M.A. Kodis

Self-consistent field theory of a helix traveling wave tube amplifier

A self-consistent relativistic field theory of a helix traveling wave tube (TWT) is presented for a configuration in which a thin annular beam propagates through a sheath helix enclosed within a loss-free wall. A linear analysis of the interaction is carried out, subject to the boundary conditions imposed by the beam, helix, and wall. A detrimental dispersion equation is obtained which implicitly includes beam space-charge effects without recourse to a heuristic model of the space-charge field. The equation is valid for arbitrary azimuthal mode number and is solved numerically for the azimuthally symmetric case. The coupled-wave Pierce theory is recovered in the near-resonant limit. Numerical comparisons between the complete dispersion equation and the Pierce model are described. A discrepancy is found between the Pierce and the field theory even for low currents in the nominally ballistic regime, owing to the dielectric effect of the beam on the helix modes. >

Field theory of a traveling wave tube amplifier with a tape helix

A self-consistent relativistic field theory for a helix traveling wave tube (TWT) is presented for a configuration in which a magnetized pencil beam propagates through a tape helix enclosed with a loss-free well. A linear analysis of the interaction is solved subject to the boundary conditions imposed by the beam, helix, and wall. The wave equation for the fields within the electron beam corresponds to the Appleton-Hartree magnetoionic wave modes that are of mixed electrostatic/electromagnetic polarization. Hence, the determinantal dispersion equation that is obtained implicitly includes beam space-charge effects without recourse to a heuristic model of the space-charge field. This dispersion equation includes azimuthal variations and all spatial harmonics of the tape helix. Solutions that correspond to both the extraordinary (X) and ordinary (O) solutions for the Appleton-Hartree modes are found numerically. >

Space charge effects on the current-voltage characteristics of gated field emitter arrays

Microfabricated field emitter arrays (FEAs) can provide the very high electron current densities required for rf amplifier applications, typically on the order of 100 A/cm2. Determining the dependence of emission current on gate voltage is important for the prediction of emitter performance for device applications. Field emitters use high applied fields to extract current, and therefore, unlike thermionic emitters, the current densities can exceed 103 A/cm2 when averaged over an array. At such high current densities, space charge effects (i.e., the influence of charge between cathode and collector on emission) affect the emission process or initiate conditions which can lead to failure mechanisms for field emitters. A simple model of a field emitter will be used to calculate the one-dimensional space charge effects on the emission characteristics by examining two components: charge between the gate and anode, which leads to Child’s law, and charge within the FEA unit cell, which gives rise to a field supp...

Operation and optimization of gated field emission arrays in inductive output amplifiers

In an inductive output amplifier, an emission-gated electron beam induces high-frequency fields in an output circuit via displacement current, not convection current. Emission-gated electron beams experience strong interactions when traversing a resonant or synchronous electromagnetic field, and this strong interaction is responsible for both the interesting nonlinear physics and the attractive efficiency and compactness of emission-gated amplifiers. Field emission cathodes, due to their extremely low electron transit time and high transconductance, offer the opportunity to extend the advantages of emission gating into C and X band. This paper presents design criteria for the joint optimization of the field emission array (FEA) structure and the RF input and output circuits of inductive output amplifiers. We find that while output circuits yielding net efficiencies of 50% or greater are well within the state of the art, the gain is likely to be moderate (10-20 dB). With todays FEA performance, a desirable operating regime is achievable, yielding a new class of compact, highly efficient, and moderate gain power booster amplifiers.

Emission gated device issues

A review of linear and nonlinear analyses applicable to emission gated devices is provided with an explicit declaration of the physical assumptions for each model. The authors consider density gating, not velocity modulation, emphasizing high-power and high-efficiency applications. Increased efficiency through the use of density gating for the RF input bunching of an electron beam is expected. The authors review the basic dynamics of bunch formation and describe the gating technologies currently available for the production of a prebunched beam. Considerable insight into the basic physics of emission gating, such as beam dynamics and frequency spectra, is obtainable from numerical modeling. Some unresolved issues are presented for investigation. >

Linearized field theory of a dielectric-loaded helix traveling wave tube amplifier

A linearized relativistic field theory of a helix traveling wave tube (TWT) is presented for a configuration where either a thin annular beam or a solid beam propagates through a sheath helix enclosed within a loss-free wall in which the gap between the helix and the outer wall is filled with a dielectric. A linear analysis of the interaction is solved subject to the boundary conditions imposed by the beam, helix, and wall. In the case of the annular beam, the electrons are assumed to be strongly magnetized. In contrast, the effect of variations in the axial magnetic field are included in the electron dynamics for the solid beam analysis. Determinantal dispersion equations are obtained for the azimuthally symmetric modes which implicitly includes beam space-charge effects without recourse to a heuristic model of the space-charge field. Numerical solutions of the dispersion equations are discussed and compared with experiments.

Design of traveling wave tubes based on field theory

A method is described for the design of helix traveling wave tubes (TWT) which is based on the linear field analysis of the coupled beam-wave system. The dispersion relations are obtained by matching of radial admittances at boundaries instead of the individual field components. This approach provides flexibility in modeling various beam and circuit configurations with relative ease by choosing the appropriate admittance functions for each case. The method is illustrated for the case of a solid beam inside a sheath helix which is loaded externally by lossy dielectric material, a conducting cylinder, and axial vanes. Extension of the analysis to include a thin tape helix model is anticipated in the near future. The TWT model may be divided into axial regions to include velocity tapers, lossy materials and severs, with the helix geometry in each region varied arbitrarily. The relations between the AC velocities, current densities, and axial electric fields are used to derive a general expression for the new amplitudes of the three forward waves at each axial boundary. The sum of the fields for the three forward waves (two waves in a drift region) is followed to the circuit output. Numerical results of the field analysis are compared with the coupled-mode Pierce theory. A method is suggested for applying the field analysis to accurate design of practical TWTs that have a more complex circuit geometry, which starts with a simple measurement of the dispersion of the helix circuit. The field analysis may then be used to generate a circuit having properties very nearly equivalent to those of the actual circuit. >

Twystrode experiments with tapered and untapered helices

A series of experiments has been performed at NRL to determine the saturation behavior and maximum conversion efficiency of emission gated electron beams in slow wave circuits. Simulations suggest that single-pass conversion efficiencies exceeding 50% to the fundamental harmonic may be achieved with moderately tight bunches in a properly tapered helix. Such an efficiency, achieved in a circuit only two to three slow-wavelengths long, points the way toward significant advances of microwave power tubes into new markets and applications. Emission gated devices, including klystrodes and twystrodes, have potential as compact and efficient power booster amplifiers. The NRL Twystrode Experiment is a flexible instrumented amplifier operating in a wide parameter space, allowing thorough verification of analytical and simulation models. The electron beam (from a gridded thermionic cathode) can be modulated in any degree, from DC, to 100% amplitude modulation, to discrete electron bunches only 90/spl deg/ wide. The beam voltage is variable from below to well above synchronism, and the beam current from the ballistic to the spacecharge regimes. We find that moderate bunching (270/spl deg/ or greater width) and velocity tapering of the output circuit improve beam conversion efficiency at the cost of an increased saturation circuit length.<<ETX>>

Interaction efficiency of an emission gated TWT

The Emission Gated Device Experiment extracts RF power from a prebunched electron beam passing through a short helix traveling wave circuit. Efficient and compact amplifiers are possible through this approach because of the large component of RF current in a tightly bunched beam. While a wideband, high gain, high power input circuit for such devices is beyond the present state of the art, high transconductance gated field emission cathodes are being developed for emission gated devices. The present experiment is designed to test the performance of the output coupler using a cavity-driven cathode circuit. Twenty percent beam coupling efficiency has been observed from a helix one slow wavelength long.<<ETX>>

Nonlinear analysis of helix traveling wave tubes

A time‐dependent nonlinear formulation of the interaction in the helix traveling wave tube is presented for a configuration in which an electron beam propagates through a sheath helix surrounded by a conducting wall. In order to describe both the variation in the wave dispersion and in the transverse inhomogeneity of the electromagnetic field with wave number, the field is represented as a superposition of waves in a vacuum sheath helix. An overall explicit sinusoidal variation of the form exp(ikz−iωt) is assumed (where ω denotes the angular frequency corresponding to the wave number k in the vacuum sheath helix), and the polarization and radial variation of each wave is determined by the boundary conditions in a vacuum sheath helix. Thus, while the field is three‐dimensional in nature, it is azimuthally symmetric. The propagation of each wave in vacuo as well as the interaction of each wave with the electron beam is included by allowing the amplitudes of the waves to vary in z and t. A dynamical equation...