Electronic Circuits for the Generation and Transfer of High-Power Pulses in Nuclear Fusion Installations

The toroidal confinement and the ohmic heating of a thermonuclear plasma as used in tokamak experiments can be achieved by strong magnetic fields and by a heavy direct current flowing parallel to the axis of the plasma torus. This current can be induced with the aid of a transformer for which the plasma torus acts as the secondary winding. The high loop voltage required for start-up is obtained by commutation of the primary current to a resistor. This commutation can be achieved by a mechanical switch or by electronic circuits. New electronic commutation circuits are described which enable very heavy direct currents to be switched without contacts. The operation of the new circuits was checked by computer calculations. Experiments have not yet been performed.     

Ion current distribution within a toroidal duct of a filteredvacuum arc deposition system

Vacuum arcs were established on a 90-mm-diameter Ti cathode in a deposition apparatus consisting of a spacer, 122 mm-diameter annular anode, quarter-torus magnetic macroparticle filter, and a deposition chamber. A toroidal magnetic field generally parallel to the torus walls of up to 20 mT was applied. The ion current in various cross-sections of the toroidal duct was measured using: 1) a disc probe of 130-mm diameter, oriented normal to the torus axis used to measure the transmitted ion current, and 2) a hollow cylindrical probe of 135-mm diameter and 25-mm height, whose axis coincided with the torus axis, used to measure ion current losses to the duct wall. The distribution of ion current loss was studied using an 8-segment hollow cylindrical multiprobe, where the individual probes were equally distributed on the circumference of a 130-mm-diameter circle. It was shown that: 1) the ratio of ion currents collected on the cylindrical and disc probes at first decreases with increasing the toroidal field, and then becomes approximately constant; 2) the presence of the large-diameter disc probe does not influence the value of the ion current on the cylindrical probe; and 3) the maximum ion current density near the torus walls is located in the +g direction and displaces in the -(B×g) direction with increasing the toroidal field, where g and B are the vectors of the centrifugal acceleration and the magnetic field, respectively     

parafermionic current algebras of torus/orbifold models

We study the quantum field theory of bosons on the torus and the orbifold. When the torus is in special moduli, the representations of the theory are equivalent to those of some rational conformal field theories. We show that there are parafermonic current algebras in Z_N orbifold models.     

Two-dimensional quantum gravity and current algebra on a torus

The euclidean generating functional of the correlation functions of the energy-momentum tensor in conformal field theory on a torus is derived. The quantization of the effective action for induced two-dimensional gravity on the torus is still related to the SU(2)×SU(2) current algebra.     

Oscillating-field current-drive experiments in a reversed field pinch

Oscillating-field current drive (OFCD) is a steady-state magnetic helicity injection method to drive net toroidal current in a plasma by applying oscillating poloidal and toroidal loop voltages. OFCD is added to standard toroidal induction to produce about 10% of the total current in the Madison symmetric torus. The dependence of the added current on the phase between the two applied voltages is measured. Maximum current does not occur at the phase of the maximum helicity injection rate. Effects of OFCD on magnetic fluctuations and dissipated power are shown.     

Microscopic Structure of Shocks and Antishocks in the ASEP Conditioned on Low Current

We study the time evolution of the ASEP on a one-dimensional torus with L sites, conditioned on an atypically low current up to a finite time t. For a certain one-parameter family of initial measures with a shock we prove that the shock position performs a biased random walk on the torus and that the measure seen from the shock position remains invariant. We compute explicitly the transition rates of the random walk. For the large scale behavior this result suggests that there is an atypically low current such that the optimal density profile that realizes this current is a hyperbolic tangent with a traveling shock discontinuity. For an atypically low local current across a single bond of the torus we prove that a product measure with a shock at an arbitrary position and an antishock at the conditioned bond remains a convex combination of such measures at all times which implies that the antishock remains microscopically stable under the locally conditioned dynamics. We compute the coefficients of the convex combinations.     

铁芯变压器对极向场的影响

本文叙述了对HL-1装置铁芯变压器作无限长均匀磁化假定后,给出了极向场线圈(包括等离子体电流环)在空气区产生的磁场解析表达式,及数值计算,并在一比四模拟变压器上做了实验,计算结果与实验结果符合。     

Potential in the “Clearance” of torus: Development on spherical functions

The method of solution of the Dirichlet problem for potentials of volume bodies with torus topology when the boundary conditions are set in the form of a series on spherical harmonics on pieces of two spherical surfaces is developed. The problem representation of an exterior potential homogeneous gravitating (or charged by static electric charge) circular torus out of a substance in a special (??intermediate??) spherical zone is presented and solved. The solution is received in the form of a combination of the Laplace series on even positive and odd negative degrees of the radius-vector of a test point. Coefficients of this series are received in a final analytical form. The general member of the series at the limit of big n tends to zero so the series converges fast and the radius of convergence are defined by torus geometry. The specified solution meets a gap in the theory, connecting together earlier discovered by us, two expansions in the Laplace series of a torus potential in ??interior?? and ??exterior?? spherical space zones. Thus, it is proved that it is possible to present the torus potential by power rows in all free space from the substance. For control of results by means of the obtained series, equipotential surfaces of the torus were calculated.     

Bootstrap current fraction scaling for spherical torus plasmas

Dependence of the bootstrap current fraction of spherical torus plasma on the aspect ratio and the triangular deformation is studied by using a simple equilibrium model, the Solov‘ev-type equilibrium. Two bootstrap current models are used: one is the single-ion collisionless regime model, the other is the recently developed arbitrary collisional regime model. It is found that besides the well known favourable effect of the small aspect ratio on the enhancement of the bootstrap current fraction, the triangularity is beneficial for raising the total bootstrap current though it does not change its fraction much.     

Laplace series expansion of the internal potential of a homogeneous circular torus

The internal potential of a homogeneous circular torus first is represented by a series expansion in spherical functions (Laplace series). Exact analytical formulas for the coefficients of this series are derived and it is shown that they can be expressed through the standard Gauss hypergeometric function depending only on the geometric parameter of the torus. Convergence of the series is proved and the radius of convergence is determined. The relation of the radius with the torus geometrical parameter is found. A special spherical shell, where the problem of expansion of the torus potential should be solved in additional investigations, is detected.     

Vortices in the Two-Dimensional Simple Exclusion Process

We show that the fluctuations of the partial current in two dimensional diffusive systems are dominated by vortices leading to a different scaling from the one predicted by the hydrodynamic large deviation theory. This is supported by exact computations of the variance of partial current fluctuations for the symmetric simple exclusion process on general graphs. On a two-dimensional torus, our exact expressions are compared to the results of numerical simulations. They confirm the logarithmic dependence on the system size of the fluctuations of the partial flux. The impact of the vortices on the validity of the fluctuation relation for partial currents is also discussed in an Appendix.     

Interactions of the directed plasma from a cathodic arc withelectrodes and magnetic fields

Curved magnetic ducts are frequently used to remove macroscopic-sized droplets from the plasma stream of cathodic vacuum arcs. The plasma of a cathodic vacuum arc in a magnetic filter is characterized by a strongly directional ion velocity (corresponding to 20-100 eV) and magnetized electrons. In the first section of this paper the effects of these features on the I-V characteristic curves of planar probes are identified and explained using a simple model. This is then used to interpret the interaction of the plasma with the walls of a biased quarter torus duct. Two small electrodes placed on the outer and inner sections of the curved duct wall show that the I-V characteristic is determined primarily by the electron-ion current balance at the wall on the outside of the curve. The application of a bias to a planar electrode on the outer wall section was found to give the same increase in throughput as a positive bias applied to the entire duct with the advantage of a much smaller electron current being drawn by the biasing power supply. The improvement in duct throughput achievable with positive-biasing of the duct wall was found to depend on both the configuration and strength of the magnetic field in the quarter torus filter. The plasma density profile and potential were unaffected by the application of the bias     

Dirac operator zero-modes on a torus

We study Dirac operator zero-modes on a torus for gauge background with uniform field strengths. Under the basic translations of the torus coordinates the wave functions are subject to twisted periodic conditions. In suitable torus coordinates the zero-mode wave functions can be related to holomorphic functions of the complex torus coordinates. Half of the twisted boundary conditions for the holomorphic part of the zero-mode wave function can be made periodic or anti-periodic. The remaining half is until coordinate dependent but diagonal. We completely solve the twisted boundary conditions and construct the zero-mode wave functions. The chirality and the degeneracy of the zero-modes are uniquely determined by the gauge background and are consistent with the index theorem.     

Efficient generation of closed magnetic flux surfaces in a large spherical tokamak using coaxial helicity injection

A method of coaxial helicity injection has successfully produced a closed flux current without the use of the central solenoid in the NSTX device, on a size scale closer to a spherical torus reactor, for a proof-of-principle demonstration of this concept. For the first time, a remarkable 60 times current multiplication factor was achieved. Grad-Shafranov plasma equilibrium reconstructions are used to verify the existence of closed flux current. In some discharges the generated current persists for a surprisingly long time approximately 400 ms.     

Hydrodynamics of a rotating torus

The hydrodynamics of a torus is important on two counts: firstly, most stiff or semiflexible ring polymers, e.g. DNA miniplasmids are modeled as a torus and secondly, it has the simplest geometry which can describe self propelled organisms (particles). In the present work, the hydrodynamics of a torus rotating about its centerline is studied. Analytical expression for the velocity of a force free rotating torus is derived. It is found that a rotating torus translates with a velocity which is proportional to its internal velocity and to the square of the slenderness ratio, epsilon, similar to most low Reynolds number swimmers. The motion of a torus along a cylindrical track is studied numerically and it is observed that a force free torus changes its direction of motion (from a propelled state (weak wall effects) to a rolling state (strong wall effects)) as the diameter of the inner circular cylinder is increased. The rolling velocity is found to depend only on epsilon when the inner cylinder diameter approaches that of the torus.     

Multifolded torus chaotic attractors: design and implementation

This paper proposes a systematic methodology for creating multifolded torus chaotic attractors from a simple three-dimensional piecewise-linear system. Theoretical analysis shows that the multifolded torus chaotic attractors can be generated via alternative switchings between two basic linear systems. The theoretical design principle and the underlying dynamic mechanism are then further investigated by analyzing the emerging bifurcation and the stable and unstable subspaces of the two basic linear systems. A novel block circuit diagram is also designed for hardware implementation of 3-, 5-, 7-, 9-folded torus chaotic attractors via switching the corresponding switches. This is the first time a 9-folded torus chaotic attractor generated by an analog circuit has been verified experimentally. Furthermore, some recursive formulas of system parameters are rigorously derived, which is useful for improving hardware implementation.     

An elementary model of torus canards

We study the recently observed phenomena of torus canards. These are a higher-dimensional generalization of the classical canard orbits familiar from planar systems and arise in fast-slow systems of ordinary differential equations in which the fast subsystem contains a saddle-node bifurcation of limit cycles. Torus canards are trajectories that pass near the saddle-node and subsequently spend long times near a repelling branch of slowly varying limit cycles. In this article, we carry out a study of torus canards in an elementary third-order system that consists of a rotated planar system of van der Pol type in which the rotational symmetry is broken by including a phase-dependent term in the slow component of the vector field. In the regime of fast rotation, the torus canards behave much like their planar counterparts. In the regime of slow rotation, the phase dependence creates rich torus canard dynamics and dynamics of mixed mode type. The results of this elementary model provide insight into the torus canards observed in a higher-dimensional neuroscience model.     

Effects of a vertical magnetic field on particle confinement in a magnetized plasma torus

The particle confinement in a magnetized plasma torus with superimposed vertical magnetic field is modeled and measured experimentally. The formation of an equilibrium characterized by a parallel plasma current canceling out the grad B and curvature drifts is described using a two-fluid model. Characteristic response frequencies and relaxation rates are calculated. The predictions for the particle confinement time as a function of the vertical magnetic field are verified in a systematic experimental study on the TORPEX device, including the existence of an optimal vertical field and the anticorrelation between confinement time and density.     

Generalized Winding Number of a Dynamical System

The generalized winding number of the BW model system stimulated by a periodic current is studied in this letter. As long as the attractors lie on the invariant torus, the winding number diagram shows the well-known devil's staircases scenario. When the system transits to chaotic state, the winding number becomes irregular.     

一类多折叠环面多涡卷混沌吸引子的仿真研究

通过构造一个新的非线性函数，研究一类多折叠环面多涡卷混沌产生器.这种混沌产生器的主要特征是随着自然数n的增加，能产生大小相等、均匀分布的2n个折叠环面混沌吸引子和大小相等、均匀分布的2n+1个涡卷混沌吸引子，且折叠环面混沌吸引子与涡卷混沌吸引子之间相互间置，最左边和最右边均为涡卷混沌吸引子.基于虚拟电子实验室EWB软件，设计具体的电路，进行了仿真实验验证. 关键词： 折叠环面混沌吸引子 多涡卷混沌吸引子 涡卷