ON THE STATISTICAL-MECHANICS OF SELF-ORGANIZED PROFILES

The radial structure of tokamak profiles determined by anomalous trans port is elucidated by studying the statistical mechanics of a sand pil e automaton for which the toppling conditions depend on local gradient , alone. In this representation, the sand pile dynamics is Markovian, and spatial profiles may be obtained from calculated expectation value s of the local gradient. The Markovian structure of the dynamics is ex ploited to analytically derive a local gradient probability distributi on function from a generalized kinetic equation. for homogeneous, weak noise, the calculated expectation value of the gradient is well below the marginally stable state. In the over-driven limit (i.e., strong h omogeneous noise), a region of super-critical gradient is shown to for m near the bottom of the pile. For the case of localized noise, the me an self-organized profile is always sub-critical. These results are co nsistent with numerical studies of simple automata. Their relevance to and implications for tokamak confinement are discussed. (C) 1996 Amer ican Institute of Physics.