二次电子分布函数对绝缘壁面稳态鞘层特性的影响

由于缺乏详细的理论计算和实验结果,在研究绝缘壁面稳态流体鞘层特性时,通常假设壁面出射的总二次电子服从单能分布(0)、半Maxwellian分布等.在单能电子轰击壁面的详细二次电子发射模型基础上,采用Monte Carlo方法统计发现:当入射电子服从Maxwellian分布时,绝缘壁面发射的总二次电子服从三温Maxwellian分布.进而,采用一维稳态流体鞘层模型进行对比研究,结果表明:二次电子分布函数对鞘边离子能量、壁面电势、电势及电子/离子密度分布等均具有明显影响;总二次电子服从三温Maxwellian分布时,临界空间电荷饱和鞘层无解,表明随着壁面总二次电子发射系数的增加,鞘层直接从经典鞘层结构过渡到反鞘层结构.     

Sheath structure in plasma with two species of positive ions and secondary electrons

The properties of a collisionless plasma sheath are investigated by using a fluid model in which two species of positive ions and secondary electrons are taken into account. It is shown that the positive ion speeds at the sheath edge increase with secondary electron emission(SEE) coefficient, and the sheath structure is affected by the interplay between the two species of positive ions and secondary electrons. The critical SEE coefficients and the sheath widths depend strongly on the positive ion charge number, mass and concentration in the cases with and without SEE. In addition, ion kinetic energy flux to the wall and the impact of positive ion species on secondary electron density at the sheath edge are also discussed.     

电子温度各向异性对霍尔推力器BN绝缘壁面鞘层特性的影响

建立多价态多组分等离子体一维流体鞘层模型,引入电子温度各向异性系数并考虑出射电子速度分布,研究了电子温度各向异性对霍尔推力器中的BN绝缘壁面鞘层特性和近壁电子流的影响.分析结果表明,相比于纯一价氙等离子体鞘层参数,推力器中的多价态氙等离子体鞘层电势降略有降低,电子壁面损失增加,临界二次电子发射系数减小.推力器中的电子温度各向异性现象可以显著地加大出射电子能量系数,进而降低鞘层电势降,增强电子壁面相互作用.数值结果表明,空间电荷饱和机制下电子温度各向异性对鞘层空间电势分布影响显著. 关键词： 霍尔推力器 电子温度各向异性 空间电荷饱和鞘层     

电子温度对霍尔推进器等离子体鞘层特性的影响

采用二维粒子模拟方法研究了霍尔推进器通道中电子温度对等离子体鞘层特性的影响, 讨论了不同电子温度下电子数密度、鞘层电势、电场及二次电子发射系数的变化规律. 结果表明: 当电子温度较低时, 鞘层中电子数密度沿径向方向呈指数下降, 在近壁处达到最小值, 鞘层电势降和电场径向分量变化均较大, 壁面电势维持一稳定值不变, 鞘层稳定性好; 当电子温度较高时, 鞘层区内与鞘层边界处电子数密度基本相等, 而在近壁面窄区域内迅速增加, 壁面处达到最大值, 鞘层电势变化缓慢, 电势降和电场径向分量变化均较小, 壁面电势近似维持等幅振荡, 鞘层稳定性降低; 电子温度对电场轴向分量影响较小; 随电子温度的增大, 壁面二次电子发射系数先增大后减少. 关键词： 霍尔推进器 等离子体鞘层 电子温度 粒子模拟     

两种温度电子对稳态等离子体鞘层的影响

建立包含冷热电子的无碰撞等离子体鞘层的流体模型,利用数值模拟研究含有两种温度电子时等离子体鞘层的产生.结果表明:对于含有两种不同温度电子的稳态等离子体,冷电子的温度越低或者冷电子的含量越多,鞘边离子的马赫数临界值就越小,鞘层的宽度就变得越窄,沉积器壁的离子动能流也就越少.此外,研究不同种类的等离子体(Ar、Ke、Xe),鞘层厚度和离子沉积器壁动能流受冷电子的影响.     

Floating Sheath Potentials in Non-Maxwellian Plasmas

The floating sheath potential in a plasma having a Maxwellian electron distribution function is e?>s = -kTe 1n (a/b)/2 where Te is the electron temperature, a is the ratio of electron temperature to ion temperature, and b is the ratio of electron mass to ion mass. This expression is derived by equating the flux of electrons and ions to a surface in the plasma. Only electrons initially having an energy greater than -e?s flow to the surface. These electrons are in the tail of the distribution, a region that differs significantly from a Maxwellian in many plasmas. An analysis is performed where the sheath potential is solved for using a two-temperature model for the electron distribution function. The two-temperature model accurately describes the distortion from a Maxwellian in the tail of the distribution function. The magnitude of the sheath potential calculated with the two-temperature distribution is significantly smaller than that obtained using a Maxwellian distribution, a result of the reduction in the relative abundance of energetic electrons in the tail of the distribution.     

Fluid Model of a Sheath Formed in Front of an Electron Emitting Electrode Immersed in a Plasma with Two Electron Temperatures

The formation of a sheath in front of a negatively biased electrode (collector) that emits electrons is studied by a one‐dimensional fluid model. Electron and ion emission coefficients are introduced in the model. It is assumed that the electrode is immersed in a plasma that contains energetic electrons. The electron velocity distribution function is assumed to be a sum of two Maxwellian distributions with two different temperatures, while the ions and the emitted electrons are assumed to be monoenergetic. The condition for zero electric field at the collector is derived. Using this equation the dependence of electron and ion critical emission coefficients on various parameters ‐ like the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons ‐ is calculated for a floating collector. A modification of the Bohm criterion due to the presence of hot and emitted electrons is also given. The transition between space charge limited and temperature limited electron emission for a current‐carrying collector is also analyzed. The critical potential, where this transition occurs, is calculated as a function of several parameters like the Richardson emission current, the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

不同成分等离子体鞘层的玻姆判据

在一维平板鞘层中采用流体模型分别研究了不同成分无碰撞等离子体鞘层的玻姆判据.通过拟牛顿法数值模拟了含有电子、离子、负离子以及二次电子的等离子体鞘层玻姆判据.结果表明二次电子发射增加了鞘层离子马赫数的临界值,且器壁发射二次电子温度越高,离子马赫数临界值越小.负离子使离子马赫数临界值减小.而在含有二次电子和负离子的等离子体鞘层中,当负离子较少时,二次电子发射对离子马赫数临界值影响较大;当负离子增加时,离子马赫数的临界值则主要受负离子的影响. 关键词： 鞘层 等离子体 玻姆判据     

霍尔推进器中磁化二次电子对鞘层特性的影响

为进一步研究霍尔推进器壁面二次电子发射对推进器性能的影响,采用流体模型数值模拟了二次电子磁化效应的等离子体鞘层特性.得到二次电子磁化鞘层的玻姆判据.讨论了不同的磁场强度和方向、二次电子发射系数以及不同种类等离子体推进器的鞘层结构.结果表明:随器壁二次电子发射系数的增大,鞘层中粒子密度增加,器壁电势升高,鞘层厚度减小;鞘层电势及粒子密度随着磁场强度和方位角的增加而增加;而对于不同种类的等离子体,壁面电势和鞘层厚度也不同.这为霍尔推进器的磁安特性实验提供了理论解释. 关键词： 霍尔推进器 磁鞘 二次电子     

Sheath in Front of a Negatively Biased Collector that Emits Electrons and is Immersed in a Two Electron Temperature Plasma

An extension of a recently published [Gyergyek T., ?er?ek M. Contrib. Plasma Phys., 45 , (2005), 89] one dimensional fluid model of the sheath formation in front of a floating electrode (collector) that emits secondary electrons and is immersed in a two‐electron temperature nonmagnetized, collisionless plasma is presented. The electron velocity distribution function is assumed to be a two‐temperature maxwellian, while the singly charged positive ions and the emitted electrons are assumed to be monoenergetic. It is assumed that the electrons in the pre‐sheath potential drop obey the Boltzmann relation, so that a larger fraction of the hot than of the cool electrons can penetrate to the sheath edge. Our model predicts that the collector can in some cases have 3 and in some cases, when the emission of electrons from the collector is critical, even 5 different floating potentials at the same hot to cool electron temperature and density ratios very far away from the collector. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

具有非广延分布电子的碰撞等离子体磁鞘的结构

很多关于等离子体鞘层的研究工作都是基于电子满足经典的麦克斯韦速度分布函数,而等离子体中的粒子具有长程电磁相互作用,使用Tsallis提出的非广延分布来描述电子更为恰当.本文建立一个具有非广延分布电子的碰撞等离子体磁鞘模型,理论推导出受非广延参数q影响的玻姆判据,离子马赫数的下限数值会随着参数q的增大而减小.经过数值模拟,发现与具有麦克斯韦分布(q=1)电子的碰撞等离子体磁鞘对比,具有超广延分布(q<1)和亚广延分布(q>1)电子的碰撞等离子体磁鞘的结构各有不同,包括空间电势分布、离子电子密度分布、空间电荷密度分布.模拟结果显示非广延分布的参数q对碰撞等离子体磁鞘的结构具有不可忽略的影响.希望这些结论对相关的天体物理、等离子体边界问题的研究有参考价值.     

Nonlinear collisional monte carlo simulations for high-temperature SOL plasma

A nonlinear Monte Carlo collisional model is applied to to investigate scrape-off layer (SOL) plasmas with high temperatures. In the proposed SOL modeling, A steady state SOL plasma, which satisfies the particle and energy balances and neutrality constraint, is determined in terms of total particle and heat fluxes across the separatrix, the edge plasma temperature, the secondary electron emission coefficient, and the SOL size. A conductive heat flux into the SOL is effectively modeled via random exchange of source particles and the SOL plasma particles. It is found that the potential drop and the electron transmission factor in the collisional SOL plasma are in good agreement with the theoretical prediction. The cooling effect of secondary electrons in the high temperature divertor operation is investigated. In such a collisionless plasma, the present nonlinear collision model is useful because the electron distribution function deviates far from a Maxwellian distribution. In the presence of strong secondary electron emission, the electron sheath energy transmission factor in the collisionless regime is found to be significantly smaller than that in the collisional regime. This fact suggests that a high-temperature divertor operation can be possible.     

Tonks-Langmuir problem for a bi-Maxwellian plasma

An analytical solution of the Tonks-Langmuir (TL) problem with a bi-Maxwellian electron energy distribution function (EEDF) is obtained for a plasma slab. The solution shows that the ambipolar potential, the plasma density distribution, and the ion flux to the wall are mainly governed by the cold electrons, while the ionization rate and voltage drop across the wall sheath are governed by the hot electrons. The ionization rate by direct electron impact is found to be spatially rather uniform, contrary to the T-L solution where it is proportional to the plasma density distribution. The temperature of hot electrons defined by the ionization balance is found to be close to that of the T-L solution for a mono-Maxwellian EEDF, and is in reasonable agreement with experiments carried out in a low pressure capacitance RF discharge. The energy balance for cold electrons in this discharge shows that their heating by hot electrons via Coulomb interaction is equalized by the cold electrons' escape to the RF electrodes during collapse of the RF sheath     

Plasma-wall interactions in DC discharges and sheath of Langmuir probes

The plasma-wall interactions in various DC discharges and sheath of Langmuir probe are analyzed and discussed. The methods of their investigations are discussed including fluid and PIC MC. Various assumptions used in fluid models e.g. plasma neutrality, Bohm criterion, Boltzmann electrons approximation, etc. are analyzed. Ion heating and electron cooling effect at the DC plasma wall is discussed and explained. Langmuir probes measurements in high-temperature and ion thruster plasma are analyzed. The secondary electron emission influences the IV characteristic of Langmuir probe especially at positive voltages. However, only elastic reflection processes really contribute significantly to the probe current. The elastic SEE processes reflect electrons from probe with the same relatively high speed. It was observed that the axial magnetic field influences probe characteristics and floating potential more significantly than radial field. The axial field deflects all electrons approaching probe.     

Control of the Interface Between Electron‐Hole and Electron‐Ion Plasmas: Hybrid Semiconductor‐Gas Phase Devices as a Gateway for Plasma Science

Coupling electron‐hole (e^–‐ h⁺) and electron‐ion plasmas across a narrow potential barrier with a strong electric field provides an interface between the two plasma genres and a pathway to electronic and photonic device functionality. The magnitude of the electric field present in the sheath of a low temperature, nonequilibrium microplasma is sufficient to influence the band structure of a semiconductor region in immediate proximity to the solid‐gas phase interface. Optoelectronic devices demonstrated by leveraging this interaction are described here. A hybrid microplasma/semiconductor photodetector, having a Si cathode in the form of an inverted square pyramid encompassing a neon microplasma, exhibits a photosensitivity in the ～420–1100 nm region as high as 3.5 A/W. Direct tunneling of electrons into the collector and the Auger neutralization of ions arriving at the Si surface appear to be facilitated by an n ‐type inversion layer at the cathode surface resulting from bandbending by the microplasma sheath electric field. Recently, an npn plasma bipolar junction transistor (PBJT), in which a low temperature plasma serves as the collector in an otherwise Si device, has also been demonstrated. Having a measured small signal current gain h_fe as large as 10, this phototransistor is capable of modulat‐ing and extinguishing the collector plasma with emitter‐base bias voltages <1 V. Electrons injected into the base when the emitter‐base junction is forward‐biased serve primarily to replace conduction band electrons lost to the collector plasma by secondary emission and ion‐enhanced field emission in which ions arriving at the base‐collector junction deform the electrostatic potential near the base surface, narrowing the potential barrier and thereby facilitating the tunneling of electrons into the collector. Of greatest significance, therefore, are the implications of active, plasma/solid state interfaces as a new frontier for plasma science. Specifically, the PBJT provides the first opportunity to control the electronic properties of a material at the boundary of, and interacting with, a plasma. By specifying the relative number densities of free (conduction band) and bound (valence band) electrons at the base‐collector interface, the PBJT's emitter‐base junction is able to dictate the rates of secondary electron emission (including Auger neutralization) at the semiconductor‐plasma interface, thereby offering the ability to vary at will the effective secondary electron emission coefficient for the base surface (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Collisionless bounce resonance heating in dual-frequency capacitively coupled plasmas

We present the experimental evidence of the collisionless electron bounce resonance heating (BRH) in low-pressure dual-frequency capacitively coupled plasmas. In capacitively coupled plasmas at low pressures when the discharge frequency and gap satisfy a certain resonant condition, the high energy beamlike electrons can be generated by fast sheath expansion, and heated by the two sheaths coherently, thus the BRH occurs. By using a combined measurement of a floating double probe and optical emission spectroscopy, we demonstrate the effect of BRH on plasma properties, such as plasma density and light emission, especially in dual-frequency discharges.     

Heat flow through a plasma sheath in the presence of secondary electron emission from plasma‐wall interaction

The formation of a plasma sheath in front of a negative wall emitting secondary electron is studied by a one‐dimensional fluid model. The model takes into account the effect of the ion temperature. With the secondary electron emission (SEE ) coefficient obtained by integrating over the Maxwellian electron velocity distribution for various materials such as Be, C, Mo, and W, it is found that the wall potential depends strongly on the ion temperature and the wall material. Before the occurrence of the space‐charge‐limited (SCL ) emission, the wall potential decreases with increasing ion temperature. The variation of the sheath potential caused by SEE affects the sheath energy transmission and impurity sputtering yield. If SEE is below SCL emission , the energy transmission coefficient always varies with the wall materials as a result of the effect of SEE , and it increases as the ion temperature is increased. By comparison of with and without SEE , it is found that sputtering yields have pronounced differences for low ion temperatures but are almost the same for high ion temperatures.     

电子和负离子的反射运动对碰撞电负性磁鞘的影响

研究了鞘层中电子和负离子的反射运动对碰撞电负性磁鞘玻姆判据和鞘层结构的影响.通过理论推导得到了考虑鞘层中电子和负离子的反射运动时鞘层玻姆判据表达式,并通过数值模拟得到了电子和负离子采用玻尔兹曼模型和反射运动模型时离子马赫数的下限随参数的变化曲线以及鞘层中带电粒子密度的分布曲线.结果表明,电子和负离子的反射运动模型和玻尔兹曼模型离子马赫数的上限完全相同,下限表达式不同,反射运动模型中下限还与基板电势有关,且随着基板电势值的增加而增大,达到与玻尔兹曼分布中相同值后保持不变,随着鞘边负离子浓度和温度的不同达到最大值的速度不同;离子马赫数的下限在玻尔兹曼和反射运动模型中都随鞘边负离子浓度的增加和温度的降低而减小,只是在反射运动模型中的最大值要小;两种模型中离子马赫数的下限都随鞘边电场的增加而增加,但在玻尔兹曼模型中增加得更快最终值更大;两种模型离子马赫数的下限都随碰撞参数或磁场角度的增加而降低,但在玻尔兹曼模型中降低更快,随着碰撞参数或者磁场角度的增加两种模型中离子马赫数的下限趋于一致;当基板电势值较小时,电子和负离子的反射运动对鞘层结构影响较大,当基板电势值较大时电子和负离子反射运动对鞘层中带电粒子密度分布的影响很小.     

霍尔推进器壁面材料二次电子发射及鞘层特性

霍尔推进器放电通道等离子体与壁面相互作用形成鞘层,不同壁面材料的二次电子发射对推进器鞘层特性具有重要影响,本文针对推进器壁面鞘层区域建立二维物理模型,研究了氮化硼(BN)、碳化硅(SiC)和三氧化二铝(Al_2O_3)三种不同壁面材料的二次电子发射特性,在改进SiC材料二次电子发射模型的基础上,采用粒子模拟方法,讨论了壁面二次电子发射系数与电子温度和磁场强度的关系,研究了三种材料(BN,SiC和Al_2O_3)的鞘层特性,结果表明:修正的二次电子发射模型拟合曲线与实验曲线几乎一致;在相同电子温度下,三种材料(BN,SiC和Al_2O_3)的二次电子发射系数和壁面电子数密度依次增大,而鞘层电场和鞘层电势降依次减小,BN材料具有合适的二次电子发生射系数,使得霍尔推进器能在低电流下稳态工作。     

Characteristics of wall sheath and secondary electron emission under different electron temperatures in a Hall thruster

In this paper, a two-dimensional physical model is established in a Hall thruster sheath region to investigate the influences of the electron temperature and the propellant on the sheath potential drop and the secondary electron emission in the Hall thruster, by the particle-in-cell(PIC) method. The numerical results show that when the electron temperature is relatively low, the change of sheath potential drop is relatively large, the surface potential maintains a stable value and the stability of the sheath is good. When the electron temperature is relatively high, the surface potential maintains a persistent oscillation, and the stability of the sheath reduces. As the electron temperature increases, the secondary electron emission coefficient on the wall increases. For three kinds of propellants(Ar, Kr, and Xe), as the ion mass increases the sheath potentials and the secondary electron emission coefficients reduce in sequence.