Theory for toroidal momentum pinch and flow reversal in tokamaks

It is demonstrated that besides the well-known toroidal momentum diffusion flux there is a pinchlike flux in the fluctuation-induced toroidal stress. A toroidal flow profile is determined up to a constant, e.g., the value of the flow at the magnetic axis, by balancing these two fluxes. The remaining residual toroidal stress determines the value of the flow at the axis. It is illustrated that the direction of the flow at the axis can change after plasma confinement is improved. The theory is applied to explain the toroidal flow reversal in tokamak experiments.     

Magnetic field in a finite toroidal domain

The magnetic field structure in a domain surrounded by a closed toroidal magnetic surface is analyzed. It is shown that ergodization of magnetic field lines is possible even in a regular field configuration (with nonvanishing toroidal component). A unified approach is used to describe magnetic fields with nested toroidal (possibly asymmetric) flux surfaces, magnetic islands, and ergodic field lines.     

基于环磁美特材料的无线传能系统

传统的四线圈磁共振耦合无线传能系统已在移动电子设备、电动汽车无线充电中得以应用,然而,其传能效率仍然因其磁场空间分布的发散性而难以提高.为了克服上述缺点,我们提出了一种基于环磁美特材料、磁场更为局域的高效无线传能系统.该系统将四线圈系统中的一对磁谐振耦合线圈替换为具有环磁谐振特性的四个非对称开口谐振环.该环磁模式具有高Q值、低金属损耗以及辐射抑制的特性.实验结果表明,相对于四线圈系统,该系统的磁场更为集中,能量传输效率更高.     

Momentum-transfer scattering cross section and the Aharonov-Bohm effect on a toroidal solenoid

The quantum-mechanical Aharonov-Bohm effect in the diffraction of charged particles by a toroidal solenoid containing a magnetic field is investigated. The total and differential elastic scattering cross sections depend on the magnetic flux inside the solenoid, even in the presence of a “black” ring-shaped screen which prevents charged particles from entering the region where the magnetic field is localized. Relations describing the momentum-transfer cross section for the elastic scattering of charged particles by a toroidal solenoid are obtained in the eikonal approximation and in a unitary model of scattering with a sharp jump in the partial amplitudes. The momentum-transfer scattering cross section is proportional to the average transfer of the longitudinal momentum of the scattered particle and can be expressed in terms of a force operator. It is shown that in the absence of a screen the momentum-transfer scattering cross section of toroidal solenoid is indeed determined only by the part of the incident beam that intersects the inner region of the toroidal solenoid, where the magnetic field intensity and, therefore, the Lorentz force are nonzero. At the same time, the momentum-transfer cross section for the scattering of charged particles by a toroidal solenoid covered by a “black” ring-shaped screen does not depend on the magnetic flux inside the solenoid and is identical to the momentum-transfer cross section for diffraction by the same screen. The contribution from scattering by an opening in the screen, which depends on the magnetic flux, is completely compensated by the contribution of the interference of the scattering amplitudes of the opening and the “black” screen.     

Observation of Fano resonance and classical analog of electromagnetically induced transparency in toroidal metamaterials

Toroidal multipoles have recently been explored in various scientific communities, ranging from atomic and molecular physics, electrodynamics, and solid‐state physics to biology. Here we experimentally and numerically demonstrate a three‐dimensionsal toroidal metamaterial where two different toroidal dipoles along orthogonal directions have been observed. The chosen toroidal metamaterial also simultaneously supports Fano resonance and the classical analog of electromagnetically induced transparency (EIT) phenomena in the transmission spectra that originate from the electric–toroidal dipole and electric–magnetic dipole destructive interference. The intriguing properties of the toroidal resonances may open up avenues for applications in toroidal moments generator, sensing and slow‐light devices.     

Neutron flux distribution on the wall of toroidal controlled thermonuclear reactor devices with elongated cross section

The neutron flux distribution on the wall of a toroidal CTR device with strongly elongated cross section is calculated. On the inner and outer cylindrical walls (belt-pinch device) the flux distribution has a plateau region with a half-width equal to about the height of the plasma. The maximum flux is found on the outer cylinder and in the symmetry plane (z ₀=0). The neutron flux asymmetry and reductionη of the mean wall loading are determined. For standard data anη of 57% is computed. This is mainly due to the flux profiles on the cylindrical walls and does not depend sensitively on the toroidal curvature. For standard parameters the inner cylinder absorbs 22.6%, the outer cylinder 68.6% and the end plates together 8.8% of the total neutron emission. The corresponding values for a straight device with the same coil and plasma cross section are 44%, 44% and 12%. A reduction of toroidal curvature diminishes flux asymmetry between the inner and outer cylinders. The maximum flux and minimumη-value are obtained at a large torus radius equal to two times the coil width. For small aspect ratios (R _t W0.5) the neutron flux through the inner cylinder becomes so small that its interior may be filled with a material other than a blanket material, e.g. with an iron core.     

Transport-driven toroidal rotation in the tokamak edge

The interaction of passing-ion drift orbits with spatially inhomogeneous but purely diffusive radial transport is demonstrated to cause spontaneous toroidal spin-up in a simple model of the tokamak edge. Physically, major-radial orbit shifts cause orbit-averaged diffusivities to depend on v(∥), including its sign, leading to residual stress. The resulting pedestal-top intrinsic rotation scales with T(i)/B(θ), resembling typical experimental scalings. Additionally, an inboard (outboard) X point enhances co- (counter)current rotation.     

单壁碳纳米管环离散谱和连续谱间的转变

考虑卷曲效应，构造了扶手形单壁碳纳米管环的单Π轨道紧束缚模型.利用波函数分解方法导出了原子间相互作用矩阵元，由此研究了扶手形碳纳米管环的电子性质.随环半径改变，观察到电子结构发生从离散谱到连续谱之间的转变.计算也表明随管半径改变，其能谱也有类似的变化. 关键词： 碳纳米管环 卷曲效应 电子结构     

Use of spherical gratings in a toroidal grating mount for vuv-soft x-ray synchrotron radiation

A toroidal grating monochromator (TGM) based beamline was designed earlier and it is being setup on the 450 MeV Indus-1 synchrotron radiation source. This beamline operates in 40–1000 Å wavelength range and gives a moderate resolution (～500) at high throughput. Now-a-days, spherical gratings are giving very high resolution in some complex monochromators. We have evaluated the use of spherical gratings in the simple rotation mount of a TGM. The motivation has been to evaluate if the existing TGM beamline, without any hardware changes, can be used with the much cheaper spherical gratings. The two monochromators, employing toroidal and spherical gratings respectively, have been compared by performing detailed ray tracing calculations. Our study shows that, with the same mechanical hardware, a real spherical grating monochromator gives better performance compared to the conventional TGM with respect to the spectral resolution and the flux. Furthermore, for moderate resolution this improvement is realized even when the exit slit is not moved to keep the spherical grating in-focus.     

Toroidicity and shape dependence of peeling mode growth rates in axisymmetric toroidal plasmas

The growth rate of the peeling mode instability with large toroidal mode number is calculated for general axisymmetric toroidal plasmas, including tokamaks and the spherical torus(ST) equilibia by using formalism presented by Connor et al.Analytic equilibia with non-zero edge current density and quasi-uniform current profiles are assumed. It is found that in sharp D-shape tokamak plasma, the derivative of the safety factor with respect to the poloidal flux becomes very large,making the perturbed poloidal motion very large, in turn making a significant reduction of the growth rate of the peeling mode, similar to the X-point effect in diverted plasma. The large aspect ratio effect is also studied, which reduces the growth rate further.     

On the toroidal distributions

The so called toroidal distributions were obtained using the method previously employed to derive the other decompositions of the electric type transition operator used in literature. Some aspects of toroidal distributions are discussed. The condition is given which has to be imposed on the decomposition generating function in order that the Siegert's theorem holds.     

A novel approach to calculate inductance and analyze magnetic flux density of helical toroidal coil applicable to Superconducting Magnetic Energy Storage systems (SMES)

In this paper, formulas are proposed for the self and mutual inductance calculations of the helical toroidal coil (HTC) by the direct and indirect methods at superconductivity conditions. The direct method is based on the Neumann’s equation and the indirect approach is based on the toroidal and the poloidal components of the magnetic flux density. Numerical calculations show that the direct method is more accurate than the indirect approach at the expense of its longer computational time. Implementation of some engineering assumptions in the indirect method is shown to reduce the computational time without loss of accuracy. Comparison between the experimental measurements and simulated results for inductance, using the direct and the indirect methods indicates that the proposed formulas have high reliability. It is also shown that the self inductance and the mutual inductance could be calculated in the same way, provided that the radius of curvature is >0.4 of the minor radius, and that the definition of the geometric mean radius in the superconductivity conditions is used. Plotting contours for the magnetic flux density and the inductance show that the inductance formulas of helical toroidal coil could be used as the basis for coil optimal design. Optimization target functions such as maximization of the ratio of stored magnetic energy with respect to the volume of the toroid or the conductor’s mass, the elimination or the balance of stress in some coordinate directions, and the attenuation of leakage flux could be considered. The finite element (FE) approach is employed to present an algorithm to study the three-dimensional leakage flux distribution pattern of the coil and to draw the magnetic flux density lines of the HTC. The presented algorithm, due to its simplicity in analysis and ease of implementation of the non-symmetrical and three-dimensional objects, is advantageous to the commercial software such as ANSYS, MAXWELL, and FLUX. Finally, using the presented algorithm, magnetic flux density lines in several examples are drawn.     

Schur duality in the toroidal setting

The classical Frobenius-Schur duality gives a correspondence between finite dimensional representations of the symmetric and the linear groups. The goal of the present paper is to extend this construction to the quantum toroidal setup with only elementary (algebraic) methods. This work can be seen as a continuation of [J, D1 and C2] (see also [C-P and G-R-V]) where the cases of the quantum groups U _q (sl(n)), Y(sl(n)) (the Yangian) and U _q (sl(n)) are given. In the toroidal setting the two algebras involved are deformations of Cherednik's double affine Hecke algebra introduced in [C1] and of the quantum toroidal group as given in [G-K-V]. Indeed, one should keep in mind the geometrical construction in [G-R-V] and [G-K-V] in terms of equivariant K-theory of some flag manifolds. A similar K-theoretic construction of Cherednik's algebra has motivated the present work. At last, we would like to lay emphasis on the fact that, contrary to [J, D1 and C2], the representations involved in our duality are infinite dimensional. Of course, in the classical case, i.e.,q=1, a similar duality holds between the toroidal Lie algebra and the toroidal version of the symmetric group. The authors would like to thank V. Ginzburg for a useful remark on a preceding version of this paper. Communicated by M. Jimbo     

Supersymmetry of the extreme rotating toroidal black hole

We study the supersymmetry of the charged rotating toroidal black hole solutions found by Lemos and Zanchin, and show that the only configurations that are supersymmetric are: (i) the non-rotating electrically charged naked singularities already studied by Caldarelli and Klemm, and (ii) an extreme rotating toroidal black hole with zero magnetic and electric charges. For this latter case, the extreme uncharged black hole, we calculate the Killing spinors and show that the configuration preserves the same supersymmetries as the background spacetime.     

RF breakdown by toroidal helicons

Bounded whistlers are well-known for their efficient plasma production capabilities in thin cylindrical tubes. In this paper we shall present their radio frequency (RF) breakdown and discharge sustaining capabilities in toroidal systems. Pulsed RF power in the electronmagnetohydrodynamic (EMHD) frequency regime is fed to the neutral background medium. After the breakdown stage, discharge is sustained by toroidal bounded whistlers. In these pulsed experiments the behaviour of the time evolution of the discharge could be studied in four distinct phases of RF breakdown, steady state attainment, decay and afterglow. In the steady state average electron density of ≈10¹² per cc and average electron temperature of ≈20 eV are obtained at 10⁻³ mbar of argon filling pressure. Experimental results on toroidal mode structure, background effects and time evolution of the electron distribution function will be presented and their implications in understanding the breakdown mechanism are discussed.     

The gyrokinetic water-bag modeling in toroidal geometry

The present paper addresses the gyrokinetic water-bag model in toroidal geometry. The previous works were focused on the water-bag concept in magnetized cylindrical plasmas. Here we report on the possibility to improve the water-bag model by taking into account the curvature and gradient drifts. After a presentation of the model, a local linear analysis with some approximations is performed. Interchange and ion temperature gradient instabilities are examined with this new gyro-water-bag model in order to show its ability and its theoretical interest in describing kinetic instabilities in toroidal geometry.     

Turbulent transport reduction and randomization of coherent fluctuations by zonal flows in toroidal plasma

Fluctuation-driven particle flux is greatly reduced in the plasma radial region where zonal flows are present in the H-1 toroidal heliac. This occurs without reduction in the fluctuation level. Statistical properties of fluctuations are significantly modified in this region. It is shown that the randomization of phases of coherent structures by zonal flows is responsible for the observed effect. This mechanism of transport reduction complements theoretically predicted random shearing of turbulence by zonal flows and does not require the fluctuations suppression.     

A geometrical template for toroidal aggregates of chiral macromolecules

The formation of toroidal aggregates by long chiral molecules of biological origin, as collagen, f-actin and DNA, or by chiral synthetic polypeptides has been observed in specific ionic environments. Such aggregates have received considerable attention in order to identify the various physical factors susceptible to contribute to this original morphogenesis, particularly in the case of those formed by DNA. We consider here the eventual role of a spontaneous uniform twist of micrometric pitch whose possible occurrence is suggested by some observations and by recent studies of DNA dense phases exhibiting cholesteric and “blue” phase structures. Following an approach inspired by the geometry and topology of fiber bundles, we show that the necessity to propagate such a twist in a dense bundle of fibers leads to the formation of aggregates having a toroidal shape and, in the case of the nanometric aggregates of DNA, characteristic sizes similar to those observed.