About generalized scaling for passive scalars in fully developed turbulence

In this paper we use a simple normal form approach of scale invariant fields to investigate scaling laws of passive scalars in turbulence. The coupling equations for velocity and passive scalar moments are scale covariant. Their solution shows that passive scalars in turbulence do not generically follow a general scaling observed for velocity field because of coupling effects.

Evolution induced catastrophe in a nonlinear dynamical model of material failure

In order to study the failure of disordered materials, the ensemble evolution of a nonlinear chain model was examined by using a stochastic slice sampling method. The following results were obtained. (1) Sample-specific behavior, i.e. evolutions are different from sample to sample in some cases under the same macroscopic conditions, is observed for various load-sharing rules except in the globally mean field theory. The evolution according to the cluster load-sharing rule, which reflects the interaction between broken clusters, cannot be predicted by a simple criterion from the initial damage pattern and even then is most complicated. (2) A binary failure probability, its transitional region, where globally stable (GS) modes and evolution-induced catastrophic (EIC) modes coexist, and the corresponding scaling laws are fundamental to the failure. There is a sensitive zone in the vicinity of the boundary between the GS and EIC regions in phase space, where a slight stochastic increment in damage can trigger a radical transition from GS to EIC. (3) The distribution of strength is obtained from the binary failure probability. This, like sample-specificity, originates from a trans-scale sensitivity linking meso-scopic and macroscopic phenomena. (4) Strong fluctuations in stress distribution different from that of GS modes may be assumed as a precursor of evolution-induced catastrophe (EIC).

Thermodynamical versus log-Poisson distribution in turbulence

The thermodynamical model of intermittency in fully developed turbulence due to Castaing (B. Castaing, J. Phys. II France 6 (1996) 105) is investigated and compared with the log-Poisson model (Z-S, She, E. Leveque, Phys. Rev. Lett. 72 (1994) 336). It is shown that the thermodynamical model obeys general scaling laws and corresponds to the degenerate class of scale-invariant statistics. We also find that its structure function shapes have physical behaviors similar to the log-Poisson's one. The only difference between them lies in the convergence of the log-Poisson's structure functions and divergence of the thermodynamical one. As far as the comparison with experiments on intermittency is concerned, they are indifferent.

Effects of magnetic configuration on hot electrons in highly charged ECR plasma

To investigate the hot electrons in highly charged electron cyclotron resonance (ECR) plasma, Bremsstrahlung radiations were measured on two ECR ion sources at the Institute of Modern Physics. Used as a comparative index of the mean energy of the hot electrons, a spectral temperature, Tspe, is derived through a linear fitting of the spectra in a semi-logarithmic representation. The influences of the external source parameters, especially the magnetic configuration, on the hot electrons are studied systematically. This study has experimentally demonstrated the importance of high microwave frequency and high magnetic field in the electron resonance heating to produce a high density of hot electrons, which is consistent with the empirical ECR scaling laws. The experimental results have again shown that a good compromise is needed between the ion extraction and the plasma confinement for an efficient production of highly charged ion beams. In addition, this investigation has shown that the correlation between the mean energy of the hot electrons and the magnetic field gradient at the ECR is well in agreement with the theoretical models.中文摘要：ECR(电子回旋共振)离子源是产生稳定的强流多电荷态离子束流最有效装置。全永磁 ECR 离子源因其独特的特点为很多中小型多电荷态离子束流实验平台与离子注入机等系统所采用，为后者产生重复性好、稳定性强的多电荷态离子束流。本文着重论述了中国科学院近代物理研究所研制的几台全永磁多电荷态ECR离子源及其特性与典型性能，如能产生强流高电荷态离子束流的高性能全永磁离子源LAPECR2，能产生强流中低电荷态离子束流的LAPECR1，能产生多电荷态重金属离子束流的LAPECR1-M等。这些性能稳定的离子源为提高近代物理研究所相关试验平台的性能提供了关键的束流品质保障。

Slow isocharged sequence ions with helium collisions: Projectile core dependence

The collisions of the isocharged sequence ions of q=6 (C6+, N6+, O6+, F6+, Ne6+, Ar6+, and Ca6+), q=7 (F7+, Ne7+, S7+, Ar7+, and Ca7+), q=8 (F8+, Ne8+, Ar8+, and Ca8+), q=9 (F9+, Ne9+, Si9+, S9+, Ar9+, and Ca9+) and q=11 (Si11+, Ar11+, and Ca11+) with helium at the same velocities were investigated. The cross-section ratios of the double-electron transfer (DET) to the single-electron capture (SEC) sigma(DET)/sigma(SEC) and the true double-electron capture (TDC) to the double-electron transfer sigma(TDC)/sigma(DET) were measured. It shows that for different ions in an isocharged sequence, the experimental cross-section ratio sigma(DET)/sigma(SEC) varies by a factor of 3. The results confirm that the projectile core is another dominant factor besides the charge state and the collision velocity in slow (0.35-0.49v(0); v(0) denotes the Bohr velocity) highly charged ions (HCIs) with helium collisions. The experimental cross-section ratio sigma(DET)/sigma(SEC) is compared with the extended classical over-barrier model (ECBM) [A. Barany , Nucl. Instrum. Methods Phys. Res. B 9, 397 (1985)], the molecular Coulombic barrier model (MCBM) [A. Niehaus, J. Phys. B 19, 2925 (1986)], and the semiempirical scaling laws (SSL) [N. Selberg , Phys. Rev. A 54, 4127 (1996)]. It also shows that the projectile core properties affect the initial capture probabilities as well as the subsequent relaxation of the projectiles. The experimental cross-section ratio sigma(TDC)/sigma(DET) for those lower isocharged sequences is dramatically affected by the projectile core structure, while for those sufficiently highly isocharged sequences, the autoionization always dominates, hence the cross-section ratio sigma(TDC)/sigma(DET) is always small.

Multi-electron processes in 4.15-11.08 keV/u(13)C(6+) on argon collisions

The relative partial cross sections for C-13(6+)-Ar collisions at 4.15-11.08 keV/u incident energy are measured. The cross-section ratios sigma(2E)/sigma(SC), sigma(3E)/sigma(SC), sigma(4E)/sigma(SC) and sigma(5E)/sigma(SC) are approximately the constants of 0.51 +/- 0.05, 0.20 +/- 0.03, 0.06 +/- 0.03 and 0.02 +/- 0.01 in this region. The significance of the multi-electron process in highly charged ions (HCIs) with argon collisions is demonstrated (sigma(ME)/sigma(SC) as high as 0.79 +/- 0.06). In multi-electron processes, it is shown that transfer ionization is dominant while pure electron capture is weak and negligible. For all reaction channels, the cross-sections are independent of the incident energy in the present energy region, which is in agreement with the static characteristic of classic models, i.e. the molecular Coulomb over-the-barrier model (MCBM), the extended classical over-the-barrier (ECBM) and the semiempirical scaling laws (SL). The result is compared with these classical models and with our previous work of C-13(6+)-Ne collisions

Multi-electron processes in C-13(6+) ions with neon collisions in energy region 4.15-11.08 keV/u

The cross-section ratios of double-, triple-, quadruple-, and the total multi-electron processes to the single electron capture process sigma(DE)/sigma(SC), sigma(TE)/sigma(SC), sigma(QE)/sigma(SC) and sigma(ME)/sigma(SC)) as well as the relative ratios among reaction channels in double-electron active, triple-electron active and quadruple- electron active are measured in C-13(6+) -Ne collision in the energy region of 4.15-11.08 keV/u by employing position-sensitive and time-of-flight coincident techniques. It is determined that the cross-section ratios sigma(DE)/sigma(SC), sigma(TE)/sigma(SC), sigma(QE)/sigma(SC) and sigma(ME)/sigma(SC) are approximately the constants of 0.20 +/- 0.03, 0.16 +/- 0.04, 0.06 +/- 0.02 and 0.42 +/- 0.05. These values are obviously smaller than the predictions of the molecular Coulomb over-the-barrier model (MCBM) [J. Phys. B 23 (1990) 4293], the extended classical over-the-barrier model (ECBM) [J. Phys. B 19 (1986) 2925] and the semiempirical scaling laws (SL) [Phys. Rev. A 54 (1996) 4127]. However, the relative ratios among partial processes of DE, TE and QE are found to depend on collision energy, which suggests that the collision dynamics depends on the collision velocity. The limitation of velocity-independent character of ECBM, MCBM and SL is undoubtedly shown.

新一代多电荷态离子源的研究

离子源发展存在两大热点问题：其一强流高电荷态离子的产生；其二强流金 属离子的产生。为了获得强流高电荷态离子，我们设计制造了全超导 ECR 离子 源 SECRAL（Superconducting ECR ion source with Advanced design in Lanzhou） ， 该离子源采用了全新的超导磁体结构形式，工作于 18～28GHz 的微波频率。根据 scaling laws 和实验经验，我们确定了 SECRAL 离子源所需要的约束磁场场形， 并针对新的磁体结构设想，通过 TOSCA 程序进行了详细的计算，成功地设计出 满足我们场形要求的超导磁体物理模型。据此，我们进一步进行了超导磁体的力 学结构分析，为磁体机械工艺设计提供了参考依据，保证了超导磁体结构设计的 可靠性。源体建成后，经过一系列的测试和调束实验，不但验证了我们的设计和 分析是合理的、可靠的，而且创造了许多项束流调试的新世界纪录，我们分别获 得了 810 A eμ O7+ 、730 A eμ Ar 11+ 、220 A eμ Ar 14+ 、73 A eμ Ar 16+ 、483 A eμ Xe 20+ 等束 流。为了获得强流中低电荷态金属离子束，我们尝试探索一种原理、结构、工作 模式全新的离子源－外部电子注入PIG离子源（E-PIG） 。目前，我们基本按照我 们的初期设想设计建造了 E-PIG离子源，设计中采用了外部电子枪注入电子、空 心阴极、特殊的场形等手段来提高金属离子的电荷态和流强。经过初步的起弧调 试，我们发现在初期的设计中还存在一些问题亟待进一步整改。

ECR等离子体的轫致辐射谱和极紫外光研究

本论文对电子回旋共振（ECR）等离子体发出的轫致辐射谱和极紫外光做了系统的实验研究，并对ECR等离子体的工作机制及新的应用前景进行了探索。 在ECR等离子体中，热电子对于离子的形成、约束以及整个等离子体的能量平衡具有重要意义，而由电子发出的轫致辐射谱则包含了电子的能量、密度等信息，因此，测量等离子体发出的轫致辐射谱作为一种非侵入式的诊断方式，成为等离子体诊断的有力手段。为了研究ECR等离子体中热电子这个重要组成部分，我们对三台高电荷态ECR离子源的轫致辐射谱进行了系统测量，并通过对实验谱的拟合得到一个代表等热电子平均能量的参量——光谱温度Tspe。通过测量不同工作参数下（例如微波频率、功率，约束磁场，掺气，负偏压等）等离子体的轫致辐射谱，深入研究了ECR离子源的这些工作参数对热电子能量及密度的影响，并对ECR等离子体中与电子加热及等离子体约束相关的一些物理问题进行了探索性的研究和讨论，在此基础上，对一些已在ECR离子源界得到广泛应用但其物理机制尚不十分清晰的经验性规律及技巧（如Scaling laws，掺气效应，负偏压效应等），做出了新的解释。其中的创新点有：通过对ECR等离子体轫致辐射谱的测量，首次从电子加热的角度诠释了在ECR源领域得到普遍认可的有关约束磁场的Scaling laws；首次实验观察到在磁场分量Blast≈Bext时，离子源的约束和引出之间的关系达到最佳，而当Bext小于Blast较多时，等离子体的约束将遭到较严重的破坏；实验观察到热电子能量随共振区磁场梯度的减弱而提高，并分别从单粒子轨道模型和电磁波在等离子体中的传播两个角度对这一现象进行了分析；基于实验现象，从抑制等离子体不稳定性的角度出发对掺气效应做出了新的解释。 由于在未来光刻及显微成像等领域的广泛应用前景，极紫外（EUV）和软X射线光源目前是国际上的研究热点，而ECR等离子体作为一种高离化态的等离子体，为EUV和软X射线光源的发展提供了一条新思路。为了研究ECR等离子体作为EUV光源的可行性，我们对其发出的波长在13.5nm附近的窄带宽EUV光功率进行了初步测量，在超导ECR离子源——SECRAL上，测量到了超过2W的窄带宽EUV光功率（2π sr），这是目前国际上利用ECR等离子体产生并测量到的EUV光功率中的最好结果，这一结果证明了ECR等离子体作为EUV光源的潜力，但在发射强度、转化效率等方面还需做出很大的改进，本论文给出了相应的研究发展思路

高电荷态ECR离子源的设计与实验研究

本文详细论述了三种各具特色的高电荷态ECR离子源的设计与研制，它们分别是：14．SGHz全永磁高电荷态ECR离子源LAPEC咫、传统常温ECR离子源GTS、混和超导ECR离子源HECRIS。另外，还从理论与实验两个方面对ECR离子源多电荷态离子束流的引出进行了详细研究。设计研制了一台高性能14．SGHz全永磁ECR离子源LAPECRZ，该离子源的设计尺寸为杯50mm*560mm，重量可达9ookg以上，为目前世界上体积与重量最大、设计参数最高的全永磁ECR离子源。全永磁离子源的尺寸增大一些，其加工与研制所存在的难度将会有质的变化。研制LAPEC形所存在的技术难度大大超过了以往所有全永磁ECR离子源。LAPECR2的磁场参数为：注入磁场1 ．4T，如果加注入端辅助铁扼，磁场可达2．6T；引出磁场为1 ．1T；六极永磁体在弧腔内壁产生的最大径向磁场的设计值为1．22T，实际加工得到的磁场大小为1．2T，与计算结果基本一致。该离子源的设计采用了多种特殊技术与方法以提高引出高电荷态离子束流强度，如：双层含铝衬底的等离子体弧腔、铝制等离子体电极、冷阴极电子枪（注入端负偏压电极）、旁轴微波直接馈入与等离子体位置相对于磁场可调等等。目前，我们已开始源体的组装。GTS离子源为目前世界上运行性能最好的常温ECR离子源之一。它的设计指导思想是ECR离子源的经验结论scaling Laws，高磁场、高磁镜比，高磁场梯度是该离子源磁场设计的主要特点。设计时充分考虑了多频加热机制，允许多频功率同时馈入弧腔：IOGHz＋14GHz＋18GHz＋ZSGHz。良好的磁场约束、灵活的磁场结构设计、高频率大功率微波馈入、大体积弧腔、足够的冷二次电子注入、优良的真空抽气系统、以及有效的束流引出系统等等都是该离子源高性能表观的原因。经过近一年半的优化与调试，该离子源运行性能优良，能产生很多领先国际伺类ECR源的离子束流，如：1.95emAO6+，O·semAArll”，o．15e拜AArl犷，31Oe瘩建叙e，哪se拼A豁岁”与0.4eμAXe39+为18GHz时调试的结果：1.OemAAr8+，1.8eμAAr17+24OeμAXe20+ ，20eμAxe30+与0.3oe从Axe38＋为在14GHz调试的最好结果。该离子源已多次为原子物理实验提供了Ar17+与Ar18+等高电荷态离子束流。HECRIS是一台高性能混和超导ECR离子源，其各项设计参数均高于GTS源，以保证该离子源能具有比GTS更好的性能。它的最小B场型设计继续沿袭现在ECR离子源设计惯用的Scaling Laws设计思想。该离子源采用较高频率的微波馈入，设计运行范围为18GHz-24GHz。该离子源着重于在运行调试中实现对轴向最小磁场Bmin的调节与匹配，这里采用两组超导线包进行辅助调节。径向磁约束由一个能在弧腔内壁产生1．6T径向磁场的六极永磁体提供，它强磁场设计与部分磁块存在的退磁问题的解决也是该离子源的一大特点与难点。文中还详细讨论一个高性能的Halbach结构六极永磁体的设计方法。分别从永磁材料选取、物理尺寸优化、结构选择等角度，结合理论分析与PolssON，PERMAG和TOscA3D程序的模拟计算结果，对六极永磁体的性能进行了全面的分析，提出两种确定六极永磁体中存在退磁磁块的办法，并且提出了一种用高极化矫顽力永磁材料替代退磁磁块中所采用的永磁材料的解决办法。对多电荷态ECR离子源的引出进行了理论与实验两方面的研究。利用PBGUNS程序，对ECR离子源的引出系统进行了一定的理论分析。通过模拟计算，详细地论述了引出系统的各主要物理参数对ECR离子源引出离子束流品质的影响。这些得到的结果，对设计一套高性能的ECR离子源引出系统具有一定的指导意义。结合理论分析，我们还设计完成了一系列关于ECR离子源引出系统的实验，来研究多电荷态离子束流的引出与短距离传输。采用电扫描发射度测量系统（ESS）探测离子束流在x与y方向的发射度，用两个荧光靶分别在束运线不同位置探测束流的束斑形状，并利用一个亮度探测器对束斑相对亮度进行探测。通过多组实验结果的处理，分别分析了离子源的几个主要参数如磁场、微波、掺气、偏压等对引出束流品质的影响并结合相关理论给予了解释，通过对混合多电荷态离子束流的三电极引出实验结果的讨论，建立了一个关于高电荷态ECR离子源束流引出的较为清晰的物理图象。

How does solvent molecular size affect the microscopic structure in polymer solutions?

Monte Carlo simulation has been used to investigate the effects of linear solvent molecular size on polymer chain conformation in solutions. Increasing the solvent molecular size leads to shrinkage of the polymer chains and increase of the critical overlap concentrations. The root-mean-square radius of gyration of polymer chains (R-g) is less sensitive to the variation of polymer concentration in solutions of larger solvent molecules. In addition, the dependency of R-g on polymer concentration under normal solvent conditions and solvent molecular size is in good agreement with scaling laws. When the solvent molecular size approaches the ideal end-to-end distance of the polymer chain, an extra aggregation of polymer chains occurs, and the solvent becomes the so-called medium-sized solvent. When the size of solvent molecules is smaller than the medium size, the polymer chains are swollen or partially swollen. However, when the size of solvent molecules is larger than the medium size, the polymer coils shrink and segregate, enwrapped by the large solvent molecules.

Scaling relationships in conical indentation of elastic perfectly plastic solids

Using dimensional analysis and finite element calculations we derive several scaling relationships for conical indentation into elastic-perfectly plastic solids. These scaling relationships provide new insights into the shape of indentation curves and form the basis for understanding indentation measurements, including nano- and micro-indentation techniques. They are also helpful as a guide to numerical and finite element calculations of conical indentation problems. Finally, the scaling relationships are used to reveal the general relationships between hardness, contact area, initial unloading slope, and mechanical properties of solids.

High-Resolution Finite Compact Difference Schemes for Hyperbolic Conservation Laws

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknown variable for third-order FC-ENO scheme and two unknown variables for fifth-order FC-ENO scheme. Numerical test results of the proposed FC-scheme were compared with traditional TVD, ENO and WENO schemes to demonstrate its high-order accuracy and high-resolution.

Scaling approach to conical indentation in elastic-plastic solids with work hardening

We derive, using dimensional analysis and finite element calculations, several scaling relationships for conical indentation in elastic-plastic solids with work hardening. Using these scaling relationships, we examine the relationships between hardness, contact area, initial unloading slope, and mechanical properties of solids. The scaling relationships also provide new insights into the shape of indentation curves and form the basis for understanding indentation measurements, including nano- and micro-indentation techniques. They may also be helpful as a guide to numerical and finite element calculations of indentation problems.