Transition region between a nonequilibrium plasma and a negative electrode

A model is developed that describes the transition region between a quasineutral plasma and a planar negative electrode and in which the electron velocity distribution is represented as the sum of two Maxwellian distributions with different temperatures or as the sum of a Maxwellian distribution and distribution corresponding to an electron beam directed toward the electrode. Criteria for the formation of a sheath of positive space charge and a secondary plasma in the transition region are derived. An analysis is made of the dependence of the structure of the transition region on the parameters of the electron distribution, the space charge density distribution in the sheath, and the density of the ion current to the electrode. The criteria obtained are compared with the Bohm criterion.     

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.     

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)     

Quasi-static surface modes of plasma layer with anisotropic electron temperature

Quasi-static surface wave propagation in a plasma layer with anisotropic electron temperature is considered. The case is analyzed where the electron temperature in the direction normal to the plasma boundary is considered to be zero, while in the direction along the boundary, electrons are described by the Maxwellian velocity distribution. It is shown that the modes of such a layer are described by equations for bulk plasma waves with renormalization of the electron density affecting the surface wave dispersion and damping.     

双麦克斯韦分布等离子体对航天器表面的充电效应

空间等离子体在有些情形下,并非单麦克斯韦分布,而是双麦克斯韦分布。为了研究双麦克斯韦分布等离子体对航天器表面的充电效应,基于等离子体动理学理论,建立表面充电平衡方程,综合考虑双麦克斯韦分布等离子体的粒子参数、航天器的单位电容、二次电子发射及光照等因素,得出了双麦克斯韦分布等离子体对航天器表面充电电位的计算表达式,给出了表面充电电位随时间的变化规律。研究结果表明:当等离子体为双麦克斯韦分布时,航天器表面充电电位低于单麦克斯韦分布等离子体环境下的表面充电电位,单麦克斯韦分布的等离子体假设会过高估计航天器表面的充电效应;双麦克斯韦分布的第二分布函数中,对最终的表面充电平衡电位影响较大的主要是离子成分;双麦克斯韦分布等离子体的粒子数密度或温度越高,则表面充电达到平衡所需的时间越长;单位电容仅影响表面充电电位达到稳定所需的时间,对最终的充电平衡电位值影响不大。     

Calculation of the inverse bremsstrahlung absorption in unmagnetized plasmas

Inverse bremsstrahlung is one important way to deliver laser energy to the plasma in inertial confinement fusion. In this article, we study the collisional absorption rate as obtained from the Fokker–Planck treatment of an unmagnetized plasma in harmonic laser field. The electron–ion collision rate is considered in the Krook approximation, and the electron distribution function is considered a Maxwellian function. We evaluate the inverse bremsstrahlung absorption near the irradiated plasma surface in the critical layer. We observe that absorption increases with shorter laser wavelength and lower electron temperatures. When the maximum electron velocity in the limit of q → 1 reaches infinity, the q-non-extensive distribution function reduces to the standard Maxwell-Boltzmann distribution.     

电感耦合氩等离子体中的碰撞截面和输运系数

本文计算了电感耦合氩等离子体中各碰撞截面及电导、热导、扩散和粘滞系数。指出热导在能量传递中起着重要作用,双极扩散则会造成冷等离子体区拥有比局部热平衡值大得多的电子密度。更重要的是,计算表明:三体复合和超弹性碰撞会导致冷等离子体区出现大量的高能电子,这种电子速度分布对Maxwell分布的偏离对作为发射光谱光源的等离子体的激发性质有着特殊的重要意义。 关键词：     

Resonance line radiative transfer for hot atom coronae using Kappa distributions

Hot atomic populations are an important component of the planetary exospheres. Usually, radiative transfer models describing the scattering of light by moving atoms assume that these populations have a Maxwellian velocity distribution. However, the velocity distributions of the hot populations could actually have some more extended wings. Popular velocity distributions often used in plasma physics and recently proposed to describe neutral planetary environments are Kappa velocity function distributions. In this paper, following the work of Hummer [Non-coherent scattering: I The redistribution functions with Doppler broadening. R Astron. Soc Month Not 1962;125:21] and Cranmer [Non-Maxwellian redistribution in solar coronal Lyα emission. Astrophys J 1998;508:925–39], we calculate the frequency redistribution functions of radiation scattered by moving atoms with Kappa velocity distribution. We also present a detailed study of a radiative transfer model taking into account Kappa velocity distribution functions, for integer and semi-integer values of κ. We apply this theory to a model of Jupiter hydrogen corona containing 0.1% column density of hot hydrogen to quantify the spectroscopic and imaging differences between Kappa velocity distributions and bi-Maxwellian velocity distributions. When assuming a Kappa velocity distribution with κ=2 for the hot population, intensity increases of 40% occur at the bright limb and 15% on the disk compared with the same calculations done using a Maxwellian velocity distribution. The line profile differs slightly from a Maxwellian distribution on the disk and at the bright limb, but the difference is larger above the limb. Kappa distributions used to study the Jovian atmosphere are speculative and further studies are needed to link the formation of the hot exospheric populations to the Kappa velocity distributions.     

Effects of Energetic Electrons on Collector and Source Potentials in a Finite Ion Temperature Plasma

Formation of the potential in a two-electron-temperature plasma region facing a floating collector was studied theoretically with a kinetic plasma-sheath model and by electrostatic particle simulation. The electrons were described by truncated full Maxwellian velocity distribution functions and the ions by an accelerated half-Maxwellian velocity distribution function. The collector potential and the plasma source sheath or presheath potential drop were evaluated as functions of the hot to cool electron temperature ratio and the hot electron density ratio using Vlasov and Poison equations. The results showed that the presheath potential drop varied continuously with electron composition ratio for lower values of the electron temperature ratio, while for higher values in a narrow composition ratio range, triple values of the potential were found. Of the two physically acceptable values, the lower was characterized by the cool electrons and the higher by the hot electrons. It is anticipated that a current-free double layer structure is formed in the plasma system between these two potential regions. The collector floating potential, as a function of electron composition ratio, is mainly dominated by the hot electrons, since already a small value of hot electron current is sufficient to compensate the ion saturation current. In order to complete the theoretical investigation we also study the hydrogen plasma system with the XPDP1 particule-in-cell simulation code composed at Berkeley. At certain plasma parameter values formation of a double layer structure was observed. The potential Values on the upper and lower side of the double layer, as well as that of the collector floating potential, corresponded very well to the calculated values. On the upper side the plasma was composed of ions, accelerated through the source sheath potential drop, and electrons consisting of cool full Maxwellian and hot truncated full Maxwellian populations. On the lower side only hot electrons and ions additionally accelerated through the double layer were found.     

双麦克斯韦分布尘埃等离子体中尘埃粒子的充电研究

根据充电方程和电荷守恒条件,导出了双麦克斯韦分布的弱电离尘埃等离子体充电频率(电荷弛豫速率),给出了充电电流的计算公式. 对结果分析表明,定向运动速度大小对充电电流和充电频率有一定的影响,充电频率随着定向速度增加而减小,当定向速度远远小于电子的热速度时,充电频率与文献给出的表达式一致. 关键词： 尘埃等离子体 双麦克斯韦分布 充电频率     

Study of the X-ray emission from Ta plasma obtained by ns laser ablation

In this work, the continuum spectrum of X-rays originated from the interaction of a moderate intensity ns Nd:YAG laser (1064 nm, 9 ns, 30 Hz, 900 mJ, 10¹¹ W/cm²) with Ta target producing plasma is investigated. Plasma expands unisotropically with a velocity, depending on the pressure of the residual gas in the vacuum chamber. The X-ray intensity is a function of the laser energy and of the gas pressure inside the chamber. The X-ray energy is measured with an X-ray filter positioned in front of the Si(Li) solid-state detector. A temperature of about ～1–2 keV of the hot electrons, responsible for the continuum spectrum emission from the plasma, is calculated from the fit of the X-ray spectrum, applying a Maxwellian distribution.     

Influence of electron energy distribution on helium recombining plasma diagnostics using line emissions

The influence of electron energy distribution on helium recombining plasma diagnostics is investigated using a helium collisional‐radiative model. The population densities of excited helium atoms are calculated for Maxwellian and non‐Maxwellian distribution plasma cases. In the case of the Maxwellian distribution plasma, the electron temperature and electron density determined by the Boltzmann plot method agree well with the input plasma parameters. On the other hand, it is indicated that the electron temperature and electron density are significantly underestimated in the bi‐Maxwellian distribution plasma case, even though the density of the hot electron components is three orders smaller than that of the bulk electrons. This result indicates that in a non‐Maxwellian helium recombining plasma, evaluation of the particle balance based on line emissions from excited helium atoms would be difficult because the reaction rate of atomic and molecular processes is strongly dependent on the electron temperature and density.     

Geschwindigkeitsverteilungsfunktionen von Atomen und Ionen in verschiedenen Anregungs- und Ionisationsstufen in Niederdruck-Entladungen bei hohem Ionisationsgrad

Supposing free-fall conditions the velocity distribution functions of atoms and ions in various levels in gas discharges at low pressures are calculated. In particular, plasmas at high degrees of ionization are considered. Solving the Boltzmann equation for the motions transverse to the wall of the discharge tube it is shown that the velocity distribution functions can considerably deviate from the Maxwellian and become non-isotropic. Inelastic collisions with electrons and the ionization by electron impacts considerably determine the velocity distribution function of the neutral atoms. The velocity distribution function of the ions is also essentially determined by the electric field within the plasma. For the motions transverse to the wall the half widths of the velocity distribution functions do not only depend on the temperature of the wall, but on the electron density and on the electron temperature as well. At small electron densities the half widths for excited atoms and for ions can be narrower than the one for the ground state atoms. The charge exchange between atoms and ions is shortly taken into consideration.     

Ion acceleration during adiabatic plasma expansion: Renormalization group approach

The renormalization group approach is applied to derive an exact solution to self-consistent Vlasov kinetic equations for plasma particles in the quasineutral approximation. The solution obtained describes the one-dimensional adiabatic expansion into vacuum of a plasma bunch with arbitrary initial velocity distributions of the electrons and ions. The ion acceleration is investigated for both a Maxwellian two-temperature initial electron distribution and a super-Gaussian initial electron distribution.     

Determination of the charge state distribution of a highly ionized coronal Au plasma

We present the first definitive measurement of the charge state distribution of a highly ionized gold plasma in coronal equilibrium. The experiment utilized the Livermore electron beam ion trap EBIT-II in a novel configuration to create a plasma with a Maxwellian temperature of 2.5 keV. The charge balance in the plasma was inferred from spectral line emission measurements which accounted for charge exchange effects. The measured average ionization state was 46.8+/-0.75. This differs from the predictions of two modeling codes by up to four charge states.     

Inverse Bremsstrahlung absorption coefficient in inhomogeneous plasma with nonextensive electron velocity distribution and Tsallis exponential electron density profile

Inverse bremsstrahlung (collisional) absorption of the laser beam is studied in plasma with a generalized (q-nonextensive) electron velocity distribution and some kind of generalized electron density profile. It is shown that for some values of parameters designating the q-nonextensive electron velocity distribution function and its generalized density profile, the calculated absorption coefficient reduces to the already known cases with Maxwellian velocity distribution with linear and exponential density profiles.     

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.     

Measurement of the velocity distribution of neutral atoms using laser-induced fluorescence

Laser-induced fluorescence has been used to measure the Doppler-shifted emission spectra in the atomic beam of gadolinium. The velocity distribution of gadolinium atoms that was deduced from these spectra shows good agreement with a Maxwellian distribution. Based on this good agreement, temperatures of the evaporating source have also been estimated. A new experimental method has been devised in our measurements, which can also be used for other multiline systems similar to gadolinium. This method allows one to effectively eliminate the distorting interference present in Doppler profile measurements for the multiline systems mentioned above. The text was submitted by the authors in English.