A running sandpile is shown to undergo a dynamical transition as diffusion is increased from zero. The transition takes place after the local diffusion has become so large as to erase the local inhomogeneities, caused by the intermittent rain of sand, before they can trigger avalanche activity. The system then undergoes an abrupt change with the self-similar structure of the dynamics being replaced with quasiperiodic, near system-size transport events. These results may have significant implications for many of the driven physical systems for which self-organized criticality based dynamical models have been proposed.

Access to the MHD second stability regime has been achieved in the ATF torsatron. Experimental p values (j3 0 < 3%, with fast ions contributing « j of the pressure at high p) are well above the theoretical transition value (p c « 1.3% for ideal modes) required to reach this regime. The relatively low p c results from operation with peaked pressure profiles. The measured magnetic fluctuations decrease with increasing /?, and the pressure profile broadens. This behavior is consistent with theoretical predictions for p self-stabilization of resistive interchange modes. PACS numbers: 52.55.Hc, 52.30.Jb, 52.35.PyThe ideal magnetohydrodynamic (MHD) second stability regime has attracted increasing attention in toroidal confinement fusion research 1 ' 2 because it offers the hope of operation at high p=2fiop/B 2 (the ratio of the plasma kinetic pressure to the magnetic pressure) with favorable confinement, which would improve the prospects for a viable D-T fusion reactor. This theory predicts that the changes in the internal magnetic surfaces (plasma axis shift and shape) caused by an increase in plasma pressure act to stabilize instabilities driven by unfavorable field-line curvature. l As a result, the plasma can become more stable as p increases ("/? self-stabilization"), with an accompanying reduction in the anomalous transport induced by the curvature-driven instabilities. In this Letter we describe experiments in which operation in the second stability regime has been achieved at relatively low p in a torsatron (a type of stellarator).Because of their external control of magnetic configuration and the absence of plasma current, stellarators are well suited for exploring the second stability regime and studying p self-stabilization. In stellarators with significant shear (dx/dr > 0, where % is the rotational transform and r is the plasma minor radius) the dominant instabilities are interchange modes. 3,4 These modes can be stabilized by the magnetic well produced by the outward magnetic axis shift at finite p (Shafranov shift), and this p self-stabilization effect can open a stable path to the second stability regime. 5 ' 6 The ATF torsatron design was optimized to explore this possibili- ty. 7ATF is an / -2, twelve-field-period torsatron with major radius /?o™2.10 m, average minor radius a *=0.27 m, magnetic field on axis 5o<2T, central rotational transform £o«0.3, and edge transform ^f l «l. For the profile assumed in the ATF design studies 6 the p selfstabilization effect should dominate at /?o«5%. Electron-beam field mapping in early 1988 revealed substantial magnetic islands (6 cm wide at the x ™ T surface and smaller at other rational surfaces). 8 These islands, now corrected, acted as a magnetic limiter and effectively reduced the plasma radius to r p *=*0.6d (increasing the effective aspect ratio A from 8 to 10) and the effective edge transform Xa » 0.5. This led to a large increase in the Shafranov shift id/accp^A/xl) that enhanced the self-stabilization effect and afforded the results reported here, which ...

Visualization of turbulent flows is a powerful tool to help understand the turbulence dynamics and induced transport. However, it does not provide a quantitative description of the observed structures. In this paper, an approach to characterize quantitatively the topology of the flows is given. The technique, which can be applied to any type of turbulence dynamics, is illustrated through the example of resistive ballooning instabilities.