TWO-DIMENSIONAL NUMERICAL SIMULATION OF LOW FREQUENCY OSCILLATIONS OF SPACE CHARGE AND POTENTIAL IN THE GYROTRON ADIABATIC TRAP

The development of oscillations of the space charge and potential in the adiabatic trap of a gyrotron between the cathode and the cavity is studied numerically. The PIC method is applied, with the real two-dimensional distributions of the electric and magnetic fields taken into account. Secondary emission is included into the numerical model, as well as such factors as the electron beam space charge, thermal velocities of electrons, and emitter roughness. The value of the trapped space charge as a function of time is calculated. Time dependences of the potential in various cross-sections of the formation system are traced. The amplitudes of its variable component have been found and then the corresponding frequency spectra have been calculated. The process of cathode bombardment is investigated. The energy distribution and time dependence of the current in the electron beam coming to the operating space are found. Some ways to reduce the oscillations of the potential and the space charge are discussed.     

Ion storage in Kingdon trap

Abstract

The characteristics of stored ions in a Kingdon trap have been investigated. The charge distribution of stored ions was measured by a time of flight (TOF) mass spectrometer. Storage of Ar^q+ (q = 1, 2, 3, 4) produced by electron beam irradiation has been confirmed. The dependences of Ar ion yields on the trapping potential and storage time have been systematically studied.

Applying a voltage to end plates is very important for the storage of ions. Remarkable oscillations of the ion yields are found in the decay curves as a function of storage time for Ar⁺, Ar²⁺ and Ar³⁺ indicating periodical motion of each ion group about the central wire. The three dimensional orbits of ions in the trap are analysed by a computer calculation to understand the experimental results.     

On the influence of the voltage pulse profile on the process of particle trapping in the adiabatic trap of the gyrotron

We analyze the process of stabilization of electron beam parameters in a gyrotron for different profiles of the front of the accelerating-voltage pulse and the case of a large space charge trapped in the adiabatic trap. The duration of the portion of the pulse front, within which the electrons are reflected from the magnetic mirror and trapped, is at least an order of magnitude shorter than the entire length of the pulse front and is comparable with the characteristic time of potential oscillation development in the trap at great values of the pitch factor. The results of numerical analysis of the electron beam within the framework of models with finite durations of the voltage pulse front and instantaneous switch-on of the voltage showed that the steady-state values of the beam parameters are only weakly dependent on the pro.le of the pulse front. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 5, pp. 425–433, May 2008.     

Collective processes in a microsecond relativistic electron beam: Basic rules and mechanisms

Collective processes taking place in the space charge of a microsecond relativistic electron beam with magnetic insulation are considered. The space-time characteristics of the low-frequency and high-frequency oscillations are found, and the effect of the magnetic compression of the beam near the cathode on these oscillations is studied. It is shown that the basic source of the low-frequency oscillations is the collective motion of the space charge, which takes place in crossed electric and magnetic fields near the cathode, while the primary reason for the high-frequency oscillations is two-stream instability in the beam. The possibility of suppressing both types of oscillations by compressing relativistic electron beams near the cathode is demonstrated. The effect of nonuniform magnetic fields, including their effect on the cathode plasma motion, is elucidated.     

储存环内电子冷却过程模拟

考虑储存环内离子的横向振荡和纵向振荡的运动特性,模拟了HIRFL-CSR内重离子束的电子冷却过程.给出了离子束的横向发射度和纵向动量散度随时间连续变化的图象,由此分析了电子束的空间电荷效应,冷却段色散函数和横向电子束温度对冷却过程快慢的影响.     

Influence of the beam-forming conditions on the development of space-charge oscillations in a long-pulse relativistic electron beam

The characteristics of the space-charge oscillations of a long-pulse relativistic electron beam in magnetically insulated diodes are determined for different geometries of the electron acceleration section and for explosive-emission cathodes of different materials. The important role of the stream of electrons having high transverse velocities in the evolution of the oscillations is demonstrated, and the laws governing the generation of this stream are determined. Possible mechanisms of the space-charge oscillations are described, taking into account the interaction of the electron stream in the beam halo with the main electron stream, the development of diocotron instability in the stream of electrons emitted by the outer lateral surface of the plasma emitter, and the instability of the space charge of “long-lived” electrons in the beam transport channel. Zh. Tekh. Fiz. 68, 102–106 (April 1998)     

Analysis of microscopic parameters of surface charging in polymer caused by defocused electron beam irradiation

The relationship between microscopic parameters and polymer charging caused by defocused electron beam irradiation is investigated using a dynamic scattering-transport model. The dynamic charging process of an irradiated polymer using a defocused 30 keV electron beam is conducted. In this study, the space charge distribution with a 30 keV non-penetrating e-beam is negative and supported by some existing experimental data. The internal potential is negative, but relatively high near the surface, and it decreases to a maximum negative value at z = 6 μm and finally tend to 0 at the bottom of film. The leakage current and the surface potential behave similarly, and the secondary electron and leakage currents follow the charging equilibrium condition. The surface potential decreases with increasing beam current density, trap concentration, capture cross section, film thickness and electron–hole recombination rate, but with decreasing electron mobility and electron energy. The total charge density increases with increasing beam current density, trap concentration, capture cross section, film thickness and electron–hole recombination rate, but with decreasing electron mobility and electron energy. This study shows a comprehensive analysis of microscopic factors of surface charging characteristics in an electron-based surface microscopy and analysis.     

非聚焦电子束照射SiO2薄膜带电效应

采用考虑电子散射、俘获、输运和自洽场的三维数值模型, 模拟了低能非聚焦电子束照射接地SiO₂薄膜的带电效应. 结果表明, 由于电子的迁移和扩散, 电子会渡越散射区域产生负空间电荷分布. 空间电荷呈现在散射区域内为正, 区域外为负的交替分布特性. 对于薄膜负带电, 电子会输运至导电衬底形成泄漏电流, 其暂态过程随泄漏电流的增加趋于平衡. 而正带电暂态过程随返回二次电子的增多而趋于平衡. 在平衡态时, 负带电表面电位随薄膜厚度、陷阱密度的增大而降低, 随电子迁移率、薄膜介电常数的增大而升高;而正带电表面电位受它们影响较小.     

The surface potential of insulating thin films negatively charged by a low-energy focused electron beam

We report on the surface potential characteristics in the equilibrium state of the grounded insulating thin films of several 100 nm thickness negatively charged by a low-energy (<5 keV) focused electron beam, which have been simulated with a newly developed two-dimensional self-consistent model incorporating electron scattering, charge transport and charge trapping. The obtained space charge is positive and negative within and outside the region, respectively, where the electron and hole densities are greater than the trap density. Thus, the surface potential is relatively high around the center, then it decreases to a maximum negative value and finally tends to zero along the radial direction. The position of the maximum value is far beyond the range of e-beam irradiation as a consequence of electron scattering and charge transport. Moreover, a positive electric field can be generated near the surface in both radial and axial directions. The surface potential at center exhibits a maximum negative value in the condition of the ～2 keV energy non-penetrating e-beam in this work, which is supported by some existing experimental data in scanning electron microscopy. Furthermore, the surface potential decreases with the increase in beam current, trap density and film thickness, but with the decrease in electron mobility.     

Influence of nonuniformities of a magnetic-mirror field on the space-time characteristics of a long-pulse relativistic electron beam

An experimental investigation is made of the influence of local nonuniformities of a mirror-configuration magnetic field on oscillations of the space charge and the structure of a long-pulse relativistic electron beam. It is found that the outcome depends on the axial configuration of the nonuniformity. A nonuniformity near the cathode can substantially reduce the amplitude of the oscillations and improve the beam transport. The creation of a nonuniformity far from the cathode leads to an accelerated increase in the oscillations and causes spreading of the transverse structure of the beam. A possible explanation is given for the mechanism responsible for the influence of these local magnetic field nonuniformities assuming reflection of the cathode plasma and electron flux from the magnetic mirror, and also allowing for a jump in the drift velocity. Zh. Tekh. Fiz. 67, 83–88 (August 1997)     

The Influence of the Fluctuation Amplitude on the Probe Characteristic

The time-averaged probe current is calculated by using a sampling method for sinusoidal and sawtooth-like oscillations of the space potential. The effect of oscillations on the measured plasma parameters obtained with the aid of the single probe method, double probe method and the method of the second derivative of the probe characteristic is discussed, with the electron saturation current being taken into account. In the ion current the values r_p/λ_D, λ/r_p and M_i characterizing the working regime are varied. The calculated results are checked by corresponding measurements in a beam generated plasma.     

Charge transport and accumulation in dielectrics upon irradiation by an electron beam

The transient process of charge accumulation in a dielectric with exposed surface is considered for the case of irradiation by a beam of electrons with path lengths less than the specimen thickness. For the case of shallow traps the characteristic method is used to solve the problem of passage of the space charge density front through the specimen volume from a virtual cathode located at a depth equal to the path length of the primary beam electrons to a grounded electrode. Transient patterns of field intensity and space charge density over dielectric layer thickness are found. Special features of the transient process are considered, related to the fact that the charge carriers are being injected into the dielectric by an electron beam. Furthermore, an expression is obtained describing the kinetics of formation of the exposed dielectric surface potential, and the dependence of these kinetics on radiation parameters and dielectric properties are considered. The conclusions of the model are compared to experiment.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 20–25, August, 1988.     

高能电子辐照绝缘厚样品的表面电位动态特性

采用数值计算和实验测量相结合的方法, 阐明了高能电子束照射下绝缘厚样品的表面电位和电子产额动态特性. 结果表明: 由于电子在样品内部的散射和输运, 沿着深度方向, 空间电位先缓慢下降到最小值, 然后逐渐升高并趋近于零; 随着电子束照射, 样品的表面电位逐渐下降, 可至负千伏量级, 电子总产额逐渐增大至一个接近于1的稳定值; 电子束停止照射后, 长时间放置下, 表面电位将逐渐升高, 但带电并不会消除; 表面电位随电子束能量的升高近似线性下降, 随入射角的增大而升高, 而随样品厚度的增大仅略有下降.     

An approximate two-dimensional theory of interaction between an electron beam and an electromagnetic wave (noise- and photo-traveling wave tubes)

Processes that occur in a traveling wave tube(TWT) equipped with a photocathode are examined within two-dimensional theory. The impact of noise fluctuations of the beam is studied, and the dependences of the amplifier’s noise factor are obtained. The interaction between an electromagnetic wave with an infinitely thin strip electron beam is described with allowance for a finite focusing magnetic field and the space charge field.     

Effect of external magnetic field on critical current for the onset of virtual cathode oscillations in relativistic electron beams

In this Letter we research the space charge limiting current value at which the oscillating virtual cathode is formed in the relativistic electron beam as a function of the external magnetic field guiding the beam electrons. It is shown that the space charge limiting (critical) current decreases with growth of the external magnetic field, and that there is an optimal induction value of the magnetic field at which the critical current for the onset of virtual cathode oscillations in the electron beam is minimum. For the strong external magnetic field the space charge limiting current corresponds to the analytical relation derived under the assumption that the motion of the electron beam is one-dimensional [D.J. Sullivan, J.E. Walsh, E. Coutsias, in: V.L. Granatstein, I. Alexeff (Eds.), Virtual Cathode Oscillator (Vircator) Theory, in: High Power Microwave Sources, vol. 13, Artech House Microwave Library, 1987, Chapter 13]. Such behavior is explained by the characteristic features of the dynamics of electron space charge in the longitudinal and radial directions in the drift space at the different external magnetic fields.     

Numerical simulation of space-charge dynamics in a gyrotron trap

The particle-in-cell (PIC) method is used to simulate the self-consistent accumulation and bunching of space charge in the trap of a gyrotron electron-optical system. It is shown that it is possible to generate charge bunches that oscillate along the direction of the magnetic field. The dependence of the characteristics of these oscillations on the magnitude of the electron current into the trap is determined, along with the effect of the accumulated charge on the velocity distribution of electrons in the current passing through the magnetic mirror. Satisfactory agreement with the experimental data is obtained. Zh. Tekh. Fiz. 67, 98–101 (September 1997)     

The positive charging effect of dielectric films irradiated by a focused electron beam

Space charge and surface potential profiles are investigated with numerical simulation for dielectric films of SiO₂ positively charged by a focused electron beam. By combining the Monte Carlo method and the finite difference method, the simulation is preformed with a newly developed comprehensive two-dimensional model including electron scattering, charge transport and trapping. Results show that the space charge is distributed positively, like a semi-ellipsoid, within a high-density region of electrons and holes, but negatively outside the region due to electron diffusion along the radial and beam incident directions. Simultaneously, peak positions of the positive and negative space charge densities shift outwards or downwards with electron beam irradiation. The surface potential, along the radial direction, has a nearly flat-top around the center, abruptly decreases to negative values outside the high-density region and finally increases to zero gradually. Influences of electron beam and film parameters on the surface potential profile in the equilibrium state are also shown and analyzed. Furthermore, the variation of secondary electron signal of a large-scale integration sample positively charged in scanning electron microscopic observation is simulated and validated by experiment.     

空间多能电子辐照聚合物充电过程的稳态特性

空间同步轨道上多能电子辐照聚合物的充电过程及其稳态特性是研究和抑制通信卫星静电放电的基础.在同步电子散射-输运微观模型的基础上,采用具有10—400 keV积分能谱分布的多能电子辐照聚酰亚胺样品,进行了多能电子辐照聚酰亚胺充电过程的数值模拟,获得了空间电荷密度、空间电位、空间电场分布和聚合物样品参数条件下的表面电位和最大场强.结果表明,多能电子与样品发生散射作用并沉积在样品内形成具有高密度的电荷区域分布,同时在迁移和扩散的作用下输运至样品底部形成样品电流;充电达到稳态、电子迁移率较小时(小于10-10cm2·V-1·s-1),表面电位绝对值和充电强度随电子迁移率的降低明显加强,捕获密度较大时(大于1014cm-3),表面电位绝对值和充电强度随捕获密度的增大明显加强;聚合物样品厚度对表面电位和充电强度的影响大于电子迁移率、捕获密度和相对介电常数的影响.研究结果对于揭示空间多能电子辐照聚合物的充电现象及微观机理、提高航天器故障机理研究水平具有重要科学意义和价值.     

Self-consistent charging in dielectric films under defocused electron beam irradiation

We clarify the transient and equilibrium charging characteristics of grounded dielectrics due to low-energy defocused electron beam irradiation by a three-dimensional self-consistent simulation model. The model incorporates the electron scattering, transport and trapping. Results show that some electrons can arrive at the grounded substrate due to the internal field and density gradient, forming the leakage current. The transient charging process tends to equilibrium as the surface potential decreases and the leakage electron current increases. The positive and negative space charges are distributed alternately along the beam incident direction. In the equilibrium state, the surface potential and leakage electron current decrease to stable values with increasing film thickness and the trap density, but with decreasing electron mobility. Moreover, the surface potential of the dielectric thin film exhibits a maximum negative value with variation of the beam energy; for example, under the condition of the film thicknesses 0.5 μm and 2 μm, the maximum negative values of surface potentials are -13 V and -98 V in beam energies 2 keV and 3.5 keV, respectively. However, for the thick film, the surface potential decreases with the increase in beam energy.