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The Korea Superconducting Tokamak Advanced Research (KSTAR) project is the major effort of the national fusion programme of the Republic of Korea. Its aim is to develop a steady state capable advanced superconducting tokamak to establish a scientific and technological basis for an attractive fusion reactor. The major parameters of the tokamak are: major radius 1.8 m, minor radius 0.5 m, toroidal field 3.5 T and plasma current 2 MA, with a strongly shaped plasma cross-section and double null divertor. The initial pulse length provided by the poloidal magnet system is 20 s, but the pulse length can be increased to 300 s through non-inductive current drive. The plasma heating and current drive system consists of neutral beams, ion cyclotron waves, lower hybrid waves and electron cyclotron waves for flexible profile control in advanced tokamak operating modes. A comprehensive set of diagnostics is planned for plasma control, performance evaluation and physics understanding. The project has completed its conceptual design and moved to the engineering design and construction phase. The target date for the first plasma is 2002.

Recently reported numerical results for axisymmetric devices with low aspect ratio A found radial transport enhanced over the expected neoclassical value by a factor of 2 to 3. In this paper, we provide an explanation for this enhancement. Transport theory in toroidal devices usually assumes large A, and that the ratio B{sub p}/B{sub t} of the poloidal to the toroidal magnetic field is small. These assumptions result in transport which, in the low collision limit, is dominated by banana orbits, giving the largest collisionless excursion of a particle from an initial flux surface. However in a small aspect ratio device one may have B{sub p}/B{sub t} {approx} 1, and the gyroradius may be larger than the banana excursion. Here, we develop an approximate analytic transport theory valid for devices with arbitrary A. For low A, we find that the enhanced transport, referred to as omniclassical, is a combination of neoclassical and properly generalized classical effects, which become dominant in the low-A, B{sub p}/B{sub t} {approx} 1 regime. Good agreement of the analytic theory with numerical simulations is obtained.

Calculations of collisional thermal and particle diffusivities in toroidal magnetic plasma confinement devices order the toroidal gyroradius to be small relative to the poloidal gyroradius. This ordering is central to what is usually referred to as neoclassical transport theory. This ordering is incorrect at low aspect ratio, where it can often be the case that the toroidal gyroradius is larger than the poloidal gyroradius. We calculate the correction to the particle and thermal diffusivities at low aspect ratio by comparing the diffusivities as determined by a full orbit code (which we refer to as omni-classical diffusion) with those from a gyroaveraged orbit code (neoclassical diffusion). In typical low aspect ratio devices the omni-classical diffusion can be up to 2.5 times the calculated neoclassical value. We discuss the implications of this work on the analysis of collisional transport in low aspect ratio magnetic confinement experiments.

Compact optimized stellarators offer novel solutions for confining high-beta plasmas and developing magnetic confinement fusion. The 3-D plasma shape can be designed to enhance the MHD stability without feedback or nearby conducting structures and provide drift-orbit confinement similar to tokamaks. These configurations offer the possibility of combining the steady-state low-recirculating power, external control, and disruption resilience of previous stellarators with the low-aspect ratio, high beta-limit, and good confinement of advanced tokamaks. Quasi-axisymmetric equilibria have been developed for the proposed National Compact Stellarator Experiment (NCSX) with average aspect ratio 4-4.4 and average elongation of approximately 1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassical-tearing modes for beta > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at beta = 4% (the rest is from the coils), thus the equilibrium is much less nonlinear and is more controllable than similar advanced tokamaks. The enhanced stability is a result of ''reversed'' global shear, the spatial distribution of local shear, and the large fraction of externally generated transform. Transport simulations show adequate fast-ion confinement and thermal neoclassical transport similar to equivalent tokamaks.more » Modular coils have been designed which reproduce the physics properties, provide good flux surfaces, and allow flexible variation of the plasma shape to control the predicted MHD stability and transport properties.« less

Absorption of fast Alfven waves by the minority fundamental ion-cyclotron resonance, coupled with finite banana width physics, generates torque distributions and ultimately rotational shear layers in the bulk plasma, even when the toroidal wavenumber k(subscript ''phi'') = n/R of the fast wave vanishes (n=0) and cyclotron absorption introduces no angular momentum nor canonical angular momentum [F.W. Perkins, R.B. White, P.T. Bonoli, and V.S. Chan, Phys. Plasmas 8 (2001) 2181]. The present work extends these results to travelling waves with non-zero n where heating directly introduces angular momentum. Since tokamak fast-wave antennas have approximately one wavelength per toroidal field coil, the toroidal mode number n lies in the range n = 10-20, independent of machine size. A zero-dimensional analysis shows that the rotation rate arising from direct torque is comparable to that of the rotational shear layer and has the same scaling. Nondimensional rotation profiles for n = (-10, 10) show modest changes from the n = 0 case in the expected direction. For a balanced antenna spectrum, the nondimensional rotational profile (averaged over n = -10, 10) lies quite close to the n = 0 profile.

The threshold for stochastic transport of high energy trapped particles in a tokamak due to toroidal field ripple is calculated by explicit construction of primary resonances, and a numerical examination of the route to chaos. Critical field ripple amplitude is determined for loss. The expression is given in magnetic coordinates and makes no assumptions regarding shape or up-down symmetry. An algorithm is developed including the effects of prompt axisymmetric orbit loss, ripple trapping, convective banana flow, and stochastic ripple loss, which gives accurate ripple loss predictions for representative Tokamak Fusion Test Reactor and International Thermonuclear Experimental Reactor equilibria. The algorithm is extended to include the effects of collisions and drag, allowing rapid estimation of alpha particle loss in tokamaks.

Coherent magnetohydrodynamic modes have been observed during neutral beam injection in TFTR and JET. Periodic bursts of oscillations were detected with several plasma diagnostics, and Fokker-Planck calculations show that the populations of trapped particles in both tokamaks are sufficient to account for fishbone destabilization. Estimates of mode parameters are in reasonable agreement with the experiments, and they indicate that the fishbone mode may continue to affect the performance of intensely heated tokamaks. 13 refs., 1 fig., 1 tab.

The presence of energetic particles is shown to qualitatively modify the stability properties of ideal as well as resistive magnetohydrodynamic (MHD) modes in tokamaks. Specifically, we demonstrate that, consistent with highpower ICRF heating experiments in JET, high energy trapped particles can effectively stabilize the sawtooth mode, providing a possible route to stable high current tokamak operation. An alternative stabilization scheme employing barely circulating energetic particles is also proposed. Finally, we present analytical and numerical studies on the excitations of high-n MHD modes via transit resonances with circulating alpha particles. 14 refs., 3 figs.

It is shown that, in present-day large-size tokamaks, finite resistivity modifies qualitatively the stability properties of magnetohydrodynamic instabilities resonantly excited by the unfavorable processional drift of energetic-trapped particles, i.e., the so-called ''fishbone''-type instabilities. Specifically, it is found that (1) the n = 1 energetic-trapped particle-induced internal kink (''fishbone'') instability is strongly stabilized by resistive dissipation and (2) finite resistivity lowers considerably the threshold conditions for resonant excitations of high-n ballooning/interchange modes. The possibility of exciting fishbones by alpha particles in ignition experiments is also considered.

A review is given of the linear theory of reconnection for a plane current layer. The three basic modes are the Rippling Mode, the Gravitational Interchange Mode, and the Tearing Mode. A derivation is given of the magnetic field energy which provides the driving force for the tearing mode. The necessary concepts for the analysis of tearing modes in cylindrical geometry are introduced. The equations governing tearing mode evolution in a tokamak are expanded to lowest order in the inverse aspect ratio. The tearing mode in a toroidal device is closely related to the ideal magnetohydrodynamic kink mode, and this relationship is stressed in the derivations of the linear growth rates for modes with poloidal model number m > 2 and for the quite different m = 1 mode. The nonlinear theory of tearing mode development and the implications of this theory for the understanding of toroidal magnetic confinement devices is reviewed.

The nonlinear saturation theory of the tearing mode is used to examine the necessary conditions for the occurrence of a major tokamak disruption. The results are compared with full three-dimensional numerical simulations, and with experimental data.

The Sweet-Parker and Petschek scalings of magnetic reconnection rate are modified to include the effect of the viscosity. The modified scalings show that the viscous effect can be important in high-..beta.. plasmas. The theoretical reconnection scalings are compared with numerical simulation results in a tokamak geometry for three different cases: a forced reconnection driven by external coils, the nonlinear m = 1 resistive internal kink, and the nonlinear m = 2 tearing mode. In the first two cases, the numerical reconnection rate agrees well with the modified Sweet-Parker scaling, when the viscosity is sufficiently large. When the viscosity is negligible, a steady state which was assumed in the derivation of the reconnection scalings is not reached and the current sheet in the reconnection layer either remains stable through sloshing motions of the plasma or breaks up to higher m modes. When the current sheet remains stable, a rough comparison with the Sweet-Parker scaling is obtained. In the nonlinear m = 2 tearing mode case where the instability is purely resistive, the reconnection occurs on the slower dissipation time scale (Psi/sub s/ approx. eta). In addition, experimental data of the nonlinear m = 1 resistive internal kink in tokamak discharges aremore » analyzed and are found to give reasonable agreement with the modified Sweet-Parker scaling.« less

Energetic trapped particles are shown to introduce a new unstable solution to the internal kink and ballooning modes in tokamaks. Both the real frequencies and growth rates of the instabilities are comparable to the trapped-particle precession frequency. Simulations including the excitation and particle-loss mechanisms of the internal kink mode are found to reproduce essential features of the fishbones. Furthermore, the energetic trapped particle-induced ballooning modes are shown to be consistent with the associated high-frequency oscillations observed experimentally. Several possible stabilizing schemes are considered.

Experiments with plasmas having nearly equal concentrations of deuterium and tritium have been carried out on TFTR. To date, the maximum fusion power has been 10.7 MW, using 39.5 MW of neutral-beam heating, in a supershot discharge and 6.7 MW in a high-{beta}{sub p} discharge following a current ramp-down. The fusion power density in the core of the plasma has reached 2.8 MWm{sup {minus}3}, exceeding that expected in the International Thermonuclear Experimental Reactor (ITTER). The energy confinement time, {tau}{sub E}, is observed to increase in D-T, relative to D plasmas, by 20% and the n{sub i}(O){center_dot}{tau}{sub E} product by 55%. The improvement in thermal confinement is caused primarily by a decrease in ion heat conductivity in both supershot and limiter-H-mode discharges. Extensive lithium pellet injection increased the confinement time to 0.27 s and enabled higher current operation in both supershot and high-{beta}{sub p} discharges. First measurements of the confined alpha particles have been performed and found to be in good agreement with TRANSP simulations assuming classical confinement. Measurements of the alpha ash profile have been compared with simulations using particle transport coefficients from helium gas puffing experiments. The loss of energetic alpha particles to a detector at the bottom ofmore » the vessel is well described by the first-orbit loss mechanism. No loss due to alpha-particle-driven instabilities has yet been observed. ICRF heating of a D-T plasma, using the second harmonic of tritium, has been demonstrated. D-T experiments on TFTR will continue both to explore the physics underlying the ITER design and to examine some of the physics issues associated with an advanced tokamak reactor.« less