Some properties of the spectral flow in semiriemannian geometry

Let be the action integral on a semiriemannian manifold ( , g) defined on the space of the curves z : [0, 1] → joining two given points z₀ and z₁. The critical points of ƒ are the geodesics joining z₀ and z₁. Let s ε [0, 1]. We study the behavior, in dependence of s, of the eigenvalues of the Hessian form of ƒ evaluated at z, restricted to the interval [0, s]. A formula for the derivative of the eigenvalues is given and some applications are shown.     

HL-2M 装置环向场线圈匝间绝缘工艺研究

HL-2M tokamak adopts the demountable toroidal field coils (TFCs) structure in order to assemble the vacuum vessel chamber and poloidal field coils (PFCs) integrally. TFCs are subjected to high shear force, which require high electrical performance and adhesive strength between the inter turn insulation and the copper plate. Baking and curing impregnated glass cloth and epoxy glass cloth under different pressure, then adhesive properties have been researched by shear tests. The results show that there are some differences in the adhesive properties between the turn to turn insulation and the copper plate under different structural combinations and different pressures. Appropriate structural combination and pressure of hot baking and curing were selected for TFCs.     

Effect of unstable MHD modes on the confinement of a stellarator plasma

The results of an experimental study of the influence of unstable MHD modes on plasma confinement in an L-2M stellarator are presented. The spectral and statistical characteristics of turbulent plasma simultaneously at both the edge and center of the plasma are investigated. It is shown that at constant power of electron-cyclotron heating of the plasma the energy content of the plasma depends strongly on the strength of the externally applied vertical magnetic field used to adjust the position of the plasma column. Appreciable degradation of plasma confinement is observed for values of the vertical field such that ideal MHD modes become unstable in the greater part of the plasma column. This in turn is due to the formation of a magnetic configuration with a magnetic “hump.” At the same time, in the edge plasma the instability of resistive-balloon modes grows, and turbulent particle transport increases. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 6, 407–412 (25 March 1999)     

Study of the plasma potential evolution during ECRH in the T-10 tokamak and TJ-II stellarator

Comparison of the plasma electric potential evolution in the T-10 tokamak and TJ-II stellarator was performed. The core potential was measured by the heavy-ion beam probing and the edge potential was measured by Langmuir probe. The intrinsic potentials in both devices are different in sign, positive in TJ-II low-density discharge and negative in T-10 higher-density discharges, but during ECRH they evolve similarly: the potential becomes more positive, and increase of ECRH power leads to stronger rise of core potential. Presented at the Workshop “Electric Fields, Structures and Relaxation in Edge Plasmas”, Tarragona, Spain, July 3–4, 2005.     

Growth and properties of Ti-Cu films with respect to plasma parameters in dual-magnetron sputtering discharges

Properties of different methods of magnetron sputtering (dc-MS, dual-MS and dual-HiPIMS) are studied and compared with respect to intermetallic Ti-Cu film formation. The quality and features of thin films are strongly influenced by the energy of incoming particles. The ion velocity distribution functions (IVDFs) were measured by time-resolved retarding field analyzer (RFA) in the substrate position. Thin films were characterized by X-ray photoelectron spectroscopy (XPS), X-ray diffractometry (XRD) and X-ray reflectometry (XR). Properties and crystallography of Ti-Cu films are discussed as a function of ion energy which is affected by the mode of sputtering. It was found that IVDFs measured in pulsed discharges exhibit double-peak distribution. The IVDFs reach the maximum at ion energies about  ~8 eV. The ion saturated current is highest in dual-HiPIMS discharge (~5 μA/cm²) and is mostly represented by Cu⁺ and Ar⁺ ions. The mode of sputtering influences chemical composition and film formation. The copper forms polycrystalline fcc-phase while much smaller Ti particles enwraps the copper crystallites or are part of a solid solution.     

A contribution to the global formulation of the higher-order Poincaré-Cartan form

The global formulation of the higher-order Poincaré-Cartan form for Lagrangian field theories in the calculus of variations is re-examined in terms of the theory of lifts of tensor fields on a manifold to its higher-order prolongated jet bundles.Partially supported by CNPq, Brazil, Proc. MA 30.1115/79.     

Geometric Structures of Fractional Dynamical Systems in Non‐Riemannian Space: Applications to Mechanical and Electromechanical Systems

Based on a non‐Riemannian treatment of geometric objects, the geometric structures of fractional‐order dynamical systems are investigated. A fractional derivative describes non‐local effects across a space or a history encoded in memory features of the system. A system of fractional‐order differential equations is formulated in film space that includes fictitious forces. Film space is a geometric space whose coordinates comprise time, and the geometric quantities vary in time. Fractional‐order torsion tensors that appear are related to the dissipated energy and the energy conversions between subsystems and power of the system. The geometric treatment is then applied to damped‐harmonic and fractional oscillators and the hybrid electromechanical Rikitake system. The damped‐harmonic oscillator is characterized by two torsion tensors, whereas the fractional oscillator is characterized by one torsion tensor. Herein, the fractional order of the derivative of the metric tensor is used to characterize the damping of the fractional oscillator. The energy conversions between electromechanical subsystems in the Rikitake system are characterized by the torsion tensor. These results suggest that the non‐Riemannian geometric objects can represent the non‐local properties of fractional‐order dynamical systems.     

On the stability of a classical plasma

A linearized self-consistent variational approach is employed to investigate the (thermodynamic) stability of a classical plasma (electrons and positive ions). It is shown, by using this approach, that a classical plasma, which consists of ions “dressed” with electrons, has a well-defined thermodynamics. In the strong-coupling regime the “plasma” is a solid, while, on passing to the weak-coupling regime, it becomes gradually a liquid, a non-ideal gas, and, finally, in the weak-coupling limit, it behaves as an ideal classical gas. A van der Waals-type equation is established for the plasma non-ideal gas.     

Observation of the coherence between the plasma density fluctuations in the core and at the edge of the plasma column in the L-2M stellarator

Results are presented from the measurements of the radial coherence between the plasma density fluctuations in the core and at the edge of the plasma column in the L-2M stellarator. It is found that the radial coherence between these fluctuations is fairly high: the coherence coefficient attains a value of higher than 0.5 for the spectral wavelet components with frequencies lying in the range from several kilohertz to 30 kHz. The statistical characteristics of density fluctuations are also studied. It is shown that the power distribution function of the plasma density fluctuations in the plasma core differs from Gaussian.     

Derivatives of the hamiltonian eigenvalues with respect to parameters

Explicit equations are obtained which define the derivatives with respect to parameters entering in the Hamiltonian of the eigenvalues of the Hamiltonian (through third order in the degenerate and nondegenerate cases). A method is indicated of introducing a basis depending on the parameters. A compact expression is obtained for the correction of arbitrary order to the energy in the Rayleigh-Schrodinger perturbation theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 3, pp. 72–75, March, 1972.     

Kinetic theory of semibounded plasma with randomly scattering boundary

The electromagnetic fields created by an arbitraty distribution of sources in a semibounded plasma with random Scattering of charged particles by the boundary surface are calculated. A model boundary condition is employed that ensures simultaneously preservation of the number of particles and the absence of particle flow through the boundary. The electric-susceptibility tensors, surface impedances, and coefficients of reflection of plane electromagnetic waves from a plasma half-space are found. Invariance of the distributions of s-polarized electromagnetic waves with respect to the selected model of a randomly scattering boundary is established.     

Compton散射强光子流在等离子体通道中的传输特性

给出了冷等离子体中高阶相对论下多光下非线性Compton散射的光子流在等离子体通道中的传输方程,研究了高阶相对论效应对散射光子流传输的影响。在近轴近似下,散射强光子流依然有较浅的“势阱”方程。当散射强光子流强度较大时,高阶相对论效应变得更加重要：它减小了散射光束宽的振荡幅度,同时加快了散射光束宽的振荡速度。当散射强光子流功率大于或等于相对论临界功率时,高阶相对论效应避免了散射强光子流强度随传输距离出现无限大的奇异性。给出了散射强光子流的平衡解存在的条件。     

基于边界元方法的超导核磁共振成像设备高阶轴向匀场线圈优化算法

在磁共振成像设备中,为了消除目标区域内的高阶谐波磁场分量,传统方法采用无源匀场,但该方法匀场精度较低,针对性较差,适用于全局匀场,而有源匀场则可以通过优化线圈分布来产生所需要的特定的磁场分布.但是,由于匀场线圈线型的复杂度会随着线圈阶数的增加而增加,难以满足设计需要,因此本文提出了一种用于磁共振成像超导匀场线圈系统的多变量非线性优化设计方法.该方法基于边界元方法,将匀场线圈所产生的磁场与目标磁场之间的偏差作为目标函数,线匝间距、线圈半径等作为约束条件,通过非线性优化算法,得到满足设计要求的线圈分布.通过一个中心磁场为0.5 T的开放式双平面磁共振成像超导轴向匀场线圈的设计案例,说明本方法具有计算效率高、灵活性好的特点.     

Average coherence with respect to complementary measurements

We investigate the average coherence with respect to a complete set of complementary measurements.By using a Wigner-Yanase skew information-based coherence measure introduced in Luo and Sun(2017 Phys.Rev.A 96,022130),we evaluate the average coherence of a state with respect to any complete set of mutually unbiased measurements and general symmetric informationally complete measurements,respectively.We also establish analytically the relations among these average coherences.     

How to measure the earth's velocity with respect to absolute space

In our absolute space-time theory the time dilation is treated as an absolute phenomenon and it appears as a result of the motion of the material systems with respect to absolute space. Hence, comparing the courses of two atomic clocks put at two antipodal points of the equator (which in the different hours of the day move with different velocities with respect to the absolute space), one can establish the velocity of the Earth as a whole.     

Scaling with respect to disorder in time-to-failure

We revisit a simple dynamical model of rupture in random media with long-range elasticity to test whether rupture can be seen as a first-order or a critical transition. We find a clear scaling of the macroscopic modulus as a function of time-to-rupture and of the amplitude of the disorder, which allows us to collapse neatly the numerical simulations over more than five decades in time and more than one decade in disorder amplitude onto a single master curve. We thus conclude that, at least in this model, dynamical rupture in systems with long-range elasticity is a genuine critical phenomenon occurring as soon as the disorder is non-vanishing. Received: 11 July 1997 / Revised: 6 November 1997 / Accepted: 10 November 1997     

Parametric study of cylindrical and spherical dust ion acoustic shock waves with two temperature electrons in dusty plasma relevant to Saturn's E ring

We have performed numerical analysis of the one-dimensional dynamics of the cylindrical/spherical dust ion acoustic shock waves in unmagnetized dusty plasma consisting of positive ions, immobile dust particles, and nonextensive distributed cold and hot electrons. A multiple-scale expansion method is used to derive Burgers Equation (BE) and modified Burgers equation (MBE) by including higher order nonlinearity. The basic characteristics of the shock waves have been analysed numerically and graphically for different physical parameters relevant to Saturn' E ring through 2D figures. The parametric dependence of dust ion acoustic shock waves on some plasma parameters nonextensive index, density, and temperature of cold and hot electrons, concentration of dust particles, thermal effects and kinematic viscosity of ions is explored. Furthermore, it is found that the nonplanar geometry effects have an important impact on the establishment of shock waves. The amplitude of the wave decreases faster as one departs away from the axis of the cylinder or centre of the sphere. Such decaying behaviour continues as time progresses. It is also found that an increasing dust concentration decreases the amplitude of the dust ion acoustic shock waves.     

激波/边界层干扰对等离子体合成射流的响应特性

利用高速纹影系统和数值模拟方法研究了激波/边界层干扰对逆流喷射的等离子体合成射流的响应特性,并揭示了流动控制机理.实验在来流马赫数Ma=3.1的风洞中进行,测试模型采用钝头体和压缩斜坡的组合模型,等离子体合成射流激励器安装在钝头体头部.纹影系统捕捉了放电频率为f=1 kHz和f=3 kHz的激励对附体激波形态和分离激波运动的控制效果.等离子体合成射流使压缩斜坡激波/边界层干扰区域的起始点向下游移动,分离泡尺寸减小,附体激波强度减弱,发生弯曲,再附点移向上游,与此同时分离激波向附体激波逼近.与f=3 kHz激励相比,f=1 kHz激励的射流流量更大,对激波/边界层干扰的影响范围更广、控制效果更好.通过数值模拟,揭示了射流与来流相互作用对下游流场的作用机理:射流与来流相互作用诱导出大尺度旋涡,大尺度旋涡耗散发展增强了近壁面流场的湍流度;压缩斜坡上游近壁面的流场性质发生变化,进而导致了压缩斜坡激波/边界层干扰区域流动的变化.     

New experimental data on the possibility of influencing fluctuational particle fluxes in a L-2M stellarator edge plasma

The results of an experiment show that in the edge plasma of a L-2M stellarator the radial electric field is one of the determining factors influencing the formation of spatial structures and fluctuational particle fluxes. A point where the poloidal velocity of the fluctuations reverses is observed in an experiment with a high neutral-gas flux from the chamber walls. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 560–565 (10 October 1998)