Stability transitions for axisymmetric relative equilibria
نویسندگان
چکیده
In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of Hamiltonian systems with Euclidean symmetry, we investigate different mechanisms of stability: stability by energy–momentum confinement, KAM, and Nekhoroshev stability, and we explain the transitions between them. We apply our results to the Kirchhoff model for the motion of an axisymmetric underwater vehicle, and we numerically study dissipation induced instability of KAM stable relative equilibria for this system. Mathematics Subject Classification: 70E50, 70H14, 37J25, 53D20 (Some figures in this article are in colour only in the electronic version)
منابع مشابه
Stability Transitions for Axisymmetric Relative Equilibria of Euclidean Symmetric Hamiltonian Systems
In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of Hamiltonian systems with Euclidean symmetry, we investigate different mechanisms of stability: stability by energy-momentum confinement, KAM, and Nekhoroshev s...
متن کاملTokamak Plasma Equilibria and Axisymmetric Stability with a Zero Total Toroidal Current
Several tokamak experiments have reported the existence of plasma equilibria with a zero total toroidal current in their AC operations. By taking a plasma profile model based on linear functions of the poloidal flux function ψ , a variety of equilibrium configurations with a zero total toroidal current have been found. The MHD_N0 stability code [1] is able to compute axisymmetric mode stability...
متن کاملStability and Bifurcation of Equilibria for the Axisymmetric Averaged Mean Curvature Flow
We study the averaged mean curvature flow, also called the volume preserving mean curvature flow, in the particular setting of axisymmetric surfaces embedded in R3 satisfying periodic boundary conditions. We establish analytic well–posedness of the flow within the space of little-Hölder continuous surfaces, given rough initial data. We also establish dynamic properties of equilibria, including ...
متن کاملTokamaks with Reversed Current Density: Stability of Equilibria with Axisymmetric Islands
Tokamak regimes with nearly zero or negative toroidal current in the central region (current hole) feature good plasma confinement properties and may be naturally attained in the advanced tokamak (AT) regime. On the other hand, quasi-steady-state AC plasma current operation in tokamaks relies upon the existence of current reversal equilibria with zero net toroidal current. In both cases a syste...
متن کاملStability to Localized Modes for a Class of Axisymmetric Magnetohydrodynamic Equilibria
Mercier's criterion is computed numerically for an exact class of axisymmetric MHD equilibria having possibly elliptical cross sections and a flat current profile. The main result is that the toroidal current density and the plasma beta can be increased by one order of magnitude if a) the eccentricity of the magnetic surfaces, b) the poloidal current, and c) the aspect ratio are adequately chos...
متن کامل