Current distribution in triodes neglecting space charge and initial velocities

We investigate the generation and distribution of high-energy electrons in the cosmic structure environment and their observational consequences by carrying out the first cosmological simulation that includes directly cosmic-ray (CR) particles. Starting from cosmological initial conditions, in addition to the gas and dark matter related quantities, we follow the evolution of CR electrons (primary and secondary) and CR ions along with a passive magnetic field. CR ions and primary electrons are injected in accordance with the thermal leakage model and accelerated in the test-particle limit of diffusive shock acceleration at shocks associated with large-scale structure formation. Secondary electrons are continuously generated through p-p inelastic collisions of the CR ions with the thermal nuclei of the intergalactic medium. The evolution of the CR electrons accounts for spatial transport, adiabatic expansion/compression, and losses due to Coulomb collisions, bremsstrahlung, synchrotron and inverse-Compton emission. The magnetic field is seeded at shocks according to the Biermann battery model, and thereafter amplified by shear flow and gas compression. We compute the emission due to the inverse-Compton scattering of the simulated primary and secondary electrons off cosmic microwave background photons and compare it with the published values of the detected radiation excesses in the hard X-ray and extreme-ultraviolet wavebands. We find that the few instances of detection of hard X-ray radiation excess could be explained in the framework of IC emission from primary electrons in clusters characterized by high accretion/merger activity. On the other hand, with the only exception of measured flux from the Coma Cluster by Bowyer, Berghoefer & Korpela, both primary and secondary CR electrons associated with the cosmic structure formation account at most for a small fraction of the radiation excess detected in the extreme-ultraviolet waveband. Next, we calculate the synchrotron emission after normalizing the magnetic field strength so that for a Coma-like cluster the volume-averaged B21/2 3 ?G. Our results indicate that the synchrotron emission from the secondary CR electrons reproduces several general properties observed in radio halos. These include the recently found P1.4 GHz versus TX relationship, the morphology and polarization of the emitting region, and, to some extent, even the spectral index. In addition, radio synchrotron emission from primary electrons turns out to be large enough to power extended regions of radio emission, resembling radio relics observed at the outskirts of clusters. Once again we find a striking resemblance between the general properties of morphology, polarization, and spectral index of our synthetic maps and those of reported in the literature.

The problem of space-current calculation is reviewed briefly to point out the inadequacy of the classic solution for modern close-spaced electron tubes. A more accurate solution for the space current is obtained by calculating the current distribution from the potential field in the grid-cathode space, corrected for space charge and initial electron velocities. A machine program set up on a large high-speed computer permits the calculation of complete voltage-current characteristics and their derivatives from basic input data. A brief account of the sequence of machine operations illustrates the large number of detailed steps and the flexibility of the program. The accuracy of the calculations is demonstrated by a comparison of the computed and measured characteristics of a nuvistor triode.

Electron space-charge lenses and spherical aberration correctors are studied theoretically. Many interesting features of space charge devices are revealed by considering some simple, but physically reasonable models. A `toroidal sub-beam' algorithm has been developed to model the evolution of the current and charge density distributions of charged particle beams taking into account space charge and initial thermal velocity effects. It is shown that a number of simple space charge distributions can compensate a large range positive spherical aberrations. Some practical structures of the space charge lenses are presented.

Using a semiclassical model, we investigate the effect of the initial longitudinal velocity of the tunnel-ionized electron on low-energy structure (LES) in above-threshold ionization (ATI) spectra. Our analysis shows that the effect (reduction or enhancement) of the initial longitudinal velocity pz0 on the LES is dependent on the direction of the initial longitudinal velocity. For the initial longitudinal velocity along the direction of the laser electric field at the moment of tunneling (i.e., pz0 > 0), the Coulomb interaction between the photoelectron and ion core is enhanced, while for the initial longitudinal velocity in the opposite direction (i.e., pz0 < 0), the Coulomb effect is reduced. Our work provides solid evidence that the initial electron longitudinal velocity has considerable effect on the photoelectron dynamics in the ATI process.

The old problem of electron distribution in crossed electric and magnetic fields, such as exist in magnetrons, has in the past proved full of pitfalls, owing to the decisive influence which even very small initial electron velocities can have on the character of the solution. A complete analysis of the plane magnetron is presented, with a thermal emitter, i.e. with Maxwellian distribution of the initial velocities. Instead of looking for self-consistent solutions, which vary strongly with the space charge, the solution is given for three simple types of prescribed electric potentials, zero, linear and parabolic. The first two are mainly for orientation, the third is of practical interest as it is approximately self-consistent. For zero or weak electric fields the distribution is ‘triangular’, i.e. the function decreases monotonically as we move away from the cathode. For strong electric fields, the distribution has a peak away from the cathode and strongly resembles that obtained in the so called ‘double-stream’ flow. Finally, for a parabolic potential distribution (linear field variation) the space charge density exhibits a pronounced plateau which is highly reminiscent of the conditions in a Brillouin or ‘single-stream’ flow, although the electron motion is anything but rectilinear.

The key to the imaging technology in the ESEM is the ionization of gas molecules by the secondary electrons from the sample and the collection of this amplified signal. Secondary electrons that are generated by the interaction of the primary electron beam with the sample are the signal of choice for high resolution imaging. The primary beam strikes a sample generating both secondary and backscattered electrons. In the ESEM, the secondary electrons are specifically collected by a confined electrostatic field that is generated by gaseous secondary electron detector above the sample. Within this field, the secondary electrons strike gas molecules generating an additional electron; a process termed cascade amplification. The image formed by collection of these electrons is very similar to the image formed by the conventional Everhart-Thornley detector, even though the signal amplification process is different. Scattering of the primary beam electrons also results in the formation of amplified electrons, but contains no relevant image information.

In this work, a “main condition” for phase stability has been employed to investigate the effects of the velocity deviation of the electrons in DC-biased single-sided multipactors (MPs). In a previous study [M. Mostajeran, Phys. Plasmas 21, 053108 (2014)], a stability equation was derived, where the secondary electron was assumed to have zero initial velocity and the phase deviation from the resonant phase was considered. In this work, both deviations in phase and velocity from the resonant condition are taken into account, assuming nonzero initial velocity for the secondary electrons. Using the main condition for stability, it is shown that MP discharge can rise in situations, where large velocity deviations from initial velocity and large phase deviations from resonant phase exist. This is contrary to what can be predicted on the basis of the “simple stability condition.” This result is further confirmed by numerical simulations.

A technique to take into account the initial transverse electron thermal velocities in converged sheet electron beams has been developed. This determines the main integral characteristics of a thermal beam in a gun and transportation region of the paraxial approximation via chosen characteristic electron trajectories. We have equations of characteristic electrons motion, initial conditions to solve equations, and formulas for the current density distribution in the thermal beam cross-section and current fraction in conventional boundary. The derived equations and formulas may be used in modeling electron-optical systems and choosing parameters in which the effect of heat electron motion on beam characteristics will lie within tolerable limits.

This paper presents some fundamental characteristics of a secondary emission electron gun using a pulsed glow discharge wire ion plasma source (WIPS). The positive helium ions extracted from WIPS are accelerated in vacuum toward the negatively biased cold cathode surface, which is set oblique to the ion loci in order to inject the emitted secondary electrons perpendicular to the foil window. The physical mechanisms governing the characteristics such as space charge and secondary electron emission have been reviewed. The dependence of such characteristics on the kinetic energy of incident ion and on the ion incidence position have been experimentally investigated. The experimental results are discussed together with the available theoretical models of each characteristic to establish the relative understanding of such phenomena in side‐extraction‐type secondary emission electron gun. The experimental results are further discussed in the light of a self‐developed numerical simulation using the finite element method, which presents a good understanding of particle trajectories as well as potential distribution inside the gun geometry.

Universal 1/f noise is shown to originate from the variations in the initial velocities of conduction electrons after collisions with defects. Defect atoms, after being struck by conduction electrons, recoil and form an impacted mass of lattice atoms. Conduction electrons emitted after a collision have an average initial velocity which steadily decreases as the impacted mass builds up. It is shown that this process yields a noise spectrum of the form f−n where n is in the vicinity of one and has an amplitude given by the Hooge empirical formula. Variations from the Hooge result are discussed. The model described applies to all semiconductors and metals.

Based on the theory of current and potential distribution for aqueous solution systems and existing analytical models, tertiary current and potential distributions over carbon and non-consumable anodes in cryolite-alumina melt are calculated. By varying different electrolysis parameters and anode surface geometry (rectangular smooth anode and section of anode sinusoidal profile), their functional relationship with current and potential distribution is established. The influence of resulting distribution pattern and the values of local current density and local anode potential on anode process stability together with related probable causes of the increased consumption of carbon and non-consumable anodes are discussed. The main factors influencing on current and potential distribution are anode overpotential and diffusion layer thickness, which represents the electrolyte properties related to electrolyte mixing conditions. Local current density on the edges of a rectangular anode is 2 times higher than in the central part. Current distribution over rough anode surface is uneven—local current density at peaks of surface defects is higher by 40% to 60%. When limiting current density is approached at these preferential spots, the values of standard potentials for perfluorocarbons evolution on carbon anodes and metal fluorides formation on inert anodes are reached. The theoretically established relationship between the anode surface structure and current and potential distribution could be the primary cause for increased anode consumption and passivation with subsequent destabilization of electrolysis in standard and low-melting electrolytes. The possible ways to equalize the current and potential distribution across the anode surface are presented.

Unwilling deformations of secondary electron (SE) images due to charging of an insulating layer on materials is one of important issues for semiconductor industry applications of scanning ion microscopes (SIM). This paper presents a Monte Carlo model of SE emission from SiO₂ in which the charging induced by ion bombardment at the energy range of tens of keV is taken into account. A self-consistent calculation is carried out for the transport of a projectile ion, recoiled material atoms and SEs, the creation of space charges trapped in the material and the resultant electric field in/out the material. Drift motion of trapped charges is calculated as well, where the recombination with a charge of opposite sign is taken into account. Therefore, the evolution of the charging is simulated with successive arrivals of ions. Since the surface voltage is positive due to ejection of SEs and injection of positive ions, some of ejected SEs are drawn back to the surface and can rebound on it; these SEs are unable to produce a net emission. Dynamic changes in the SE yield and surface voltage are compared among He ions, Ga ions and low-energy (&lt;1 keV) electrons, along with the space charge distributions and the in/out electric fields. The net SE yield is decreased during ion bombardment and finally it vanishes, which is different from the case of electron bombardment where the net SE yield (including BSEs) is kept to one due to a balance between coming and outgoing electrons. Even if there is not net emission of SEs, the surface voltage does not reach any steady-state condition but progressively increases due to successive injection of positive ions. The growth rate of the surface voltage depends on both the SE yield with no charging and the spatial distribution of the ions penetrating into the material.

We theoretically study the high-order harmonic generation (HHG) from Rydberg hydrogen atom driven by a mid-infrared linearly polarized chirped laser pulse. It is shown that the high-order harmonic spectrum demonstrates an excessive high-yield broad-band supercontinuum. Based on the analyses of quantum-mechanical and classical models, it is found that the enhancement is caused by the motion of the Rydberg electron perpendicular to the polarization direction of the chirped laser pulse, which is induced by the attraction of the nucleus and initial orbital velocity of the Rydberg electron. This mechanism is different from the previous study (Chen et al 2015 Phys. Rev. A 91 043403), in which the motion of the Rydberg electron perpendicular to the polarization direction has little contribution to HHG.

Summary form only given. In a low-pressure hot-filament discharge, the primary electrons induce the emission of secondary electrons from the walls of the plasma chamber. The generation rate of these secondary electrons typically exceeds the rate of ionization. The plasma thus has three electron components: fast electrons from the filament, secondary electrons from the walls, and plasma electrons confined in the potential well of the plasma. The performed experiments show that the latter two components make most of the electron current to a cylindrical Langmuir probe immersed in the plasma. It is shown that this current to the probe may be accurately fit by orbit-motion-limited probe theory applied to both the secondary and the bulk electrons. The analysis takes into consideration that the secondary and plasma electrons have different reference potentials. The secondary electrons originate from the grounded walls and the plasma electrons are born at the more positive plasma potential. A method to evaluate probe traces is presented that allows the separation of the two components and to calculate their parameters. The secondary electrons have a distribution close to a Maxwellian with a temperature /spl sim/2-3 eV. It is shown that the probe current of the bulk electrons alone goes to zero for probe potentials more negative than the wall potential, indicating that there are indeed no bulk electrons with energies exceeding the ambipolar potential.

We have added some features to our library of computer-aided design codes for design of depressed collectors and to the code for tracing the trajectories of backscattered electrons. In the former case, the process of optimization of depressed potentials is facilitated. The computer code changes the combinations of potentials by controllable amounts. The trajectory tracing code runs the modified input files sequentially and feeds data to post processors. This generates charts of important parameters in the performance of the collectors. The parameter space can, thus, be explored quickly for optimum operation. In the second case, we have automated the iterative simulation of trajectories of primary and secondary electrons, which interact by virtue of their space charge. This is with a view to obtaining enhanced mutual consistency between them. Furthermore, a specified number of orders of backscattered electrons can be traced. These codes have been used for exploring the dependence of depressed collector performance on various geometrical and electrical parameters for megawatt continuous wave power gyrotrons.