Numerical study of plasmas start-up by electron cyclotron waves in NCST spherical tokamak and CN-H1 stellarator

According to the physics of tokamak start-up,this study constructs a zero-dimensional(0D)model applicable to electron cyclotron(EC)wave assisted start-up in NCST spherical torus(spherical tokamak)and CN-H1 stellarators.Using the constructed 0D model,the results obtained in this study under the same conditions are compared and validated against reference results for pure hydrogen plasma start-up in tokamak.The results are in good agreement,especially regarding electron temperature,ion temperature and plasma current.In the presence of finite Ohmic electric field in the spherical tokamak,a study on the EC wave assisted start-up of the NCST plasma at frequency of 28 GHz is conducted.The impact of the vertical magnetic field B_(v)on EC wave assisted start-up,the relationship between EC wave injection power P_(inj),Ohmic electric field E,and initial hydrogen atom density n_(H0)are explored separately.It is found that under conditions of Ohmic electric field lower than ITER(~0.3 V m^(-1)),EC wave can expand the operational space to achieve better plasma parameters.Simulating the process of28 GHz EC wave start-up in the CN-H1 stellarator plasma,the plasma current in the zerodimensional model is replaced with the current in the poloidal coil of the stellarator.Plasma startup can be successfully achieved at injection powers in the hundreds of kilowatts range,resulting in electron densities on the order of 10^(17)-10^(18)m^(-3).

The scattering fields for a spherical target irradiated by a plane electromagnetic wave in an arbitrary direction

The relation between corresponding trigonometric functions in two rotating coordinate systems is presented. The transformation formula for a vector in the two rotating spherical coordinate systems is obtained. The scattering fields for a spherical target irradiated by a plane electromagnetic wave in an arbitrary direction are derived. These fields in a particular case retrogress to those available in the literature. The obtained results have great potential in practical applications.

Chirping instabilities produced by a runaway electron beam at a spherical tokamak

Two different types of MHD instabilities with rapidly chirping frequency were found to arise in the Globus-M2 spherical tokamak in substantially different frequency ranges.The first type arises at frequencies of an order of 1 MHz in ohmic plasmas at relatively low density(n_(e))<2×10^(19) m^(-3) in a wide range of toroidal magnetic fields and plasma currents.This type of instability was identified as compressional Alfven waves,driven by electrons,accelerated during a sawtooth crush.It was found that the mode frequency is sweeping in time,according to the Berk-Breizman hole-clump nonlinear chirping model.The second type of wave arises in a specific single-swing regime of the central solenoid current with a very narrow plasma column,when the plasma tends to decay at extremely low density(n_(e))<2×10^(18) m^(-3) and,in fact,is an instability of the runaway electron beam.The exited modes cover the whole observed frequency range and are divided into several(two or three)frequency regions:approximately 0-30 MHz,60-120 MHz and sometimes 30-60 MHz.Reconnection of the branches was also observed.Single chirps are more rapid than for 1 MHz Alfven instability and follow an exponential law.This paper,to our knowledge,is the first report of frequency chirping instabilities excited by accelerated electrons at a spherical tokamak.

SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONSⅡ, NONLINEAR CAUSTIC

This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L^∞ norms, it analyzes the relative errors in approximate solutions.

SPHERICAL WAVE PROPAGATION IN SATURATED SOILS

Based on the generally adopted soil model for engineering, an analytic solution of spherical wave propagation problem in a special case for an equally pressurized spherical cavity in saturated space by Laplace transformation which is compared with that of the same problem in a one-phase elastic space. The influence of fluid on dynamic response of saturated soil is examined. The authors propose an effective way for dynamic analysis of underground structure.

Converging spherical and cylindrical elastic–plastic waves of small amplitude

Converging spherical and cylindrical elastic-plastic waves in an isotropic work-hardening medium is investigated on the basis of a finite difference method. The small amplitude pressure is applied instantaneously and maintained on the outer surface of a spherical or a cylindrical medium. It is found that for undercritical loading, the induced wave structure is an elastic front followed in turn by an expanding plastic region and an expanding elastic region. For supercritical loading, the elastic front is followed in turn by an expanding plastic region, a narrowing elastic region and an expanding plastic region. After yielding is initiated, the strength of the elastic front is constant and equal to the critical loading pressure. The motion of the continuous elastic-plastic interface is discussed in detail. Spatial distributions of pressure near the axis show the strength of the converging wave is nearly doubled in the reflecting stage.

Particle Velocity Measurement for Spherical Wave in Solid

An experimental technique for research on spherical divergent wave propagation in a solid has been developed, in which the source of generating spherical wave is a center initiating explosive charge designed in a mini-spherical shape with yield equivalent to 0.125?g and 0.486?g TNT and a set of circular electromagnetic particle velocity gages is used to record the particle velocity histories. By using the circular electromagnetic particle velocity gages, the signal outputs not only are unattenuated due to the geometrical divergence, but also represent the average of the measured dynamic states of the medium over a circle on the wavefront. The distinctive features of this technique are very useful for the study of spherical divergent wave propagation in a solid, especially in an inhomogeneous solid, and the corresponding material dynamics. Many experimental measurements were conducted in polymethylmethacrylate (PMMA) and granite by means of the technique, and the reproducibility of tests was shown to be good. The measurement technique of the circular electromagnetic particle velocity gages is also suitable to the case of cylindrical wave.

Relativistic Spherical Plasma Waves in a Collisional and Warm Plasma

Under Lagrange coordinates, the relativistic spherical plasma wave in a collisional and warm plasma is discussed theoretically. Within the Lagrange coordinates and using the Maxwell and hydrodynamics equations, a wave equation describing the relativistic spherical wave is derived. The damped oscillating spherical wave solution is obtained analytically using the perturbation theory. Because of the coupled effects of spherical geometry,thermal pressure, and collision effect, the electron damps the periodic oscillation. The oscillation frequency and the damping rate of the wave are related to not only the collision and thermal pressure effect but also the space coordinate. Near the center of the sphere, the thermal pressure significantly reduces the oscillation period and the damping rate of the wave, while the collision effect can strongly influence the damping rate. Far away from the spherical center, only the collision effect can reduce the oscillation period of the wave, while the collision effect and thermal pressure have weak influence on the damping rate.

Focusing of Spherical Nonlinear Pulses for Nonlinear Wave Equations Ⅲ. Subcritical Case

This paper studied spherical pulses of solutions of the system of semilinear wav e equations with the pulses focusing at a point in three space variables. It is shown that there is no nonlinear effect at leading terms of pulses, when the ini tial data is subcritical.

Source localization with minimum variance distortionless response for spherical microphone arrays

To improve localization accuracy, the spherical microphone arrays are used to capture high-order wavefield in- formation. For the far field sound sources, the array signal model is constructed based on plane wave decomposition. The spatial spectrum function is calculated by minimum variance distortionless response （MVDR） to scan the three-dimensional space. The peak values of the spectrum function correspond to the directions of multiple sound sources. A diagonal loading method is adopted to solve the ill-conditioned cross spectrum matrix of the received signals. The loading level depends on the alleviation of the ill-condition of the matrix and the accuracy of the inverse calculation. Compared with plane wave decomposition method, our proposed localization algorithm can acquire high spatial resolution and better estimation for multiple sound source directions, especially in low signal to noise ratio （SNR）.

Characteristics of supersonic flow in new type externally pressurized spherical air bearings

In order to predict accurately the characteristics of supersonic flow in new type externally pressurized spherical air bearings under large bearing clearance and high air supply pressure,which could decrease their load carrying capacity and stability,a CFD-based analysis was introduced to solve the three-dimensional turbulent complete compressible air flow governing equations.The realizable κ-ε model was used as a turbulent closure.The supersonic flow field near air inlets was analyzed.The flow structures illustrate that the interaction exists between shock waves and boundary layer,and the flow separation is formed at the lower corner and the lower wall around the point of a maximum velocity.The numerical results show that the conversion from supersonic flow to subsonic flow in spherical air bearing occurs through a shock region(pseudo-shock),and the viscous boundary layer results in the flow separation and reverse flow near the shock.The calculation results basically agree with the corresponding experimental data.

SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRM SPACE-TIME

In this article, we concern the motion of relativistic membranes and null mem- branes in the Reissner-Nordstrom space-time. The equation of relativistic membranes moving in the Reissner-Nordstrom space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-NordstrSm space-time.

An efficient algorithm for generating a spherical multiple-cell grid

This paper presents an efficient algorithm for generating a spherical multiple-cell(SMC)grid.The algorithm adopts a recursive loop structure and provides two refinement methods:(1)an arbitrary area refinement method and(2)a nearshore refinement method.Numerical experiments are carried out,and the results show that compared with the existing grid generation algorithm,this algorithm is more flexible and operable.

Analytical Solutions to Definite Integrals for Combinations of Legendre, Bessel and Trigonometric Functions Encountered in Propagation and Scattering Problems in Spherical Coordinates

Mie theory is a rigorous solution to scattering problems in spherical coordinate system. The first step in applying Mie theory is expansion of some arbitrary incident field in terms of spherical harmonics fields in terms of spherical which in turn requires evaluation of certain definite integrals whose integrands are products of Bessel functions, associated Legendre functions and periodic functions. Here we present analytical results for two specific integrals that are encountered in expansion of arbitrary fields in terms of summation of spherical waves. The analytical results are in terms of finite summations which include Lommel functions. A concise analytical expression is also derived for the special case of Lommel functions that arise, rendering expensive numerical integration or other iterative techniques unnecessary.

The Investigation and Study of Hydrogen Atom in Spherical Cavity Using B-Spline Basis Functions: A Mathematical Approach

The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site.

单摆永磁直驱式波浪能发电装置的性能研究

为解决海洋仪器的长期能源供应问题,基于永磁材料的电磁特性,结合易于起振的摆式俘能机制,提出了一种与小体积球形浮标相结合的永磁式波浪能发电装置。详细论述了装置的发电原理和设计方案,推导了装置在波浪激励下的运动模型。依靠AQWA与Maxwell软件进行了联合仿真并对装置进行了参数优化,最终仿真结果表明:在波浪入射角度β=0°,波浪周期T=3.5s,波浪高度H=0.6m的波况下摆锤做周期T_(p)=2s,幅值A_(p)=15°的往复振荡运动,单相绕组产生的感应电动势最大可达27.7V,最佳输出功率为2.07W,可有效满足海洋仪器的供电要求。

A More Accurate Determination of the Magnitude of Cosmic Inflation in the Big Bang Model

According to our hypothesis, at the very beginning of the Big Bang, a hyperenergetic spherical wave was created. We described its characteristics in our previous work, and the present work is based on them. Logically, we saw that in cosmic inflation the frequency of such a wave would decrease sharply. Based on the temperature that prevailed immediately after inflation according to the hot Big Bang model, we determined a measure of the size of the inflation in this model, in accordance with our hypothesis.

基于均匀分布偶极子的天线辐射场建模方法

针对雷达观测目标近场电磁散射的天线相关问题,发展了基于偶极子模型的天线辐射场建模方法。偶极子模型包括电偶极子与磁偶极子,其位置均匀分布于天线辐射口面,通过偶极子辐射场坐标变换和天线辐射场球面波展开(spherical wave expansion,SWE),建立了偶极子参数与天线辐射场SWE系数之间的线性矩阵方程,并采用奇异值分解(singular value decomposition, SVD)方法实现了偶极子参数的最小二乘估计。对喇叭天线、波导缝隙天线和微带贴片阵天线进行偶极子建模实验,建立了这三种天线辐射场建模误差小于1%的等效偶极子模型,通过对等效偶极子模型预测任意观测距离天线辐射场精度的评估,验证了基于均匀分布偶极子建模天线辐射场的有效性。

Effects of the shape and size of a mooring line surface buoy on the mooring load of wave energy converters

This paper describes the physical model testing of a wave energy converter (WEC) undertaken in the Heriot-Watt wave basin during October 2010 as part of the SUPERGEN2 project funded by the British government,and provides a preliminary analysis of the extreme mooring loads.Tests were completed at 1/20 scale on a single oscillating water column device deployed with a 3-line taut mooring configuration.The model was fully instrumented with mooring line load cells and an optical motion tracker.The tests were preceded by calibration of instrumentation and the wave test environment,and carried out in long crested waves regimes with 12 combinations of peak period T p and significant wave height H s.The main objective for these experiments was to examine the effect of shape and size of the tethered buoy on the leading mooring line on the maximum mooring loads and the excursion of the device.Comparison of the loads at different configurations of the tethered buoy suggests that the results are consistent with the hypothesis that the mooring forces should depend on the change in stiffness of the mooring system.In particular,the results indicate that with the spectral peak period close to the natural period of the moored device of 8 s,peak loads in a configuration with a smaller buoy may be considerably higher than those with a larger buoy.However,when T p was dissimilar,a harder mooring with a smaller spherical buoy appears to result in lower peak loads.The exact configuration should,therefore,be chosen according to the prevalent conditions of any particular location,and will also depend on the design and expected maintenance schedule,as well as matters related to the risk to navigation,environmental effects and the conservation status of the area.

Flow structures, nonlinear inertial waves and energy transfer in rotating spheres

We investigate flow structures,nonlinear inertial waves and energy transfer in a rotating fluid sphere,using a Galerkin spectral method based on helical-wave decomposition(HWD).Numerical simulations of flows in a sphere are performed with different system rotation rates,where a large-scale forcing is employed.For the case without system rotation,the intense vortex structures are tube-like.When a weak rotation is introduced,small-scale structures are reduced and vortex tubes tend to align with the rotation axis.As the rotation rate increases,a large-scale anticyclonic vortex structure is formed near the rotation axis.The structure is shown to be led by certain geostrophic modes.When the rotation rate further increases,a cyclone and an anticyclone emerge from the top and bottom of the boundary,respectively,where two quasi-geostrophic equatorially symmetric inertial waves dominate the flow.Based on HWD,effects of spherical confinement on rotating turbulence are systematically studied.It is found that the forward cascade becomes weaker as the rotation increases.When the rotation rate becomes larger than some critical value,dual energy cascades emerge,with an inverse cascade at large scales and a forward cascade at small scales.Finally,the flow behavior near the boundary is studied,where the average boundary layer thickness gets smaller when system rotation increases.The flow behavior in the boundary layer is closely related to the interior flow structures,which create significant mass flux between the boundary layer and the interior fluid through Ekman pumping.