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The usage of permanent magnets to shape the confining magnetic field of a stellarator has the potential to reduce or eliminate the need for non-planar coils. As a proof-of-concept for this idea, we have developed a procedure for designing an array of cubic permanent magnets that works in tandem with a set of toroidal-field coils to confine a stellarator plasma. All of the magnets in the design are constrained to have identical geometry and one of three polarization types in order to simplify fabrication while still producing sufficient field accuracy. We present some of the key steps leading to the design, including the geometric arrangement of the magnets around the device, the procedure for optimizing the polarizations according to the three allowable magnet types, and the choice of magnet types to be used. We apply these methods to design an array of rare-Earth permanent magnets that can be paired with a set of planar toroidal-field coils to confine a quasi-axisymmetric plasma with a toroidal magnetic field strength of about 0.5 T on axis., Comment: 17 pages, 11 figures

A strong interaction of fast ions with ion Bernstein waves has been observed in TFTR. It results in a large increase in the fast ion loss rate and heats the lost particles to several megaelectronvolts. The lost ions are observed at the passing-trapped boundary and appear to be either DD fusion produced tritons or accelerated deuterium neutral beam ions. Under some conditions, enhanced loss of DT alpha particles is also seen. The losses provide experimental support for some of the elements required for alpha energy channelling

The deuterium-tritium (D-T) experimental program on the Tokamak Fusion Test Reactor (TFTR) is underway and routine tritium operations have been established. The technology upgrades made to the TFTR facility have been demonstrated to be sufficient for supporting both operations and maintenance for an extended D-T campaign. To date fusion power has been increased to {approximately}9 MW and several physics results of importance to the D-T reactor regime have been obtained: electron temperature, ion temperature, and plasma stored energy all increase substantially in the D-T regime relative to the D-D regime at the same neutral beam power and comparable limiter conditioning; possible alpha electron heating is indicated and energy confinement improvement with average ion mass is observed; and alpha particle losses appear to be classical with no evidence of TAE mode activity up to the P{sub FUS} {approximately}6 MW level. Instability in the TAE mode frequency range has been observed at P{sub FUS} > 7 MW and its effect on performance is under investigation. Preparations are underway to enhance the alpha particle density further by increasing fusion power and by extending the neutral beam pulse length to permit alpha particle effects of relevance to the ITER regime to be more fullymore » explored.« less

High poloidal beta (βp approximately 5) discharges produced with nearly balanced tangential neutral beam injection into low current discharges in the TFTR tokamak are described. As βp exceeds approximately 1.2 times the aspect ratio, a separatrix with an inside poloidal field null is observed to limit the outer boundary of the plasma. Since the curvature of TFTR's applied vertical field is constant, the appearance of the poloidal field null corresponds to the equilibrium poloidal beta limit

Compact stellarators have the potential to make steady-state, disruption-free magnetic fusion systems with beta approximately 5% and relatively low aspect ratio (R/ < 4.5) compared to most drift-optimized stellarators. Magnetic quasi-symmetry can be used to reduce orbit losses. The National Compact Stellarator Experiment (NCSX) is designed to test compact stellarator physics in a high-beta quasi-axisymmetric configuration and to determine the conditions for high-beta disruption-free operation. It is designed around a reference plasma with low ripple, good magnetic surfaces, and stability to the important ideal instabilities at beta approximately 4%. The device size, available heating power, and pulse lengths provide access to a high-beta target plasma state. The NCSX has magnetic flexibility to explore a wide range of equilibrium conditions and has operational flexibility to achieve a wide range of beta and collisionality values. The design provides space to accommodate plasma-facing components for divertor operation and ports for an extensive array of diagnostics.

Compact quasi-axisymmetric stellarators 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 approximately 4.4 and average elongation approximately 1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassical-tearing modes for b > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at b = 4% (the rest is from the coils). Transport simulations show adequate fast-ion confinement and thermal neoclassical transport similar to equivalent tokamaks. 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.

A strong interaction of fast ions with ion Bernstein waves has been observed in TFTR. It results in a large increase in the fast ion loss rate, and heats the lost particles to several MeV. The lost ions are observed at the passing/trapped boundary and appear to be either DD fusion produced tritons or accelerated D neutral beam ions. Under some conditions, enhanced loss of DT alpha particles is also seen. The losses provide experimental support for some of the elements required for alpha energy channeling.

A quantitative comparison is made between the tearing-type modes observed supershot plasmas and the nonlinear, neoclassical pressure gradient ({nabla}{sub p}) driven tearing mode theory. Good agreement is found on the nonlinear magnetic island evolution of a single helicity mode (m/n = 3/2, 4/3 or 5/4, where m and n are the poloidal and toroidal mode numbers, respectively). Statistical data on the island width and growth rate are also found to be consistent with this theory. The results imply that the supershot plasmas are the classical current-driven tearing modes.

Local thermal particle and energy transport studies of balanced-injection L-mode and Supershot deuterium plasmas with the same toroidal field, plasma current, and neutral beam heating power have been performed on TFTR. The particle transport of He{sup 2+} and electrons following a small helium gas puff and Fe{sup 24+} induced by laser ablation has been examined and compared to the local energy transport characteristics inferred from power balance analysis. All particle perturbation diffusivities are radially hollow and are similar in magnitude and shape to the effective thermal conductivities found by power balance analysis. All particle diffusivities are 1--2 orders of magnitude larger than neoclassical values, except near the magnetic axis. A reduction in the helium diffusivity D{sub He} in the Supershot as compared to the L-mode is accompanied by a similar reduction in the effective single fluid thermal conductivity {chi}fluid. Also, the helium core convective velocity V{sub He} is found to increase in the Supershot over the L-Mode for r/a < 0.5. A quasilinear model of electrostatic drift waves has been used to calculate ratios between particle and energy fluxes in the Supershot. The measured ratios of the helium and iron particle diffusivities are in good accord with predictions, as aremore » predicted ratios of V{sub He}/D{sub He}. Modelling indicates that the similarity in magnitude and profile shape of D{sub He} and {chi}fluid has generally favorable implications for helium ash content in a future fusion reactor. The core convection found in the Supershot increases the helium concentration on axis but does not reduce the plasma reactivity significantly.« less

A transport code (TRANSP) is used to simulate future deuterium-tritium experiments (DT) in TFTR. The simulations are derived from 14 TFTR DD discharges, and the modeling of one supershot is discussed in detail to indicate the degree of accuracy of the TRANSP modeling. Fusion energy yields and {alpha}-particle parameters are calculated, including profiles of the {alpha} slowing down time, average energy, and of the Alfven speed and frequency. Two types of simulations are discussed. The main emphasis is on the DT equivalent, where an equal mix of D and T is substituted for the D in the initial target plasma, and for the D{sup O} in the neutral-beam injection, but the other measured beam and plasma parameters are unchanged. This simulation does not assume that {alpha} heating will enhance the plasma parameters, or that confinement will increase with T. The maximum relative fusion yield calculated for these simulations is Q{sub DT} {approx} 0.3, and the maximum {alpha} contribution to the central toroidal {beta} is {beta}{sub {alpha}}(0) {approx} 0.5%. The stability of toroidicity-induced Alfven eigenmodes (TAE) and kinetic ballooning modes (KBM) is discussed. The TAE mode is predicted to become unstable for some of the equivalent simulations, particularly after the terminationmore » of neutral beam injection. In the second type of simulation, empirical supershot scaling relations are used to project the performance at the maximum expected beam power. The MHD stability of the simulations is discussed.« less

Local particle and heat transport coefficients have been measured in a controlled temperature scan of neutral-beam-heated plasmas with n, I{sub p}, and B{sub {var phi}} held constant. The electron particle transport is ascertained from a general flux analysis of a small density perturbation, and the heat transport is obtained from the equilibrium power balance. The local particle and heat transport coefficients vary as T{sub e}{sup {alpha}}, where {alpha} = 1.5--2.5. The observed temperature dependence for these plasmas is predicted by numerical calculations of anomalous transport due to trapped-particle drift-type microinstabilities.

The calculated heating-beam deposition profile is experimentally verified for a variety of target plasma densities for the first time. The calculation of the heating-beam deposition is found to be consistent with the measurement for the discharges without MHD activity. It is also demonstrated that the radial electron flux is unchanged from the ohmic phase to the initial auxiliary heating phase ({le}100 msec).

Measurements on the TFTR tokamak of the electron temperature profile evolution and soft x-ray emissivity on a fast (10 {mu}sec) time scale during a sawtooth crash, show that significant heat is deposited beyond the mixing (or reconnection) radius within 200 {mu}sec following a sawtooth crash. This extended region in which electron heat is redistributed during the sawtooth crash substantially complicates the determination of heat transport properties from the subsequent heat pulse propagation. It is shown that the relaxation of this extended perturbation is consistent with the power balance estimates of the local thermal diffusivity. 19 refs., 6 figs.

Neutral-beam-heated plasmas in TFTR show evidence of substantial non-ohmically-driven toroidal current, even for balanced beam momentum input. The observations are inconsistent with calculations including only ohmic and beam-driven currents, and presently can only be matched by models including the neoclassical bootstrap current. 28 refs., 9 figs., 1 tab.

Praxis is the practice of the programming art, science, and skill. It is a high-order language designed for the efficient programming of control and systems applications. It is a comprehensive, strongly typed, block-structured language in the tradition of Pascal, with much of the power of the Mesa and Ada languages. It supports the development of systems composed of separately compiled modules, user-defined data types, exception handling, detailed control mechanisms, and encapsulated data and routines. Direct access to machine facilities, efficient bit manipulation, and interlocked critical regions are provided within Praxis.

Electron heat transport on TFTR and other tokamaks is several orders of magnitude larger than neoclassical calculations would predict. Despite considerable effort, there is still no clear theoretical understanding of this anomalous transport. The electron temperature profile T/sub e/(r), shape has shown a marked consistency on many machines, including TFTR, for a wide range of plasma parameters and heating profiles. This could be an important clue as to the process responsible for this enhanced thermal transport. In this paper 'profile consistency' in TFTR is described and an experiment which uses a fast current ramp to transiently decouple the current density profile J(r), and the T/sub e/(r) profiles is discussed. From this experiment the influence of J(r) on electron temperature profile consistency can be determined.

Measurements of the plasma ion temperature and toroidal rotation speed profiles have allowed the study of ion thermal transport in the TFTR hot ion enhanced confinement regime. Central ion temperatures up to 30 keV and rotation speeds up to 8 x 10/sup 5/ m/sec have been confirmed with new diagnostic measurements, and the ion thermal diffusivity is found to be non-neoclassical and comparable to the anomalous electron thermal diffusivity. The dominant effects of strong rotation are the down-shifting of the neutral beam energies in the plasma frame, which results in reduced ion and electron heating on axis, and the presence of off-axis ion heating from viscous damping of the plasma rotation. 14 refs., 3 figs.

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