Space Charge Density Profiles Research Articles

Characteristics of plasma sheath in multi-component plasmas with three-ion species

The plasma sheath of a three ion species plasma is studied numerically, relying on the results of the experiment by Yip et al. (Phys. Plasmas 23:050703 (2016) to measure the positive ion velocities at the sheath edge. The positive ion species (Ar^+, Kr^+, and Xe^+) are assumed to be singly charged and to be characterized by the same temperature. It is shown that the sheath characteristics, viz. the particle number densities, the electrostatic potential and the space charge density profile in the sheath all depend on the Kr^+ concentration that is gradually added to the argon-xenon plasma as the third positive ion species. Also, the effect of ion-neutral collisions on the sheath properties is investigated numerically. Our results may be extended to a multi-ion plasma with more than two species of positive ions.

Formation of an inverted sheath in a one-dimensional bounded plasma system studied by particle-in-cell simulation

Formation of an “inverted sheath” is studied by particle-in-cell (PIC) simulation using the code XPDP1 [Verboncoeur et al., J. Comp. Phys. 104, 321–328 (1993)]. Examples of current carrying and floating sheaths are presented. It is shown that the results of the PIC simulation are in excellent agreement with the model developed recently [Gyergyek et al., Phys Plasmas 27, 023520 (2020)]. In this work, it is shown how to normalize the results from the simulations, which are given in SI units, to the dimensionless variables of the model. The procedure can also be reversed. From a given solution of the model, the input parameters of the simulation can be determined. Excellent matching between the results of the model and of the simulations is obtained in both cases. The length of the system is an eigenvalue of the model, while for the simulations, it has to be selected in advance and it is fixed. The appropriate selection of the length of the system is briefly discussed, and so it is the role of the external circuit in the XPDP1 code. Injection of particles into the system is such that monotonically decreasing potential profiles are enforced. A monotonic space charge density profile with surplus of negative charge at the left (collector) electrode and surplus of positive charge at the right (source) electrode must be created. As a consequence, a neutrality point must exist somewhere between the electrodes. The “inverted sheath” is the region between the neutrality point and the collector. By appropriate injection of the particles, the location of the neutrality point can be enforced to any position between the electrodes including the electrodes themselves.

Space charge profile study of AlGaN-based p-type distributed polarization doped claddings without impurity doping for UV-C laser diodes

The space charge density profile of the nondoped AlGaN-based p-type cladding layer for UV-C laser diodes realized by distributed polarization doping is examined theoretically and experimentally. The analysis of the capacitance-voltage measurement revealed that the average effective acceptor density of 4.2 × 1017 cm–3 is achieved even without impurity doping, and it is in good agreement with the theoretical prediction from the measured Al composition profile. This result suggests that the cladding layer is ideal for UV-C LDs because it provides sufficient hole injection while potentially avoiding internal losses due to impurity doping.

Methodology for extraction of space charge density profiles at nanoscale from Kelvin probe force microscopy measurements

To understand the physical phenomena occurring at metal/dielectric interfaces, determination of the charge density profile at nanoscale is crucial. To deal with this issue, charges were injected applying a DC voltage on lateral Al-electrodes embedded in a SiNx thin dielectric layer. The surface potential induced by the injected charges was probed by Kelvin probe force microscopy (KPFM). It was found that the KPFM frequency mode is a better adapted method to probe accurately the charge profile. To extract the charge density profile from the surface potential two numerical approaches based on the solution to Poisson’s equation for electrostatics were investigated: the second derivative model method, already reported in the literature, and a new 2D method based on the finite element method (FEM). Results highlight that the FEM is more robust to noise or artifacts in the case of a non-flat initial surface potential. Moreover, according to theoretical study the FEM appears to be a good candidate for determining charge density in dielectric films with thicknesses in the range from 10 nm to 10 μm. By applying this method, the charge density profile was determined at nanoscale, highlighting that the charge cloud remains close to the interface.

Towards 3D charge localization by a method derived from atomic force microscopy: the electrostatic force distance curve

Charges injection and accumulation in the dielectric remains a critical issue, mainly because these phenomena are involved in a great number of failure mechanisms in cables or electronic components. Achieving a better understanding of the mechanisms leading to charge injection, transport and trapping under electrical stress and of the relevant interface phenomena is a high priority. The classical methods used for space charge density profile measurements have a limited spatial resolution, which prevents them being used for investigating thin dielectric layers or interface processes. Thus, techniques derived from atomic force microscopy (AFM) have been investigated more and more for this kind of application, but so far they have been limited by their lack of in-depth sensitivity. In this paper a new method for space charge probing is described, the electrostatic force distance curve (EFDC), which is based on electrostatic force measurements using AFM. A comparison with the results obtained using kelvin force microscopy (KFM) allowed us to highlight the fact that EFDC is sensitive to charges localized in the third-dimension.

On the modeling of electrical boundary layer (electrode layer) and derivation of atmospheric electrical profiles, eddy diffusion coefficient and scales of electrode layer

Electrode layer or electrical boundary layer is one of the charge generators in the global atmospheric electric circuit. In spite of this we find very few model studies and few measurements of it in the literature. Using a new technique it is shown that in this layer, the space charge density varies exponentially in vertical. A new experimental method based on the surface measurements is discussed to determine all the characteristic scales and an average electrical and meteorological state of an electrode layer. The results obtained are in good agreement with the previous studies. So, it is suggested that an exponential space charge density profile will no longer be an assumption in the case of electrode layer studies. The profiles of atmospheric electric field and electrical conductivity are also derived and a new term named as electrode layer constant is introduced.

Sheath structure in front of an electron emitting electrode immersed in a two-electron temperature plasma: a fluid model and numerical solutions of the Poisson equation

A one-dimensional fluid model of sheath formation in front of a large, planar, floating, electron emitting electrode (collector) immersed in a two-electron temperature plasma is presented. For certain values of the parameters the Bohm criterion is triple valued. Three methods to select the correct Bohm velocity are compared. The simplest is to find the parameters, where the floating potentials that correspond to the high and to the low Bohm velocity are equal. But sometimes—when the electron emission is small—such parameters cannot be found. The second method is the ‘maximum positive ion flux criterion’, proposed recently by Fernández Palop et al (2002 J. Appl. Phys. 91 2587), for electronegative plasmas. In this work it is modified for a two-electron temperature plasma with emitted electrons and applied successfully. This method is sometimes—when the electron emission from the collector is increased—not applicable because the positive ion flux as a function of potential has only 1 maximum. The third method is a numerical solution of the Poisson equation. The transition from the low to the high Bohm velocity occurs at the parameters where the numerically found space charge density profile indicates the formation of a double layer in the sheath. These parameters are always identical to the parameters found with the maximum positive ion flux method, when the latter can be applied. The ‘shooting method’ for the correct determination of electric field at the collector is presented. This method reveals the existence of regular and irregular numerical solutions of the Poisson equation. The irregular solutions of the Poisson equation fulfill only one of the two sheath edge conditions and they correspond to the solutions of the fluid model, that are not physically acceptable. The parameters, where the numerical solutions of the Poisson equation become irregular, are identical to those found with the ‘positive square of electric field’ test, which is also presented.

Effect of the space charge layer created by corona at ground level on the inception of upward lightning leaders from tall towers

Electric field measurements above ground have shown that the space charge layer created by corona at ground level shields the background electric field produced by the thundercloud. Therefore it is expected that this space charge layer can also influence the conditions required to initiate upward lightning from tall objects. For this reason, a numerical model that describes the evolution of the main electrical parameters below a thunderstorm is used to compute the space charge layer development. The time variation of the electric field measured at 600 m above ground during the 1989 rocket triggered lightning experiment at the Kennedy Space Center (Florida) is used to drive the model. The obtained space charge density profiles are used to compute the conditions required to initiate stable upward lightning positive leaders from tall towers. Corona at the tip of the tower is neglected. It is found that the space charge layer significantly affects the critical thundercloud electric fields required to initiate upward lightning leaders from tall objects. The neutral aerosol particle concentration is observed to have a significant influence on the space charge density profiles and the critical thundercloud electric fields, whereas the corona current density does not considerably affect the results for the cases considered in the analysis. It is found that a lower thundercloud electric field is required to trigger a lightning flash from a tall tower or other tall slender grounded structure in the case of sites with a high neutral aerosol particle concentration, like polluted areas or coastal regions.

Streaming current development in a rectangular channel

In this paper, we fast analyse the flow distribution in a metallic pipe of rectangular cross section. In the case of a laminar flow, an analytical solution has been found for the velocity distribution in the pipe cross section. Concerning the space charge density profile, in the case of weak space charge density in the whole section, the general system of equations for a rectangular channel have first been solved. Thus, the space charge density profile can be expressed in terms of the channel dimensions, the diffusion constants and the total charge in the diffuse layer, which is an indicator of the diffuse layer development. Indeed, in the case of a diffuse layer development controlled by a weak wall current ( as it is very often the case ), the space charge density profile is close to a quasi fully developed diffuse layer profile for which the total charge in the diffuse layer increases slowly in order to reach a constant value. Then, the space charge density convected in a such rectangular pipe has been computed, in terms of the geometry of the pipe and the state of development of the diffuse layer, that is to say, in terms of the total space charge in a given cross section. In the case of a turbulent flow, an analysis shows that in our experimental results, a large part of the diffuse layer is perturbed by the turbulence even for a relatively low Reynolds number. Therefore, the space charge density convected in a given cross section is nearly proportional to the mean space charge density in the whole section, or the total charge in this section. Thus, the mesurement of the space charge density convected in a given section indicates the mean space charge density in that section, and so the state of development. We present new experimental streaming current results for a rectangular channel. The experiments were conducted for Reynold's numbers varying from 2000 to 5000 and channel lengths from the entry of the pipe varying from a few centimeters to one meter. These results give the evolution of the space charge density development for different Reynolds numbers and for different lengths from the entry of pipe.

Studies of an artificially generated electrode effect at ground level

Abstract. The outdoor experiments, using a metallic grid above the ground surface, have yielded well-defined vertical profiles of the space-charge density. The profiles showed strong evidence for the existence of an electrode effect, which could be named the artificial electrode effect and can serve as a very useful and well-controlled model for the study of atmospheric electric processes in the atmospheric surface layer. The build-up or break-down of an electrode-effect layer occurred in a time of the order of 10 s under the experimental conditions realized. The artificially generated electrode effect is dependent on the electrical field strength supplied, wind speed, turbulent mixing and ion mobilities. Wind speed and ion mobility seem to be the dominant factors, defining space-charge density profiles. A theoretical model for the artificial electrode effect has been developed, taking into account turbulent mixing of charged particles in the air flow with the logarithmic profile of the wind velocity. The numerical analysis of the boundary value problem for the two-dimensional equations for the light ion concentrations has been performed. The model presented shows a qualitative agreement of calculated space-charge profiles with measured ones, and explains the dependence of the artificial electrode effect on the dominant control parameters. The limiting conditions for the developed theory are discussed.

Measurements of the electrode effect over flat, snow-covered ground

Space charge density profiles up to 3 m above ground were recorded with the Obolensky-filter method. A measuring technique with two instruments was used, where one reference instrument was placed on a fixed level and the other was moved up and down. The space charge difference between the reference and the actual level, and the correlation coefficient were calculated. From the analysis of the recordings, made under very similar atmospheric and ground conditions (snow-covered ground), we found strong evidence for the existence of the electrode effect. Very good agreement between the experimental results and theoretical calculations were observed.

Space charge layers created by coronae at ground level below thunderclouds: Measurements and modeling

High electric fields created by thunderclouds at ground level are enhanced by the irregularities of the surface. This causes corona discharges to occur. The generated ions, when they are not blown away, form a space charge layer which reduces the magnitude of the electric field at ground level. During the LANDES 79 experiment (south western France), electric field soundings have been performed. The sensor is a balloon‐borne double field‐mill device designed for measuring the vertical and horizontal components of the external electric field. At several occasions, a strong vertical field increase with height was detected in the lower part of the sounding. This reveals the existence of important space charge layers near the ground. Space charge density profiles are deduced from electric field soundings. They display density values running from 2 to 7 nC m−3, distributed over shallow layers. A numerical model taking into account ion capture by the neutral aerosol particles leads to theoretical charge density profiles which display features close to those of the experimental profiles. Computation shows that the initial number of neutral aerosol particles has a drastic effect on both density maximum values and layer depths. According to aerosol density, charge density values run from 0.6 nC m−3 (in clean air) up to 3.1 nC m−3 (high aerosol density).

A simple approximation technique for the solution of the Poisson-Boltzmann equation for fixed charge systems

A simple two step approximation technique is described which yields expressions for the mobile ion concentration, electrostatic potential and space charge density profiles inside a lattice of fixed (immobilized) charges when the latter is immersed in an ionic solution. Examples are presented of the results obtained with the approximation technique for a single fixed charge lattice and a membrane consisting of two fixed charge lattices (of opposite sign) in contact. It is shown that the results obtained are in close agreement with iterative computer solutions for the profiles.