In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; there exist stable Hamiltonian structures that are not homotopic to a positive contact structure; stable Hamiltonian structures are generically Morse-Bott (i.e. all closed orbits are Bott nondegenerate) but not Morse; the standard contact structure on S 3 is homotopic to a stable Hamiltonian structure which cannot be embedded in R 4 . Moreover, we derive a structure theorem in dimension three and classify stable Hamiltonian structures supported by an open book. We also discuss implications for the foundations of symplectic field theory.

In the l = 3/m = 9 Uragan-3M (U-3M) torsatron (R 0 = 1 m, ā ≈ 0.12 m, B φ = 0.72 T, ι( ā)/2π ≈ 0.4), an open helical divertor is realized. A hydrogen plasma with ne ≈ 2 × 10 18 m −3 , T e ≈ 0.3 keV, T i ≈ 0.1 keV is produced and heated by RF fields (ω ≈ ω ci ). The flows of diverted plasma are detected by 78 plane Langmuir probes aligned poloidally in the spacings between the helical coils in two geometrically symmetric poloidal cross-sections of the torus. In measurements of the distributions of ambipolar (e.g. the ion saturation current I s ) and non-ambipolar (e.g. the current to a grounded probe I p ) plasma flows, a strong vertical asymmetry of these distributions is observed, its main characteristics being a many-fold difference in the values of I s in the outgoing flows in the upper and lower parts of the torus and the opposite signs of I p in these flows, with the positive current corresponding to the larger ambipolar flow of the diverted plasma. Reversal of the direction of the toroidal magnetic field results in the reversal of the asymmetry, with the larger flux (and I p > 0) always flowing in the ion B × ∇B drift direction. On this basis, it is concluded that the asymmetry is related to direct (non-diffusive) losses of charged particles from the confinement volume. This conclusion is validated by numerical modelling of thermal and fast particle orbits in U-3M, where qualitative agreement has been revealed between the calculated distribution of the angular co-ordinates of lost particles and the measured poloidal distributions of the flows of diverted plasma.

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The magnetic field configuration of the Uragan-3M l=3 torsatron, which has a p=4 multipole vertical magnetic field compensation system, was studied using two methods to map the contours of the magnetic flux surfaces. The first method, the so-called triode method with a constant voltage electron source, measures the current emitted by an open thermoelectron emitter and the portion drawn by a highly transparent grid located in a poloidal cross-section of the torus. The second method involves the use of a conducting luminescent rod which scans the torus cross-section and lights up when struck by electrons emitted by an electron gun. The information on the magnetic surface structure obtained by these two techniques is compared. The characteristics of the two methods are discussed, giving special attention to the triode method because it allows an objective criterion for the quality of the magnetic surface structure to be introduced. It is shown how advantageous both methods are for rapid adjustment and optimization of the magnetic configurations in a stellarator when perturbations are present and what improvements could be achieved on Uragan-3M. Also discussed are experiments on generating electron clouds in Uragan-3M during the ramp-up phase of the magnetic field pulse

This note concerns stationary solutions of the Euler equations for an ideal fluid on a closed 3-manifold. We prove that if the velocity field of such a solution has no zeroes and real analytic Bernoulli function, then it can be rescaled to the Reeb vector field of a stable Hamiltonian structure. In particular, such a vector field has a periodic orbit unless the 3-manifold is a torus bundle over the circle. We provide a counterexample showing that the correspondence breaks down without the real analyticity hypothesis.Comment: 28 pages, no figures, counterexample adde