Investigation of the compact torus plasma motion in the KTX-CTI device based on circuit analyses

Compact torus (CT) injection is one of the most promising methods for the central fuelling of next-generation reactor-grade fusion devices due to its high density, high velocity, and self-contained magnetised structure. A newly compact torus injector (CTI) device in Keda Torus eXperiment (KTX), named KTX-CTI, was successfully developed and tested at the University of Science and Technology in China. In this study, first, we briefly introduce the basic principles and structure of KTX-CTI, and then, present an accurate circuit model that relies on nonlinear regression analysis (NRA) for studying the current waveform of the formation region. The current waveform, displacement, and velocity of CT plasma in the acceleration region are calculated using this NRA-based one-dimensional point model. The agreement between the model results and the experimental results is better than in the previous general model results estimated by the device dimensions in previous. The next-step upgrading reference scheme of the KTX-CTI device is preliminarily investigated using this NRA-based point model. This research can provide insights for the development of experiments and future upgrades of the device.

Kähler–Einstein metrics on symmetric general arrangement varieties

We calculate Chow quotients of some families of symmetric T-varieties. In complexity two we obtain new examples of Kähler–Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine the homeomorphism class of the orbit space of the compact torus action.

Manifolds of Isospectral Matrices and Hessenberg Varieties

We consider the space $X_h$ of Hermitian matrices having staircase form and the given simple spectrum. There is a natural action of a compact torus on this space. Using generalized Toda flow, we show that $X_h$ is a smooth manifold and its smooth type is independent of the spectrum. Morse theory is then used to show the vanishing of odd degree cohomology, so that $X_h$ is an equivariantly formal manifold. The equivariant and ordinary cohomology rings of $X_h$ are described using GKM theory. The main goal of this paper is to show the connection between the manifolds $X_h$ and regular semisimple Hessenberg varieties well known in algebraic geometry. Both spaces $X_h$ and Hessenberg varieties form wonderful families of submanifolds in the complete flag variety. There is a certain symmetry between these families, which can be generalized to other submanifolds of the flag variety.

Fujiki class 𝒞 and holomorphic geometric structures

For compact complex manifolds with vanishing first Chern class that are compact torus principal bundles over Kähler manifolds, we prove that all holomorphic geometric structures on them, of affine type, are locally homogeneous. For a compact simply connected complex manifold in Fujiki class [Formula: see text], whose dimension is strictly larger than the algebraic dimension, we prove that it does not admit any holomorphic rigid geometric structure, and also it does not admit any holomorphic Cartan geometry of algebraic type. We prove that compact complex simply connected manifolds in Fujiki class [Formula: see text] and with vanishing first Chern class do not admit any holomorphic Cartan geometry of algebraic type.

Twisted Weyl Groups of Compact Lie Groups and Nonabelian Cohomology

Given a compact connected Lie group G with an S 1 -module structure and a maximal compact torus T of G S 1 , we define twisted Weyl group W ( G , S 1 , T ) of G associated to S 1 -module and show that two elements of T are δ -conjugate if and only if they are in one W ( G , S 1 , T ) -orbit. Based on this, we prove that the natural map W ( G , S 1 , T ) \ H 1 ( S 1 , T ) → H 1 ( S 1 , G ) is bijective, which reduces the calculation for the nonabelian cohomology H 1 ( S 1 , G ) .

Nuclear molecular outflow in the Seyfert galaxy NGC 3227

ALMA observations have revealed nuclear dusty molecular disks or tori with characteristic sizes 15−40 pc in the few Seyferts and low -luminosity AGN that have been studied so far. These structures are generally decoupled both morphologically and kinematically from the host galaxy disk. We present ALMA observations of the CO(2–1) and CO(3–2) molecular gas transitions and associated (sub-) millimeter continua of the nearby Seyfert 1.5 galaxy NGC 3227 with angular resolutions 0.085 − 0.21″ (7–15 pc). On large scales, the cold molecular gas shows circular motions as well as streaming motions on scales of a few hundred parsecs that are associated with a large-scale bar. We fit the nuclear ALMA 1.3 mm emission with an unresolved component and an extended component. The 850 μm emission shows at least two extended components, one along the major axis of the nuclear disk, and the other along the axis of the ionization cone. The molecular gas in the central region (1″ ∼ 73 pc) shows several CO clumps with complex kinematics that appears to be dominated by noncircular motions. While we cannot conclusively demonstrate the presence of a warped nuclear disk, we also detected noncircular motions along the kinematic minor axis. They reach line-of-sight velocities of v − vsys = 150 − 200 km s−1. Assuming that the radial motions are in the plane of the galaxy, we interpret them as a nuclear molecular outflow due to molecular gas in the host galaxy that is entrained by the AGN wind. We derive molecular outflow rates of 5 M⊙ yr−1 and 0.6 M⊙ yr−1 at projected distances of up to 30 pc to the northeast and southwest of the AGN, respectively. At the AGN location we estimate a mass in molecular gas of 5 × 105 M⊙ and an equivalent average column density N(H2) = 2 − 3 × 1023 cm−2 in the inner 15 pc. The nuclear CO(2–1) and CO(3–2) molecular gas and submillimeter continuum emission of NGC 3227 do not resemble the classical compact torus. Rather, these emissions extend for several tens of parsecs and appear connected with the circumnuclear ring in the host galaxy disk, as found in other local AGN.

Complex manifolds with maximal torus actions

In this paper, we introduce the notion of maximal actions of compact tori on smooth manifolds and study compact connected complex manifolds equipped with maximal actions of compact tori. We give a complete classification of such manifolds, in terms of combinatorial objects, which are triples {(\Delta,\mathfrak{h},G)} of nonsingular complete fan Δ in {\mathfrak{g}}, complex vector subspace {\mathfrak{h}} of {\mathfrak{g}^{\mathbb{C}}} and compact torus G satisfying certain conditions. We also give an equivalence of categories with suitable definitions of morphisms in these families, like toric geometry. We obtain several results as applications of our equivalence of categories; complex structures on moment-angle manifolds, classification of holomorphic nondegenerate {\mathbb{C}^{n}}-actions on compact connected complex manifolds of complex dimension n, and construction of concrete examples of non-Kähler manifolds.