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[en] A simple one-field L-H transition model is studied in detail, analytically and numerically. The dynamical system consists of three equations coupling the drift wave turbulence level, zonal flow speed, and the pressure gradient. The fourth component, i.e., the mean shear velocity, is slaved to the pressure gradient. Bursting behavior, characteristic for predator-prey models of the drift wave - zonal flow interaction, is recovered near the transition to the quiescent H-mode (QH) and occurs as strongly nonlinear relaxation oscillations. The latter, in turn, arise as a result of Hopf bifurcation (limit cycle) of an intermediate fixed point (between the L- and H-modes). The system is shown to remain at the QH-mode fixed point even after the heating rate is decreased below the bifurcation point (i.e., hysteresis, subcritical bifurcation), but the basin of attraction of the QH-mode shrinks rapidly with decreasing power. This suggests that the hysteresis in the H-L transition may be less than that expected from S-curve models. Nevertheless, it is demonstrated that by shaping the heating rate temporal profile, one can reduce the average power required for the transition to the QH-mode.
[en] Transport barriers and L-H transitions in Tokamak plasmas are often attributed to suppression of turbulence by a shear flow related to a plasma gradient, eg. of density. However, such shear flow is also affected by the second derivative of density. When this is introduced there is no unique relation between flux and gradient - it depends on the source distribution within the plasma and on conditions at the plasma edge (eg. imposed by the scrape-off layer). This edge gradient must lie within prescribed limits if a stationary plasma profile (which may include an improved confinement zone) is to exist. (author)
[en] We discuss the effect of shearing on transport and the formation of transport barriers. The focus is primarily on laboratory plasmas where the formation of transport barrier (the L-H transition or the formation of internal transport barrier) is thought to originate from turbulence regulation by shearing by (coherent) mean E x B flows and (random) zonal flows. We provide quantitative discussion on the reduction of turbulent transport by these flows and elucidate their roles in the barrier formation
[en] The basic in–out divertor asymmetry with respect to ion B × ∇B direction has been examined in EAST by changing the divertor configuration from upper single null (USN) to lower single null (LSN) during the same discharge without reversing BT. It is remarkable that the in–out asymmetry is reversed when moving from USN to LSN. However, modeling with SOLPS, taking into account classical drifts, shows little difference. The divertor magnetic configuration also affects the access to H-modes, favoring DN or near-DN divertor configurations on EAST. ELMs further enhance the in–out divertor asymmetry, leading to greater particle and heat deposition on the outer target with a broader footprint, presumably arising from enhanced ELM transport in the outboard region
[en] Turbulence, and turbulence-driven transport are ubiquitous in magnetically confined plasmas, where there is an intimate relationship between turbulence, transport, instability driving mechanisms (such as gradients), plasma flows, and flow shear. Though many of the detailed physics of the interrelationship between turbulence, transport, drive mechanisms, and flow remain unclear, there have been many demonstrations that transport and/or turbulence can be suppressed or reduced via manipulations of plasma flow profiles. This is well known in magnetic fusion plasmas [e.g., high confinement mode (H-mode) and internal transport barriers (ITB's)], and has also been demonstrated in laboratory plasmas. However, it may be that the levels of particle transport obtained in such cases [e.g. H-mode, ITB's] are actually lower than is desirable for a practical fusion device. Ideally, one would be able to actively feedback control the turbulent transport, via manipulation of the flow profiles. The purpose of this research was to investigate the feasibility of using both advanced model-based control algorithms, as well as non-model-based algorithms, to control cross-field turbulence-driven particle transport through appropriate manipulation of radial plasma flow profiles. The University of New Mexico was responsible for the experimental portion of the project, while our collaborators at the University of Montana provided plasma transport modeling, and collaborators at Lehigh University developed and explored control methods.
[en] The thickness of the transport barrier at the plasma edge is discussed, by analyzing the structure of the interface region between the turbulent L-mode region and the region where the transport is strongly-stabilized by the electric field. The effect of this localized radial electric field is prescribed. The spatial profile of turbulence intensity is analyzed by using a simplified model, in which the suppression and transport of turbulence intensity are introduced. The scaling property of the transport barrier is discussed. (paper)
[en] Full text: The L-H transition is a more-or-less sudden change in the state of a con ed plasma with increasing power input, having the desirable, but counter-intuitive, quality that confinement is dramatically improved. We are interested in understanding why this transition to good confinement properties occurs and how to control it. In this work we present a singularity and stability analysis of an economical model for L-H transition dynamics and clarify the relationship between the qualitative structure of the model and the physics of the process. By economical, or minimal, model we mean the smallest, functionally simplest, and mathematically consistent model that captures qualitatively the dynamical traits that are typically observed over many experiments in different machines. The strength and power of a minimal model is just this universality; its apparent disregard for numbers and unit dimensions is sometimes perceived as a weakness. In keeping with this ideology we compose a consensus dynamical model that incorporates coupled rates and feedback processes as indicated in the following schematic. A constant power input creates a pressure gradient, which feeds the turbulent density fluctuations, which in turn feed energy into the poloidal shear flow via the Reynolds stress. The shear flow has an external source, and is damped through viscosity. Nonlinear behaviour arises through the bipartite, pressure-gradient dependent form of the viscosity function. A high pressure gradient has the effect of reducing or blocking the shear flow damping. Under these circumstances shear flow energy can 'accumulate', but having no other avenue for egress it feeds back into suppressing the turbulence. It can readily be appreciated how such processes can balance out | or rather, un-balance out - so as to give rise to the oscillatory and hysteretic dynamics that are characteristic of L-H transitions. Copyright (2002) Australian National University- Research School of Physical Sciences and Engineering
[en] After a general discussion of the experimental characteristics of the L-H transition and consideration of basic theoretical principles underlying models for it, this paper reviews the various theories of the L-H transition available in the literature, providing some background information on each theory and expressing the transition criteria in forms suitable for comparison with experiment. Some conclusions on the relevance of these models for explaining the experimental data on the transition are drawn. (author)
[en] It is well known that there is an up-down difference in temperature in tokamaks. In the collisional case this difference for ions is on the order of 1/(ωBi τ)>>1 for a circular cross section tokamak, where ωBi and τi are the ion cyclotron frequency and collision time, respectively. Here we show that the presence of an X-point amplifies this effect and can lead to effects of order of unity, depending on the ion drift direction. This in turn leads to a strong increase of the pressure gradient in the vicinity of the X-point (if the drift of the ions is in the X-point direction). In the framework of the Alfven-drift paradigm for the L-H transition, it provides an explanation for the difference in the power threshold for the L-H transition arising from the ion drift direction. (author)
[en] Full text: We report on recent progress on several closely related theoretical problems with a common focus on the multi-scale dynamics of drift wave turbulence. These topics are: (a) low q resonances and the fate of turbulence energy in an inverse cascade, (b) turbulence propagation and transport barrier dynamics. Topic (a) deals with narrow, m not equal zero secondary flows, which are generated by turbulence and resemble zonal flows. These vortex modes can produce local flat spots and corrugations on profiles, and sink energy from the inverse cascade. Topic (b) deals with the theory of turbulence spreading. In particular, we validate simple turbulence propagation models via a rigorous theory, which yields a flux-gradient relation for turbulence intensity. We also show which classes of wave interactions facilitate spreading and that zonal flows do not. We also solve exactly for the phase co-existence region in a simple two-field model of the L to H transition. We show that profile curvature must be retained in order to obtain a regularizable solution, and that hysteresis is weaker than conventionally assumed. (author)