Compact Torus Research Articles

Formation of a compact toroid for enhanced efficiency

We report here our results on the formation of a plasma configuration with the generic name of compact toroid (CT). A method of compact toroid formation to confine, heat and compress a plasma is investigated. Formation of a compact torus using an additional toroidal magnetic field helps to increase the plasma current to a maintainable level of the original magnetic field. We design the Compact Toroid Challenge (CTC) experiment in order to improve the magnetic flux trapping during field reversal in the formation of a compact toroid. The level of the magnetic field immersed in the plasma about 70% of the primary field is achieved. The CTC device and scheme of high level capturing of magnetic flux are presented.

GKM-sheaves and nonorientable surface group representations

Let T be a compact torus and X a nice compact T-space (say a manifold or variety). We introduce a functor assigning to X a GKM-sheaf F_X over a GKM-hypergraph G_X. Under the condition that X is equivariantly formal, the ring of global sections of F_X are identified with the equivariant cohomology, H_T^*(X; C). We show that GKM-sheaves provide a general framework able to incorporate numerous constructions in the GKM-theory literature. In the second half of the paper we apply these ideas to study the equivariant topology of the representation variety R_K := Hom(\pi_1(S), K) under conjugation by K, where S is a nonorientable surface and K is a compact connected Lie group. We prove that R_{SU(3)} is equivariantly formal for all S and compute its equivariant cohomology. . We also produce conjectural betti number formulas for some other Lie groups.

Sur le volume arithmétique sur les schémas torique lisses

Let X be a smooth projective toric scheme over Spec(Z). Let D¯ be an equivariant line bundle on X, endowed with a continuous Hermitian metric which is invariant by the action of the compact torus of X(C). We show that its arithmetic volume is given in terms of the Legendre–Fenchel transform associated to the metric. When D¯ is supposed admissible, we characterize when it is arithmetically ample, nef, or big in terms of combinatorial date.

Translation of an FRC Plasma into a Quasi-spherical Confinement Region

Translation of a Field-Reversed Configuration (FRC) into a quasi-spherical confinement region with super-alfvénic translation speed has been successfully conducted. Translation speed can be controlled in the range from 80 to 150km/s by changing statically filled gas pressure. The translated FRC experiences radial decompression process rapidly when it enters into the confinement chamber. The separatrix shape of translated FRC is controlled through the translation process. Especially, in the case of FRC translation into deuterium gas atmosphere, elongation of the FRC is roughly unity. It indicates possible application of center solenoid onto the high-beta compact torus of FRC. Also, as a new finding, a rotational instability with an n=2 deformation has been observed in the translated FRC.

A Particle-Fluid Hybrid Modeling of Neutral Gas Flow Generation from a CT Neutralization Fuel-Injector

The feasibility of compact torus (CT) neutralization fuel injection method is studied by a simulation model using particle and MHD hybrid techniques. The neutralization process is simulated by using rate-coefficients. The magnetic and electric fields are found to respond sluggishly to the neutralization process. Slow ions generated by charge-exchange have been added to the model, although the CT neutralization process is not significantly affected by this.

Quasimap Floer Cohomology for Varying Symplectic Quotients

AbstractWe show that quasimap Floer cohomology for varying symplectic quotients resolves several puzzles regarding displaceability of toric moment fibers. For example, we present a compact Hamiltonian torus action containing an open subset of non-displaceable orbits and a codimension four singular set, partly answering a question of McDuff, and we determine displaceability for most of the moment fibers of a symplectic ellipsoid.

A characterization of compact complex tori via automorphism groups

We show that a compact Kähler manifold \(X\) is a complex torus if both the continuous part and discrete part of some automorphism group \(G\) of \(X\) are infinite groups, unless \(X\) is bimeromorphic to a non-trivial \(G\)-equivariant fibration. Some applications to dynamics are given.

On Hermitian structure on [formula omitted

Let G be a connected complex Lie group, and let Γ be a cocompact discrete subgroup of G. If G/Γ admits an astheno-Kähler metric, then we show that G is abelian and G/Γ is a compact complex torus.

Effects of compact torus injection on toroidal flow in the STOR-M tokamak

In compact torus injection (CTI) experiments on the STOR-M tokamak, an ion Doppler spectrometer is installed to observe the effects of CTI on toroidal plasma flows. The intrinsic toroidal flow in ohmic discharges without CTI is sheared with counter plasma current flow in the core region and co-current direction at the periphery. With tangential CTI along the co-current direction, the flow velocity in the core region decreases by more than 5 km s−1, while in the periphery the flow velocity increases by 3–4 km s−1. These data indicate that the observed flow change is due to the injection of toroidal momentum. Density increase and high soft x-ray emission after CTI are observed during the changes in the toroidal flow.

Ramified Satake isomorphisms for strongly parabolic characters

For certain characters of the compact maximal torus of a reductive p -adic group, which we call strongly parabolic characters, we prove Satake-type isomorphisms. Our results generalize those of Satake, Howe, Bushnell and Kutzko, and Roche.

RANK ONE CONNECTIONS ON ABELIAN VARIETIES, II

Given a holomorphic line bundle L on a compact complex torus A, there are two naturally associated holomorphic ΩA-torsors over A: one is constructed from the Atiyah exact sequence for L, and the other is constructed using the line bundle [Formula: see text], where α is the addition map on A × A, and p1 is the projection of A × A to the first factor. In [I. Biswas, J. Hurtvbise and A. K. Raina, Rank one connections on abelian varieties, Internat. J. Math.22 (2011) 1529–1543], it was shown that these two torsors are isomorphic. The aim here is to produce a canonical isomorphism between them through an explicit construction.

Development of a low-energy and high-current pulsed neutral beam injector with a washer-gun plasma source for high-beta plasma experiments

We have developed a novel and economical neutral-beam injection system by employing a washer-gun plasma source. It provides a low-cost and maintenance-free ion beam, thus eliminating the need for the filaments and water-cooling systems employed conventionally. In our primary experiments, the washer gun produced a source plasma with an electron temperature of approximately 5 eV and an electron density of 5 × 10(17) m(-3), i.e., conditions suitable for ion-beam extraction. The dependence of the extracted beam current on the acceleration voltage is consistent with space-charge current limitation, because the observed current density is almost proportional to the 3/2 power of the acceleration voltage below approximately 8 kV. By optimizing plasma formation, we successfully achieved beam extraction of up to 40 A at 15 kV and a pulse length in excess of 0.25 ms. Its low-voltage and high-current pulsed-beam properties enable us to apply this high-power neutral beam injection into a high-beta compact torus plasma characterized by a low magnetic field.

Polyhedral surfaces and determinant of Laplacian

An explicit formula for the determinant of the Laplacian on a compact polyhedral surface of genus g > 1 g>1 is found. This formula generalizes previously known results for flat surfaces with trivial holonomy and compact polyhedral tori.

Modeling of neutral beam injection into a compact spherical torus by a Monte Carlo deposition and a Fokker–Planck code

The numerical codes NFREYA and FIFPC have been applied to optimize the neutral beam injection (NBI) parameters for a high-β, highly elongated, compact spherical tokamak plasma.The Monte Carlo code NFREYA uses the 2D-flux surface and the 3D beam line geometry, such as the focal lengths, duct length, and beamlet divergences, beam tangency radius and the position of the ion source to calculate the beam deposition profile H(ρ) in an arbitrarily shaped axisymmetric plasma. The deposition profile H(ρ), depending on the radial coordinate ρ, for an arbitrarily shaped axisymmetric plasma is computed by a Monte Carlo method. H(ρ) is proportional to the source terms in the Fokker–Planck equation to be solved at selected flux surfaces.The deposition profile is used in the FIFPC code to compute the fast ion distribution function and thus the neutron yield. FIFPC accounts for the slowing down of the fast deposited particles due to the drag of the ions and electrons, the energy diffusion and pitch angle scattering.Results concerning the beam geometry and the neutron generation by the injection of (D,T) ions into (D,T) background plasmas of different compositions are presented.

Box splines and the equivariant index theorem

AbstractIn this article, we begin by recalling the inversion formula for the convolution with the box spline. The equivariant cohomology and the equivariant $K$-theory with respect to a compact torus $G$ of various spaces associated to a linear action of $G$ in a vector space $M$ can both be described using some vector spaces of distributions, on the dual of the group $G$ or on the dual of its Lie algebra $\mathfrak{g}$. The morphism from $K$-theory to cohomology is analyzed, and multiplication by the Todd class is shown to correspond to the operator (deconvolution) inverting the semi-discrete convolution with a box spline. Finally, the multiplicities of the index of a $G$-transversally elliptic operator on $M$ are determined using the infinitesimal index of the symbol.

A remark on the orbit structure of the complexification of a semisimple symmetric space

We consider the action of a real semisimple Lie group G on the complexification GC/HC of a semisimple symmetric space G/H and we present a refinement of Matsukiʼs results (Matsuki, 1997 [1]) in this case. We exhibit a finite set of points in GC/HC, sitting on closed G-orbits of locally minimal dimension, whose slice representation determines the G-orbit structure of GC/HC. Every such point p¯ lies on a compact torus and occurs at specific values of the restricted roots of the symmetric pair (g,h). The slice representation at p¯ is equivalent to the isotropy representation of a real reductive symmetric space, namely ZG(p4)/Gp¯. In principle, this gives the possibility to explicitly parametrize all G-orbits in GC/HC.

Computation of Neutral Gas Flow Generation From a CT Neutralization Fuel-Injector

The feasibility of compact torus (CT) neutralization fuel injection method is studied by a simulation model using particle and MHD hybrid techniques. The neutralization process is simulated by using rate-coefficients. The magnetic and electric fields are found to respond sluggishly to the neutralization process. Slow ions generated by charge-exchange have been added to the model, although the CT neutralization process was not significantly affected by this. Finally, the minimum length for the CT neutralizer is proposed as 2 m from the simulation run time 10µs at a CT injection speed of 200 km/s. c

Completely integrable torus actions on complex manifolds with fixed points

We show that if a holomorphic n-dimensional compact torus action on a compact connected complex manifold of complex dimension n has a fixed point then the manifold is equivariantly biholomorphic to a smooth toric variety.

T-duality and homological mirror symmetry for toric varieties

Let X Σ be a complete toric variety. The coherent-constructible correspondence κ of Fang et al. (2011) [14] equates P erf T ( X Σ ) with a subcategory Sh c c ( M R ; Λ Σ ) of constructible sheaves on a vector space M R . The microlocalization equivalence μ of Nadler and Zaslow (2009) [27] and Nadler (2009) [25] relates these sheaves to a subcategory Fuk ( T ⁎ M R ; Λ Σ ) of the Fukaya category of the cotangent T ⁎ M R . When X Σ is nonsingular, taking the derived category yields an equivariant version of homological mirror symmetry, DCoh T ( X Σ ) ≅ DFuk ( T ⁎ M R ; Λ Σ ) , which is an equivalence of triangulated tensor categories. The nonequivariant coherent-constructible correspondence κ ¯ of Treumann (preprint) [33] embeds P erf ( X Σ ) into a subcategory S h c ( T R ∨ ; Λ ¯ Σ ) of constructible sheaves on a compact torus T R ∨ . When X Σ is nonsingular, the composition of κ ¯ and microlocalization yields a version of homological mirror symmetry, DCoh ( X Σ ) ↪ DFuk ( T ⁎ T R ; Λ ¯ Σ ) , which is a full embedding of triangulated tensor categories. When X Σ is nonsingular and projective, the composition τ = μ ∘ κ is compatible with T-duality, in the following sense. An equivariant ample line bundle L has a hermitian metric invariant under the real torus, whose connection defines a family of flat line bundles over the real torus orbits. This data produces a T-dual Lagrangian brane L on the universal cover T ⁎ M R of the dual real torus fibration. We prove L ≅ τ ( L ) in Fuk ( T ⁎ M R ; Λ Σ ) . Thus, equivariant homological mirror symmetry is determined by T-duality.

Asymptotics of Szegö kernels under Hamiltonian torus actions

Let X be the circle bundle associated to a positive line bundle on a complex projective (or, more generally, compact symplectic) manifold. The Tian-Zelditch expansion on X may be seen as a local manifestation of the decomposition of the (generalized) Hardy space H(X) into isotypes for the S 1-action. More generally, given a compatible action of a compact Lie group, and under general assumptions guaranteeing finite dimensionality of isotypes, we may look for asymptotic expansions locally reflecting the equivariant decomposition of H(X) over the irreducible representations of the group. We focus here on the case of compact tori.