Table of contents

Filamentation instability, which develops mainly due to plasma acceleration in dynamic pinches, is studied using the ideal MHD model in the linear approximation. For the cases of implosion of a Z pinch, expansion of an inverse Z pinch, implosion of a theta pinch and magnetic flux compression by an annular plasma liner, exact solutions describing the growth of the azimuthal perturbations in a cold plasma are found. For a theta pinch geometry the Rayleigh-Taylor mode of filamentation instability is shown to be the dominating mode, its effective growth rate for large wavenumbers being given by the known expression (gk)¹2/. For an annular Z pinch or liner the effective growth rate of the dominating mode differs from this expression by a factor smaller than unity. The concept of an effective growth rate is found to be inapplicable to the development of filamentation instabilities in the course of implosion of a solid Z pinch: in this case perturbations do not propagate with the plasma particles, they converge to the axis faster than the pinch itself.

Ion acoustic waves on the forward branch of the dispersion relation (also known as electrostatic ion cyclotron waves, ESICW, particularly when the frequency is close to an ion gyrofrequency) have been studied at angles from 40 degrees to 90 degrees , with a constant magnetic field in a relatively homogeneous plasma. Waves on the ion Bernstein backward wave branch were not detected. The wave vectors and damping coefficients have been deduced from interferograms and compared with theory, showing good agreement.

The surface wave evolution in a waveguide with a plasma column upon changing the external longitudinal magnetic field from 0 to infinity is investigated. It is shown that a family of anisotropic plasma modes EH_l1^ap exists when the magnetic field has intermediate values. When Omega < omega _p (where Omega is the cyclotron frequency and omega _p the plasma frequency), the EH_l1^ap modes have a surface wave field distribution. When Omega > omega _p, they exist only for some system parameters and their field distribution has a quasi-surface character and when k_z to infinity (where k_z is the longitudinal wave number), the fields have a volume wave distribution.

The resonant layer equations governing tearing and micro-tearing modes in toroidal geometry are formulated and solved for a plasma in the banana regime and for wavelengths in the intermediate collisionality range nu _e< omega _*e< nu _e/ epsilon . It is shown that stability of such tearing modes is determined by a competition between destabilizing trapped electron dissipation and stabilizing effects arising from ion magnetization and collisional broadening of the passing-electron Landau resonance. Analytic stability criteria are derived, but for realistic parameters these modes are predicted to be stable.

The new entropy concept for the collective magnetic equilibria developed in preceding papers is applied to the description of the states of a Tokamak subjected to Ohmic and auxiliary heating. The condition of existence of steady-state plasmas with vanishing entropy production implies, on the one hand, the resilience of specific current density profiles and, on the other, severe restrictions on the scaling of the confinement time with power and current in the presence of Ohmic relaxation. These restrictions are consistent with the Goldston scaling and with the existence of a heat pinch.