Scale size of magnetic turbulence in tokamaks probed with 30-MeV electrons

Measurements of synchrotron radiation emitted by 30-MeV runaway electrons in the TEXTOR-94 tokamak show that the runaway population decays after switching on neutral beam injection (NBI). The decay starts only with a significant delay, which decreases with increasing NBI heating power. This delay provides direct evidence of the energy dependence of runaway confinement, which is expected if magnetic modes govern the loss of runaways. Application of the theory by Mynick and Strachan [Phys. Fluids 24, 695 (1981)] yields estimates for the "mode width" (delta) of magnetic perturbations: delta<0.5 cm in Ohmic discharges, increasing to delta = 4.4 cm for 0. 6 MW NBI.     

Symmetry and phaselocking in chains of weakly coupled oscillators

Weakly coupled chains of oscillators with nearest-neighbor interactions are analyzed for phaselocked solutions. It is shown that the symmetry properties of the coupling affect the qualitative form of the phaselocked solutions and the scaling behavior of the system as the number of oscillators grows without bound. It is also shown that qualitative behavior of these solutions depends on whether the coupling is “diffusive” or “I synaptic”. terms defined in the paper. The methods include the demonstration that the equations for phaselocked solutions can be approximated by a singularly perturbed two-point (continuum) boundary value problem that is easier to analyze; the issue of convergence of the phaselocked solutions to solutions of the continuum equation is closely related to questions involving numerical entropy in computation schemes for a conservation law. An application to the neurophysiology of motor behavior is discussed briefly.     

Target pattern and spiral solutions to reaction-diffusion equations with more than one space dimension

We prove the existence of homogeneous target pattern and spiral solutions to equations of the form

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; the spatial dimension is greater than one. As in the one-dimensional case, such solutions exist for discrete values of the asymptotic wave number (or equivalently, the frequency of oscillation of the entire solution). For target patterns, we construct solutions for a sequence of frequencies. For spirals, we construct only the “lowest mode” solution.     

A complete analysis of a model nonlinear singular perturbation problem having a continuous locus of singular points

Consider the boundary value problem ?y′′ = (y² ? t²)y′, ? 1 ≤ t ≤ 0, y(? 1) = A, y(0) = B. Depending on the choice of A and B, one can ensure the existence of “turning points,” $\text{t}\text{?}\text{; y(t, ?)}{}^2\text{?}\text{t}\text{?}{}^2\text{= 0}$. However, due to the nonlinear nature of the problem, one does not know the position or number of such turning points. In the case when A >f 0 = B Kedem, Parter and Steuerwalt gave a development of this problem based on an abstract bifurcation analysis which in turn was based on “degree theory.” In this paper we give a complete analysis of the problem based entirely on a priori estimates and the “shooting” method.     

Target Patterns and Horseshoes from a Perturbed Central-Force Problem: Some Temporally Periodic Solutions to Reaction-Diffusion Equations

Existence and construction of some time-periodic solutions of a class of reaction-diffusion equations is described. These give examples of center-structures from which emanate trains of waves with outward directed group velocity, in an infinite one-dimensional spatial domain. A discrete set of distinct types of center-structures is found. Similar results are found for sufficiently large finite regions with impermeable boundaries. The existence of many other time periodic solutions corresponding to spatially infinite irregular arrays of center-structures of different types is also demonstrated for these systems. Some numerical examples are presented.