Generic structure of externally driven tearing modes instabilities

A major limit to steady state and advanced high operation of tokamaks of reactor class is due to the onset of tearing modes that develop magnetic and may cause loss of energy confinement or a major disruption. Here the structure of a classical problem about the effects of external control helical fields is analysed and it is shown to offer a general paradigm of response of low order classical and neoclassical tearing modes to a wide class of external perturbations. New results of principle on the structural stability of the response model are obtained, leading to a clear interpretation of the role of “seed islands" in the onset of neo-classical tearing modes and the role of finite ion larmor radius corrections to Ohm's law. Received 12 November 2001 and Received in final form 4 January 2002     

OPCPA系统中光栅对不平行度对脉冲时间波形的影响

 利用光线追迹法和四阶龙格-库塔法分析了光参量啁啾脉冲放大系统中实际展宽器和压缩器所带来的各阶色散，并将其代入放大过程数值模拟了脉冲变化的情况，讨论了压缩器光栅对表面不平行、刻线不平行、信号光强度、泵浦光强度等因素对输出脉冲宽度和时间波形的影响。结果表明，光栅对表面不平行将引起脉冲宽度变大，且光栅顺时针旋转对脉冲宽度和波形影响更大。而光栅刻线不平行时，当仅考虑二阶色散时，夹角为0.8°时脉宽最小，考虑到三阶色散时，夹角为1°脉宽最小，且光栅顺时针和逆时针旋转对脉冲的作用相同。对实际OPCPA系统，当放大晶体材料及长度一定时，尽量调整压缩器光栅平行，信号光强度和泵浦光强度有一最佳值能使输出脉冲宽度达到最小。     

Parametric amplification at low-frequency pumping and generation of four-mode entangled states

We show that parametric amplification at low-frequency pumping can be implemented in aperiodic nonlinear photonic crystals. In this process, the intensities of the waves with frequencies higher than the pumping frequency increase with increase in the interaction length as in the case of the standard process of parametric amplification at high-frequency pumping. The process under consideration includes a nondegenerate parametric down-conversion followed by two parametric up-conversions in the same pumping wave. As a result, generation at four new frequencies arises. Quantum analysis of the process demonstrates the presence of entanglement in the states of four modes. Talk presented at the oral issue of J. Russ. Laser Res. dedicated to the memory of Professor Vladimir A. Isakov, Professor Alexander S. Shumovsky, and Professor Andrei V. Vinogradov held in Moscow February 21–22, 2008.     

A procedure for one-parametric linear programming

A procedure is proposed for the parametric linear programming problem where all the coefficients are linear or polynomial functions of a scalar parameter. The solution vector and the optimum value are determined explicitly as rational functions of the parameter. In addition to standard linear programming technique, only the determination of eigenvalues is required. The procedure is compared to those by Dinkelbach and Zsigmond, and a numerical example is given.     

An O(n 2) Active Set Algorithm for Solving Two Related Box Constrained Parametric Quadratic Programs

Recently, O(n ²) active set methods have been presented for minimizing the parametric quadratic functions (1/2)x Dx–a x+| x–c| and (1/2)x Dx–a x+(/2)( x–c)², respectively, subject to lxb, for all nonnegative values of the parameter . Here, D is a positive diagonal n×n matrix, and a are arbitrary n-vectors, c is an arbitrary scalar; l and b are arbitrary n-vectors such that lb. In this paper, we show that each one of these algorithms may be used to simultaneously solve both parametric programs withno additional computational cost.     

Amplification Coefficient of the Anti‐Stokes Component of Raman Scattering

The theory of intracavity parametric interaction of the components of Raman scattering is developed in the prescribedintensity approximation, which takes into account the reverse reaction of the excited waves to the pumpingwave phase. It is shown that one can substantially improve the conversion efficiency or the amplification coefficient of the antiStokes component by selection of the intracavity geometry, the optimum phase relation between the interacting waves, the pumping level, and the phase mismatch.     

Primal-Dual Solution Perturbations in Convex Optimization

Solutions to optimization problems of convex type are typically characterized by saddle point conditions in which the primal vector is paired with a dual multiplier vector. This paper investigates the behavior of such a primal-dual pair with respect to perturbations in parameters on which the problem depends. A necessary and sufficient condition in terms of certain matrices is developed for the mapping from parameter vectors to saddle points to be single-valued and Lipschitz continuous locally. It is shown that the saddle point mapping is then semi-differentiable, and that its semi-derivative at any point and in any direction can be calculated by determining the unique solutions to an auxiliary problem of extended linear-quadratic programming and its dual. A matrix characterization of calmness of the solution mapping is provided as well.     

Parametric Transducers for the Advanced Cryogenic Resonant-Mass Gravitational Wave Detectors

It is shown that a large improvement in liquid helium and ultra-cryogenically cooled resonant-mass gravitational wave detectors can be achieved through improved parametric transducers using either low loss sapphire dielectric resonators or niobium re-entrant cavities. Performance is analysed in relation to the existing resonant bar antenna Niobe and to massive spherical detectors. Applied to Niobe, a millisecond burst sensitivity of order 10^–20 can be achieved, corresponding to a spectral strain sensitivity of 2 × 10^-22 Hz with a 50 Hz bandwidth. Applied to an ultra-cryogenic 117 tonne spherical detector made from CuAl, a spectral strain sensitivity of better than 2 ×10^-23/ Hz with a bandwidth of order 100 Hz can be achieved, which is close to the quantum limit. This sensitivity is comparable to that of advanced interferometer detectors at this frequency.     

发散光束抽运的宽带光参量啁啾脉冲放大系统的理论研究

对发散光束抽运的光参量啁啾脉冲放大器的增益带宽进行了系统的理论研究.采用空间傅里叶变换和四阶Runge-Kutta算法，分别模拟了非衍射极限情况下的高斯光束和空间频谱为矩形的发散光束作为抽运光时的增益曲线.结果表明：不管是在可见光或是在近红外光谱区，用发散光束均可以明显地改善光参量啁啾脉冲放大系统的增益带宽.选取合适的发散角和抽运光强，可以获得高增益、宽谱带的信号光输出. 关键词： 光参量啁啾脉冲放大 增益带宽 发散角 高斯光束