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.     

New approach to transport improvement in a helical magnetic axis system by introduction of effective toroidal curvature

A new approach to transport improvement in a helical magnetic axis stellarator is proposed. First of all, the proposal is presented for the L = 1 system. The effective toroidal curvature term epsilon(T), defined as the sum of the usual toroidal curvature and one of the nearest satellite harmonics of the helical field, determines confinement conditions of localized trapped particles. There exists a certain correlation between the smallness of epsilon(T) and the omnigeneity. This approach would give rise to the possibility of a stellarator design study in a wider parameter domain than quasisymmetry approaches.     

New approach to perturbation theory of many-particle systems

We derive an infinite hierarchy of integral equations for the Green functions of a many-particle system. This set of equations forms the basis of a unified approach to the perturbation theory of many boson and many fermion systems and avoids the introduction of the adiabatic hypothesis. It is demonstrated how a well-known ground state perturbation theory of a system of interacting fermions is obtained without introducing disconnected diagrams. It is shown that the formalism allows a self-consistent determination of the condensate Green function of a condensed Bose system and a derivation of the Beliaev, Hugenholtz, and Pines result for the single-particle k 0 Green function is given. A new self-consistent equation for the k = 0 Green function is solved to yield the well-known self-energy relation ₁₁ – ₀₂ = which plays the role of a self-consistency condition on the theory.     

Collective coordinates in Fermi systems

The problem of developing a consistent perturbation theory for a Fermi system in the case in which the unperturbed system exhibits dynamical symmetry breaking is discussed, by using collective coordinate methods. By adapting to this problem the methods used in the quantization of gauge theories, it is shown how to deal with composite zero-frequency excitations in such a way that the resulting perturbation theory is free of infrared divergencies. Explicit calculations are carried out in the case of a simple quantum mechanical model representing a superfluid Fermi system.     

Transition to special canonical coordinates for systems with constraints

When using the Dirac hamiltonization of Lagrange systems with constraints, it is convenient to perform a canonical transformation such that the constraints become linear combinations of only a subset of the new variables, while the primary constraints can be identified with some of the variables belonging to this subset. We prove the existence of such canonical transformation, as well as the possibility of separation of first-class constraints.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 93–97, August, 1983.     

On superintegrable systems separable in Cartesian coordinates

We continue the study of superintegrable systems of Thompson's type separable in Cartesian coordinates. An additional integral of motion for these systems is the polynomial in momenta of N-th order which is a linear function of angle variables and the polynomial in action variables. Existence of such superintegrable systems is naturally related to the famous Chebyshev theorem on binomial differentials.     

AC Stark effect in toroidal carbon nanotubes threaded with an ac magnetic flux

The ac Stark effect is investigated in the toroidal carbon nanotube system threaded with an ac magnetic flux. The Floquet theory is employed to deal with the time-dependent quantum problems. The time-averaged energy of the system is derived and is found to exhibit a strong relationship with an external field, and the modified energy gap has been presented. The ac flux enhances energy gaps to cause metal-semiconductor transition. The steady current has been obtained by employing the free energy approach, and the persistent current is a special case as the magnitude of the ac flux approaches zero. The photon-assisted current is quite different from the persistent current due to the absorption and emission of photons. The local density of states is obtained by calculating the Green's function in the Floquet state, and photon-resonant structures are observed. All of the novel features are associated with the ac Stark effect, which is caused by the modification of energy levels. Received 20 November 2002 / Received in final form 7 February 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: zhaohonk@yahoo.com     

An alternative approach to field-aligned coordinates for plasma turbulence simulations

In this work, a new approach to field-aligned coordinates for plasma turbulence is presented, in which the position along the field lines is identified by the toroidal angle. The several advantages of the new approach are discussed. It is also shown that the approach can be generalised to get rid of magnetic coordinates in the poloidal plane altogether. Tests are carried out by comparing codes implementing a basic ion temperature gradient turbulence model with the old and the new methods. Results show an unexpected property of the model, that localized large parallel gradients can intermittently appear in the turbulent regime.     

Genetic estimation of iron losses in strip wound toroidal cores under PWM flux conditions

Recently estimation of iron losses in electrical steels have become very significant for the manufacture of well-designed magnetic devices that are to be subjected to electronically generated voltage excitations such as pulse width-modulated (PWM) voltage excitation. In this study, iron loss components were estimated by means of the genetic algorithms method and electrical steel manufacturers’ data. The results were compared with those obtained by a widely used classical method. The comparison has shown that the genetic algorithms method improved loss estimation with respect to the classical method under both sinusoidal and PWM flux conditions.     

Self-reversal phenomena of toroidal current by reversing the external toroidal field in helicity-driven toroidal plasmas

In order to understand self-organization in helicity-driven systems, we have investigated the dynamics of low-aspect-ratio toroidal plasmas by decreasing the external toroidal field and reversing its sign in time. Consequently, we have discovered that the helicity-driven toroidal plasma relaxes towards the flipped state. Surprisingly, it has been observed that not only toroidal flux but also poloidal flux reverses sign spontaneously during the relaxation process. The self-reversal of the magnetic fields is attributed to the nonlinear growth of the n=1 kink instability of the central open flux.     

一维变系数耗散系统Lagrange函数和Hamilton函数的新构造方法

提出构造二阶微分方程的Lagrange函数和Hamilton函数的新路径. 将二阶方程写成一阶方程组并构造出对应的一阶Lagrange函数后,直接从一阶Lagrange函数导出二阶Lagrange函数和Hamilton函数. 利用上述方法得到若干耗散和类耗散系统的一阶和二阶Lagrange函数以及Hamilton函数;讨论了这种方法的优点. 举例说明所得结果的应用. 关键词： 逆问题 耗散系统 Lagrange函数 Hamilton函数     

Quantum description of five-particle systems in principal-axis hyperspherical coordinates

To describe a 5-particle system, ‘principal-axis hyperspherical’ coordinates (made up of one hyperradius and eight angles as internal coordinates) and three Euler angles as external (rotational) coordinates are used. A mathematical procedure to derive, in a systematic manner, the exact quantum mechanical Hamiltonian of the system in terms of these coordinates is presented. A generalized angular momentum vector operator, which allows the generation of a profitable standard representation for the angular part of the problem, is introduced.     

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.     

Information-theoretic approach to the study of control systems

We propose an information-theoretic framework for analyzing control systems based on the close relationship of controllers to communication channels. A communication channel takes an input state and transforms it into an output state. A controller, similarly, takes the initial state of a system to be controlled and transforms it into a target state. In this sense, a controller can be thought of as an actuation channel that acts on inputs to produce desired outputs. In this transformation process, two different control strategies can be adopted: (i) the controller applies an actuation dynamics that is independent of the state of the system to be controlled (open-loop control); or (ii) the controller enacts an actuation dynamics that is based on some information about the state of the controlled system (closed-loop control). Using this communication channel model of control, we provide necessary and sufficient conditions for a system to be perfectly controllable and perfectly observable in terms of information and entropy. In addition, we derive a quantitative trade-off between the amount of information gathered by a closed-loop controller and its relative performance advantage over an open-loop controller in stabilizing a system. This work supplements earlier results (Phys. Rev. Lett. 84 (2000) 1156) by providing new derivations of the advantage afforded by closed-loop control and by proposing an information-based optimality criterion for control systems. New applications of this approach pertaining to proportional controllers, and the control of chaotic maps are also presented.