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.     

Interaction and “apparent” reconnection of 3D vortex tubes via direct numerical simulations

We present evidence of: “binding” of anti-parallel vortex tube segments; strong noncircular core development; evolution of new secondary finger-like vortex structures: and finally “apparent” vortex reconnections due to entanglement. The latter three processes are not present in Biot-Savart filament simulations.     

Shock-bubble interactions : Generation and evolution of vorticity in two-dimensional supersonic flows

We present high resolution simulations with the PPM code of shock-bubble interactions coresponding to the recent Haas-Sturtevant experiments. VCR cinemas show and diagnostic interpretations quantify the variety of shock-vortex interactions     

Measures of chaos and equipartition in integrable and nonintegrable lattices

We have simulated numerically the behavior of the one-dimensional, periodic FPU-alpha and Toda lattices to optical and acoustic initial excitations of small--but finite and large amplitudes. For the small-through-intermediate amplitudes (small initial energy per particle) we find nearly recurrent solutions, where the acoustic result is due to the appearance of solitons and where the optical result is due to the appearance of localized breather-like packets. For large amplitudes, we find complex-but-regular behavior for the Toda lattice and "stochastic" or chaotic behaviors for the alpha lattice. We have used the well-known diagnostics: Localization parameter; Lyapounov exponent, and slope of a linear fit to linear normal mode energy spectra. Space-time diagrams of local particle energy and a wave-related quantity, a discretized Riemann invariant are also shown. The discretized Riemann invariants of the alpha lattice reveal soliton and near-soliton properties for acoustic excitations. Except for the localization parameter, there is a clear separation in behaviors at long-time between integrable and nonintegrable systems.     

Computational synergetics and the exploration of nonlinear science

In 1960, S. Ulam demonstrated, in A Collection of Mathematical Problems, how computers would be used as heuristic tools to allow us to explore complex nonlinear dynamical motions and to discover unexpected linkages and new concepts. Recent developments in two-dimensional vortex dynamics illustrate the synergetic working mode.