Bifurcation effects on the plasma edge of tokamaks with ergodic limiter.

In the present paper, we solve a twist symplectic map for the action of an ergodic magnetic limiter in a large aspect-ratio tokamak. In this model, we study the bifurcation scenarios that occur in the remnants regular islands that co-exist with chaotic magnetic surfaces. The onset of atypical local bifurcations created by secondary shearless tori are identified through numerical profiles of internal rotation number and we observe that their rupture can reduce the usual magnetic field line escape at the tokamak plasma edge.

Divertor map with freedom of geometry and safety factor profile

An explicit, area-preserving and integrable magnetic field line map for a single-null divertor tokamak is obtained using a trajectory integration method to represent equilibrium magnetic surfaces. The magnetic surfaces obtained from the map are capable of fitting different geometries with freely specified position of the X-point, by varying free model parameters. The safety factor profile of the map is independent of the geometric parameters and can also be chosen arbitrarily. The divertor integrable map is composed of a nonintegrable map that simulates the effect of external symmetry-breaking resonances, so as to generate a chaotic region near the separatrix passing through the X-point. The composed field line map is used to analyze escape patterns (the connection length distribution and magnetic footprints on the divertor plate) for two equilibrium configurations with different magnetic shear profiles at the plasma edge.

Harmonic deformation of Delaunay triangulations

We construct harmonic functions on random graphs given by Delaunay triangulations of ergodic point processes as the limit of the zero-temperature harness process. (C) 2012 Elsevier B.V All rights reserved.

Nontwist symplectic maps in tokamaks

We review symplectic nontwist maps that we have introduced to describe Lagrangian transport properties in magnetically confined plasmas in tokamaks. These nontwist maps are suitable to describe the formation and destruction of transport barriers in the shearless region (i.e., near the curve where the twist condition does not hold). The maps can be used to investigate two kinds of problems in plasmas with non-monotonic field profiles: the first is the chaotic magnetic field line transport in plasmas with external resonant perturbations. The second problem is the chaotic particle drift motion caused by electrostatic drift waves. The presented analytical maps, derived from plasma models with equilibrium field profiles and control parameters that are commonly measured in plasma discharges, can be used to investigate long-term transport properties. (C) 2011 Elsevier B.V. All rights reserved.

An analysis of Taguchi's on-line quality monitoring procedure for variables based on the results of a sequence of inspections

In this paper, a procedure for the on-line process control of variables is proposed. This procedure consists of inspecting the m-th item from every m produced items and deciding, at each inspection, whether the process is out-of-control. Two sets of limits, warning (µ0 ± W) and control (µ0 ± C), are used. If the value of the monitored statistic falls beyond the control limits or if a sequence of h observations falls between the warning limits and the control limits, the production is stopped for adjustment; otherwise, production goes on. The properties of an ergodic Markov chain are used to obtain an expression for the average cost per item. The parameters (the sampling interval m, the widths of the warning, the control limits W and C(W < C), and the sequence length (h) are optimized by minimizing the cost function. A numerical example illustrates the proposed procedure.