Theory of the Spatio-Temporal Dynamics of Transport Bifurcations

The development and time evolution of a transport barrier in a magnetically confined plasma with non-monotonic, nonlinear dependence of the anomalous flux on mean gradients is analyzed. Upon consideration of both the spatial inhomogeneity and the gradient nonlinearity of the transport coefficient, we find that the transition develops as a bifurcation front with radially propagating discontinuity in local gradient. The spatial location of the transport barrier as a function of input flux is calculated. The analysis indicates that for powers slightly above threshold, the barrier location $x_b(t) \sim ( D_n t (P-P_c)/P_c)^{1/2},$ where $P_c$ is the local transition power threshold and $D_n$ is the neoclassical diffusivity . This result suggests a simple explanation of the high disruptivity observed in reversed shear plasmas. The basic conclusions of this theory are insensitive to the details of the local transport model.Comment: 21 page Tex file, 10 postscript file

Effects of ExB Velocity Shear and Magnetic Shear on Turbulence and Transport in Magnetic Confinement Devices

One of the scientific success stories of fusion research over the past decade is the development of the ExB shear stabilization model to explain the formation of transport barriers in magnetic confinement devices. This model was originally developed to explain the transport barrier formed at the plasma edge in tokamaks after the L (low) to H (high) transition. This concept has the universality needed to explain the edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines. More recently, this model has been applied to explain the further confinement improvement from H (high)-mode to VH (very high)-mode seen in some tokamaks, where the edge transport barrier becomes wider. Most recently, this paradigm has been applied to the core transport barriers formed in plasmas with negative or low magnetic shear in the plasma core. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to a higher energy state with reduced turbulence and transport when an additional source of free energy is applied to it. The transport decrease that is associated with ExB velocity shear effects also has significant practical consequences for fusion research. The fundamental physics involved in transport reduction is the effect of ExB shear on the growth, radial extent and phase correlation of turbulent eddies in the plasma. The same fundamental transport reduction process can be operational in various portions of the plasma because there are a number ways to change the radial electric field Er. An important theme in this area is the synergistic effect of ExB velocity shear and magnetic shear. Although the ExB velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of ExB velocity shear and facilitate turbulence stabilization

Characterization of density fluctuations during ELMs in the DIII-D tokamak

Bursts of turbulence associated with ELMs have been studied systematically in DIII-D with a multichannel phase contrast imaging (PCI) diagnostic, which is sensitive to the long poloidal wavelength components of the density fluctuations in the outer edge of the tokamak. A comparison of the temporal dynamics of the turbulence with the signature D-alpha signal from the divertor has revealed systematic differences between type I and type III ELMs: even though precursor fluctuations are sometimes seen before type I ELMs, the PCI signal level remains high until the peak in the D-alpha signal: by contrast, in type III ELMs the fluctuation burst precedes the D-alpha peak by 0.4-0.6 ms. Type I ELMs can generate 'echoes', i.e. secondary bursts. in the scrape-off layer, Coherent modes are observed during type III ELMs only. The radial and temporal correlation structures and the spectral properties of the turbulence during the transient ELM phase have been reconstructed by averaging over multiple ELMs. in order to improve the statistical accuracy. ELM turbulence is found to share many properties with L mode turbulence, including the main qualitative features of radial wavenumber and frequency spectra and radial dispersion relations. However, features unique to ELM turbulence are also identified

Decorrelation of edge plasma turbulence at the transition from low- to high-confinement mode in the DIII-D Tokamak

The modification of turbulence in the edge plasma of the DIII-D tokamak at the transition from the low to the high mode of confinement is investigated with a phase-contrast imaging diagnostic. The amplitude and radial correlation length of the turbulence in the confinement region decrease at the transition, whereas the decorrelation time increases. The transition model of Biglari, Diamond, and Teny [Phys. Fluids B 2 (1990) 1], based on turbulence decorrelation by E x B velocity shear, is quantitatively substantiated by measurements of the theoretical control parameter. Further quantitative predictions of the theory are tested for the first time. (C) 2000 Published by Elsevier Science B.V

Signature of turbulent zonal flows observed in the DIII-D tokamak

The spectrum of turbulent density fluctuations at long poloidal wavelengths in the edge plasma of the DIII-D tokamak peaks at nonzero radial wave number. The associated electric-potential fluctuations cause shearedẼ 3 B flows primarily in the poloidal direction. These zonal flows have been predicted by theory and are believed to regulate the overall level of turbulence and anomalous transport. This study provides the first indirect experimental identification of zonal flows

Partial-wave analysis of p⃗p⃗→ppπ∘\vec{p}\vec{p}\to pp\pi^\circ data

We present a partial-wave analysis of the polarization data for the reaction $\vec{p}\vec{p}\to pp\pi^\circ$, based solely on the recent measurements at IUCF for this channel. The fit leads to a $\chi^2$ per degree of freedom of 1.7. Methods for an improved analysis are discussed. We compare the extracted values to those from a meson exchange model.Comment: 14 pages, 11 figure

Axisymmetric equilibria of a gravitating plasma with incompressible flows

It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the pressure. This set of equations is amenable to analytic solutions. As an application, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov, Catto, and Hazeltine [Phys. Rev. Lett. {\bf 82}, 2689 (1999)] are extended to plasmas with finite poloidal currents, subject to gravitating forces from a massive body (a star or black hole) and inertial forces due to incompressible sheared flows. Explicit solutions are obtained in two regimes: (a) in the low-energy regime $\beta_0\approx \gamma_0\approx \delta_0 \approx\epsilon_0\ll 1$, where $\beta_0$, $\gamma_0$, $\delta_0$, and $\epsilon_0$ are related to the thermal, poloidal-current, flow and gravitating energies normalized to the poloidal-magnetic-field energy, respectively, and (b) in the high-energy regime $\beta_0\approx \gamma_0\approx \delta_0 \approx\epsilon_0\gg 1$. It turns out that in the high-energy regime all four forces, pressure-gradient, toroidal-magnetic-field, inertial, and gravitating contribute equally to the formation of magnetic surfaces very extended and localized about the symmetry plane such that the resulting equilibria resemble the accretion disks in astrophysics.Comment: 12 pages, latex, to be published in Geophys. Astrophys. Fluid Dynamic