The maximum normalized beta achieved in long-pulse tokamak discharges at low collisionality falls significantly below both that observed in short pulse discharges and that predicted by the ideal MHD theory. Recent long-pulse experiments, in particular those simulating the International Thermonuclear Experimental Reactor ͑ITER͒ ͓M. Rosenbluth et al., Plasma Physics and Controlled Nuclear Fusion ͑International Atomic Energy Agency, Vienna, 1995͒, Vol. 2, p. 517͔ scenarios with low collisionality e * , are often limited by low-m/n nonideal magnetohydrodynamic ͑MHD͒ modes. The effect of saturated MHD modes is a reduction of the confinement time by 10%-20%, depending on the island size and location, and can lead to a disruption. Recent theories on neoclassical destabilization of tearing modes, including the effects of a perturbed helical bootstrap current, are successful in explaining the qualitative behavior of the resistive modes and recent results are consistent with the size of the saturated islands. Also, a strong correlation is observed between the onset of these low-m/n modes with sawteeth, edge localized modes ͑ELM͒, or fishbone events, consistent with the seed island required by the theory. We will focus on a quantitative comparison between both the conventional resistive and neoclassical theories, and the experimental results of several machines, which have all observed these low-m/n nonideal modes. This enables us to single out the key issues in projecting the long-pulse beta limits of ITER-size tokamaks and also to discuss possible plasma control methods that can increase the soft ␤ limit, decrease the seed perturbations, and/or diminish the effects on confinement.

A quasi-linear analytical model is used to describe the nonlinear growth and saturation of tearing modes with mode number m⩾2. The saturation of the magnetic island growth is the quasi-linear development of a single mode rather than a mode coupling process. The saturation amplitude, which is dependent on the form of the resistivity, is in good agreement with results obtained previously by numerically advancing the full set of nonlinear equations.

Larqe-amplitude rotating maqnetohydrodynamic modes have been observed to induce significant hiqh-energy-beam particle loss durinq hiqh _ power perpendicular neutral-beam injection on PDX. A Hamiltonian formalism for drift-orbit trajectories in the presence of such modes is used to study induced particle loss analytically and numerically. Results are in qood agreement with experiment.

levels which might have a significant role in the light shift of the 22p level due to the 1.06-/im laser field are 6s, 7s, Ad, and 5d. These are far from being resonantly coupled to the 22p level, at least 1700 cm" 1 away. Their relative positions are such that their combined effects are partially cancelled* A rough evaluation showed that under these conditions the 5d level, which is expected to be responsible for the largest effect, contributes to the shift of the 22p level an amount of approximately 3xl0" 3 MHz/ MW-cm' 2 . This is at least 4 orders of magnitude less than the measured shift, and is thus completely negligible, With respect to the shift Lv g of the ground state, since it cannot be measured alone the best procedure is to calculate it as carefully and precisely possible. A calculation based on Fig. 1 has been carried out. 6 The result is &v g = -26.3 MHz/MW-cm" 2 . The dashed line in Fig. 3 corresponds to the sum of the two calculated shifts Ai/ e + Ay g , whereas the straight line corresponds to a least-squares fit on the measured shifts. Agreement between experimental and theoretical results is satisfactory.To conclude, this experiment provides clear evidence for the shift of a Rydberg level, due to an intense and strongly nonresonant em field. It is of interest to note that in a pure quantum treat-PACS numbers: 52.55.Gb, 52.35.Py On the PDX tokamak, large-amplitude magnetohydrodynamic (MHD) fluctuations have been observed during plasma heating by injection of high-ment, radiative corrections can be interpreted as the sum of spontaneous and stimulated radiative corrections. The net effect of spontaneous radiative corrections due to vacuum fluctuations is well known to be responsible for the Lamb shift. In the same spirit, the light shifts which have been studied in our experiment can perhaps be viewed as resulting from the stimulated radiative corrections induced by an intense and nonresonant em field.We thank Professor CI. Cohen-Tannoudji for many helpful discussions concerning both the experiment and its interpretation. We are indebted to Dr. M. Aymar and Dr. M. Crance for their calculation of the shift of the ground state.Strong magnetohydrodynamic activity has been observed in PDX neutral-be am-heated discharges. It occurs for fi T q^ 0.045 and is associated with a significant loss of fast ions and a drop in neutron emission. As much as 20%~-40% of the beam heating power may be lost. The instability occurs in repetitive bursts of oscillations of ^ 1 msec duration at 1-6-msec intervals. The magnetohydrodynamic activity has been dubbed the "fishbone instability" from its characteristic signature on the Mirnov coils.

A three-dimensional (3-D) hybrid gyrokinetic-MHD (magnetohydrodynamic) simulation scheme is presented. To the 3-D toroidal MHD code, MH3D-K the energetic particle component is added as gyrokinetic particles. The resulting code, mh3d-k, is used to study the nonlinear behavior of energetic particle effects in tokamaks, such as the energetic particle stabilization of sawteeth, fishbone oscillations, and alpha-particle-driven toroidal Alfvén eigenmode (TAE) modes.

Compact optimized stellarators offer novel solutions for confining high-β plasmas and developing magnetic confinement fusion. The three-dimensional plasma shape can be designed to enhance the magnetohydrodynamic (MHD) stability without feedback or nearby conducting structures and provide driftorbit 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 β limit, and good confinement of advanced tokamaks. Quasiaxisymmetric equilibria have been developed for the proposed National Compact Stellarator Experiment (NCSX) with average aspect ratio 4-4.4 and average elongation ∼1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassicaltearing modes for β > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at β = 4% (the rest is from the coils); thus the equilibrium is much less non-linear 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. 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.

The Sweet–Parker and Petschek scalings of the 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-β 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 (ψ̇s∼η). In addition, experimental data of the nonlinear m=1 resistive internal kink in tokamak discharges are analyzed and are found to give reasonable agreement with the modified Sweet–Parker scaling.

The time scales for sawtooth repetition and heat pulse propagation are much longer (10's of msec) in the large tokamak TFTR than in previous, smaller tokamaks. This extended time scale coupled with more detailed diagnostics has led us to revisit the analysis of the heat pulse propagation as a method to determine the electron heat diffusivity, x e) in the plasma. A combination of analytic and computer solutions of the electron heat diffusion equation are used to clarify previous work and develop new methods for determining x e-Direct comparison of the predicted heat pulses with soft X-ray and ECE data indicates that the space-time evolution is diffusive. However, the x e determined from heat pulse propagation usually exceeds that determined from background plasma power balance considerations by a factor ranging from 2 to 10, Some hypotheses for resolving this discrepancy are discussed.