RF)-induced breakdown experiments in QUEST (Q-shu University Experiment with Steady-State Spherical Tokamak) and a one-point model of hydrogen ionization. Experimental results with two different frequencies of 2.45 GHz and 8.2 GHz showed that the clear threshold on connection length, L , existed for breakdown with a negative n- index configuration n =(dR/dBv)/(dBv/dR) , where R is the major radius and Bv the is vertical magnetic field. In contrast, breakdown was always obtained with positive n -index when changing L. It indicates that a lifetime of an incubated electron plays a significant role in the plasma breakdown. According to one-point model calculation, the experimental threshold of L is well predicted by the lifetime of the incubated electron estimated by employing the loss term along with L . The model calculation also describes the requirement of the minimum electron temperature Te for RF-induced breakdown to realize an avalanche of electrons in the tokamak magnetic structure.

The direct measurements of high-frequency electric fields in a plasma bring about significant advances in the physics and engineering of various waves. We have developed an electro-optic sensor system based on the Pockels effect. Since the signal is transmitted through an optical fiber, the system has high tolerance for electromagnetic noises. To demonstrate its applicability to plasma experiments, we report the first result of measurement of the ion-cyclotron wave excited in the RT-1 magnetosphere device. This study compares the results of experimental field measurements with simulation results of electric fields in plasmas.

This paper reports on the behaviour of high-energy ions created by ion cyclotron range of frequency (ICRF) heating on the Large Helical Device (LHD). In the third experimental campaign conducted in 1999, it was found that minority heating has good heating performance, and high-energy particles were observed. In the fourth campaign in 2000, the temporal behaviour of high-energy ions was investigated in the minority heating regime using turnoff or modulation of ICRF power. The time evolution of the high-energy particle distribution was measured using a natural diamond detector (NDD) and a time-of-flight neutral particle analyser (TOF-NPA). It was found that the count number of higher-energy particles declines faster than that of lower-energy particles after ICRF turnoff. In the modulation experiments, the phase difference of the flux of high-energy particles with respect to the ICRF power modulation increased with energy. These results were explained qualitatively by the Fokker-Planck equation with a simple model. The pitch-angle dependence of the distribution function was also measured in the experiment by changing the line of sight of the TOF-NPA, and an anisotropy of the high-energy tail was found. This anisotropy was reproduced by solving the bounce-averaged Fokker-Planck equation. The second harmonic heating was conducted successfully for the first time in the LHD in high-β plasma, and high-energy particles were also detected in this heating regime.

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.

The controllability of current profile driven by the fundamental resonance of the O-mode wave is examined for the parameters of the Intermediate Aspect ratio Machine option of the International Thermonuclear Experimental Reactor (ITER). The driven current is numerically evaluated by using the full relativistic adjoint method which we have extended from the non-relativistic one. By changing both the toroidal and poloidal injection angles, the optimum direction to drive a current with maximum current density at the aimed position is obtained. The position of wave launching affects the optimum injection angles and the driven current profile. The dependence of driven current profile on beam divergence is also examined. When the beam is injected from the equatorial plane, the maximum current density is reduced and the width of current profile becomes wide in the outer region of r≳0.5a. The localized current profile is kept well within the region of r≳0.4a by injection from a location away from the equatorial plane.

Current drive by the electromagnetic waves in the electron cyclotron range of frequency was numerically studied by the newly developed code TASK/EC. The dependence on the poloidal injection angle and the effect of negative magnetic shear associated with the internal transport barriers are studied.

Correlation between electron heat diffusivity and short wavelength ( kρ i ∼5) fluctuation amplitude was observed in the TFTR tokamak in the core of ERS plasmas (Phys. Lett. A 236 (1997) 339). These fluctuations propagate in the ion diamagnetic drift direction with wave number comparable to ω pe / c . Further analysis of these data yields the ratios χ e / χ i and χ e / D e , and their values are consistent with the picture that the electron transport is mainly induced by the short wavelength fluctuations in the plasma core where the long wavelength ( kρ i ∼1) fluctuations are absent. Although there is not enough information to identify these short wavelength modes, the values of χ e is found to be comparable to theoretical predictions based on the current diffusive ballooning mode theory (Plasma Phys. Control. Fusion 36 (1994) 279).

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.

The influence of plasma flow inhomogeneity on the magnetic surface, which is driven by anisotropic hot ions, on the micro-turbulence of the low/negative magnetic shear tokamak is investigated. It is found that the poloidal inhomogeneity is effective in suppressing the current-diffusive ballooning mode turbulence which has a large nonlinear growth rate. This new mechanism of turbulence suppression provides the model of improved confinement associated with the reversed magnetic shear.

A simple physical model for toroidal flow shear stabilization of a hybrid dissipative trapped electron-ion temperature gradient mode (namely, the hybrid electron-ion drift mode) is presented. Coupling between the sheared flows and non-adiabatic electrons is proposed as the stabilization mechanism of the hybrid electron-ion drift mode. This implies that the confinement improvement can be achieved not only through the poloidal sheared rotation flow in the edge region of tokamaks for the L-H transition but also through the toroidal sheared rotation in the core region for further confinement improvement associated with the internal transport barrier and negative shear.

A simple physical model for the flow-shear stabilization of ion temperature gradient (ITG)-driven instability in the presence of dissipative trapped electrons is presented. Reduced fluid equations and magnetic sheared slab geometry are adopted. From analytical analyses and numerical calculations, it was found that the coupling between the sheared flows and non-adiabatic electrons will result in the stabilization of both toroidal sheared flow and poloidal sheared flow on hybrid dissipative trapped electron ITG mode. This implies that the confinement improvement in tokamaks can be obtained not only through the poloidal sheared rotation in the edge region of tokamaks for the H-mode (high-confinement mode), but also through the toroidal sheared rotation in the core region for further confinement improvement associated with internal transport barrier (ITB) and negative shear (or reversed magnetic shear). When the poloidal and toroidal sheared flows are simultaneously considered, it was found that in the presen...

The crash of the temperature profile associated with a propagating transport bifurcation between the L-mode and the magnetic braiding mode (M-mode) in a tokamak plasma is presented. The magnetic braiding mode is induced by the magnetic stochasticity. If the pressure gradient exceeds a threshold value a magnetic stochasticity sets in and the heat conductivity is much enhanced (M-mode). The back transition to the L-mode occurs when the pressure gradient decreases to another threshold value. The model of the transport bifurcation is included in the 1D transport code. The crash of the temperature profile and the propagation of the crash front (avalanche) are realized by this model. The collapse without a precursor oscillation is revealed.

The eigenvalue equation for the current diffusive ballooning mode in tokamaks is derived taking the geometrical effects, i.e., triangularity and ellipticity into account. The stability boundary is obtained in the strong ballooning limit. It is found that the ellipticity plays an important role on the stability of the current diffusive ballooning mode. On the other hand, the effect of the stabilization by the triangularity appears indirectly through the magnetic well term. The geometrical effect on the transport coefficient is also discussed.

It is desirable to self-consistently describe two-dimensional transport in a whole tokamak plasma including both core and peripheral regions, since the pedestal region lying between the core and peripheral regions strongly affects the confinement property of the core plasma. The set of two-dimensional transport equations with poloidal angle dependence has been formulated from Braginskii’s multi-fluid equations and the neoclassical transport theory and has been coupled with electromagnetic equations in order to develop a two-dimensional transport simulation code TASK/T2. The set of transport equations consists of equations of the particle density and the momentum (radial, parallel, and toroidal), and the heat transport equation, which provide the consistent description of transport phenomena through the whole region. In this paper, we focus on the derivation of the heat transport equation.

A theory of the anomalous transport coefficient in toroidal helical systems (such as stellarators, torsatron and Heliotron devices) is developed. The theoretical formalism of self-sustained turbulence is applied to the interchange mode turbulence and ballooning mode turbulence. The nonlinear destabilization of microscopic modes by the current diffusivity is the key for the anomalous transport. A general form of the anomalous transport coefficient in toroidal plasmas is derived. The intrinsic importance of the pressure gradient, collisionless skin depth and Alfven transit time is confirmed. The geometrical factors which characterize the magnetic configurations are also obtained. The theory is extended to study the influence of parallel compressibility. The ion viscosities of the perpendicular and parallel momenta, electron viscosity and energy diffusion coefficient are obtained. The comparison with experimental results is also given.

Circulating power for the sustenance and profile control of the steady state tokamak plasmas is discussed. The simultaneous fulfillment of the MHD stability at high beta value, the improved confinement and the stationary equilibrium requires the rotation drive as well as the current drive. In addition to the current drive efficiency, the efficiency for the rotation drive is investigated. The direct rotation drive by the external torque, such as the case of beam injection, is not efficient enough. The mechanism and the magnitude of the spontaneous plasma rotation are studied.

A model of giant edge localized modes in tokamaks is developed. The theory of self-sustained turbulence of a current-diffusive ballooning mode is extended. A bifurcation from the H mode to a third state with magnetic braiding, the M mode, is found to occur if the pressure gradient reaches a critical value. Nonlinear excitation of magnetic perturbation takes place, followed by catastrophic increase of transport. With backtransition to the $H\left(L\right)$ mode, a new hysteresis is found in the gradient-flux relation. The process then repeats itself. Avalanche of transport catastrophe across the plasma radius is analyzed.

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 unified model of the L-mode confinement in tokamaks and the improved modes associated with current profile modification is investigated by means of a one-dimensional transport simulation. The thermal transport coefficient employed is based on the theory of self-sustained turbulence due to the current-diffusivity-driven modes. In the case of low beta p ( beta p being the ratio of the plasma pressure to the pressure of the poloidal magnetic field), the simulation results show fairly good agreement with empirical L-mode scaling laws of the thermal energy confinement time tau E, indicating favourable dependence on the plasma current. When beta p exceeds about unity, however, the transport in the core region is strongly reduced. This confinement improvement is attributed to the weak or negative magnetic shear due to the bootstrap current and the Shafranov shift of the magnetic surface. The enhancement factor of tau E scales as beta p0.76 and is consistent with experimental observation. The effect of current profile modification due to the current ramp down and the lower hybrid current drive is also studied.

The transport coefficient for a magnetized plasma, which has been obtained by the use of the method of self-sustained turbulence, is applied to the reverse field pinch (RFP). The dependence beta p alpha n34//Ip is obtained ( beta p is the plasma pressure divided by the poloidal magnetic pressure, n is the plasma density and Ip the plasma current). This result gives an explanation of the experimental observation of the RFP scaling, beta p alpha n/Ip. This theory of anomalous transport unifies the L-mode scaling laws in tokamaks, stellarators and heliotron/torsatrons as well as the RFP.

Based on the method of self-sustained turbulence, the anomalous transport coefficient is derived for various toroidal plasmas. The L-mode confinements in the tokamaks, stellarators, H/T systems and RFP are explained by this formula, showing the influence of the magnetic geometry. The mechanism of the confinement improvement is discussed. Associated with the H-mode, the bifurcation physics is described. The catastrophic event at the {beta}-limit is described. 30 refs., 5 figs.

In order to study the particle transport and the mechanism of the L/H transition in tokamaks, a one-dimensional transport code which describes the toroidal and poloidal plasma rotation as well as the radial electric field has been developed. The neoclassical transport, turbulent transport and ion orbit loss are included. Using a turbulent transport model based on the current diffusive high-n ballooning mode and a fixed temperature profile, the density profile in a steady state and the dependence on the edge temperature are studied. With high edge temperature, the density gradient near the edge becomes steep and a H-mode like density profile is obtained. The preliminary calculation including heat transport is also presented. 10 refs., 3 figs.

Preliminary key issues for a synchrotron radiation-enhanced compact fusion advanced Brayton (CFAB) cycle fusion reactor similar to the CFAR (compact fusion advanced Rankine) cycle reactor are presented. These include plasma operation windows as a function of the first wall reflectivity and related issues, to estimate an allowance for deterioration of the first wall reflectivity due to dpa effects. It was found theoretically that first wall reflectivities down to 0.8 are still adequate for operation at an energy confinement scaling of 3 times Kaye-Goldston. Measurements of the graphite first wall reflectivities at Nagoya University indicate excellent reflectivities in excess of 90% for CC-312, PCC-2S, and PD-330S in the submillimeter regime, even at high temperatures in excess of 1000 K. Some engineering issues inherent to the CFAB cycle are also discussed briefly in comparison with the CFAR cycle which uses hazardous limited-resource materials but is capable of using mercury as coolant for high heat removal. The CFAB cycle using helium coolant is found to achieve higher net plant conversion efficiencies in excess 60% using a non-equilibrium magnetohydrodynamic disk generator in the moderate pressure range, even at the cost of a relatively large pumping power, and at the penalty of high temperature materials, although excellent heat removal characteristics in the moderate pressure range need to be guaranteed in the future.

The averaged toroidal flow of energetic minority ions during ICRF (ion cyclotron range of frequencies) heating is investigated in the Alcator C-Mod plasma by applying the GNET code, which can solve the drift kinetic equation with complicated orbits of accelerated energetic particles. It is found that a co-directional toroidal flow of the minority ions is generated in the region outside of the resonance location, and that the toroidal velocity reaches more than 40% of the central ion thermal velocity (Vtor ∼ 300 km/s with PICRF ∼ 2 MW). When we shift the resonance location to the outside of |r/a|∼0.5, the toroidal flow immediately inside of the resonance location is reduced to 0 or changes to the opposite direction, and the toroidal velocity shear is enhanced at r/a ∼ 0.5. A radial diffusion equation for toroidal flow is solved by assuming a torque profile for the minority ion mean flow, and good agreements with experimental radial toroidal flow profiles are obtained. This suggests that the ICRF driven min...

For integrated modeling of core and peripheral plasmas and analysis of transient transport phenomena where poloidal dependence of quantity is important, describing transport phenomena in the entire tokamak plasma as two-dimensional problems is desirable and becoming feasible owing to recent remarkable progress in computational resources. The set of two-dimensional transport equations with poloidal angle dependence is formulated from Braginskii’s equations and the neoclassical theory in order to develop an integrated two-dimensional transport simulation code.

The toroidal flow generation of minority ions by the local ion cyclotron range of frequencies (ICRF) heating is investigated in a tokamak plasma by applying the GNET code, which can solve the drift kinetic equation in the 5-D phase space. An asymmetry of velocity distribution function in the parallel direction is found and two types of toroidal averaged flow of minority ions are observed. One is the sheared flow near the RF power absorption region depending on the sign of k||, and the other is the toroidal flow, which is larger than the previous one, independent of the sign of k||. It is found that the k||-sign-independent toroidal flow is generated by the net toroidal motion of energetic tail ions and that the k||-sign-dependent flow is related to the mechanism proposed by Ohkawa [Phys. Plasmas 12, 094506 (2005)].