Table of contents

A ballooning eigenmode equation, taking into account the presence of energetic particles i n a tokamak, is derived from the Vlasov equation. The numerical solution of this equation demonstrates that the finite-Larmor-radius effect of the energetic particles can have a strong stabilizing effect on ballooning modes. This result supports the observed lack of high-mode-number ballooning instabilities in ISX-B injection experiments.

Toroidal effects on the outer magnetic surfaces of a configuration having a large toroidal plasma current that is stabilized by a pitch reversal produced by an external helical coil (OHTE) are investigated by both field-line tracing and an analytic expansion of the magnetic surfaces. Results of the two methods are compared. It is shown that both plasma position control and the helical coil winding law can be used to compensate undesired toroidal effects at both low and high beta.

The stability of the hot-electron annulus in the ELMO Bumpy Torus (EBT) is not yet completely understood despite considerable attention. Most stability studies have dealt with localized analysis of simplified models in which the actual magnetic configuration is replaced by a straight-line slab with a gravity to emulate the effects of curvature and gradients n i the actual magnetic field. Here, a more realistic geometry, a 'bumpy' cylinder with a 2:1 magnetic mirror ratio, is considered and the response of the hot-electron rings to various non-local perturbations, specifying only the mode number in the ignorable co-ordinate, is examined. Guiding-centre theory (with p_⊥ > p_||) is used and the second variation in the plasma energy (δW) using a finite-element representation to identify the least stable mode for the plasma is studied. All the equilibria that are examined are found to be unstable for all poloidal mode numbers m ⩾1, with growth rates increasing with increasing ring beta, plasma beta, and poloidal mode number. It is concluded that two-fluid and/or kinetic effects are required to explain the observed global stability of EBT-I.

The usual predictions of linear coupling theory for lower hybrid waves are altered by including an overdense edge plasma (ω < ω_pe) in the plasma model. Coupling is found to depend strongly on the value of the edge density, as well as the density gradient. The regimes, where one or the other of these parameters is important, are investigated. Typically, only the first few millimetres of the edge plasma are important in determining coupling. The major implications of the problem of coupling to an overdense plasma can be derived from a simple impedance-matching argument. In general, coupling is optimum for an edge density, n₀, determined by , where n_c = ω²m_e/4πe² and n_|| is the parallel index of refraction of the lower hybrid wave.

Self-consistent electrostatic potential variations are considered in a spatial region of weak magnetic field, as in the proposed tandem mirror thermal barriers (with no trapped ions). For some conditions, equivalent to ion distributions with a sufficiently high net drift speed along the magnetic field, the desired potential depressions are found. When the net drift speed is not high enough, potential depressions are found only in combination with strong electric fields on the boundaries of the system. These potential depressions are not directly related to the magnetic field depression.

The authors consider longitudinal plasma confinement in a centrifugal trap which is a modification of the rotating-plasma trap. The values of nτ, T and Q are calculated for a reactor based on this type of trap. New methods for solving the Fokker-Planck equation are used in these calculations.

Diffusion due to non-linear convective cells, excited by the ponderomotive force of interchange modes, is calculated. For a spectrum of linear modes measured in recent tokamak experiments, an ion energy diffusion close to that measured in the 6.5-keV PLT experiments is obtained. It is also found that, for a given spectrum of linear modes, the diffusion due to the driven non-linear mode is insensitive to shear.

Plasma transport is studied in a simulated magnetic divertor in the Wisconsin single-ring DC machine. The transport perpendicular and parallel to the magnetic field is shown to be non-ambipolar by a variety of measurements. The degree of the non-ambipolarity can be reduced by an appropriately designed divertor target plate, but not eliminated altogether. The density and temperature profiles in the scrape-off zone agree with the solutions of one-dimensional transport equations that assume classical cross-field diffusion due to ion-neutral collisions, classical cross-field conductivity due to electron-neutral collisions, and plasma flow parallel to the field at the local ion acoustic velocity.

Toroidal plasma rotation in the Princeton Large Torus, PLT, has been measured for various plasma and neutral-beam injection conditions. Measurements of the plasma rotational velocities were made from Doppler shifts of appropriate spectra lines and include data from both hydrogen and deuterium beams and co- and counter-injection at several electron densities. Without injection, a small but consistent toroidal rotation exists in a direction opposite to the plasma current (counter-direction) in the plasma centre but parallel to the current (co-direction) in the plasma periphery. Using these velocities measured in the absence of injection, and the plasma density and temperature gradients, radial electron fields can be determined from theory, giving E_r ≈ 40 V · cm⁻¹ in the plasma centre and E_r ≈ 10 V · cm⁻¹ near the plasma edge. Insertion of a local, 2.5% magnetic well produced no observable effect on the beam-driven rotation. Modelling of the time evolution and radial distribution of the rotation allows one to deduce an effective momentum diffusivity of the order of (1–5) × 10⁴ cm² · s⁻¹.

In this letter, collisionless α-particle losses in tokamak reactors are studied. Orbit losses of high-energy α-particles are calculated. The results are presented in a parameterized form which allows the fraction of α-particles lost and the load on the first wall in tokamaks of practical interest, circular and both with elliptical cross-sections, to be determined. The possibility of α-particle losses due to the excitation of various types of thermonuclear instabilities in the plasma is also examined.

A one-dimensional variational principle for the stability of external kink modes in a free-boundary high-β tokamak with skin currents is derived by the application of conformal mapping techniques. It is shown that these modes are stable above a certain critical value of aεβ_p if the wall is sufficiently close to the plasma.

Experimental studies of electron cyclotron pre-ionization and heating have been carried out in the JIPP T-II torus by injecting a power of 36 kW at the frequency of 35.5 GHz. Pre-ionization effectively decreases the loop voltage at the initial stage and eliminates strong spikes in the signals of electron density and of light and hard-X-ray emission which is due to runaway electrons in the initial breakdown phase of the Joule heating. From the measurement of the central electron temperature only, it is seen that electron cyclotron heating of a stellarator plasma with ordinary-mode radiation shows a heating efficiency of 1.6 eV·kW⁻¹ and, from power balance considerations, the absorption rate of microwave power is estimated to be around 50%.

The generation of a steady current in a resistive plasma cylinder by means of a travelling-wave magnetic field has been studied by using the resistive MHD equations. The non-linear initial-boundary value problem has been solved numerically. Hollow DC current profiles, similar to the experimental data obtained by other workers, have been found. A simple analytical argument, of a more general nature, shows that classical resistive diffusion cannot lead to a more uniform current distribution.

Gun injection of plasma parallel to the magnetic field in the Proto-Cleo stellarator results in particle confinement times of 3.5 – 4 ms while injection of plasma perpendicular to the magnetic field results in confinement times of 1.5 – 2 ms. Calculations of confinement times based on convective-cell theory that includes shear show good agreement with experimentally measured values.

A plasma current about a factor of two above the design value for ETF/INTOR is found to provide ideal magnetohydrodynamic (MHD) stability when a poloidal divertor is assumed. Ignition-scale devices may require plasma currents much larger than those presently considered.