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The reversed field pinch (RFP) configuration at an aspect ratio of 8.8 is studied numerically by means of the three-dimensional magnetohydrodynamic code DEBS [D. D. Schnack et al., J. Comput. Phys. 70, 330 (1987)]. This aspect ratio is equal to that of the Extrap T1 experiment [S. Mazur et al., Nucl. Fusion 34, 427 (1994)]. A numerical study of a RFP with this level of aspect ratio requires extensive computer achievements and has hitherto not been performed. The results are compared with previous studies [Y. L. Ho et al., Phys. Plasmas 2, 3407 (1995)] of lower aspect ratio RFP configurations. In particular, an evaluation of the extrapolation to the aspect ratio of 8.8 made in this previous study shows that the extrapolation of the spectral spread, as well as most of the other findings, are confirmed. An important exception, however, is the magnetic diffusion coefficient, which is found to decrease with aspect ratio. Furthermore, an aspect ratio dependence of the magnetic energy and of the helicity of the ...

A phenomenological derivation of a one‐dimensional model of crossfield plasma diffusion in toroidal multipole geometry is presented. Experimental studies have shown previously that this one‐dimensional model describes the observed density profile shape and decay in the Wisconsin levitated octupole in certain regimes. Simplified mathematical studies of the model (which did not give adequate attention to geometrical effects) have also shown that a stable profile should evolve from an arbitrary initial particle distribution. Here, a numerical treatment and a discussion of the effects of multipole geometry are given. Comparison is made with experimental results. Finally, analytical studies give additional evidence that the observed rapid evolution toward a stable profile should be expected theoretically. It is concluded that the phenomenological model is generally useful for determining diffusion coefficient magnitude and scaling with density once the density profiles have been determined experimentally.

Measurements of cross‐field diffusion were made in the levitated octupole using two independent methods. First, the magnitude and scaling of D⊥ with density, n, and field strength, B, were determined by direct measurements of the particle flux onto an internal ring surface. Second, the shape of the density profile and the time decay of the density at the separatrix were compared with solutions of a diffusion equation model. Both methods indicated that D⊥ was proportional to n−1/2 and independent of B. The plasma was created by gun injection into the purely poloidal magnetic field and the initial parameters were ne∼5 ×109 cm−3, Ti∼20 eV, Te∼5 eV. The observed diffusion scaling can be understood within the framework of vortex diffusion in a high‐dielectric constant plasma if the spectrum of waves is enhanced in energy over thermal levels with an effective temperature, T*, of 104 eV.

Two unstable modes were observed in the average minimum‐B region of the levitated octupole operating with a weak toroidal field (safety factor of approximately 0.25) and collisionless ions. One mode propagated in the electron diamagnetic drift direction and the other mode propagated in the ion diamagnetic drift direction. The frequencies of the modes were much greater than the ion detrapping collision frequency and slightly less than the trapped ion bounce frequency. The electron collisionality was intermediate between the collisionless trapped ion mode and the dissipative trapped ion mode regimes. Density fluctuation levels from 5% to 50% and enhanced transport approaching Bohm diffusion were the manifest effects of the instabilities. When the ion collisionality was increased by cooling the ion temperature, the unstable fluctuations were not seen.