Chaotization of the virtual cathode oscillations in the external magnetic field created by a ring magnet

The physical mechanisms leading to the chaotization of the virtual cathode oscillations in a low-voltage vircator system at an increase in the amplitude of the external inhomogeneous magnetic field created by a ring magnet have been studied within a two-dimensional numerical model. It has been established that the chaotization of the virtual cathode oscillations in a strongly inhomogeneous external magnetic field is due to the formation of the secondary electronic structure (electron beam) in the electron flow resulting from the magnetic trap in the outer layers of the electron beam.     

Study of transients in the formation of heavy-current nanosecond electron beams

Results are presented from experimental and numerical studies of the spatial and temporal microstructure of a relativistic heavy-current electron beam of nanosecond duration. The beam is formed in a magnetically insulated coaxial diode with an edge-emitting cathode. Microcurrent oscillations and azimuthal nonuniformity of the beam are seen, the scale of the latter depending on the maximum cyclotron radius of the electrons. Two- and three-dimensional numerical calculations performed by the macroparticle method show that space-charge oscillations near the cathode produce these phenomena even in the case of a uniform emission surface. It is shown that the increase in the full current of the beam that occurs during the pulse in a weak magnetic field is connected with the gradual propagation of emission to the cylindrical outside surface of the cathode. A study is made of the effect of the discreteness of the emission surface on the impedance and current of the vacuum diode. The linear increase seen in current during the pulse with a small number of emission centers is attributed to an increase in their size as a result of expansion of the cathode plasma. Institute of Heavy-Current Electronics, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 12, pp. 31–48, December, 1996.     

Dynamics of magnetic insulation failure and self-organization of an electron flow in a magnetron diode

The dynamics of back cathode bombardment (BCB) instability in a magnetron diode (a coaxial diode in a magnetic field, B ≡ B _0z ≡ B ₀) is numerically simulated. The quasi-stationary regime of electron leakage across the high magnetic field (B ₀/B _cr > 1.1, where B _cr is the insulation critical field) is realized. An electron beam in the electrode gap is split into a series of bunches in the azimuthal direction and generates the electric field component E _θ(r, θ, t), which accelerates some of the electrons. Having gained an extra energy, these electrons bombard the cathode, causing secondary electron emission. The rest of the electrons lose kinetic energy and move toward the anode. Instability is sustained if the primary emission from the cathode is low and the secondary emission coefficient k _se=I _se/I _{e, BCB} is greater than unity. The results of numerical simulation are shown to agree well with experimental data. A physical model of back-bombardment instability is suggested. Collective oscillations of charged flows take place in the gap with crossed electric and magnetic fields (E × B field) when the electrons and E × B field exchange momentum and energy. The self-generation and self-organization of flows are due to secondary electron emission from the cathode.     

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.     

On envelope equations for electron beams in magnetic fields

A self-similarity approach is used to obtain envelope equations for an annular beam propagating along a magnetic field, and also an electron beam injected at an angle to a magnetic field. An exact solution is constructed for the self-consistent problem of transverse oscillations of a cold annular beam in a magnetic field, and a comparison is made with approximate results from the method of envelope equations. Zh. Tekh. Fiz. 68, 103–107 (January 1998)     

Improvement of the helical electron beam quality and the gyrotron efficiency by controlling the electric field distribution near a magnetron injection gun

A technique for controlling the electric field distribution near the cathode of a magnetron injection gun is developed. The feasibility of improving the quality of a helical electron beam by optimizing the electric field distribution in a pulsed 4-mm-wave gyrotron is studied theoretically and experimentally. Field distributions are obtained that minimize the electron velocity spread in the beam, coefficient of electron reflection from a magnetic mirror, and intensity of parasitic low-frequency oscillations. It is demonstrated that the gyrotron efficiency can be increased through a rise in the beam quality at the optimized electric field distribution.     

Nonlinear dynamics of a generator on a virtual cathode with modulated emission

A numerical study of a low-voltage vircator with controlled emissions from a thermocathode is performed for when an external signal effects on the electron beam and modulates the emission. The strong influence of the modulation parameters on characteristics of oscillations of the beam with virtual cathode is noted. It is shown that when the modulation frequency is tuned to the one of harmonics of a virtual cathode’s free oscillations, there is a considerable increase in the power of high-frequency harmonics of the virtual cathode’s free oscillations in the output spectrum.     

Influence of positive ions on oscillatory processes in an electron beam with virtual cathode

We numerically simulate the influence of positive ions on characteristics of the microwave oscillations in a nonrelativistic electron beam with the virtual cathode formed in a decelerating field (low-voltage vircator). A numerical scheme allowing for ionization of a residual gas by an electron flow is proposed. It is shown that the residual-gas ionization in the operating chamber of a low-voltage vircator leads to a forcing of the virtual cathode out of the transit gap and to a cutoff of microwave oscillations. The obtained numerical data are confirmed by an experimental study using a low-voltage vircator model. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 10, pp. 853–863, October 2006.     

Dynamics of neutralized charged particle beams in external magnetic and self fields

The dynamics of charged particle beams under the influence of their self-magnetic field and an external magnetic field is examined on the basis of equations for the trajectory of a boundary particle. A study is made of the change in the dynamics of fast particles due to the influence of the electric field of the partially neutralized space charge of the beam, the stationary electric field, and the field of the oscillations in the quasineutral beam plasma. Changes in the total beam energy caused by the self-electric field and in the longitudinal velocity owing to the self-magnetic field are taken into account. Zh. Tekh. Fiz. 68, 106–109 (August 1998)     

Generation of a submillisecond electron beam with a high-density current in a plasma-emitter diode under the conditions of open plasma boundary emission

The generation of a 250-μs-wide electron beam in a plasma-emitter diode is studied experimentally. A plasma was produced by a pulsed arc discharge in hydrogen. The electron beam is extracted from a circular emission hole 3.8 mm in diameter under open plasma boundary conditions. The beam accelerated in the diode gap enters into a drift space in the absence of an external magnetic field through a hole 4.1 mm in diameter made in the anode. The influence of electron current deposition at the edge of the anode hole on the beam’s maximum attainable current, above which the diode gap breaks down, is studied for different accelerating voltages and diode gaps. The role of processes occurring on the surface of the electrodes is shown. For an accelerating voltage of 32 kV, a mean emission current density of 130 A/cm² is achieved. The respective mean strength of the electric field in the acceleration gap is 140 kV/cm. Using the POISSON-2 software package, the numerical simulation of the diode performance is carried out and the shape of steady plasma emission boundaries in the cathode and anode holes is calculated. The influence of the density of the ion current from the anode plasma surface on the maximum attainable current of the electron beam is demonstrated.     

EXPERIMENTAL STUDY ON THE UNIFORMITY OF LARGE AREA INTENSE RELATIVISTIC ELECTRON BEAMS

The uniformity of intense relativistic electron beams under a converging magnetic guide field is studied experimentally in this paper. In the experiments, fluence calorimeter and X-ray pinhole photograph were used to measure the beam uniformity. The experimental results show that the externally applied magnetic flux density at the cathode and the shape of cathode face have considerable influence on the beam uniformity, The beam uniformity better than 80% is obtained over an area of 200cm² when the externally applied magnetic flux density at the cathode is about 0.6T and the cathode face is concave to a depth of 1.5 mm, relative to the cathode edge.     

Power of microwave generation in an ultrarelativistic electron beam in the regime of virtual cathode formation in an externally applied magnetic field

A numerical study of the output power characteristics of microwave radiation from a relativistic electron beam (REB) with a virtual cathode in the presence of externally applied longitudinal magnetic field is performed. Typical dependences of the output microwave power of the relativistic vircator system on the external magnetic field strength are obtained, showing a number of local maxima. It is found that the characteristic behavior of the radiation power is determined by the conditions and mechanisms of virtual cathode formation in the presence of external longitudinal magnetic field and a self-magnetic REB field.     

Numerical study of chaotic oscillations in the electron beam with virtual cathode in the external non-uniform magnetic fields

In this Letter the results of theoretical investigations of the chaotic microwave oscillator based on the electron beam with a virtual cathode are presented. Nonlinear non-stationary processes in these electron systems are studied by means of numerical analysis of 2.5D model. It was discovered that the non-uniform external magnetic field value controls the dynamical regime of oscillations in the virtual cathode oscillator. The processes of the chaotization of output microwave radiation are described and interpreted from the point of view of the formation and interaction of electron structures (bunches) in the electron beams. The numerical results have shown that the investigated electron system with virtual cathode could be considered as a promising controlled source of wideband chaotic oscillations in the microwave range.     

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.     

Localization of plasma in the extended hollow cathode of a ribbon-electron-beam plasma source at forevacuum pressures

The results of a study of the plasma density distribution in the slit aperture of a right-angled extended hollow cathode used in a ribbon-electron-beam plasma source operating at forevacuum pressures (1–10 Pa) are presented. It is shown that a local peak of plasma density appears in some region of the slit aperture as the slit width is decreased. This results in the appearance of a region of increased current density when the ribbon beam forms. The uniformity of the beam current density distribution is additionally disturbed by the reverse ion flow whose effect on the emission properties of the plasma is significant in the region of elevated pressure. A model which describes the development of plasma density nonuniformity in a hollow cathode is proposed which is based on the idea that the electron current flows predominantly through the slit aperture regions that are associated with local openings of the cathode layer ion sheaths. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 3–9, June, 2007.     

Electron beam halo formation in high-power periodic permanentmagnet focusing klystron amplifiers

Electron beam halo formation is studied as a potential mechanism for electron beam losses in high-power periodic permanent magnet focusing klystron amplifiers. In particular, a two-dimensional (2-D) self-consistent electrostatic model is used to analyze equilibrium beam transport in a periodic magnetic focusing field in the absence of a radio frequency (RF) signal, and the behavior of a high-intensity electron beam under a current-oscillation-induced mismatch between the beam and the periodic magnetic focusing field. Detailed simulation results are presented for choices of system parameters corresponding to the 50-MW, 11.4-GHz periodic permanent magnet (PPM) focusing klystron experiment performed at the Stanford Linear Accelerator Center (SLAC). It is found from the self-consistent simulations that sizable halos appear after the beam envelope undergoes several oscillations, and that the residual magnetic field at the cathode plays an important role in delaying the halo formation process     

强流相对论多注电子束研究进展

研制了基于爆炸发射的扇形和圆柱形多注阴极系统,并开展了强流相对论多注电子束的实验研究。研究发现:扇形多注阴极由于发射端面电场分布严重不均,电子束主要由尖端发射,束斑畸变明显,当每注扇形电子束进入到多注扇形漂移管内时,在空间电磁场的作用下电子束会绕束心旋转,导致束斑的畸变和束流的损失;圆柱形多注阴极发射端电场分布相对均匀,电子束斑畸变较小,每注电子束在多注漂移管内绕束心的旋转不会引起束斑的畸变和束流的损失;由于阴极杆和多注阴极柱的发射,多注电子束品质较差,进入多注漂移管时存在电子束轰击管壁现象,造成束流的损失甚至截止。采用大内径磁场可增大阳极筒内半径,明显提高束流的传输效率。目前,采用功率约6.5 GW、传输效率约89%的相对论多注电子束驱动的多注速调管,可实现GW量级的微波输出。     

微秒长脉冲有磁场高功率微波二极管真空界面设计

介绍了一种微秒长脉冲有磁场的真空二极管界面的设计和实验结果。采取了三种措施来抑制沿面闪络:一是阴极电子束挡板,用来拦截来自阴极和电子束漂移管的回流电子束;二是接地屏蔽板,使电场等势线和界面成约45°角,使阴极三结合点处发射的电子远离绝缘板;三是降低阴极三结合点处的场强,并使用一悬浮电位的金属环阻止电子倍增过程。计算了二极管内电场、磁场分布和电子束的运动轨迹并据此优化了真空界面的结构,实验验证了该二极管真空界面可以在400 kV、800 ns条件下正常工作,可以支持长脉冲高功率微波器件的研究。     

Characteristics of electron beams formed in a diode with magnetic insulation

The problems of the formation of relativistic electron beams in a cylindrical diode with an annular cathode are discussed in the approximation of an infinitely strong guiding magnetic field. The beams are treated as infinitely thin. The following cases are investigated: 1) The formation of an electron beam moving off the cathode with an initial velocity. The case in which the field on the cathode is not equal to zero is investigated. It is shown that the potential of the electron beam can be determined in a nonunique fashion in the drift region. 2) The formation of a two-velocity electron beam. The possibility of controlling the flow of kinetic energy of the beam by varying the fraction of fast electrons in it is shown. 3) The formation of an electron beam in a diode with the help of two opposed cathodes at different potentials. A strong dependence of the current in the diode on the potential difference between the cathodes is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 36–39, December, 1981.     

Characteristics of the statistical distribution of the current transmitted by a cathode spot of a vacuum arc in variously oriented magnetic fields

The influence of variously oriented uniform magnetic fields on the cathodic attachment of a low-current vacuum arc with electrodes made of oxygen-free copper and CuCr30 composition is studied. It is found that, if the current is fixed, cathode spots in the arc attachment are distributed by the normal law in the entire range of variation of the amplitude of magnetic induction vector B and angle α between this vector and the normal to the cathode surface. The parameters of the distribution depend on the magnetic field and cathode material. The magnetic field dependence is appreciable only when angle α exceeds some critical value α* (α* ≈ 30° and ≈45° for cathodes made of copper and CuCr30, respectively). At α > α*, the parameters of the distribution become strongly dependent on α, while the B dependence remains weak. Only when α → π/2 does the field amplitude have a pronounced effect on the parameters of the distribution. From the obtained results, we determine the statistical characteristics of the distribution of the mean current transmitted by a cathode spot in variously oriented magnetic fields. The found relationships make it possible to explain the peculiarities of the structure of the cathodic attachment of the high-current vacuum arc stabilized by an external axial magnetic field.