Turbulent transport in mixed states of convective cells and sheared flows

W. Horton, G. Hu, and G. Laval


Low-order mode coupling equations are used to describe recent computer simulations of resistive-g turbulent convection that show bifurcations for the onset of steady and pulsating sheared mass flows. The three convective transport states are identified with the tokamak confinement regimes called low mode (L-mode), high mode (H-mode), and edge-localized modes (ELMs). The first bifurcation (L -> H) and the second bifurcation (H -> ELMs) conditions are derived analytically and compared with direct solutions of the 6-ode mode coupling equations. First an exact expression is given for the energy transfer rate from the fluctuations to the sheared mass flow through the triplet velocity correlation function. Then the time scale expansion required to derive the Markovian closure formula is given. Markovian closure formulas form the basis for the thermodynamic-like L-H models used in several recently proposed models.


Stabilization of the Resistive Wall Mode Using a Fake Rotating Shell

Richard Fitzpatrick and Torkil H. Jensen


Tokamak plasma performance can, in theory, be greatly improved if the so called "resistive wall mode" is stabilized. This can be achieved by spinning the plasma rapidly, but such a scheme is not reactor relevant. A more promising approach is to apply external feedback in order to make a resistive shell placed around the plasma act like a perfect conductor. A scheme is outlined by which a network of feedback controlled conductors surrounding the plasma can be made to act like a rotating shell. This fake rotating shell combined with a satisfactory conventional shell (e.g. the vacuum vessel) can completely stablize the resistive wall mode. The gain, bandwidth, current, and power requirements of the feedback amplifiers are extremely modest. A previously proposed stabilization scheme (the intelligent shell) is also investigated, and is compared with the fake rotating shell concept. The main disadvantage of the former scheme is that it requires high gain.


Ion transport analysis of a high beta-poloidal JT-60U discharge

W. Horton, T. Tajima, J.Q. Dong, Y. Kishimoto, and J. Y. Kim


The high beta-poloidal discharge number 17110 in JT-60U that develops an internal transport barrier is analyzed for the transport of ion energy and momentum. First the classical ion temperature gradient stability properties are calculated in the absence of sheared plasma flows to establish the L-mode trasport level prior to the emergence of the transport barrier. Then the evolving toroidal and poloidal velocity profiles reported by Koide et al [Phys. Rev. Lett. 72, 3662 (1994)] are used to show how the sheared flows control the stability and transport. Coupled momentum-energy transport equations predict the creation of a transport barrier.


Stabilization of External Kink Modes in Magnetic Fusion Experiments Using a Thin Conducting Shell

Richard Fitzpatrick


In nearly all magnetic fusion devices the plasma is surrounded by a conducting shell of some description. In most cases this is the vacuum vessel. What effect does a conducting shell have on the stability of external kink modes? Is there any major difference between the effect of a perfectly conducting shell and a shell of finite conductivity? What happens if the shell is incomplete? These, and other, questions are explored in detail in this lecture using simple resistive magnetohydrodynamical (resistive MHD) arguments. Although the lecture concentrates on one particular type of magnetic fusion device, namely, the tokamak, the analysis is fairly general and could also be used to examine the effect of conducting shells on other types of device (e.g. Reversed Field Pinches, Stellerators, etc.).


Driven Reconnection in Magnetic Fusion Experiments

Richard Fitzpatrick


Error fields (i.e. small non-axisymmetric perturbations of the magnetic field due to coil misalignments, etc.) are a fact of life in magnetic fusion experiments. What effects do error fields have on plasma confinement? How can any detrimental effects be alleviated? These, and other, questions are explored in detail in this lecutre using simple resistive magnetohydrodynamical (resistive MHD) arguments. Although the lecture concentrates on one particular type of magnetic fusion device, namely, the tokamak, the analysis is fairly general and could also be used to examine the effects of error fields on other types of device (e.g. Reversed Field Pinches, Stellerators, etc.).


Nonlinear Response of Driven Systems in Weak Turbulence Theory

H. L. Berk, B. N. Breizman, J. Fitzpatrick, M. S. Pekker, H. V. Wong, and K. L. Wong


A method is presented for predicting the saturation levels and particle transport in weakly unstable systems where there are a discrete number of modes. Conditions are established for either steady sate or pulsating responses when several modes are excited for cases where there is and there is not resonance overlap. The conditions for achieving different levels of saturation are discussed. Depending on details, the saturation level can be quite low, where only a small fraction of the available free energy is released to waves, or the saturation level can be quite high, with almost a complete conversion of free energy to wave energy coupled with rapid transport.


Studies of Impurity Mode and ITG Mode in Toroidal Plasmas

J. Q. Dong and W. Horton


The impurity mode and hi mode driven by impurity ions with outwardly peaked density profiles, just as it is at the boundary of tokamak plasmas, and the ion temperature gradient, respectively, are studied in high temperature toroidal plasmas. The gyrokinetic theory is applied and finite Larmor radius effects of both hydrogenic and impurity ions are included. It is found that the impurity mode is enhanced by the ion temperature gradient. In addition, the impurity ions with outwardly peaked density profiles are demonstrated to have destabilizing effects on the hi mode. These two modes are strongly coupled to each other so that it is impossible to distinguish between them when both the driving mechanisms are stong enough to drive the corresponding mode unstable independently. The correlation of the results with nonlinear simulations and the experimental observations are discussed.


Revisit to Self-Organization of Solitons for Dissipative Korteweg-de Vries Equation

Y. Kondoh and J. W. Van Dam


The process by which self-orgainzation occurs for solitons described by the Korteweg-de Vries (KdV) equation with a viscous dissipation term is reinvestigated theoretically, with the use of numerical simulations in a periodic system. It is shown that, during nonlinear interactions, two basic processes for the self-organization of solitons are energy transfer and selective dissipation among the eigenmodes of the dissipative operator. It is also clarified that an important process during nonlinear self-organization is an interchange between the dominant operators, which has hitherto been overlooked in conventional self-organization theories and whilch leads to a final self-similar coherent structure determined uniquely by the dissipative operator.


Ion Temperature Gradient Driven Transport

W. Horton


The steep ion temperature gradients produced in the large tokamaks are analyzed in terms of the anomalous transport of ion energy and momentum. The transport equations take into account that for low viscosities and high effective Rayleigh numbers both neutral fluids and plasma show the spontaneous generation of sheared mass flows. The self-generated flows are driven by the ion temperature gradient through the turbulence and are one method for creating the transport barrier. In addition, the external control parameter from the direct injection of perpendicular ion (angular) momentum gives a second method for creating three confinement regimes of L-mode, H-mode, and a super-suppressed transport (SST) confinement regime.