Yaduvendra Choyal

Linear dispersion relation of backward-wave oscillators with finite-strength axial magnetic field

The linear dispersion relation of backward wave oscillators (BWOs) with finite strength axial magnetic field is derived and calculated numerically. Axisymmetric mode radiation in a slow wave structure (SWS) with corrugated metal wall including a column of relativistic electron beam streaming along the lines of a finite strength axial magnetic field is analyzed. Three theoretical achievements viz. (1) the dielectric tensor derived by Bogdankevich et al. (1981), (2) the formulation of EM waves in the beam column that are expressed as a linear combination of extraordinary and ordinary modes elucidated by Antonsen et al., and (3) a consideration of boundary conditions in the beam-SWS system initiated by Swegle et al. (1985) are combined in our numerical code to be exact and universal under the scope of linear treatment. Our dispersion relation can include effects of interaction between a structure mode and electron cyclotron modes in addition to conventional beam space charge modes. Numerical analysis is carried out using the parameters of a BWO experiment at the University of Maryland. The results show the well-known cyclotron absorption of radiation from the BWO at a particular value of magnetic field that was previously analyzed in various ways different from ours.

Saddle-point analysis of a high-power backward-wave oscillator Near Cyclotron absorption

Using the dielectric tensor for a relativistic electron beam with finite strength axial magnetic field, saddle-point analysis for absolute and convective instabilities in the corrugated metal-wall slow-wave structure of backward-wave oscillators (BWOs) has been carried out. The parameters used in experiments at the University of Maryland were assumed. It is shown that the absolute instability of the BWO ceases, and a convective instability appears instead for a wide range of B near the condition of cyclotron absorption. The experimental results can be explained quantitatively taking into account the effect of finite length of the BWOs.

Slow cyclotron instability in a high-power backward-wave oscillator

The linear dispersion relation of a backward-wave oscillator (BWO), derived earlier by the authors, is modified to include effects of RF surface current at the beam-vacuum interface. This modified dispersion relation results in an unstable interaction between the slow cyclotron mode (SCM) and the structure mode in addition to the conventional Cherenkov instability caused by the slow space charge mode. Numerical analysis is then carried out using parameters of a BWO experiment at University of Maryland. Fine structure of the SCM instability is elucidated. The analysis indicates that BWO radiation would not be suppressed near cyclotron absorption in an infinitely long system.

Microwave excitation by a constrained large-orbit electron Beam-a unified dispersion relation for slow- and fast-wave devices

A unified linear dispersion relation that describes both slow- and fast-wave devices excited by a constrained large gyration orbit (LO) monoenergetic electron beam of infinitely small thickness has been derived and studied numerically. Beam electrons in a sufficiently long sinusoidally corrugated metal slow-wave structure are assumed completely neutralized by the background ions in equilibrium state. An exact dispersion relation of an LO backward-wave oscillator that can reasonably describe instabilities in the slow-wave device region has been obtained. A parameter a, defined as a ratio of the transverse to the longitudinal component of the electron velocity, is found to have a critical value above which the excitation of a nonaxisymmetric quasi-TE/sub 11/ mode caused by the fast cyclotron instability dominates the conventional Cherenkov instability. However, for an SWS having infinitely small amplitude of corrugation, radiation with w<W in the fast- wave device region is obtained. Here, w and W are, respectively, microwave angular frequency and relativistic electron cyclotron frequency. The conventional cyclotron resonance maser (CRM) instability with w>W is altogether suppressed; instead, an alternate mechanism, namely, Cherenkov instability in the azimuthal direction with w<W found first in the current paper leads to the excitation of microwaves. This suggests that the radiation from some previous CRM experiments with a high current density electron beam neutralized by ions might have been caused not by CRM instability but by the present Cherenkov instability in the azimuthal direction.

A comparative study of PPM and solenoid focusing in multibeam electron gun

This paper represents the comparison of periodic permanent magnet (PPM) and solenoid focusing for dual anode multi-beam electron gun using OPERA3D code. The electron gun has been operated at 6 kV having 75 mA beam current with 0.45 mm beam waist radius. The design has an additional feature of cathode protection from ion bombardment with the application of extra ion barrier anode.

Thermal analysis of multi-beam electron gun collector

This paper represents the thermal analysis of a multi-beam electron gun collector and the effect of different types of grooves on the collector temperature has also been analyzed. The design of the grooves has been optimized to enhance the efficiency of the collector using mixed (axial and radial) grooves. Finite element analysis codes OPERA 3D, ANSYS and CST have been used for the thermal study. The values of the water flow rate and the hydraulic diameter of the outer jacket have been optimized.

Effect of Thickness and Radial Position of Aperture in a Pole Piece in Focusing of Multibeam Electron Gun

A four-beam electron gun has been designed using OPerating environment for Electromagnetic Research and Analysis (OPERA) 3-D to demonstrate the dependence of beam focusing on the thickness and the radial position of anode aperture in a pole piece with reference to the gun axis. The study is important in the sense that focusing the off-axis electron beamlets are a bit difficult with a common focusing system. The OPERA simulated results have been also compared with computer simulation technique simulated results. An example of four-beam electron gun to deliver a total of 428-mA (107 4) current at 6-kV beam voltage has been considered for carrying out the aforementioned study. The four electron beamlets are generated through four individual cathodes, surrounded by electrically isolated four beam focusing electrode and corresponding four individual anodes and a common focusing system.

The range of validity of the Rayleigh hypothesis

Summary form only given. The parameter range over which the Rayleigh hypothesis (RH) for optical gratings might be validly applied to analysis of high power backward wave oscillators (BWOs) has been investigated numerically. A widely used method to analyze high power backward wave oscillators (BWOs) is to represent the electromagnetic (EM) fields in axisymmetric slow wave structure (SWS) in terms of a Floquet harmonic expansion (FHE). EM fields, E and B, are expressed in a form as, [E B]=/spl Sigma//sub n=-N//sup N/[E/sub n/(r) B/sub n/(r)]exp i(k/sub zn/z+l/spl theta/-/spl omega/t) where k/sub zn/=k/sub z/+nK/sub 0/, K/sub 0/ is wavenumber of SWS periodicity, and n=0, /spl plusmn/1, /spl plusmn/2,.../spl plusmn/N is the Floquet harmonic number. Expansion similar to (1) was firstly introduced by Lord Rayleigh for diffraction of waves from planar grating. He assumed that the expansion was applicable both outside and inside the corrugation, and this assumption is called as RH. It was argued by some mathematician that our numerical analysis was applied to deep corrugation of hK/sub 0/=1.67 which was beyond the limiting value hK/sub 0/=0.448 for validity in RH for planar sinusoidal grating, consequently the results were invalid. Here, h is the amplitude of corrugation. To respond the doubt, EM fields and dispersion relation in the SWS are numerically analyzed with and without RH for a given set of size parameters. The field patterns and eigen frequency for the SWS are solved for a given k/sub z/ numerically by using finite difference code HIDM (Higher Order Implicit Difference Method) that is free from RH. The results are compared with those using (1). For a deep corrugation, hK/sub 0/=5/spl times/0.448, using RH is still valid for obtaining the dispersion relation, although the Floquet Harmonic Expansion (FHE) fails to correctly represent the field patterns inside the corrugation. Accordingly, there exists a discrepancy between the validity of using RH for obtaining dispersion relations and for an exact convergence of FHE everywhere in the SWS.

Analysis of a large-orbit backward wave oscillator

Summary form only given, as follows. The effect of finite axial magnetic field on excitation of a backward wave oscillator (BWO) is investigated. The driver beam is assumed to be a mono-energetic helical electron beam with all the constituent electrons having their gyration centers on the axis of the slow wave structure (SWS). Such a beam supports negative energy fast cyclotron modes (FCMs) that can excite structure modes in the SWS. This may contribute to microwave generation in the BWO, which is solely due to the Cherenkov mechanism.

Saddle point analysis of a high power backward wave oscillator near cyclotron absorption

Using the dielectric tensor for a relativistic electron beam with finite strength axial magnetic field, saddle-point analysis for absolute and convective instabilities in the corrugated metal-wall slow-wave structure of backward-wave oscillators (BWOs) has been carried out. The parameters used in experiments at the University of Maryland were assumed. It is shown that the absolute instability of the BWO ceases, and a convective instability appears instead for a wide range of B near the condition of cyclotron absorption. The experimental results can be explained quantitatively taking into account the effect of finite length of the BWOs.