30GHz RF脉冲展宽器

RF脉冲展宽器用来把高功率窄脉冲变换为较低功率的长脉冲,CLIC实验装置CTFⅡ中的功率提取结构已经可以提供功率达280MW,脉宽16ns的30GHz RF脉冲,为了用它来研究加速结构的最高表面场强和脉宽的关系,设计了30GHz RF脉冲展宽器,完成了系统设计,微波部件的设计及加工,系统的调试,最后安装在CTFⅡ上,并成功进行了高功率实验.     

Numerical solutions to the time-dependent Bloch equations revisited

The purpose of this study was to demonstrate a simple and fast method for solving the time-dependent Bloch equations. First, the time-dependent Bloch equations were reduced to a homogeneous linear differential equation, and then a simple equation was derived to solve it using a matrix operation. The validity of this method was investigated by comparing with the analytical solutions in the case of constant radiofrequency irradiation. There was a good agreement between them, indicating the validity of this method. As a further example, this method was applied to the time-dependent Bloch equations in the two-pool exchange model for chemical exchange saturation transfer (CEST) or amide proton transfer (APT) magnetic resonance imaging (MRI), and the Z-spectra and asymmetry spectra were calculated from their solutions. They were also calculated using the fourth/fifth-order Runge-Kutta-Fehlberg (RKF) method for comparison. There was also a good agreement between them, and this method was much faster than the RKF method. In conclusion, this method will be useful for analyzing the complex CEST or APT contrast mechanism and/or investigating the optimal conditions for CEST or APT MRI.     

On the analytical solution of the optical Bloch equations

We present in this note the analytical solution of the optical Bloch equations for different scenarios of the parameter space. Our method partially follows the reported by H-R. Noh and W. Jhe [Opt. Commun. 283, (2010) 2353]. However, it differs substantially with the analytical solution reported by these authors. We use the exact solution provided by numerical standard algorithms as a pattern for comparison purposes. We find out a perfect matching of our solution and the numerical one.     

Analytic solutions of the optical Bloch equations

We present analytic solutions of optical Bloch equations. We found that the solutions exhibit two different types of the behavior: one is oscillatory, and the other is a simple decay. The boundary dividing the two different types of solutions is exactly calculated in a two-dimensional space of the laser detuning and Rabi frequency. We also obtained simple analytic solutions for special conditions.     

Chaos Synchronization of Nonlinear Bloch Equations Based on Input-to-State Stable Control

In this paper, we propose a new input-to-state stable （ISS） synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality （LMI） approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.     

射频场照射下扩展的Solomon方程及射频场的照射对异核体系弛豫速率与NOE的影响

根据WBR理论,采用“改进的矩阵计算方法”,推导出了射频场照射下扩展的Solomon方程,并据此研究了射频场的照射对异核体系各种弛豫速率与NOE的影响,得出了如下结论:1)给出的方程比Boulat和Bodenhausen的方程更准确、更具普遍性,能够具体描述射频场对各种弛豫速率与NOE的影响.2)射频场的照射对纵向与横向弛豫速率的影响甚微,可以忽略,而交叉弛豫速率在射频场的照射下则有一定程度的降低.3)射频场的照射将使NOE变弱,且射频场越强,NOE越弱. 关键词： 核磁共振 Solomon方程 弛豫 射频场     

Bloch方程的精细时程积分及其在射频脉冲设计中的应用

射频脉冲的频率选择性直接影响磁共振成像的质量，而射频脉冲的优化设计又归结为对Bloch方程的求解.尽管在某些情况下Bloch方程存在解析解，但由于其缺乏通用性而且形式上过于复杂而难于得到实用.本文提出一种Bloch方程的精细时程积分算法，并结合全局优化算法给出一个完整的射频脉冲设计方案.精细积分算法具有高效、高精度的特点，对于射频脉冲的设计很有裨益.数值算例表明，设计所得的射频脉冲具有较好的频率选择性. 关键词： 磁共振成像 射频脉冲 Bloch方程 精细时程积分     

Extended Hyperbola Function Method and Its Application to Nonlinear Equations

An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.     

A New General Algebraic Method and Its Application to Shallow Long Wave Approximate Equations

A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.     

On the investigation of nonlinear waves of the Hirota and the Maxwell–Bloch equation in nonlinear optics

In this paper, considering the Hirota and Maxwell-Bloch (H-MB) equations which is governed by femtosecond pulse propagation through two-level doped fibre system, we construct the Darboux transformation of this system through linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions (both bright and dark breathers) of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.     

Design of self-refocused pulses under short relaxation times

The effect of using self-refocused RF pulses of comparable duration to relaxation times is studied in detail using numerical simulation. Transverse magnetization decay caused by short T2 and longitudinal component distortion due to short T1 are consistent with other studies. In order to design new pulses to combat short T1 and T2 the relaxation terms are directly inserted into the Bloch equations. These equations are inverted by searching the RF solution space using simulated annealing global optimization technique. A new T2-decay efficient excitation pulse is created (SDETR: single delayed excursion T2 resistive) which is also energy efficient. Inversion pulses which improve the inverted magnetization profile and achieve better suppression of the remaining transverse magnetization are also created even when both T1 and T2 are short. This is achieved, however, on the expense of a more complex B1 shape of larger energy content.     

A Solution to Einstein's Equations for the Mixmaster Universe in Complex General Relativity

Starting from Einstein's equations of the Classical General Relativity, new kinds of solutions for the Mixmaster model are explored. By dispensing with the extension to the complex variable field, which is usual in problems such as the Laplace equation or the harmonic oscillator, in a similar manner to that of Quantum Mechanics, the equations appear to have solutions that belong to the complex General Relativity. A first integral is performed by establishing a separation of the first derivatives. Then a second integral is obtained once the respective equations with separate variables are found and whose integrals provide a family of complex solutions. However, reality conditions do not seem to be easily imposed at this stage. Above all, it is significant that the classical Einstein's equations for the debatably integrable Mixmaster model present complex solutions.     

Lame Function and Its Application to Some Nonlinear Evolution Equations

In this paper, based on the Lame function and Jacobi elliptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions.     

光学Maxwell-Bloch方程的数值算法研究及其应用

建立了高准确度快速求解均匀展宽二能级体系光学Maxwell-Bloch耦合方程的数值算法.通过与特定条件得到的解析解的比较,验证了算法所具有的高收敛性和稳定性,并可保持算法的误差阶数,因此算法是可靠并实用的.应用该算法数值求解了一般条件下的MB方程,并由计算结果分析了失谐量、弛豫时间、初始光强对光脉冲在介质中的传播及对Bloch矢量演化的影响.所建立的数值算法对MB方程以及修正的这类偏微分方程组具有普适性.     

Lame Function and Its Application to Some Nonlinear Evolution Equations

In this paper, based on the Lame function and Jacobi emptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions.     

The Bloch Equations for an AB System and the Design of Spin-State-Selective RF Pulses for Coupled Spin Systems

Optimized AM/FM pulses are described which excite an arbitrary coherence of a coupled spin system with optimal intensity. These pulses may become important for creating maximum signal intensity in MQC-filtered and polarization-transfer experiments in HRNMR and in vivo spectroscopy. For an AB system, for example, a pure DQC or ZQC state is obtained (100%) compared to maximal 50% with a conventional π/2-π/2 MQC pulse sequence. The design and numerical optimization of these pulses, with pulse times of about 1/2J (J is the coupling constant), are described. Examples of three of these spin-state-selective pulses (SSSP) for an AB system are given; simulations and experiments confirm their expected performance. To get some insight in the relations between the expectation values of the several coherences under the influence of Zeeman, J-coupling, and RF terms, Bloch-like equations for a proton AB system are derived, with neglection of relaxation. A system of 15 first-order coupled differential equations is found. A solution to these equations is given for the evolution of the zero-quantum coherence and longitudinal magnetization.     

面向超短波接收机射频前端的电磁脉冲效应仿真与效应分级方法

针对接收机射频前端在电磁脉冲环境作用下的电磁损伤过程模拟问题,以超短波接收机为具体研究对象,基于超外差式接收机电路功能模型,采用Verilog-a和SPICE网表联合建模方法,建立了射频前端低噪声放大器（LNA）电磁脉冲效应仿真模型(Extended LNA Model),并通过S参数仿真和瞬态仿真验证了LNA电磁脉冲效应模型具备正常功能仿真能力;为验证该模型的电磁脉冲损伤模拟能力,以标准电磁脉冲波形作为激励,以偶极子天线作为简化的天线前门耦合通道,在不同强度电磁脉冲作用下,接收机中频电路信号输出表现出了无影响、干扰、损毁的电磁脉冲效应过程,说明了建模方法的有效性;最后以EMP-天线耦合电压峰值作为阈值指标,分析得到了超短波接收机不同电磁脉冲效应等级对应的电压峰值阈值数据。     

用于长脉冲多束团直线加速器的SLED系统

根据长脉冲多束团直线加速器对输入微波波形的要求,系统研究了带有SLED的微波系统,由SLED基本理论推导了输出RAMP波形和平顶波形脉冲时SLED所需的输入波形,给出SLED的参数优化方法.用冷测实验对所发展的理论进行了验证,第一次用SLED产生了RAMP波形和平顶波形的RF脉冲.