New universal estimates for free boundary problems arising in plasma physics

On a Free Boundary Problem Arising in Plasma Physics

INTRODUCTION THE PROBLEM we study in this paper has its origin in plasma physics. It stems from a model describing the equilibrium of a plasma confined in a toroidal cavity (a “Tokamak machine”). For a detailed presentation of this model the reader is referred to [l, 21 and also to the appendix in [3]. Let 51 denote the meridian cross section of the cavity and Oz the axis of toroidal symmetry, ...

Solution of strongly nonlinear oscillator problem arising in Plasma Physics with Newton Harmonic Balance Method

In this paper, Newton Harmonic Balance Method (NHBM) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. Periodic solution is analytically verified and consequently the relation between the Natural Frequency and the amplitude is obtained in an ana...

A Multilevel Jacobi--Davidson Method for Polynomial PDE Eigenvalue Problems Arising in Plasma Physics

The simulation of drift instabilities in the plasma edge leads to cubic polynomial PDE eigenvalue problems with parameter dependent coefficients. The aim is to determine the wave number which leads to the maximum growth rate of the amplitude of the wave. This requires the solution of a large number of PDE eigenvalue problems. Since we are only interested in a smooth eigenfunction corresponding ...

Asymptotic Stability of Boundary Layers to the Euler-Poisson Equations Arising in Plasma Physics

Numerical Solution of a Class of Boundary Value Problems Arising in the Physics of Josephson Junctions

In this paper we propose a method of numerical solution of non-linear boundary value problems for systems of ODEs given on the embedded intervals. The algorithm is based on the continuous analog of Newton method coupled with spline-collocation scheme of fourth order of accuracy. Demonstrative examples of similar problems take place in physics of stacked Jo-sephson junctions with different layer...