FUNDAMENTAL AND APPLIED FUNDAMENTAL RESEARCH•High Power Laser and Accelerator 137

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 Laser

With 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 pressure, 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

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 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, 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 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 Features

Generated 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 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 k1k2… 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 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 g 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.