Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy


MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark

TWO LECTURES

by Luis Garcia Gonzalo
Departamento de Fisica
Universidad Carlos III
Madrid, Spain

Wednesday May 5, 1999, 13.00 h
and Thursday May 6, 1999 at 10.00

at Meeting Room of the Physics Department Fys-108
Risø National Laboratory;

Lecture 1: TURBULENCE IN TOROIDAL DEVICES

Abstract: Fusion plasmas are far from thermodynamic equilibrium. Many forms of random, non-growing oscillations are observed experimentally in a plasma. The interest in these random fluctuations is that they may drastically modify the transport properties of the plasma. On the other hand, according to plasma theory, almost all plasmas are unstable to the growth of a variety of waves. The main sources of free energy that are available for driving instabilities are of two types: Gradients of density and temperature or velocity space anisotropy. Linearly, these instabilities give rise to exponentially growing modes. The nonlinear interaction of these modes brings about a turbulent saturated state. The main theoretical task is to identify for each case the saturation mechanism and to calculate the steady-state fluctuation levels in order to compare with the experimental results. The importance of different mode types (interchange, ballooning, ITGs, etc.) will be discussed. Also, the theory for a particular type of instability will be developped.

Lecture 2: ROTATION AND ENHANCED CONFINEMENT IN TOKAMAKS

Abstract: One of the common features that are seen in all devices which achieve enhanced confinement is the formation of a transport barrier in the plasma. The results obtained in many magnetic configurations show that the formation of transport barriers is closely related to increased shear in ExB velocity. During the last years, several theoretical models have been developed to explain the transition to enhanced confinement regimes. The models are based on the generation of averaged flows. Linearly, a shear flow in a plasma confined by a sheared magnetic field has generally a strong stabilizing effect. Nonlinearly, the effective turbulence decorrelation time is reduced, leading to a reduction in fluctuation levels and induced transport. For ExB shear decorrelation of turbulence, the shearing rate must be comparable to the nonlinear decorrelation rate in the absence of ExB shear. There are several possible sources for the generation of the ExB velocity shear. One of these is the plasma turbulence. The turbulent fluctuations modify the mean flow and pressure profiles that simultaneously control the level of fluctuations. Therefore, self-consistent calculations of plasma turbulence in the presence of flows are needed. The more complete models describe the simultaneous evolution of the fluctuation spectrum and the ExB velocity shear.