Table of contents

Ideal magnetohydrodynamic stability analysis has been carried out for configurations expected in the Big Dee tokamak, an upgrade of the Doublet III tokamak into a non-circular cross-section device which began operation early in 1986. The results of this analysis support theoretical predictions as follows: Since the maximum value of beta stable to ballooning and Mercier modes, which we denote β_c, increases with inverse aspect ratio, elongation and triangularity, the Big Dee is particularly suited to obtain high values of β_c and there exist high β_c Big Dee equilibria for large variations in all relevant plasma parameters. The beta limits for the Big Dee are consistent with established theory as summarized in present scaling laws. High beta Big Dee equilibria are continuously accessible when approached through changes in all relevant input parameters and are structurally stable with respect to variations of input plasma parameters. Big Dee beta limits have a smooth dependence on plasma parameters such as β_p and elongation. These calculations indicate that in the actual running of the device the Big Dee high beta equilibria should be smoothly accessible. Theory predicts that the limiting plasma parameters, such as beta, total plasma current and plasma pressure, which can be obtained within the operating limits of the Big Dee are reactor relevant. Thus the Big Dee should be able to use its favourable ideal MHD scaling and controlled plasma shaping to attain reactor relevant parameters in a moderate sized device.

The stability properties of currentless high beta plasmas have been investigated over a wide range of density profiles n_e(r), by varying the gas puffing conditions and by pellet injection. Line density fluctuations correlated with a pressure driven MHD instability were measured by a multi-channel far-infrared laser interferometer. When an increase in the plasma beta was accompanied by a peaking of n_e(r), line density fluctuations with a frequency of 2–5 kHz periodically appeared. The repetition time of the fluctuations was typically 2–5 ms. The poloidal and toroidal mode numbers of the fluctuations were identified as m=l and n=l. For plasmas with an extremely peaked profile, density fluctuations corresponding to the m=3/n=2 mode were observed. With the growth of this mode, internal disruptions occurred. Because of these disruptions, the profile of n_e(r) rapidly changed from a peaked one to a broader one. The normalized average radius, r/a, of the phase reversal in the density profile variation caused by the disruption is about 0.5, which roughly corresponds to the ι =2/3 surface, ι being the rationalized rotational transform. It is most likely that the large amplitude mode with m=3/n=2 triggers the internal disruptions. The onset regions for MHD instability have also been investigated for various density profiles and beta values.

On the assumption that the distribution function of ions heated by ion cyclotron resonance absorption is essentially isotropic, analytical and semi-analytical approximations are derived for the distribution function. The result is used to evaluate the weighted velocity space averages of the distribution, which determine the fusion reactivity and the collisional power transfer to plasma background particles, and to study their scaling with RF parameters such as absorbed power and perpendicular wave number. The importance of higher order finite Larmor radius effects on the formation of RF induced high energy tails is particularly emphasized. Comparisons based on full 2-D numerical calculations show good agreement with the semi-analytical results.

The horizontally scanning, multi-angle charge exchange analysers on the Princeton Large Torus (PLT) and the Poloidal Divertor Experiment (PDX) were used to study the effects of MHD activity on the background ion distribution function and on the beam ion slowing-down process during high power neutral injection. Sawtooth oscillations were observed in the fast ion flux on PLT and PDX, and measurements with neutral beams providing local neutral density enhancement indicated that the ions were transported radially when these events occurred. With nearperpendicular injection in PDX, at the lower toroidal fields necessary to maximize the plasma beta, repetitive bursts of greatly enhanced charge exchange flux were observed. These were associated with the 'fishbone' MHD instability, and a substantial depletion of the perpendicular slowing-down spectrum below the injection energy was seen. A simple phenomenological model for this loss mechanism was developed, and its use in simulation codes has been successful in providing good agreement with the experimental data. The behaviour and characteristics of this model are well matched by direct theoretical calculations.

The neoclassical transport theory of a plasma with an RF wave source is formulated in the Pfirsch-Schliiter regime. Particle and heat fluxes across the magnetic surfaces induced by RF wave injection are calculated numerically for a two ion species plasma. Analytic expressions for these fluxes are obtained when the parallel phase velocity of the wave is approximately two to three times as high as the ion thermal velocity. When the parallel phase velocity is lower than the ion thermal velocity, the effect of the RF wave source is shown to be approximately that of the momentum, energy and heat flow sources.

A simple quadratic dispersion relation is derived for electrostatic ion temperature gradient driven modes without expansion in the inverse aspect ratio. It is also shown that these modes experience the local curvature only on the outside of the magnetic surface.

The problem of driving quasi-steady-state currents in tokamak plasmas with pulsed RF sources is examined in the regime , where τ_RF is the length of the RF pulse, is the electron collision time, T_RF is the period between RF pulses, and T_L/R is the L over R time of the tokamak plasma. This regime is appropriate to the proposed Microwave Tokamak Experiment (MTX) in which a pulsed free electron laser will be used to drive current in Alcator C. It is found that δI/Ī ≈ T_RF/T_L/R ≪ 1, where δI/Ī is the fractional variation in the plasma current. The production of runaway electrons can be a problem in the collisional limit, ν_e T_RF ≫ 1. This will be avoided in the proposed MTX experiment if the electron temperature exceeds 1.5 keV.

The fusion neutron yield during hydrogen neutral beam injection into deuterium plasmas is examined and compared with the neoclassical model, using the Doublet III data obtained in 1983. This provides scalings of thermonuclear fusion neutron yields for the discussion of ion energy transport in tokamak devices. – Experimental data show that fusion neutron yield appears to have a scaling of in low recycling divertor discharges (so called H mode). The neoclassical theory for ion heat conduction satisfactorily described the scaling of fusion neutron yield. With a neutral injection power of P_inj = 4.6 MW, the Doublet III deuterium plasma yields thermonuclear neutrons at a rate of 1.2 × 10¹³ n·s⁻¹ in low recycling divertor discharge, which is equivalent to a D⁺ T⁺ plasma with a thermonuclear fusion power multiplication factor of Q = 7.8 × 10⁻⁵ or a beam driven T⁺ plasma with Q = 8.6 × 10⁻². A limiter discharge yields fewer neutrons.

It is shown that a class of disturbances exists which have a cumulative effect on the migration of the stable (or feedback stabilized) toroidal burning plasma along the curve of marginal ignition. However, the migration path can be compensated for and the working point on the ignition curve can be adjusted along a stable path by suitable prescriptions for the feedback system of the vertical field. Regulation of the burn and position of the plasma column on a finer scale, using a succession of small stable cycles around the chosen working point, is also discussed. Since the path R(t) = const is unstable in the pressure-position space (near the thermally unstable points of the ignition curve), the stable cycles do not involve isovolumic branches.

In linear wave-particle interaction models, the coupling between cold electrons and microwaves with frequency equal to twice the electron gyrofrequency is so weak that the ionization of a significant number of neutral hydrogen atoms would seem impossible in practical applications. However, the non-linear interaction of a cold electron with the wave is very large if the electron becomes trapped near resonance in a shallow, static magnetic well. A model has been developed to describe the breakdown of a neutral gas when these non-linear interactions are considered, and it is in reasonable agreement with the limited amount of available experimental data. For gas pressures that are too large, electron-neutral collisions inhibit the non-linear interaction and prevent breakdown. For gas pressures that are too low, the growth rate of the free electron population is limited because electrons capable of causing ionization are lost before suffering a collision with a neutral. Quantitative growth rate predictions are presented for stellarators, and formulae for rough estimates are given.

A formulation is presented for evaluating the spectral broadening, due to an extended nonuniform scattering region, of waves scattered from the electron diamagnetic drift waves in a tokamak plasma. The spectral distribution is evaluated numerically and compared with the experimental results obtained in JIPP T-IIU. Good agreement is obtained when the amplitude of the density fluctuation, ñ_e(r), is assumed to vary parabolically with the radius, just like the local time averaged density. It is also shown that non-uniformity of the plasma parameters in the scattering volume has a significant effect on the apparent form factor, S(k), and on the spatial distribution of the density fluctuations.

The effects of sawtooth activity on the poloidal magnetic flux and energy balances in tokamak plasmas on a diffusive time-scale are evaluated through the application of conservation principles to Maxwell's equations. Poloidal magnetic flux (volt-second) consumption can be partitioned into internal and dissipative components by two methods: the 'axial method' based on a magnetic flux balance and the 'Poynting method' based on a magnetic energy balance. Both methods require additional terms that specifically account for the poloidal flux and magnetic energy changes during magnetic reconnection derived from analysis on a magnetohydrodynamic time-scale. In experimental analyses these terms are absorbed in the inferred resistive dissipation, while in predictive analyses they must be evaluated directly. The dissipation of poloidal flux by sawtooth activity can exceed the normal resistive dissipation when the axial method of accounting is used.

In the reversed field pinch STP-3(M), plasma flow propagating in the direction of the electron movement along the magnetic field lines of force is found by measurements of magnetic fluctuations and Doppler shift of impurity lines. The magnitude of the flow velocity is smaller than the thermal speed of the plasma ions by about a factor of three. Thus, it is demonstrated experimentally that the theoretical assumption of no mass flow in a reversed field pinch is justified.

Initial measurements of the 15 MeV protons produced in TFTR by the d(³He, p)α fusion reaction have been used to determine the time evolution of the central ³He density. The signals following short ³He gas puffs indicate inward transport times of about 100 ms.

Non-linear MHD calculations of the m/n = 2/1 free boundary kink mode in a cylindrical tokamak are carried out by taking account of the parallel diffusion of resistivity. 'Vacuum bubbles' are formed inside the plasma for q_a somewhat smaller than 2. When 1.75 < q_a < 1.9 for q₀/q_a = 0.5 (q₀ is the safety factor at the magnetic axis and q_a is that at the plasma surface), the plasma column shrinks with elliptic deformation, the value of q_a decreases in time, the plasma becomes stable against the m/n = 2/1 mode, and finally, a damped oscillation is observed. Interaction between the plasma and the material limiter causes the shrinkage for all unstable values of q_a. When q₀ is nearly equal to or larger than unity, the plasma shrinks rapidly, and q_a can be reduced to values below unity, upon which the m/n = 1/1 kink mode becomes unstable. The plasma shrinkage is a candidate for major disruptions in a tokamak discharge with q_a less than or equal to 2.

The quantity c/ω_pe is shown to be the radial propagation wavelength rather than the evanescent skin depth for low frequency magnetic perturbations in tokamaks. This may provide an explanation for Ohkawa's postulate that c/ω_pe should play the role of random walk distance.

The 1.01 MeV triton burnup in FT deuterium discharges has been investigated by the measurement of 14.1 MeV and 2.45 MeV neutron emission. At large values of q_L, the burnup is found to increase with plasma current as expected; around q_L = 3, a reduction is observed, while for lower q_L values the burnup seems to increase again, but is more erratic.

It is shown that the density independent flute mode observed in Base-Ball II mirror becomes explosively unstable in the presence of ion cyclotron oscillations. The nonlinear growth times agree fairly well with the bursting time-scale of the amplitude of flute perturbations.