S. Yoshikawa

Adiabatic Compression of Tokamak Discharges

Adiabatic compression in minor and major radius is shown to facilitate the attainment of dense, high‐temperature plasmas in the tokamak configuration.

Application of the Virial Theorem to Equilibria of Toroidal Plasmas

Necessary conditions for equilibrium of a current‐carrying toroidal plasma are derived under the assumption of azimuthal symmetry. It is demonstrated that an azimuthally symmetric toroidal plasma can be in equilibrium only if an additional transverse magnetic field is present, which absorbs the expanding force of the plasma. An expression of parabolic pressure distribution is obtained, when the plasma minor radius is much smaller than the major radius. Stability criterion of the plasma ring against displacement is discussed. The weak focusing can be employed to stabilize the plasma ring.

Alfven wave cyclotron resonance heating

The resonance absorption of fast Alfven waves at the proton cyclotron resonance of a predominately deuterium plasma is investigated. An approximate dispersion relation is derived, valid in the vicinity of the resonance, which permits an exact calculation of transmission and reflection coefficients. For reasonable plasma parameters significant linear resonance absorption is found.

Equilibrium of a Toroidal Plasma with a Conducting Aperture Limiter

A conducting limiter brings about equilibrium of a toroidal plasma by anchoring magnetic field lines. Charge separation arising from the curvature effect can be short circuited by the limiter. This way of achieving equilibrium is not possible if the charge separation current exceeds the maximum ion saturation current to the limiter. Experiments with the Model C stellarator are consistent with this model. An observed instability is related to the loss of equilibrium due to the excess charge separation current.

Toroidal equilibrium of current‐carrying plasmas

A general method was developed to determine a toroidal equilibrium of plasmas, once a cylindrically symmetric linear solution is known. Arbitrary current distribution can be treated. The application to an equilibrium calculation to toroidal E layer is also given. This azimuthally symmetric toroidal E layer has an advantage of stable configuration with poloidal magnetic field comparable to the toroidal magnetic field offering the possibility of high β toroidal plasma containment.

Observation of Collisionless Electron Heating by Ion Cyclotron Waves

Electron heating is observed on application of the ion cyclotron wave in the C stellarator. The observed heating rate is an increasing function of the electron heating, suggesting that the heating is not due to the simple collisional process. The observed heating rate is consistent with the theoretical heating rate due to Landau damping of the wave by the resonant electrons. The generation of a dc electric current was observed when the wave was allowed to propagate in one direction, suggesting that the momentum of the wave is transmitted to electrons by Landau damping. The quasi‐linear treatment of the current generation is compared with the observed current generation.

On Equilibrium of a Current‐Carrying Toroidal Plasma. II. Experiments with the Model C Stellarator

A series of experiments with the Model C stellarator showed that a previously detected asymmetry in the device could be removed by applying such a magnetic field BT, transverse to the main confining magnetic field, that an inherent lack of closure of the flux lines of the confining field was removed. The symmetrized stellarator was then used to demonstrate that an equilibrium (discussed theoretically elsewhere) could be achieved in the plasma by applying a uniform magnetic field transverse to the plane of the stellarator. With current IOH flowing toroidally in the plasma, the tendency for the toroid to expand, due to the hoop force and the U‐bend drift, is counterbalanced by the IOH × BT force. The observed transverse field required for equilibrium is in good agreement with the value predicted theoretically. Improvement at equilibrium of such plasma parameters as electron temperature, particle confinement time, and energy replacement time is demonstrated.

Equilibrium of a Current‐Carrying Toroidal Plasma

A current‐carrying plasma confined in a smooth toroidal magnetic field tends to expand due to the nonuniformity of the field and the self‐interaction of the current. This expansion can be nullified, in the absence of externally imposed rotational transform, by means of a vertical magnetic field (perpendicular to the plane of the toroid). Macroscopically considered, such a vertical magnetic field interacts with the Ohmic heating current to supply an inward ponderomotive force. This paper derives the magnitude of the plasma expansion tendency and of the vertical field required to achieve steady state conditions. It is also demonstrated that if the plasma configuration is determined by an aperture limiter, helical fields are equivalent to an applied vertical field, insofar as the plasma equilibrium is concerned.

Stabilization of the collisionless trapped-particle instability by shaping of the tokamak cross section

Distortion of the cross sections of a tokamak has been suggested as a means of improving Ohmic heating and raising β. The effects of such distortion on the collisionless, electrostatic trapped‐particle mode have been investigated and it is found that under certain conditions a maximum‐J configuration can be approached. Results are presented for finite elliptic and triangular distortions, indicating significant stabilization.

Limitation on Ion Cyclotron Heating in the Local Mirrors of the C Stellarator

The experimental observation of the limiting phenomena of ion cyclotron resonance heating in the shallow magnetic beach is described and its explanation by the reflection of the wave is discussed. The temperature‐anisotropic plasma dispersion relation is solved with the aid of an electronic computer. The unexpected singular point which causes the reflection of waves is found in the unstable region of the ion cyclotron wave. The calculated limiting value of the ion temperature due to the wave reflection is given by β⊥c ≈ 4(T∥/T⊥)2, in reasonable agreement with the experiment.