1.Introduction

Dusty plasmas,or complex plasmas,comprise heavy dust grains,electrons and ions[1].The charged heavy grains are often in the 1pm to 1cm size range.Dusty plasmas can be found nearly everywhere in space,such as in comet tails and planetary rings[2],as well as in many industrial and laboratory plasmas,for instance laser-driven ablation and tokamak plasmas[3–6].In this type of plasma,the dust grains are mostly composed of graphite,silicates and amorphous carbon and their radii are of the order of several nanometers to several micrometers.The electrostatic charge of these heavy dust grains is in the range of several orders of the electronic charge e[7,8].These heavy and charged dust grains change the temporal and spatial behaviors of the plasma,which leads to new waves,instabilities,etc[1,9].specifically,the presence of these dust particles plays an important role in wave propagation in plasmas and their associated instabilities.It has already been shown that a large variety of electrostatic[10–12],and electromagnetic[13–16]modes are supported by dusty plasmas which become unstable provided that free energy sources are available[17].Detailed critical reviews about waves and instabilities in non-gravitating dusty plasmas are reported elsewhere[18,19].

对43篇期刊研究文献和80篇硕博士论文的文献内容进行阅读分析整理，将硕博论文与期刊文献分别总结各划分为30个关键词，根据期刊文献与硕博论文内容与分析得出的关键词将民居的植物文化的123篇文献进行整理（见图3），归纳出民居植物文化的四大研究方向：民居内的植物文化、民居装饰的植物文化、园林景观的植物文化、传统聚落的植物文化，下面分别对这四个主要方向的研究进展进行阐述。

ORNL的卷对卷技术证明，该方法可用于大规模生产下一代复合材料的涂层纤维。此自我感知复合材料可由可再生聚合物基质和低成本的碳纤维材料制成。

图2为包埋反应后的石墨片试样照片．从图2可见：无涂层的石墨片表面是深灰色的且有少许白色斑点(图2(g))，而有涂层的石墨片(图2(a)～图2(f))表面白色斑点与无涂层的相比明显增多，而且白色斑点闪闪发亮；放在炉中下层的1～3号试样的颜色比放在上层的4～6号试样以及原始石墨片的更偏深黑色，特别是2号试样颜色比上层5号试样深，尽管两者包埋粉成分相同．这是由于下层1～3号试样的温度比上层的4～6号试样的要高一些，而且隔绝空气效果比上层要好一些．

In space plasmas,the dynamics of the larger objects is effectively controlled by gravitation.However,the dynamics of the electrons and ions is mainly controlled by electromagnetic interactions.It is well established that these two forces can become comparable in micron and submicron sized dust grains[20].Self-gravitation between the heavy dust grains may lead to the collapse of the dusty plasma,resulting in the formation of massive astrophysical objects.This instability effect was first studied by Jeans(later,the term‘Jeans instability’was coined)[21],and is considered to be responsible for the formation of astrophysical objects.In this process,some tiny disturbance in the uniformly distributed mass,caused by self-gravity between the grains,leads to their further localized condensation.For charged dust grains,the electrostatic force between these grains becomes important,and intriguing deviations from the main processes for neutral grains are expected.In a non-uniform dusty plasma with a density gradient,the existence of an external electric field deforms the Debye sheath of the dust grains(polarization),and the plasma–grain interaction force(polarization force)changes their dynamics[22].Recently,several authors[2,23–25]have investigated the self-gravity effects of heavy dust grains that modify the existing waves in collisionless dusty plasmas.Prajapati has studied the self-gravity effect by considering the polarization force between the charged dust grains,and has derived the dispersion relation of the Jeans instability[2].In that paper,the effect of self-gravity between the dust grains is studied in the case where the polarization force exceeds the electrical force.It is concluded that the polarization force greatly affects the collapse of dust grains with radii of about 10 μm.However,dusty plasmas can be highly collisional—for instance in dense molecular clouds—and therefore investigating the instability of a self-gravitating collisional dusty gas against different types of disturbances is crucial[26].Shukla and Verheest have investigated the instability of self-gravitating collisional dusty plasmas against electrostatic disturbances by treating the electrostatic,gravitational and drag forces simultaneously[27].Their analytical results exhibit new classes of dissipative instabilities in collisional dusty plasmas due to the effect of self-gravity between the dust grains.specifically,they have found two types of purely growing modes whose growth rates strongly depend on the dust-neutral and ion-neutral drags.The two studies mentioned can be combined to investigate the concurrent effects of polarization and collisions between the charged dust grains in dusty plasmas on the Jeans instability.

Now,we generalize the results for collisional dusty plasmas in the intermediate frequency regime.By intermediate frequency we mean frequency of electrostatic disturbances in the range[27].In this regime,the electron number density is still given by equation(1).However,in the limit ofthe dynamics of the dust and the ion fluids must be considered in tandem.Since the gravitational,electrostatic and polarization forces balance the inertial accelerations of the dust and the cold ion fluids,the corresponding momentum and continuity equations can be combined and,using plane wave analysis,the density perturbations for the ion and dust fluids can be obtained[27].Combining equations(12),(14)and(15),δndcan be obtained as follows:

2.Instability analysis

Let us consider multicomponent collisional dusty plasmas comprising charged dust grains,ions and electrons when the polarization force also exists.For a plasma system in equilibrium,the gravitational and the plasma pressure forces are in balance.The instability of such a system is studied for electrostatic waves whose frequency ω is much smaller than the electronic and ionic collision frequencies(νe,　 νi)and their wavelengths are shorter thanandVtiare the electron and ion thermal velocities(low phase velocities),respectively.The electrons and ions thermalize rapidly in the wave potential φ and the corresponding electron and ion density fluctuations are

where　Tj ( j　=　i,e)and　n　j0　(j　=　i,e)are the temperature and unperturbed number density of the ions and electrons,eis the electronic charge(＜0)andkBis the Boltzmann constant,respectively.It is shown that the polarization force acts on a charged dust grain according to the following equation[22]

whereQ=-zd e is the total charge of the dust grain andλDis the linearized Debye radius[2]

whereλDiandλDeare the linearized Debye radius of ions and electrons,respectively.The continuity and the motion equations in the presence of the polarization force can respectively be written as

区域认知是高中学生学习地理的重要载体，以本地区域认知为前提开展高中地理教学，在帮助学生进行具体区域下学习地理知识的同时，更是将地理知识与区域发展有机联系起来。因此，密切联系区域认知，以本土化或本地区域为案例，对教学内容与教学知识进行有效互动，是提高高中地理教学效果的较好手段。一方面学生在熟悉的素材中进行教学互动，可以更大胆发表自己的认识；另一方面，地理知识渗透到教学互动中，更有助于学生理解掌握。

眼前这个被称作铜绿山的山丘，若从远处看，的确看不出它与周边山头的形状、植被有什么不同。但走到它的身边，可以看出差别不仅明显，而且巨大。铜绿山随处裸露着山岩，岩体透出铜锈般的暗绿色，用地质探矿专业术语表述，这是岩体含铜品位高的缘故。眼前这座不起眼的山包里，已经探明贮藏有丰富的孔雀石、赤铜矿、自然铜等矿藏，把铜绿山说成是宝物聚集地一点也不为过。

whereUd,md,Zd,νdandndare the velocity,mass,magnitude of the charge,collision frequency with neutral gas background and number density of the dust grains,respectively.ψ also represents the gravitational potential.The Poisson equations for the overall charge and the gravitational mass are also respectively given by

改革、开放，引进、消化、吸收国外先进技术，从那时起成为印刷产业变革的主旋律。此后，中国印刷工业迈向发展的快车道，从告别铅与火，走进光与电，再到数与网。而在每个关键节点的背后，我们都能看到中国印工协的身影，典型如：1987年12月，《经济日报》率先使用的“计算机—汉字激光照排系统”顺利通过国家级验收，宣告“世界上第一家采用计算机—汉字激光屏幕组版、整版输出的中文报纸”诞生；90年代中期，我国重点书刊印刷厂全部采用国产激光照排系统。

Combining equations(12)–(15),the dust acoustic wave dispersion relation in the presence of the self-gravitational,collisional and polarization force effects is obtained:

用进样针吸取20μL浓度为10mg·kg-1的氯标准样品（或样品）缓缓地插入裂解管进样口处的硅橡胶垫，再平放在液体进样器的针槽内。单击“启动”按钮，仪器自动测定分析样品，即可得出样品浓度。

The differential equations can be solved using the plane wave approximation

Using equations(8)and(9),equation(5)can be recast as

with

Using　this equation,the　electron　number density(equation(1)),and the ion number density in this frequency regime[23]:

where G is the gravitational constant.As has already been proved[2,28],the polarization force can be written as

whereandare the squares of the Jeans and the dust plasma frequencies,respectively.Equation(16)can be rewritten as

进入发展壮大阶段，企业的规模不断增大，并开始走向正规化。规模扩大使企业管理的专业化分工成为必然，企业主已经没有能力或体力将所有企业事务都由自己来决策和处理，专业人才的加盟成为必然。因此需要内部提升和引进职业经理人来解决发展问题。同时，企业制度的不断完善，给非家族成员提供了相对平等的发展机会，同时规范的管理和监控，减少了企业引进职业经理人的道德风险。但规范化往往是局限在非决策层，因此，非决策层仍存在职业经理人的道德风险。

whereis the dust acoustic frequency.

In this study,the polarization force effect on the Jeans instability in collisional dusty plasmas is studied against low frequency perturbations(perturbations whose phase velocity is smaller than the electrons’velocity in thermal equilibrium).Employing the plane wave approximation,a dispersion relation is derived for collisional dusty plasmas when the polarization force exists,and it is shown that it significantly affects the growth rate of the unstable modes.We first consider the instability of electrostatic waves whose frequency is much smaller than the electronic and ionic collision frequencies,and where the dynamics of the dust fluid will be predominant.Subsequently,we generalize the analysis by focusing on electrostatic disturbances with an intermediate frequency where the ion dynamics will also be predominant in collisional dusty plasmas.

whereω is harmonic disturbance frequency and k=kx　i　+　kz　kis the xz plane wave vector.By substitution of equation(11)into equations(4),(6),(7)and(10),one finds,respectively,the following relations

whereis the square of the electron Debye radius,is the plasma–ion collision frequency andνiis the ion-neutral collision frequency.One must note that reducing the amount of dust grain charge will weaken the polarization force according to equation(8).In the limiting case of zero polarization force,equation(18)will be correctly reduced to the dispersion relation obtained by Shukla and Verheest in the absence of the polarization force in dusty plasmas[27].

3.Instability growth rate analysis

The instability growth rate is obtained by knowing that in the limits ofandω　≪　νi,one can rearrange and approximate equation(20)as

whereωs　s　=kλ　Deωpiis the Shukla–Silin frequency[11]and ωd　a　=kλ　Deωpdis the dust acoustic frequency[27].In the limiting situation ofω≪　νd,equation(16)can be further approximated as

This equation can be rearranged into the form

By solving this quadratic equation and finding its imaginary roots,the instability growth rate of the system can be obtained as follows:

in equation(13),after a little algebra the following dispersion relation will be obtained:

Again in the limiting case ofχ =0,where the polarization force is absent,the instability growth rate correctly reduces to its counterpart in the Shukl aet al work,namely[27]

Figure 1.The effect of increasing the polarization force on the growth rate of Jeans instability.

In the other interesting limit ofω　≫ νd,the resulting cubic polynomial in ω from equation(16)cannot be solved analytically and one must resort to numerical analysis methods in order to obtain the instability growth rate.

To evaluate the influence of polarization force on the instability growth rate,its normalized values are plotted againstχ in figure 1.According to equation(8),χ determines the strength of the polarization force.Normalization is performed by dividing the calculated instability growth rates from equation(24)by the instability growth rate calculated from equation(25)in the absence of polarization force(χ =0).For numerical calculations,the values of Ti,Te,νi,νd,neand ni0are also,respectively,chosen as 0.03 eV[2,29],3eV[28],0.2 s−1[30],4.6s−1[31],1000 cm−3[29]and 2 × 10−3cm−3[29,32].The triangle on the curve shows the normalized instability growth value for the typical values of Q,λDand Tiequal to −103e,10−2cm and 0.03 eV,respectively,which leads to χ =0.12[2,28].Figure 1 indicates that when the polarization force increases,the contraction rate of the plasma,and hence the instability growth rate,also increase.

4.Conclusions

In short,a dispersion relation is analytically derived for collisional dusty plasmas in the presence of a polarization force,and the Jeans instability growth rate is derived.The effects of gravitational force and the collision frequency of the dust grains on the instability growth rate are studied.The results of the present study can be used to gain a proper understanding of the Jeans instability in collisional dusty plasmas when a polarization force exists due to the presence of an external electrical field.In future studies,our analysis can be extended further,to include the magnetic field and electromagnetic effects.

References

[1]Pandey B P,Avinash K and Dwivedi C 1994 Phys.Rev.E 49 5599

[2]Prajapati R P 2011 Phys.Lett.A 375 2624

[3]Winter J 1998 Plasma Phys.Control.Fusion 40 1201

[4]Winter J 2004 Plasma Phys.Control.Fusion 46 583

[5]Farmanfarmaei B,RashidianVaziri M R and Hajiesmaeilbaigi F 2014 Quantum Electron.44 1029

[6]Rashidian Vaziri M R,Hajiesmaeilbaigi F and Maleki M H 2010 J.Phys.D:Appl.Phys.43 425205

[7]Mendis D A 1979 Astrophys.Space Sci.65 5

[8]Xie B S and Mitchell C J 2000 Plasma Sci.Technol.2 171

[9]He C X and Xue J K 2013 Chin.Phys.B 22 025202

[10]Rao N N,Shukla P K and Yu M Y 1990 Planet.Space Sci.38 543

[11]Shukla P K and Silin V P 1992 Phys.Scr.45 508

[12]Liu C B et al 2015 Plasma Sci.Technol.17 298

[13]Shukla P K 1992 Phys.Scr.45 504

[14]Shukla P K and Rahman H U 1996 Phys.Plasmas 3 430

[15]Ma D L,Zhang X J and Zhang L P 2013 Plasma Sci.Technol.15 7

[16]Hong Y H et al 2017 Plasma Sci.Technol.19 055301

[17]Winske D et al 1995 Geophys.Res.Lett.22 2069

[18]Mendis D A and Rosenberg M 1994 Ann.Rev.Astron.Astrophys.32 419

[19]Verheest F 1996 Space Sci.Rev.77 267

[20]Alfvén H and Mendis D A 1983 Adv.Space Res.3 95

[21]Jeans J H 1902 Phil.Trans.R.Soc.A 199 1

[22]Hamaguchi S and Farouki R T 1994 Phys.Rev.E 49 4430

[23]Avinash K and Shukla P K 1994 Phys.Lett.A 189 470

[24]Shukla P K and Rahman H U 1996 Planet.Space Sci.44 469

[25]Shan S A and Mushtaq A 2011 Chin.Phys.Lett.28 075204

[26]Baruah M B 2009 Studies on structure formation in certain diffuse astrophysical plasmas PhD Thesis Gauhati University,Guwahati,India

[27]Shukla P K and Verheest F 1998 Astrophys.Space Sci.262 157

[28]Khrapak S A et al 2009 Phys.Rev.Lett.102 245004

[29]Prajapati R P 2013 Phys.Lett.A 377 291

[30]Wierling A,Bednarek V J and Röpke G 2000 Dynamical structure factor of dustry plasmas including collisions Frontiers in Dusty Plasmas ed Y Nakamura,T Yokota and P K Shukla(Amsterdam:Elsevier)p 153

[31]Pieper J B and Goree J 1996 Phys.Rev.Lett.77 3137

[32]Shukla P K and Sandberg I 2003 Phys.Rev.E 67 036401