Two-Dimensional Mathematical Models of Strict Plasma Equilibrium in Galatea Magnetic Traps and Numerical Analysis of Stability

The article continues the series of works on the numerical analysis of the stability of equilibrium plasma configurations confined by a magnetic field in Galatea traps, using as a specific example a toroidal Galatea–Belt straightened into a cylinder. The numerical analysis of the time behavior of small perturbations in a linear approximation was carried out in a refined equilibrium model: the boundary value problem with the Grad–Shafranov equation in a not simply connected region of a cylinder takes into account the real geometry of the current-carrying conductors immersed in it. Calculations of the time behavior of two-dimensional perturbations and their detailed analysis drew attention to the specificity of the previously observed rather large velocity values. They are concentrated only at the outer boundary of the configurations, are caused by arbitrarily small density values, do not penetrate deep into the main plasma configuration, and do not grow with time. This type of instability does not belong to the traditional type of Lyapunov instability and is apparently less dangerous. Calculations of 3D perturbations of the Belt were carried out for their harmonics corrugated along the cylinder axis and showed instability in the Lyapunov sense for any values of the oscillation frequency. Quantitative patterns of instability depend on this frequency and are represented by the calculation results.