FUNDAMENTAL AND APPLIED FUNDAMENTAL RESEARCH•High Power Laser and Accelerator 136

High Power Laser and Accelerator

1 Application of CHEL3300 Excimer Laser in Heaven-I System

GAO Zhi-xing, TONG Xiao-hui, XIANG Yi-huai, DAI Hui, TANG Xiu-zhang

The discharge pumping laser of CHEL3300(China Highpower Excimer Lab 3×300 mJ) was developed by the Department of Experimental Physics of University of Szeged(DEP) and the High Power Excimer Laser Laboratory (HPELL) of China Institute of Atomic Energy. It has an unique configuration with three parallel channels controlled by one thyratron and one common “distributed” magnetic switch.

The uniformity of its ASE is about 2% with 40 mJ effective energy output for each channel, which is compatible with LPX-150. To make full use of the electronic beam power, it acts as an amplifier with 50 mJ×3 input and 500 mJ×3 output in the Heaven-I system. On this condition, all the amplifiers in the system keep gain saturation so that the uniformity of the beam profile on target maintains 2%.

2 Experimental Investigation of Interaction of Ultra-Short Pulse LaserWith Atomic Clusters

LI Ye-jun , WANG Lei-jian, XI Xiao-feng, ZHANG Hai-feng, ZHANG Ji, TANG Xiu-zhang

Effects of experimental conditions to laser absorption coefficient at the interaction of ultra-short pulse laser with atomic clusters are investigated. Big clusters are easily formed for high Z rare gases at same backing gas pressure. The size of cluster is large at high backing gas pre ssure, and absorption coefficient is high at large cluster condition. The effects of laser wavelength (744 and 248 nm) and laser intensity and laser polarization to absorption coefficient are also investigated. Experiment results indicate short wavelength laser is easily absorbed by clusters. At the range of 1015-1016 W/cm2, laser absorption coefficient increases with laser intensity. P-polarization laser is easily absorbed than S-polarization laser by clusters. Absorption coefficients of different experiment conditions are measured by using energy meter. The absorption coefficient of Xe clusters is up to 50% at 2 MPa backing gas pressure at room temperature. Ion spectrum is measured by time of flight (TOF) spectrometer. A simple theory modeling of laser-cluster interaction is founded.

3 Measurements of Free-Surface Velocity Using Optically Recording Velocity Interferometer System in Equation of State Experiments

LU Jian-xin, WANG Zhao, LIANG Jing, SHAN Yu-sheng, ZHOU Chuang-zhi, TANG Xiu-zhang

137 Annual Report of China Institute of Atomic Energy 2005

Recent development of high-power laser facilities leads us to investigate the equations of state (EOS) of condensed matters in the laboratory. But the shockwave induced by laser is an instantaneous process, and the existing time of shockwave is about several nanosecond or shorter. An optically recording velocity interferometer system (ORVIS) is developed to research the free-surface velocity of targets in the equations of state experiments. The electronic streak camera is used to record the fringe shifts which are proportional to the free-surface velocity. The whole velocity history can be got by analyzing the fringe shift data. The experiments are carried in the High Power Excimer Laser Laboratory of China Institute of Atomic Energy.

The experiment setup is illustrated in Fig. 1. Laser produced by argon-ion laser (Beamlock 2060-10 s, Spectra) whose intensity is 0.8 W operating in a single mode at 514.5 nm pass through a 3 mm hole in the mirror M3. Through the lens L2(f=100 mm, Φ=20 mm), the laser is focused on the target back-surface whose velocity is to be monitored. The diffuse light is collected by L2 and separated from the incoming light by M3. The collimated light enters a wide-angel Michelson interferometer. The interference pattern is focused in the streak camera by a cylindrical lens CL1. The time resolution of ORVIS in the experiments is about 179 ps.

Fig.1 Schematic description of ORVIS and the equation of state experiment

L1, L2─lenses; L3─telescope; M1, M2, M3─high reflection mirrors; PS1, PS2─beam splitters; CL─cylindrical lens;

PD1, PD2, PD3─photoelectric diodes; E1─etalon

The experiments were carried out on the six laser beams of high power KrF laser Heaven-I of China Institute of Atomic Energy. The wavelength and the maximum energy of the laser beams are 248.4 nm and 200 J with pulse duration 26 ns and focus spot diameter 500 μm. The beam is smoothed with echelon-free induced spatial incoherence (EFISI).

The single-layer iron targets (20 μm) are used in the experiments. Figure 2 shows a fringe pattern (a streak camera image), time proceeds from right to left. The fringe pattern shift can be seen in Figure 2. When a shock wave arrives at the rear surface of the driver, the fringes shift to the top by about 2.6 fringes spacing.

The free-surface velocity of the target can be calculated by Figure 2. Figure 3 is the velocity history of the target. The maximum velocity of the iron target is 3.86 km/s with shifts of 2.68 fringes spacing. There is no fringe loss in the experiments.

The main advantages of the ORVIS over previous interferometers used in the equation of state

FUNDAMENTAL AND APPLIED FUNDAMENTAL RESEARCH•High Power Laser and Accelerator 138 experiments are the improved time resolution and the simple data reduction. It meets the need of measuring the equation of state and more experiments will be carried.

Fig.2 Fringe shift results in the rear surface velocity of iron

Fig.3 Free surface velocity of iron

Experimental data by 20 μm iron and 6.24×1011 W/cm2

4 Theoretical Analysis for Steps of the Velocity Curves for Double Layer Flyers by Numerical Simulation

LIANG Jing, SHAN Yu-sheng, LU Jian-xin, WANG Zhao, ZHOU Chuang-zhi

Hyades is a one-dimensional, three-temperature Lagrangean hydrodynamic code, mainly used for physical simulations of the laser driven shock wave in the flyer or target, from which we can get some parameters of the shock wave and offer instructions for target design.

We got the velocity curves for double layer flyer with Hyades, for the case of the same laser intensity and the same thickness of 4 μm tantalum flyers, but different thickness of Kapton films. As shown in Fig.1, x-coordinate is time, y-coordinate is flyer velocity. We can see for the case of 90 μm, it has a step at the velocity about 7 km/s. For the case of 110 μm and 130 μm, it has a similar result, but more and more indistinct. For the case of 150 μm, the step has disappeared. From the velocity distribution of the layers in the code, we can find that the velocity discrepancy for the case of 90 μm is even large, which means the flyer has a poor stability. However, for the case of 150 μm, the velocity discrepancy is rather uniform,

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which means the flyer is steady.

Fig.1 Velocity curves of the double layer flyers with different ablator thickness

1－90 μm Kapton; 2－110 μm Kapton; 3－130 μm Kapton; 4－150 μm Kapton

Changing the laser intensities and the material of the flyer, we redo the simulation. The same results are repeated. So, it must be some universal rules, and we can get the theoretical hydrodynamical explain.

For a certain density of the ablator and a certain laser intensity, we can get a critical thickness by theoretical deduction:

If the thickness of the ablator is smaller than the critical thickness, the shock wave increases while it reaches the interface of the ablator and the flyer. If the thickness of the ablator is larger than the critical thickness, the shock wave is stable when it reaches the interface. So, for the first case, there remains a large part of laser energy not transforming to the kinetic energy of the flyer, but back into the ablator by the reflect shock wave, which can lead the second shock wave after a time, accordingly the velocity curve of the flyer appears step. For the second case, the laser energy is mainly transformed to the kinetic energy of the flyer, the step disappear. Thus, we find a theoretical model for the above simulation result, and it offers some convenience to know the characteristics of double layer flyer and instruct the target design.

5 Development of New MOPA System for Heaven-Ⅰ

XIANG Yi-huai, GAO Zhi-xing, TONG Xiao-hui, DAI Hui, TANG Xiu-zhang, SHAN Yu-sheng

At present, a new MOPA system provided with smoothing function is built. The scheme is shown in

Fig.1, which includes a excellent beam profile ASE source(rebuild from LPX-150), one three-channel

discharge pumped KrF laser, two stage two-electron-pumped KrF amplifiers(pre-amplifier and main-

amplifier), the optical code system and decode system, the optical focusing system. A technique called of

echelon-free induced spatial incoherence is adopted for producing smooth target beam profiles. The target

FUNDAMENTAL AND APPLIED FUNDAMENTAL RESEARCH•High Power Laser and Accelerator 140 is irradiated by six beams with image plane at the same time.

Fig.1 Scheme of the MOPA system

The system passed the test and check. The basic parameters are as follows: the total energy is 158 J, the stability of energy is 4%, the pulse duration is 25 ns, the effective size of focusing spot is 400 μm, the ununiformity is about 1.6%, and the power density on the target is about 3.7×1012 W/cm2.

6 Topological Properties and Transition FeaturesGenerated by Hybrid Preferential Attachment Method

FANG Jin-qing, LIANG Yong

A simple question is: Are the real networks fundamentally random preferential attachment? Is it truth that real-world networks really are of random process without any determination process? Why most real-world growing networks have both of scale-free and small world properties? Answer of our intuition is inappropriate to describe so many real-world systems. Because a fundamental fact is that the real world basically is dominated by both of regular and random factors for a unified world. Although regular networks and random networks are both useful idealizations, interactions in real world are neither completely regular nor completely random, and lie in somewhere between the extremes of order and randomness.

Based-on fundamental fact of abundant in nature and the background above, it is very natural and

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reasonable to investigate the topological transition from random to regular in the scale-free model proposed by Barabasi and Albert (so-called BA model), in contrast to the study of the transition from regular to random in the small-world model. Therefore we propose a new hybrid preferential attachment model with both of random and determination preferential attachment, which can apply to a class of complex networks and has both scale-free and small-world properties. That means that the real world is a unified one with both of random and determination world, in which random factor is not dominated but play very important construct role in it. Determination factor with complex interaction is often dominated in real-world networks, especially for nonlinear dynamical and chaotic dynamical complex networks. In our model the original random preferential attachments in the BA model are replaced alternatively by determination preferential attachment according to a certain hybrid ratio d/r of random preferential attachment to determination preferential attachment. In this work, numerical simulations results show that hybrid network model (HNM) of random and determination preferential attachment can produce a better power-law distribution and eliminate heavy random tails in the original BA model.

Our main ideas and algorithms of the HNM are as follows. 1) We not only consider random preferential attachment (RPA) but also introduce determination

preferential attachment (DPA) in the model. The first step of the algorithm of the HNM is described by growth which version is the same as the BA model. Starting with a small number m0 of node, at every time step, then adding a new node with m (≤m0 ) edges that link the new node to m different nodes already present in the network.

2) The second step of the algorithm of the HNM is to apply hybrid preferential attachment. To do this, a new quantity, a ratio d/r is introduced, which is defined as

(1)

Here intervals are the number of uniform time steps. The ratio d/r can be selected from zero to infinity. There two types of preferential attachment are as follows.

3) Starting with the general rule of the RPA, which is the same as the BA model, apply the connective-adding possibility Pi (ki). Assume that the Pi (ki) that a new node will be connected to node i depends on the degree ki of node i, and is given by

(2)

After r time steps of the RPA, this procedure creates a network with N=r+m0 nodes. Rank of node’s degree is then reordered from largest to smallest as k1>k2>…> kn after the RPA.

4）The DPA is to be conducted for d time steps according to rank of node degree above when choosing the nodes to which the new node connects. After d time steps, this procedure creates a network with N=r+d+m0 nodes. Then steps 3) and 4) of the algorithm procedure are repeated.

In this algorithm, two kinds of preferential attachment are applied in turns. Firstly, the RPA are applied for r time steps according to value of d/r. Secondly, the DPA are applied for d times. The procedure is carried on, until the desired total number N of network size is finally reached.

Following the ideas and the algorithm described above, some simulations were performed. The resulting scale-free properties and its transition from random to regular in the hybrid network model are briefly summarized as follows.

Firstly, the average path length is decreased but average clustering coefficient is increased in the HNM, respectively, when the ratio d/r is increased. Clearly, the topological properties of the HNM have

FUNDAMENTAL AND APPLIED FUNDAMENTAL RESEARCH•High Power Laser and Accelerator 142 both scale-free and small-world effects. Secondly, the exponent of the power-law is changed significantly from 2 to very big as the radio d/r is increased significantly in the proposed HNM. That implies that the exponent of the power-law is very sensitivity to the radio d/r in the HNM. Moreover, there exists a threshold at d/r = 1/1 beyond which the exponent in the power law increases rapidly and it may tend to infinity if there is completely DPA instead of the RPA ( r=0, d/r), in this extreme case, the power-law disappears. Thirdly, the RPA is the key mechanism for generating scale-free but the DPA can plays an important role in generating power-law without random tail and in enhancing “rich-gets-richer” phenomenon. In comparison of the HNM with the BA model and the random graph, the HNM scheme is closer to real-world complex networks than the other two models. Therefore the hybrid preferential attachment may be a unified and coherent mechanism for generating scale-free distribution and small-world effects in a network.

7 Virtual Design and Installation of Linacs

YIN Meng

The virtual installation and the virtual control become more and more important in accelerator design. By using the design software, we can achieve virtual design and installation quickly and easily.

When designing, we can amend them easily. Intuitionistic 3D parts can be used to analyze strengths and weaknesses, to analyze stress and to manage design data. It also offers a wide variety of specialized features that help us design accelerators.

Computer aided software will reduce our design time, simplify our data management, make accelerator development more efficient, and provide a comprehensive and integrated design solution with broad functionality at an outstanding value.

8 Rebuilding of the UHV System of a 10 MeV Electron Linac

YIN Meng, HAN Guang-wen

A 10 MeV electron linac with the beam power of 15 kW was developed for the irradiation of food. The main goal of the vacuum system is to maintain a mean pressure of 5×10－6 Pa.

The pumping system was rebuilt in order to improve the vacuum system. Three of the five sputter ion pumps were changed. The sputter ion pump near the electron gun was changed from 3 L/s to 8 L/s, the sputter ion pump near the entrance of the accelerating tube was changed from 25 L/s to 50 L/s and the sputter ion pump near the exit of the accelerating tube was changed from 50 L/s to 100 L/s.

The new system runs well and the linac is under testing now.

9 Ultra-high Vacuum System of 350 keV Cockcroft-Walton Accelerator

YIN Meng, HAN Guang-wen

143 Annual Report of China Institute of Atomic Energy 2005

A 350 keV Cockcroft-Walton accelerator was developed for irradiation of plastic film. The main goal of the vacuum system is to maintain a mean pressure of 5×10－ 6 Pa. The vacuum

chamber is almost entirely made of stainless steel. The vacuum system is completely oil free and all of the vacuum components are all metallic type.

The design of the pumping system is optimized in order to install the required pumping speed. A 200 L/s sputter ion pump was chosen. The sputter ion pump is between the exit of the accelerating tube and the scan horn.

The system runs well and provides the Cockcroft-Walton accelerator with a good ultra-high vacuum environment.

10 A Unifying Hybrid Preferential Model of Complex Network and Its Universal Properties

FANG Jin-qing, BI Qiao, LU Xin-biao

Why existing many generalized random network models could not have both scale-free (SF) and small world (SW) properties so far? The key reason for this is most models ignored deterministic factor. A new unified hybrid preferential model (UHPM) with a hybrid ratio d/r is proposed for both unweighted and weighted networks in this article as both the SF and the SW. The UHPM includes the BA model, the BBV model, and the TDE model. Compared the UHPM with the BA model, random graph weighted BBV models, the UHPM has smallest average path length L and biggest average clustering coefficient C, which are much better and closer to real-world networks. It is found that the exponent of the power-law in the UHPM is very sensitive to the ratio d/r. It is also found that there exists a threshold at the ratio of d/r = 1/1 which the exponent value of the power law increases rapidly and will tend to infinity when the r in this extreme case, the power-law disappears. All findings for the UHPM above are held not only for the unweighted models but also for the weighted models. The UHPM have all characteristics of the topology and dynamics in the unweighted and weighted networks. These findings imply that the UHPM is of universal properties for many complex networks. The ideas and method of the UHPM provide a wide variety of scale-free, small-world properties and transition features, only depending on the hybrid ratio d/r which control the properties of topology and dynamics in many complex networks.

As typical examples, the UHPM is applied to the BA model, the BBV model and the TDE model successfully. The most important common finding above is that the exponent of the power-law is very sensitive to the hybrid ratio d/r. Compared with the BA network and the random graph models, the average path length L in the UHPM is the smallest and the average clustering coefficient C is the biggest in the UHPM. Clearly, the UHPM have both scale-free and small-world effects. All the results show that the random preferential attachment is the main mechanism for generating the scale-free feature but the deterministic preferential attachment can play an important construction role in generating a power-law without heavy random tail and in enhancing the “rich gets richer” phenomenon, and that reveals a unified and more coherent mechanism which is consistent with real-world networks. The comparisons with three kinds of network model demonstrate the unified hybrid preferential attachment scheme is much closer to real-world complex networks not only for unweighted networks but also for the weighted networks. Therefore, our present the UHPM, for a large class of complex networks, will has its potential for applications in both theory and practice, may design desired new complex networks for some engineering

FUNDAMENTAL AND APPLIED FUNDAMENTAL RESEARCH•High Power Laser and Accelerator 144 fields. Of course, many important issues existing in complex network models, including exact analytical topological property and dynamical behavior of complex networks, spatiotemporal evolution, synchronization, and above all, are still open for research.

11 On-Off Intermittency in Small-World Networks of Chaotic Maps

LI Chun-guang1, FANG Jin-qing (1 University of Electronic Science and Technology of China)

Small-world networks are highly clustered networks with small average distance among the nodes. There are many natural and technological networks that present this kind of connections. Recently, the so called on-off intermittency has been reported in literatures. This type of intermittency is characterized by a two-state nature. The “off” state, which is nearly constant, and remains so for long periods of time and is suddenly changed by a burst, the so called “on” state, which departs quickly, and returns quickly to the “off” state. Moreover, the power-law distributions of the laminar phases was also observed and discussed in the literatures. However, connection topology in real-world networks is usually not completely regular. And it is well-known that usually topology structure affects network dynamics critically. It is interesting to investigate how small-world topology would affect the on-off intermittency of coupled chaotic map networks. In this work, we study this topic numerically. We fix the coupling coefficient to a constant so that the globally coupled lattice is synchronous. Then we decrease the connection-adding probability gradually. We found when the connection-adding probability slightly less than a critical value, the synchronous chaos is no longer stable and on-off intermittency appears. When further decrease this connection-adding probability, the intermittent dynamics is eventually replaced by fully developed asynchronous chaos.

12 Dynamical Synchronization and Controlin Coupled Map Lattices With Scale-Free Topology

CHEN Wei1, FANG Jin-qing(1 School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China)

In the work, we study dynamical synchronization and control in coupled map lattices (CML) with scale-free (SF) topology. Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength for the first time-delayed feedback control is increased linearly as the coupling strength is increased linearly. The CML with SF loses synchronization and intermittency occurs if the feedback strength >critical feedback strength c. Numerical examples are presented to demonstrate all results.

13 Control of Halo-Chaos in Beam Transport Network

145 Annual Report of China Institute of Atomic Energy 2005

LIU Qiang, FANG Jin-qing, LI Yong

Beam halo-chaos in periodic focusing channel of high-current accelerators has become a key concerned issue because it always causes excessive radioactivity. Therefore, it is very necessary to find more effective control methods of beam halo-chaos in beam transport network. To do so, we have developed some methods in this work from a view of point.

First, to realize synchronization of particle envelope via control method. The equation of each point the particle beam envelope at each node is described as follows:

（1） （2）

（3）

Where the parameters are a=1.65, b=1.25, ω=2π. To control halo-chaos, we add an controller G into the right hand side of Eq.(2), G(i)=m (x(i,2)－n) 2, we have controlled equation:

（4）

Through lots of numerical simulation, it is found that when m=0.1, n=5, the system is controlled to the fixed point quickly, as shown in Figs.1, 2. It is seen that the synchronization error for total particle path and three directions approach to zero very quickly. This implies that the synchronization state in the 100 periodic focusing channel is achieved.

Fig. 1 Total particle path error versus time for N=100 (periodic number)

FUNDAMENTAL AND APPLIED FUNDAMENTAL RESEARCH•High Power Laser and Accelerator 146

Fig. 2 Particle path error versus time in three directions for N=100, respectively

Second, to carry out controlling the halo-chaos synchronization by the variable replacement method. To do so, we apply x(i,1)=x(k,1), where k is the any node. The simulation results are given in Figs.3, 4 for periodic focusing channel with N= 200. We see that particles path can achieve synchronization.

Fig. 3 Total path total error along versus time for N=200

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Fig. 4 Particle path error versus time in three directions respectively for N=200(periodic number)

Third, to synchronize via nonlinear feedback method. To realize synchronization of the halo-chaos,

we design a variable nonlinear feedback controller G as follows:

（5）which is added to the right hand side of Eq. (2). Our simulation results are shown in Figs.5, 6. It can be seen that the synchronization is reached very well.

Fig.5 Total path total error along versus time for N=200

Fig.6 Particle path error versus time in x1, x2 directions respectively for N=200

14 Soliton Control Method for Beam Halo-Chaos in Periodic Focusing Channel

BIA Long, WENG Jia-qiang, FANG Jin-qing

Recently, we have proposed the soliton controller of strong nonlinear and stability for controlling the

FUNDAMENTAL AND APPLIED FUNDAMENTAL RESEARCH•High Power Laser and Accelerator 148 halo-chaos in a quadrupole focusing system, which is another type of PFC. Based on the particle-core model, main idea of the soliton control is follows as. We consider the Kapchinsky-Vladimirsky (K-V) beam, the dimensionless nonlinear equation of the beam envelope and the transverse equations of motion for a single ion in the quadrupole focusing system. In the particle-core-interaction model, any effective controller will be added to the right-hand side of the proton forced equation. It is critical to select an effective controller G for controlling the halo-chaos. In this work, we select the soliton function u for constructing G, that is u(x)= Asech2[B(x, x0)], where A and B are constant parameters, and x0 is the initial value. We put forward a soliton feedback controller G for the K-V beam, i.e., G =(Asech2 rrms－sech2am), where rrms is the average rms radius, am is the match radius. The purpose of controlling the halo-chaos is to reach rrms－am=0, which is achieved by using the numerical simulation PIC method for solving controlled equations under the quadrupole focusing channel. Conclusions can be drawn in this work. First, not only the halo-chaos is removed, but also the proton radial density becomes uniform, and at the same time that the ratio of the phase diagram after to the one before controlling in is 1/9. Secondly, the transverse energy of the proton beam is reduced largely after controlling the halo-chaos, which means that the tendency of protons escaping from the core is controlled effectively, the protons distribution of beam becomes uniform compared with the initial nonuniform distribution. Thirdly, the halo-chaos strength factor H is reduced from bigger to 0 after the controlling the halo-chaos. In the matter of fact, all statistical properties of the proton beam can reach in good condition after the controlling. The soliton control method can be also extended to control the other initial beam distributions.

15 Synchronization in Weighted Complex Networks

LU Xin-biao1,2, FANG Jin-qing2, WANG Xiao-fan1, LI Xiang1

(1 Department of Automation, Shanghai Jiaotong University, Shanghai 200030, China;

2 China Institute of Atomic Energy, P.O. Box 275-81, Beijing 102413, China)

Recently, the weighted networks become a hot research project. The synchronizability is enhanced in asymmetrically coupled weighted networks; however, the networks do not change the edges’ weight during the generation process of networks. Barrat, Barthelemy and Vespignani (BBV) proposed a weighted network model with tunable parameter δ to change the edges’ weight during the generation process of networks. Kocarev et al. clearly proposed two complete synchronization conditions (CSC): The first CSC is d>׀a/λ2׀; the second CSC which is <b. Where d is the coupling strength of the networks, λ1=0>λ2≥…≥λN are eigenvalues of the coupling matrix with network size N, a and b are constant which depend only on dynamical function, output function and synchronization state. In this work, we use the BBV model to study the complete synchronization of weighted networks with symmetrical coupling and asymmetrical coupling respectively. Our main result is that the synchronizability for the first CSC symmetrically coupled weighted networks is enhanced, while the synchronizability for the second CSC symmetrically coupled weighted networks is weakened. However, the synchronizability of the first CSC asymmetrically coupled weighted networks and the second CSC asymmetrically coupled weighted networks is enhanced.

16 Topological Transition Features and Synchronizability

149 Annual Report of China Institute of Atomic Energy 2005

of Two New Hybrid Preferential Weighted Networks

LU Xin-biao1,2, WANG Xiao-fan1, FANG Jin-qing1

(1 Department of Automation, Shanghai Jiaotong University, Shanghai 200030, China;

2 China Institute of Atomic Energy, P.O. Box 275-81, Beijing 102413, China)

It is very important to find a new weighted model to describe the features of the real-world weighted networks. Inspired by the unweighted hybrid preferential (HP) network proposed by J.Q. Fang and Y. Liang, we apply the HP idea and method to investigate two typical weighted networks above. Numerical simulations show that the HP idea and method with both of random and determination preferential attachment can be extended to a class of weighted complex networks and to improve topological properties which have both scale-free and small-world properties.

In our first model, that is BBV hybrid network model (BBVHNM), the original random preferential attachments in the BBV model are replaced alternatively by determination preferential attachment according to a certain ratio d/r of random preferential attachment to determination preferential attachment. In our second model, that is the traffic-driven hybrid network model (TDHNM), the original random preferential attachments in the traffic-driven network model are replaced alternatively by determination preferential attachment according to the ratio d/r. We find that the two hybrid networks have both scale-free and small-world properties, while the exponent γ of the power-law is very sensitivity to the hybrid ratio or dependent of the hybrid ratio. Moreover, when the ratio d/r is increased, the power-law exponent of the degree distribution, and the average clustering coefficient are increased; while the average path length and the assortative coefficient are decreased.

The synchronizability for the first condition weighted hybrid networks is enhanced with the increase of the ratio d/r; however, the synchronizability of the second condition weighted hybrid networks is weakened with the increase of the ratio d/r.

17 Impulsive Stabilization of Uncertain Dynamical Systems and Chaos Control

LIU Bin1, YAO Jian2, FANG Jin-qing(1 Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;

2 Department of Electronic Engineering, Chinese University of Hong Kong, Shatin, N.T., Hong Kong)

Chaos control and synchronization have received significant attention. Impulsive control is one of main methods among them and arises in a wide variety of applications except at chaotic systems, such as orbital transfer of satellites, ecosystems management and control of money supply in a financial market. There are many cases where the impulsive control can give better performance than the continuous control. Systems for secure communications is a very promising practical application but the major shortcoming of recently proposed chaos-based communication schemes is their susceptibility to noise and distortions in communication channels. To avoid this problem, a way that using chaotically timed pulse sequences rather than continuous chaotic waveforms is proposed by Rulkov and his coworkers. Recently, with the development of the theories of impulsive dynamical systems, the impulsive control has attracted the interests of many researchers. In this work, we consider a general impulsive control problem for uncertain dynamical systems. There usually are some uncertainties in practical engineering systems and

FUNDAMENTAL AND APPLIED FUNDAMENTAL RESEARCH•High Power Laser and Accelerator 150 physics-mathematical models used in the design process. So the robust control strategy becomes very important issue. Of course, our consideration also includes chaos control problem in deterministic nonlinear systems. Since the stability is a fundamental issue in the control system analysis and design, we shall use the method of Lyapunov functions to establish a set of robustly impulsive stabilization criteria for the uncertain impulsive control system concerned. These results are then applied to the well-known Lorenz chaotic system with perturbed items. It is shown that all the solutions of the Lorenz system with perturbed items will robustly converge to an equilibrium point by using the impulsive feedback control.

18 Neural Network Adaptation Control of Beam Halo-Chaos

HANG Guo-xian, LUO Xiao-shu, FANG Jin-qing

Neural networks (NN) are very useful for a vast array of applications because the NN have some advantages, such as adaptation ability, self-learning, self-organization and suitable for high-dimension dynamical systems. Especially self-adaptation control method of the feed-forward back-propagating neural networks is suitable for control of nonlinear systems. Since the envelop equation of the particle has chaotic behaviors due to strong nonlinearity and sensitivity to external perturbations, we proposed the directive adaptation control method of the feed-forward back-propagating neural networks. Thus it can adaptively adjust the system parameter to reach minimum error for controlled subject. To do so, we have proposed a multiple-level neural network to learn self-adaptive ability for control of beam halo-chaos.

Using adaptive control on line during the control process, at the time-delayed radius of proton beam envelop, x(t), is taken as the input signal of the NN. AS a controller G=u, the feedback perturbation force u(t)= gf(t) of the NN is added to the right hand side of the envelop equation of proton beam. The system is turn on automatically to be controlled if the radius of beam envelop x(t) is greater than the beam matched radius, x(t) >am (matched radium). Control of beam halo-chaos can be realized only if the control structure of the NN and the linear feedback coefficient of the NN are selected suitably. Control results show the time evolution of the root-mean-square radius of the beam envelop and imply the control goal of beam halo-chaos is realized basically.

19 Small World Properties Generated by Constant-Degree Model

LI Yong, FANG Jin-qing, LIU Qiang

For depicting the transition process from local order system to random network, Watts-Strogatz (WS) proposed small-world (SW) model. Based on the WS model, we proposed a new method for generating small-world properties and we call it constant-degree model (CDM).

In our CDM the main algorithm is to keep a constant in the number of degrees for each node during randomly rewriting connections. To do this, we start from regular network. We put forward the so-called “spread all over boundaries” (SAB) algorithm and “spread all over vertices” (SAV) algorithm model. The difference between them is nodes rewriting algorithm is different. We made comparison of our CDM with the WS model, which show they have the same topological properties of SW network, small average path length, and big clustering coefficient (as shown in Figs.1, 2). However, one of advantages for our model is

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that all degree of nodes is a constant but can be selected according to practical need. Two algorithms offer good examples of diverse formation of SW networks since their distribution of node degrees are quite different. At the same time, we research the relationship between the network size N and average path length (APL). We get the whole dynamic APL behavior through rewiring connections of some nodes under the same degree (Fig. 3).

We offer the SW network topology properties generated in our new method. We believe that our model may help engineers in topology-designing and performance analysis of the SW network. It may be helpful for researching the mutual oscillator kinetics inside nodes and the automation related to networks.

Fig. 1 L(P)/L(0) verses P comparison of SAB and SAV algorithms

with WS model for N = 1 000 and k = 4

Fig. 2 Clustering coefficient C verses P comparison of SAB and SAV algorithms

with the WS model for N = 1 000 and k = 4

FUNDAMENTAL AND APPLIED FUNDAMENTAL RESEARCH•High Power Laser and Accelerator 152

Fig.3 APL verses N for different P logarithmically for N = 1 000 and k = 4

20 Controlling Chaos of Semiconductor LaserUsing Sliding Variable Structure Strategy

HUANG Liang-yu1, LUO Xiao-shu1, Fang jin-qing(1 College of Physics and Information Technology, Guangxi Normal University, Guilin 541004, China)

In this paper, a semiconductor laser with external optical feedback is entered into chaotic motion by

increasing the time of the external optical feedback at first. And then, the sliding mode variable structure

control method is used to control the chaotic motion of this laser system. The advantage of this method is

that the stable output laser can be obtained in a short time and the output power strength of the laser can

be adjusted flexibly in accordance with the engineering requirement. Theory analysis and simulation

results show that the results of the control have powerful stability and robust. Our research results have

many helpful values to improve the speed of stable output, flexible adjustment of laser output power as

well as efficiency of energy transformation for real laser system.

21 Debugging of Midas-VME Data Acquisition System at Tandem Laboratory

YANG Xiao-qing, ZHOU Jian-ming, ZHANG Bu-gang, ZHANG Xin, ZHANG Xiu-hua

The front-end of Data Acquisition Systems (DAQ) have been based on CAMAC at Tandem

Accelerator Nuclear Physics Nuclear Laboratory (BTANL) since 1980’s. The VME specification become

very popular and has been widely used in many domestic and foreign laboratories, it is a typical set of

DAQ system. To satisfied the increasing amount of data, it is urgent to build a VME based DAQ system.

We have investigated many DAQ system Since 2003, building a VME+Midas+Linux DAQ solution in

2005.

1 System Components

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Hardware include computer(any PC in market), crate control(SIS1100/3100(struck)), VME modules

(ADC CAEN V785/ TDC CAEN V775 / Scaler CAEN V560), data transmission(1000M optical fiber).

Software include operation system(Redhat9.0 (Linux kernel 2.4.20)), DAQ software(Midas), online

monitoring(Roody-root-based User Graphic Interface (GUI)), offline analysis(Root/Paw).

2 Debugging the system

System debugging is following: 1) Crate Control (SIS1100/3100), modified device driver and coded

interface with operation system, providing basic access to VME; 2) VME Modular (ADC/TDC/Scaler),

tested V785 mode, buffer analysis, addressing mode etc. providing subroutine to use ADC; 3) Installed

and configured Midas DAQ software and related device drivers; 4) Installed and configured data analysis

software(Cernlib/Root etc.) and integration with Midas; 5) Programmed the front-end and back-end with

C; 6) Simulated DAQ data taking and controlling processes; 7) Compiled online monitoring Roody.

　　At the end of September 2005, with the help of Midas’s author, Dr. Stefan Ritt from PSI and Dr.

Pierre-André Amaudruz from Triumf, we debugged the system in the following: 1) Set-up computer busy

logic using NIM modules and VMEIO, modified front-end code for multiple VME ADC readout in

relation to the computer-busy implementation, modified analyzer and ODB for multiple VME ADCs; 2)

Remote MIDAS installation, with xinetd and mserver set-up, having remote front-end, mdump; 3)

Defined new Midas VME standard, implemented this standards for SIS3100, SBS618 and VMIC interface

and tested it in laboratory with local hardware; 4) Provided advice for writing CAMAC drivers under

Midas CAMAC standard and VME drivers under Midas VME standard for Wiener VMEMM interface; 5)

Speed was tested for three different VME interfaces in single long word access, result is VMIC (Linux),

1.0 μs, SIS3100 (Linux), 4.4 μs, SBS618 (Linux),7.2 μs; 6) Compiled and demonstrated ROOT and

HBOOK analyzers with ROODY and PAW; 7) Tested in NTOF experiment.

3 Summary

At present, the new DAQ can provide less than 16 channels. We are continuing to improve the

system. It will be a good beginning to develop a versatile and scalable DAQ system.