E.G. Zaidman

Electron emission from a single spindt-type field emitter: Comparison of theory with experiment

A simple analytic model of the electron emission from a single tip field emitter is correlated with experimental measurements made on a single Spindt-type molybdenum field emitter using a nanofabricated anode whose position from the emitter was determined using laser interferometry. It is shown how the model may be extended to find the trajectories needed for particle simulations. Methods used to correlate theory with experiment are explained, and the dependence of the beam profile on tip sharpness, gate diameter, anode distance, and tip work function are examined. A simple analysis of the effects of space charge on field emission is presented and correlated with experimental data. Analysis has shown that the rms spread angle is approximately 20°.

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...

Nonlinear time-domain analysis of coupled-cavity traveling-wave tubes

A time-dependent nonlinear analysis of a coupled-cavity traveling-wave tube (CCTWT) is presented. The coupled-cavity structure is modeled by a set of equivalent circuit equations where the equations for currents and voltages are coupled to the nearest neighbor cavities. Input and output coupler models as well as sever cavities are included in the formulation. The electron dynamics are treated using the three-dimensional Lorentz force equations although the RF field representation is an analytic model based on cylindrically symmetric geometry. The magnetic focusing fields are also cylindrically symmetric and can be either a solenoid or a periodic permanent magnet stack. The space-charge fields are found by mapping charge to a two-dimensional grid (r, z) and solving Poissons equation by a finite difference grid formulation. The circuit and Lorentz force equations are integrated in time in a self-consistent manner. The formulation is capable of treating multiple drive frequencies and the associated intermodulation products as well as oscillations and backward wave instabilities. Hence, the model can be used to perform stability analyses. Furthermore, the cavity parameters can be varied to model dynamic velocity tapering for efficiency enhancement. The simulation is applied to the analysis of a sample C-Band CCTWT, and comparisons with measured performance of a Ka-Band CCTWT at Communications and Power Industries, Palo Alto, CA, are made.

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.

Simulation of field emission microtriodes

Vacuum microtriode RF amplifier performance, based upon a unit cell with a conical field emitter tip, gate, and anode, was evaluated using computer simulation. Electron emission was calculated from the Fowler-Nordheim equation. The dependence of emitted current, transconductance, and field enhancement upon geometrical factors, e.g., tip sharpness, tip height, cone half-angle, and gate hole radius, is shown. The device design parameters of transconductance, cutoff frequency, small signal gain, and efficiency have been calculated. Electron streamlines and current flux are shown for time-dependent RF input. Because a compact electron beam source has wide application, the normalized beam emittance, brightness, and beam quality are calculated for a typical case. Potential difficulties with anode power deposition are noted. >

Theory of helix traveling wave tubes with dielectric and vane loading

A time‐dependent nonlinear analysis of a helix traveling wave tube (TWT) is presented for a configuration where an electron beam propagates through a sheath helix surrounded by a conducting wall. The effects of dielectric and vane loading are included in the formulation as is efficiency enhancement by tapering the helix pitch. Dielectric loading is described under the assumption that the gap between the helix and the wall is uniformly filled by a dielectric material. The vane‐loading model describes the insertion of an arbitrary number of vanes running the length of the helix, and the polarization of the field between the vanes is assumed to be an azimuthally symmetric transverse‐electric mode. The field is represented as a superposition of azimuthally symmetric 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 var...

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. >

Nonlinear theory of collective effects in helix traveling wave tubes

A time-dependent collective nonlinear analysis of a helix traveling wave tube including fluctuating (ac) space-charge effects is presented for a configuration where an electron beam propagates through a sheath helix surrounded by a conducting wall. The effects of dielectric and vane loading of the helix are included, as is efficiency enhancement by tapering the helix pitch, and external focusing by means of either a uniform solenoidal magnetic field or a periodic field produced by a periodic permanent magnet stack. Dielectric loading is described under the assumption that the gap between the helix and the wall is uniformly filled by a dielectric material. Vane loading describes the insertion of an arbitrary number of vanes running the length of the helix. The electromagnetic field is represented as a superposition of azimuthally symmetric waves in a vacuum sheath helix. The propagation of each wave in vacuo, as well as the interaction of each wave with the electron beam, is included by allowing the amplit...

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.

Time-dependent simulation of helix traveling wave tubes

A time-dependent nonlinear analysis of a helix traveling wave tube (TWT) is presented for a configuration where an electron beam propagates through a three-dimensional tape helix surrounded by a conducting wall. The effects of dielectric- and vane-loading are included as is efficiency enhancement by tapering the helix pitch and external focusing by means of either a uniform solenoidal magnetic field or a periodic field produced by a periodic permanent magnet stack. Dielectric-loading is described under the assumption that the gap between the helix and the wall is uniformly filled by a dielectric material. Vane-loading describes the insertion of an arbitrary number of vanes running the length of the helix. The electromagnetic field is represented as a superposition of waves in a vacuum tape helix. The propagation of each wave 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. The field equations are solved in conjunction wi...