Calculations of the Critical Levitron's Tilts

The magnetic surfaces' equations and their rotational transforms are derived for the axisymmetric levitron. In the nonaxisymmetric levitron the magnetic island-contour equations are obtained and some of these island contours are plotted. The critical perturbations for the complete destruction of the ?-and 2?-resonances are calculated. The analytical results derived here are compared and shown to be in good agreement with the numerical results.     

Nonlinear resonances in the absorption spectrum of the three-level atomic V system in strong polyharmonic and weak biharmonic fields

A three-level atomic system with a strong three-mode field and a probing biharmonic field at transitions 1→2 and 1?3 (1 is a common lower level), respectively, is studied theoretically by numerical simulation and an analysis of the mathematical expressions derived for the particular case of a symmetric arrangement of the strong field components relative to the transition frequency ω₂₁. The absorption spectrum of the probing field components contains parametric supernarrow resonances against the background of resonances of the nonlinear interference effect. The ratios of the differences in the frequencies of the strong and probing fields, at which the supernarrow resonances appear, are found analytically. The results coincide with those obtained from numerical simulation.     

Theoretical Optimization of Stellarators

Net current free toroidal ("stellarator") confinement is studied with a combination of several methods: a complete set of analytical vacuum fields for finding favorable vacuum field configurations; three-dimensional MHD codes for finite-?, equilibrium computations; the expansion of a general toroidal equilibrium around its magnetic axis as guideline for the computational search in configurational space and for finite-?, MHD stability; Monte Carlo simulations for particle containment; continuous modular coil systems generating the configurations considered. Results are: vacuum field configurations with sizeable Q = 0, 1, 2, 3 helical fields, substantial twist number (? 1/2), significant reduction of the parallel current density, and vacuum magnetic well exist for a toroidal aspect ratio of 15-20 and can be generated by modular coils whose excursions from meridional planes are small compared to the toroidal period length. In these configurations, the finite-? toroidal shift is strongly reduced, so that a larger ? value (factor 2-4) than in the equivalent Q = 2 stellarator can be achieved. Stability calculations do not exclude the possibility of stable equilibria of this kind with (?) ? 0.05-0.1; transport calculations without electrical field show improvement-as compared to the Q = 2 stellarator-in the collisional and plateau regimes.     

Gravitational Waves Interacting with a Spinning Charged Particle in the Presence of a Uniform Magnetic Field

The equations which determine the response of a spinning charged particle moving in a uniform magnetic field to an incident gravitational wave are derived in the linearized approximation to general relativity. We verify that 1) the components of the 4-momentum, 4-velocity and the components of the spinning tensor, both electric and magnetic moments, exhibit resonances and 2) the co-existence of the uniform magnetic field and the GW are responsible for the resonances appearing in our equations. In the absence of the GW, the magnetic field and the components of the spin tensor decouple and the magnetic resonances disappear.     

High magnetic shear gain in a liquid sodium stable Couette flow experiment: a prelude to an α-Ω dynamo

The Ω phase of the liquid sodium α-Ω dynamo experiment at New Mexico Institute of Mining and Technology in cooperation with Los Alamos National Laboratory has demonstrated a high toroidal field B(?) that is ?8×B(r), where B(r) is the radial component of an applied poloidal magnetic field. This enhanced toroidal field is produced by the rotational shear in stable Couette flow within liquid sodium at a magnetic Reynolds number Rm?120. Small turbulence in stable Taylor-Couette flow is caused by Ekman flow at the end walls, which causes an estimated turbulence energy fraction of (δv/v)(2)～10(-3).     

关于磁悬浮陀螺稳定悬浮条件的探讨

利用牛顿力学中的稳定性理论对磁悬浮陀螺稳定悬浮的条件进行了分析,在实验上对磁悬浮陀螺底座磁场的空间分布进行了测量,将理论分析和测量的数据结合起来从理论上预测陀螺稳定悬浮的区域范围,再将实验上实际观察到的稳定悬浮区域与之对比,得到了一致性的结论,由此得出了磁悬浮陀螺稳定悬浮的条件.     

手性环状碳纳米管的电子结构及磁化特性

基于石墨平面π电子的紧束缚模型,导出了手性(chiral)环状碳纳米管(TCNTs)在磁场中的电子结构,从而对TCNTs量子特性和磁化规律进行了较深入研究.第Ⅰ,Ⅱ类TCNTs在磁场中存在金属—半导体的连续转变.计算分析表明:在T=0K时,第Ⅰ,Ⅱ类TCNTs的磁化强度随磁通量Φ呈线性周期性变化(以磁通量子Φ₀=h/e为周期),并且磁化强度对手性角θ、管口半径r,以及温度T极为敏感,但与环半径R无关.手性TCNTs的磁化强度比椅形或锯齿形TCNTs的磁化强度强很多;而第Ⅲ类TCNTs 关键词： 手性环状碳纳米管 电子结构 磁化特性     

Toroidal plasma rotation induced by the dynamic ergodic divertor in the TEXTOR tokamak

The first results of the Dynamic Ergodic Divertor in TEXTOR, when operating in the m/n=3/1 mode configuration, are presented. The deeply penetrating external magnetic field perturbation of this configuration increases the toroidal plasma rotation. Staying below the excitation threshold for the m/n=2/1 tearing mode, this toroidal rotation is always in the direction of the plasma current, even if the toroidal projection of the rotating magnetic field perturbation is in the opposite direction. The observed toroidal rotation direction is consistent with a radial electric field, generated by an enhanced electron transport in the ergodic layers near the resonances of the perturbation. This is an effect different from theoretical predictions, which assume a direct coupling between rotating perturbation and plasma to be the dominant effect of momentum transfer.     

铁芯托卡马克中二维和三维极向磁场计算模型的对比分析

为方便计算托卡马克磁场分布,建立了一些二维解析铁芯模型。由于前提假设的不同而给磁场分布的计算带来了不同的边界条件,因而得到的磁场分布计算结果与实际情况有所偏差。为了获得铁芯托卡马克的极向磁场三维分布,建立了带铁芯的极向磁场线圈三维数值模型,计算铁芯托卡马克的三维磁场,与不同铁芯模型的磁场计算结果进行比较,并且研究铁芯托卡马克的三维磁场的极向分量在环向上的不对称性。     

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For simplifying the calculation the magnetic distribution on tokamak, some two-dimensional analytic models including the effect of the iron core were established, such as the infinite long iron core model and the spool model. The assumptions of these two-dimensional analytic models lead to different results with the actual magnetic field due to the distinctive boundary condition. In order to accurately calculate the three-dimensional magnetic field distribution in the tokamak with iron core, a three-dimensional numerical finite element model was established based on J-TEXT tokamak. In two conditions, where the total toroidal current is nonzero or zero respectively, more comparison were carried out between the derived results of two-dimensional models and the results at different toroidal positions in three-dimensional models. Furthermore, the toroidal asymmetry of the magnetic field distribution of the three-dimensional model of tokamak with iron core was investigated. The results indicate that the three-dimensional construction of iron core causes the toroidal asymmetric poloidal magnetic field and the difference between the two- and three-dimensional models in the condition with total current of nonzero. However, in the condition with total current of zero, the intensity of toroidal asymmetric is reduced and the difference between the two- and three-dimensional models is smaller.     

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.     

Propagation of vacuum arc plasma beam in a toroidal filter

An analytical solution to the problem of plasma beam transport in a toroidal magnetic filter for unmagnetized ions is derived. A two-fluid model taking into account electromagnetic and pressure forces, electron-ion collisions, magnetic force line curvature, and radial dependence of centrifugal force is used. From comparison with experimental data it is shown that the obtained solution describes well the main properties of plasma beam behavior in the filter, e.g. (1) the relative value of the ion current along the torus decreases exponentially, (2) the deflection of the plasma beam from the center of the torus correlates with the centrifugal drift of the plasma beam across a magnetic field, and (3) experiment and theory agree well on the weak correlation between magnetic field strength and filter efficiency     

Hamilton flow generated by field lines near a toroidal magnetic surface

A method is described for obtaining the Hamiltonian of a vacuum magnetic field in a given 3D toroidal magnetic surface (superconducting shell). This method is used to derive the expression for the integrable surface Hamiltonian in the form of the expansion of a rotational transform of field lines on embedded near-boundary magnetic surfaces into a Taylor series in the distance from the boundary. This expansion contains the value of the rotational transform and its shear at the boundary surface. It is shown that these quantities are related to the components of the first and second quadratic forms of the boundary surface.     

On the symmetry and topology of plasmonic eigenmodes in heptamer and hexamer nanocavities

Plasmonics is expected to play a key role in nanotechnology, leading to intriguing routes in many engineering and biological applications. Recently, it has been realized that toroidal resonances could be an alternative to electric and magnetic resonances, which have governed the innovation of plasmonic applications so far. In a previous contribution, we proved the existence of toroidal moments in an oligomeric void-plasmonic structure [1]. In this article, we investigate the role of topology and symmetry in decomposing the various dipolar, quadrupolar, and toroidal moments, using energy-filtering transmission electron microscopy supported by three-dimensional finite-difference time-domain method simulations. The consequences of changing the topology on the toroidal character are discussed by comparing results obtained from nanoholes forming heptamer and hexamer nanocavity systems that were drilled into a thin silver film.     

Plasma Response to Resonant Perturbations at Tokamak Edge

In certain circumstances, plasma response suppresses magnetic islands expected at perturbed resonant magnetic surfaces. We investigate the plasma response to the resonant magnetic perturbations in a large aspect ratio tokamak perturbed by external resonant helical windings, considering polar toroidal coordinates for which analytical toroidal equilibrium solutions and perturbing fields are available. We apply an empirical approach to mimic the plasma screening effects by introducing presumed plasma current sheets on the resonance surfaces to cancel the RMP effects. Numerical examples show the effect of plasma response reducing magnetic islands at the plasma edge and also regularizing field lines around the resonant surface. The distribution of connection lengths along the plasma cross section indicates that the plasma response increases the connection lengths since more toroidal turns are performed until a field line reaches the tokamak wall.     

The Topolotron: A High Beta Device with Topological Stability

The concept of topological or structural stability is introduced and its importance in the magnetic confinement of plasmas is discussed. Topological stability requires the presence of a pair of limit cycles in the magnetic field configuration. This paper deals with the design of an experimental device possessing limit cycles. The design includes a high beta (? ? 1), high density (~1016), hot (~100 eV) hygrogen plasma which is to be compressed by a factor of about 5 in a toroidal device of 25 cm average major radius with a capacitor bank rise time of less than 2 ?sec. Two shaped toroidal coils with opposing currents and the poloidal compression coils have been designed to give a pressure balance equilibrium and establish the limit cycles. This device could be used to determine the physical significance of topological stability in plasma confinement.     

Resonances of orientation and alignment of atoms in the case of inclined optical pumping

It is shown that, with pumping inclined relative to a constant magnetic field H₀, the radio-frequency (RF) magnetic field rotating at frequency Ω induces new resonances ω₀ = γ H ₀ and 2Ω for the Fourier components of orientation and ω₀ = ?Ω, Ω/2, 3Ω/2, 2Ω, and 3Ω for the components of alignment. New resonances excited by the oscillating RF field are also considered.     

The Brunt–Väisälä frequency of rotating tokamak plasmas

The continuous spectrum of analytical toroidally rotating magnetically confined plasma equilibria is investigated analytically and numerically. In the presence of purely toroidal flow, the ideal magnetohydrodynamic equations leave the freedom to specify which thermodynamic quantity is constant on the magnetic surfaces. Introducing a general parametrization of this quantity, analytical equilibrium solutions are derived that still posses this freedom. These equilibria and their spectral properties are shown to be ideally suited for testing numerical equilibrium and stability codes including toroidal rotation. Analytical expressions are derived for the low-frequency continuous Alfvén spectrum. These expressions still allow one to choose which quantity is constant on the magnetic surfaces of the equilibrium, thereby generalizing previous results. The centrifugal convective effect is shown to modify the lowest Alfvén continuum branch to a buoyancy frequency, or Brunt–Väisälä frequency. A comparison with numerical results for the case that the specific entropy, the temperature, or the density is constant on the magnetic surfaces yields excellent agreement, showing the usefulness of the derived expressions for the validation of numerical codes.     

A model for predicting magnetic targeting of multifunctional particles in the microvasculature

A mathematical model is presented for predicting magnetic targeting of multifunctional carrier particles that are designed to deliver therapeutic agents to malignant tissue in vivo. These particles consist of a nonmagnetic core material that contains embedded magnetic nanoparticles and therapeutic agents such as photodynamic sensitizers. For in vivo therapy, the particles are injected into the vascular system upstream from malignant tissue, and captured at the tumor using an applied magnetic field. The applied field couples to the magnetic nanoparticles inside the carrier particle and produces a force that attracts the particle to the tumor. In noninvasive therapy, the applied field is produced by a permanent magnet positioned outside the body. In this paper, a mathematical model is developed for predicting noninvasive magnetic targeting of therapeutic carrier particles in the microvasculature. The model takes into account the dominant magnetic and fluidic forces on the particles and leads to an analytical expression for predicting their trajectory. An analytical expression is also derived for predicting the volume fraction of embedded magnetic nanoparticles required to ensure capture of the carrier particle at the tumor. The model enables rapid parametric analysis of magnetic targeting as a function of key variables including the size of the carrier particle, the properties and volume fraction of the embedded magnetic nanoparticles, the properties of the magnet, the microvessel, the hematocrit of the blood and its flow rate.