Table of contents

Single Langmuir probes used in the JET Tokamak environment have shown spuriously high values of electron temperatures when the voltage scan is allowed to exceed the floating potential. This note presents a theoretical explanation for this anomaly in terms of a suppression of electron current in the strong magnetic field. The theory is supported by experimental evidence.

The scattering of a uniform plane electromagnetic wave form an inhomogeneous cylindrical plasma in the presence of an axial static magnetic field has been treated in the eikonal approximation. A simple expression is presented for the scattering function for ordinary wave scattering. This expression is expected to be a good approximation at small angles and for refractive indices close to unity ( omega ²<< omega _p²). In order to show the accuracy of the eikonal approximation numerical comparisons with the exact results have been presented for the simple model of homogeneous plasma. Implications of the eikonal results in the plasma diagnostics have been discussed.

The linear dissipationless two-fluid stability of currentless stellarators is investigated using a Lyapunov approach developed in earlier work. General three-dimensional toroidal equilibria are considered. A sufficient condition for stability is derived which depends only on the electron drift parameter (ratio of electron parallel drift velocity to ion sound velocity). In particular, it is shown that for typical currentless stellarator conditions for modes with frequencies much smaller than ion cyclotron and electron sound frequencies, stability prevails irrespective of beta .

The spectrum of global eigenmodes of the Alfven wave omega < omega _ci offers the possibility of a very simple method for diagnosing the centre of a Tokamak plasma. The frequencies of these modes depend on the central mass density and the current profile, and can be adequately estimated by MHD theory in cylindrical geometry including ion cyclotron effects. A simple unshielded bar antenna has been used to launch the waves at a power level of a few watts, detected by magnetic field probes in the boundary layer. Applications investigated on the TCA and PETULA Tokamaks include estimates of the core current density over a wide variety of discharges, measurements of changes of the effective mass during impurity puffing and the observation of profile changes during sawtooth activity. A method for the measurement of the deuterium-tritium ratio in a Tokamak is proposed.

Electrostatic perturbations are considered in a model where a plasma is situated in a homogeneous magnetic field and is subject to an equivalent gravitation force representing the magnetic inhomogeneity effects. The perturbations are strongly affected by large Larmor radius (LLR) effects when their wavelength becomes comparable to the ion Larmor radius. In the case of a dilute plasma, two time-dependent constants of he motion are found from which a solution can be deduced for the perturbations. The LLR effects are show to 'chop up' the time development of the macroscopic density and electric field perturbations into a pulse-shaped periodic patterns. The latter is repeated at every half of a gyro period and becomes strongly damped between a set of arising narrow peaks. The LR effects have been demonstrated in a simple special case, but similar results are likely to be obtained in more complicated situations, such as in denser plasmas where the electric field from the space charges affects particle dynamics. Consequently, the fine structure of a number of plasma perturbation is expected to become strongly distorted by LLR effects, and this becomes important to plasma stability.

A broad family of Tokamak current profiles is found to be stable against ideal and resistive MHD king modes for 1<or=q(0), with q(a) as low as 2. For 0.5<or=q(0)<1 and q(a)>1, current profiles can be found that are unstable only to the m=1, n=1 mode. A specific 'optimal' Tokamak profile can be selected from the range of stable solutions, by imposing a common upper limit on dj/dr-corresponding in ohmic equilibrium to a limitation of dT₃/dr by anomalous transport.

The linear Fokker-Planck equation for external charged particles slowing down in a fully ionized D-T plasma has been solved in one-dimensional plane geometry by the technique of Legendre polynomial and Fourier series expansion. The vacuum boundary condition at the plasma surface has been treated by appending to it a fictitious medium in which angular dispersion is absent. For alpha particles slowing down in a fully ionized D-T plasma the effect of the angular dispersion term on the energy deposition profiles has been estimated quantitatively and found to be small. It is found that it may be masked by errors introduced by the discretisation procedures employed in the numerical solutions of the Fokker-Planck equation.

The reflection of an ordinary wave from its cut-off at the electron plasma frequency can be exploited to measure the density profile of laboratory plasmas. Because of the large shear characteristic of reversed field pinches, however, coupling between the ordinary and the extraordinary modes in the plasma can be important. Mode mixing is investigated by solving the full wave equation for nearly equatorial waves, with a finite element code using cubic Hermite interpolating functions. The results show that indeed a nonnegligible amount of power can be transferred from the launched O-mode to the unwanted X-mode of (vice-versa). Although stronger in small devices with large shear, the effect can also be substantial when the shear length is much greater than the wavelength, if the optical path is sufficiently long. The mixing coefficient is found to be an oscillating function of frequency, due to the excitation of standing waves between the plasma edge and the cut-offs. Nevertheless, it is argued that the implementation of reflectometry should still be possible in sufficiently large RFP plasmas.

The author develops a general formulation for the free energy of a hot Fermionic plasma confined in an arbitrary smooth potential barrier and a weak magnetic field. The well-known Wigner-Kirkwood expansion turns out to be powerful computational technique in the investigation. The explicit formulae obtained enable one to calculate exchange and confining effects on various physical properties of such systems. As an example, they are applied to calculations of exchange and confining corrections to the diamagnetic susceptibility and the specific heat. The author also constructs some examples by simple choices of the confining potential barrier.

It is demonstrated that the non-linear bubble growth in Rayleigh-Taylor (RT) unstable laser targets is quasi-static and obeys a gt² law. Smoothing mechanisms acting on the spikes, such as tip broadening or tip ablation, will not stabilise the RT growth once bubble growth is established, hence shell lifetime is determined by bubble growth in the target. The authors also show that mass perturbations of initial amplitude A and wavelength lambda satisfies A/_lambda >0.04 will grow according to a gt² law almost immediately, with no observable linear growth phase. Results are presented from 2D computer simulations of spherical laser targets which support the conclusions.

Resonant absorption of p-polarized light shone on a plane-layered plasma with a step profile, is discussed as a function of wavelength (or critical density n_c) of the light; for simplicity the incidence angle is assumed small. If n_c lies within or above the step, the absorption A is given by Ginzburg's result (1970) modified by strong reflections at the foot and top of the step. The absorption above is total for particular values of n_c and theta . For n_c crossing the top of the density step the absorption is not monotonical; it exhibits a minimum that vanishes for zero radius of curvature sigma there (A approximately mod ln sigma mod ²), and zero collision frequency nu (A approximately mod 1n nu mod ^-2). The results are applied to the profile produced by irradiating a solid target with a high-intensity pulse that steepens the plasma by radiation pressure.

The strong nonlocal effect seen about cyclotron harmonics in a previous numerical study accounting for magnetic inhomogeneity along B₀ is described analytically and interpreted in terms of an echo-like mechanism. Though this effect is found to cause a redistribution of power deposition in the resonance zone, agreement is found with earlier work insofar as the total power deposition is unaltered.

The Langmuir soliton stability is considered by the method of catastrophe theory.