RESUMEN
The scaling of turbulence-driven heat transport with system size in magnetically confined plasmas is reexamined using first-principles based numerical simulations. Two very different numerical methods are applied to this problem, in order to resolve a long-standing quantitative disagreement, which may have arisen due to inconsistencies in the geometrical approximation. System size effects are further explored by modifying the width of the strong gradient region at fixed system size. The finite width of the strong gradient region in gyroradius units, rather than the finite overall system size, is found to induce the diffusivity reduction seen in global gyrokinetic simulations.
RESUMEN
The theoretical study of plasma turbulence is of central importance to fusion research. Experimental evidence indicates that the confinement time results mainly from the turbulent transport of energy, the magnitude of which depends on the turbulent state resulting from nonlinear saturation mechanisms, in particular, the self-generation of coherent macroscopic structures and large scale flows. Plasma geometry has a strong impact on the structure and magnitude of these flows and also modifies the mode linear growth rates. Nonlinear global gyrokinetic simulations in realistic tokamak magnetohydrodynamic equilibria show how plasma shape can control the turbulent transport. Results are best described in terms of an effective temperature gradient. With increasing plasma elongation, the nonlinear critical effective gradient is not modified while the stiffness of transport is decreasing.
RESUMEN
A Suydam-unstable circular cylinder of plasma with periodic boundary conditions in the axial direction is studied within the approximation of linearized ideal magnetohydrodynamics (MHD). The normal mode equations are completely separable, so both the toroidal Fourier harmonic index n and the poloidal index m are good quantum numbers. The full spectrum of eigenvalues in the range 1< or = m < or = m(max) is analyzed quantitatively, using asymptotics for large m, numerics for all m, and graphics for qualitative understanding. The density of eigenvalues scales like m(2)(max) as m(max) -->infinity . Because finite-m corrections scale as 1/ m(2)(max) , their inclusion is essential in order to obtain the correct statistics for the distribution of eigenvalues. Near the largest growth rate, only a single radial eigenmode contributes to the spectrum, so the eigenvalues there depend only on m and n as in a two-dimensional system. However, unlike the generic separable two-dimensional system, the statistics of the ideal-MHD spectrum departs somewhat from the Poisson distribution, even for arbitrarily large m(max) . This departure from Poissonian statistics may be understood qualitatively from the nature of the distribution of rational numbers in the rotational transform profile.