Stationary excitation of plasma oscillations by an external a!ternating electric field in a collisionless onedimensional plasma layer (plasma condenser) is examined. For this the linearized onedimensional VLASOV equation is integrated along the one-electron characteristics, assuming the electrons are reflected specularly a t the boundaries. In the case of a homogeneous plasma the resulting FREDHOLM integral equation for the electric field is solved exactly. Tho resulb agree with SHORE'S, received on the basis of distributional analysis it la VAN KAMPEN and CASE. In view of T O N K S -D A~E Rresonances the resonance properties of the homogeneous plasma condenser are discussed. Contrary to the hydrodynamics1 theory here we receive only a finite number of resomnces, increasing with the ratio r of layer diameter to DEBYE length.The ratio of series limit to main resonance position is nearly constant for r not too small. This agrees with DATTNER'S qualitative statements about TONICS-DATTNER resonances found experimentally. However, the kinetical effect of series limit and another one of a second serio of resonances a t lower frequencies are masked by strong LANDAU damping in this region of dispersion.The method of characteristics used here has the advantage of easily being generalized for the case of an inhomogeneous plasma condenser. For this case an integral equation €or the electric field is derived in full analogy to the procedure employed for the homogeneous plasma. Finally the kernel of this equation is specialized for a parabolic static potential.

Onedimensional fluid theory of Tonks-Dattner resonances in inhomogeneous, bounded plasmas is extended to stronger exciting electric fields. The relation of parametric instabilities and harmonic generation with To&-Dattner reaonances will be worked out in a more direct way than in previous work. Electric field thresholds and growth rates for parametric instabilities will be obtained from theory of homogeneous Mathieu equation. Stationary excitation a t the driving frequency and its harmonics follows from a particular solution of an inhomogeneoiis Mathieu equation.

A common explanation is given for ion transport and strong broadband density fluctuations in tokamaks as a result of large anomalous electron transport near dominant magnetic surfaces (resp. in small magnetic islands). The main mechanism is local density flattening connected with an anomalous electron transport induced instationary radial electric field, which forces the ions via polarization drift to follow the electrons. For the density flattening process an exact solution of the time-dependent diffusion equation for a linear initial profile over the island width is used. From this we also derive a n expression for a temporal growing radial electric field. This positive field reaches its maximum at the density plateau. Strong viscous diffusion or instability-indnced transport, between high and low electric field regions may now reverse the density flattening. Therefore relaxation oscillations result which may also explain the observed strong density and potential fluctuations in tokamaks. Several details of recent measurements of impurity ion behaviour and density fluctuations in tokamaks may be better explained with the theory given here.

It is shown a t first that the ponderomotive laser force appreciably may enhance the values of the dielectric function E(Z) near the critical plasma density. If in some spatial region near c: = 0 a large anomalous collision frequency i R assumed, sharply rising a t some point, pump field depletion may also lead to strong changes in the density scale length. As a first approach we have ciilculated the laser reflectivity in the case when the anomalous collision frequency a i d the density scale length jump a t some point near the critical one. We obtain temporal oscillations of the reflectivity if due t o thermal plasma expansion the density scale length increases with time. The mlculated frequency and amplitude of the reflectivity oscillations are shown to be in good agreement with measured values in the case of Nd-laser heating of solid targets.