J. Juul Rasmussen

Blow-up in Nonlinear Schroedinger Equations-I A General Review

The general properties of a class of nonlinear Schroedinger equations: iut + p:∇∇u + f(|u|2)u = 0 are reviewed. Conditions for existence, uniqueness, and stability of solitary wave solutions are presented, along with conditions for blow-up and global existence for the Cauchy problem.

Computations of Intermittent Transport in Scrape-Off Layer Plasmas

Two-dimensional fluid simulations of interchange turbulence for geometry and parameters relevant for the scrape-off layer of magnetized plasmas are presented. The computations, which have distinct plasma production and loss regions, reveal bursty ejection of particles and heat from the bulk plasma in the form of blobs. These structures propagate far into the scrape-off layer where they are dissipated due to transport along open magnetic field lines. From single-point recordings it is shown that the blobs have asymmetric conditional wave forms and lead to positively skewed and flattened probability distribution functions. The radial propagation velocity may reach one-tenth of the sound speed. These results are in excellent agreement with recent experimental measurements.

Attraction of nonlocal dark optical solitons

We study the formation and interaction of spatial dark optical solitons in materials with a nonlocal nonlinear response. We show that unlike in local materials, where dark solitons typically repel, the nonlocal nonlinearity leads to a long-range attraction and formation of stable bound states of dark solitons.

Interchange turbulence in the TCV scrape-off layer

Probe measurements of electrostatic plasma fluctuations in the scrape-off layer (SOL) of the TCV tokamak are compared with the results from two-dimensional interchange turbulence simulations. Excellent agreement is found for both the radial variation of statistical moments and temporal correlations, clearly indicating that turbulent transport in the tokamak SOL is due to radial advection of blob-like filamentary structures. This offers an explanation both for the basic mechanism driving the anomalous SOL particle transport and the now commonly observed broad particle density profiles, extending deep into the SOL and thought to be the cause of high levels of main chamber plasma-wall interactions.

Turbulence and intermittent transport at the boundary of magnetized plasmas

Numerical fluid simulations of interchange turbulence for geometry and parameters relevant to the boundary region of magnetically confined plasmas are shown to result in intermittent transport qualitatively similar to recent experimental measurements. The two-dimensional simulation domain features a forcing region with spatially localized sources of particles and heat outside which losses due to the motion along open magnetic-field lines dominate, corresponding to the edge region and the scrape-off layer, respectively. Turbulent states reveal intermittent eruptions of hot plasma from the edge region, propagating radially far into the scrape-off layer in the form of field-aligned filaments, or blobs. This results in positively skewed and flattened single-point probability distribution functions of particle density and temperature, reflecting the frequent appearance of large fluctuations. The conditional fluctuation wave forms and transport statistics are also in a good agreement with those derived from the experiments. Associated with the turbulence bursts are relaxation oscillations in the particle and heat confinements as well as in the kinetic energy of the sheared poloidal flows. The formation of blob structures is thus related to profile variations, which are here triggered in a quasiperiodic manner by a global dynamical regulation due to the self-sustained sheared flows.

Observations of Solitary Structures in a Magnetized, Plasma Loaded Waveguide

Two types of solitary structure were investigated experimentally and numerically in a magnetized, plasma-loaded waveguide. One was identified as an ordinary KdV soliton and its properties were investigated with particular attention to the damping by resonant particles. The other type of pulse was identified as a purely kinetic phenomenon being associated with a vortex in phase space.

Mechanism and scaling for convection of isolated structures in nonuniformly magnetized plasmas

Large-scale radial advection of isolated structures in nonuniformly magnetized plasmas is investigated. The underlying mechanism considered is due to the nonlinear evolution of interchange motions, without any presumption of plasma sheaths. Theoretical arguments supported by numerical simulations reveal an inertial scaling for the radial velocity of isolated structures in the ideal limit. This velocity increases as the square root of the structure size relative to the length scale of the magnetic field. The magnitude of the radial advection velocity, as well as the dynamical evolution of the structures, compares favorably with recent experimental measurements of radially propagating blob structures in the scrape-off layer of magnetically confined plasmas.

Self-guiding light in layered nonlinear media

We study the propagation of intense optical beams in layered Kerr media. With appropriate shapes, beams with a power close to the self-focusing threshold are shown to propagate over long distances as quasi-stationary waveguides in cubic media supporting a periodic nonlinear refractive index.

Fluctuations and transport in the TCV scrape-off layer

Fluctuations and particle transport in the scrape-off layer of TCV plasmas have been investigated by probe measurements and direct comparison with two-dimensional interchange turbulence simulations at the outer midplane. The experiments demonstrate that with increasing line-averaged core plasma density, the radial particle density profile scale length becomes broader. The particle and radial flux density statistics in the far scrape-off layer exhibit a high degree of statistical similarity with respect to changes in the line-averaged density. The plasma flux onto the main chamber wall at the outer midplane scales linearly with the local particle density, suggesting that the particle flux here can be parameterized in terms of an effective convection velocity. Experimental probe measurements also provide evidence for significant parallel flows in the scrape-off layer caused by ballooning in the transport of particles and heat into the scrape-off layer. The magnitude of this flow estimated from pressure fluctuation statistics is found to compare favourably with the measured flow offset derived by averaging data obtained from flow profiles observed in matched forward and reversed field discharges. An interchange turbulence simulation has been performed for a single, relatively high density case, where comparison between code and experiment has been possible. Good agreement is found for almost all aspects of the experimental measurements, indicating that plasma fluctuations and transport in TCV scrape-off layer plasmas are dominated by radial motion of filamentary structures.

Blob/hole formation and zonal-flow generation in the edge plasma of the JET tokamak

The first experimental evidence showing the connection between blob/hole formation and zonal-flow generation was obtained in the edge plasma of the JET tokamak. Holes as well as blobs are observed to be born in the edge shear layer, where zonal-flows shear off meso-scale coherent structures, leading to disconnection of positive and negative pressure perturbations. The newly formed blobs transport azimuthal momentum up the gradient of the azimuthal flow and drive the zonal-flow shear while moving outwards. During this process energy is transferred from the meso-scale coherent structures to the zonal flows via the turbulent Reynolds stress, resulting in nonlinear saturation of edge turbulence and suppression of meso-scale fluctuations. These findings carry significant implications for the mechanism of structure formation in magnetically confined plasma turbulence.