Tokamak and Ohmically heated stellarator plasmas have been compared in the CLEO apparatus, using gas current in the range 10-25 kA at a toroidal field of 12.7 kG. It is found that the vacuum poloidal field due to the helical winding has a considerable influence on the containment properties. In particular, for the same current the electron energy per unit length is a factor of 2 greater in the stellarator than in the tokamak.CLEO' is a seven-field period, l =3 toroidal stellaretor with a major radius, Ro of 90 cm and a minor radius, r&, of 13 cm as defined by two circular stainless-steel limiters, fixed inside the 28-cm bore stainless-steel vacuum vessel. The maximum available toroidal field B~is 20 kG, and the helical winding is designed to carry current I, up to 120 kA turns. 25Vo of the torus inner surface is covered by an active film of titanium before, and if necessary during, the day' s run. The base pressure is -10 ' Torr.A tokamak configuration can be set up in this apparatus by not energizing the helical winding, with equilibrium provided by a vertical field. A vertical field is also required for stellarator operation, the typical values at 20-kA externally induced ohmic heating current (I,) being 70 and 30 G for tokamak and stellarator, respectively. By using Ohmically heated hydrogen plasma with I, in the range 5-26 kA, a comparison has been made between stellarator and tokamak configurations, most extensively at 17 kA. For the &~of 12.7 kG and I, of 61 kA turns used in this comparison, the separatrix lies outside the limiter. The calculated value of rotational transform for the stellarator vacuum magnetic surface which touches the limiter is &=0.3. The same value of + at the plasma edge would be produced in the tokamak mode by an equivalent current I, of 21 kA.We have chosen to compare the tokamak with the Ohmically heated stellarator when the plasma edge is determined by the limiter rather than by the separatrix in order to ensure that limiter effects (e.g. , recycling) and wall effects are as similar as possible in the two configurations. The diagnostics used in these experiments were the following: (i) Current and loop voltage mea. -surements. (ii) Position coils. When the vertical field is optimized to produce the longest-lasting tokamak current, these show the current channel to be centered to + 1 cm. (iii) A single-channel 0 Z 10 (a) 10-0-10 'r" Fp'gl-0 (c) E 2 V o l.2 m E 1i 0 10 20 30 Time (ms) A 40 10 20 30 40 Time (ms) B FIG. l. Oscillograms of (a) loop volts, (b) gas current, (c) mean electron density for (A) tokamak and (B) stellarator at 12.7-kG toroidal field. 2-mm microwave interferometer for measurement of n, over a minor diameter. (iv) Photon scattering with a 10-J ruby laser for measurement of n, , T,(&).(v) A neutral particle analyzer, using charge exchange, for measurement of T& (vi) .A detector of the absolute intensity of H emission, to assess recycling and estimatẽ ", the average particle containment time. Figure 1 shows oscillograms of current, loop voltage, and n, for both to...

Assemblies of one-dimensional filaments appear in a wide range of physical systems: from biopolymer bundles, columnar liquid crystals, and superconductor vortex arrays; to familiar macroscopic materials, like ropes, cables, and textiles. Interactions between the constituent filaments in such systems are most sensitive to the distance of closest approach between the central curves which approximate their configuration, subjecting these distinct assemblies to common geometric constraints. In this paper, we consider two distinct notions of constant spacing in multi-filament packings in 3  : equidistance, where the distance of closest approach is constant along the length of filament pairs; and isometry, where the distances of closest approach between all neighboring filaments are constant and equal. We show that, although any smooth curve in 3  permits one dimensional families of collinear equidistant curves belonging to a ruled surface, there are only two families of tangent fields with mutually equidistant integral curves in 3  . The relative shapes and configurations of curves in these families are highly constrained: they must be either (isometric) developable domains, which can bend, but not twist; or (non-isometric) constant-pitch helical bundles, which can twist, but not bend. Thus, filament textures that are simultaneously bent and twisted, such as twisted toroids of condensed DNA plasmids or wire ropes, are doubly frustrated: twist frustrates constant neighbor spacing in the cross-section, while nonequidistance requires additional longitudinal variations of spacing along the filaments. To illustrate the consequences of the failure of equidistance, we compare spacing in three 'almost equidistant' ansatzes for twisted toroidal bundles and use our formulation of equidistance to construct upper bounds on the growth of longitudinal variations of spacing with bundle thickness.

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