D. Chernin

Stability of Laminar Electron Layers.

The stability of a finite thickness, laminar cylindrical shell of electrons rotating azimuthally and enclosed in a coaxial waveguide is considered. The equilibrium rotation of the electrons is supported either by a radial electric field, an axial magnetic field, or a combination of both. The stability problem is formulated exactly as an eigenvalue problem, including all relativistic and electromagnetic effects as well as all effects of self and applied equilibrium fields. An approximate dispersion relation, valid for thin beams, is obtained analytically and the classical results for the ‘‘longitudinal’’ modes, i.e., the negative mass, cyclotron maser, and diocotron instabilities and for the ‘‘transverse’’ mode are recovered in appropriate limits. The dispersion relation is relatively simple and is valid for arbitrary values of the equilibrium electric and magnetic fields and for arbitrary beam energy. It therefore provides a ready comparison of the small signal properties of such devices as the Astron, gy...

Quantum extension of Child-Langmuir law.

1407_69Using a simple mean field model of the electron-electron interaction, study has been done of the effect of space charge in a planar diode. Results show, in particular, that the classical value for the limiting current in such a diode can be exceeded by a large factor due to the effect of tunneling. The smooth transition of the solutions from the quantum to the classical (non-quantum) regime is demonstrated.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Simulation of microwave devices with external cavities using MAGY

A self-consistent large-signal beam-field interaction model for vacuum electronic microwave sources with external cavities is described. The model includes a self-consistent solution of the three-dimensional equations of electron motion and the time-dependent field equations. The RF fields are decomposed into the fields inside the beam region and the fields inside outer resonators. The RF fields inside the beam region are represented as a superposition of local waveguide modes. The RF fields inside resonators are represented as a sum over resonator modes. The various modes are coupled together due to gaps connecting cavities with each other and with the beam region. The numerical implementation of the model requires additional analytical steps to obtain an effective, convergent, and stable numerical solution. The modified version of the code MAGY has been tested by a comparison with known results and also with measured data.

Limiting current in a crossed-field gap

An analytic theory is presented that yields the maximum transmittable current across an anode–cathode gap that is embedded in an arbitrary transverse magnetic field (B). The limiting current is found to be relatively insensitive to B for all B<BH, where BH is the Hull cutoff magnetic field required for magnetic insulation. The classical Child–Langmuir solution is recovered in the limit B→0.

Theory of electron multipactor in crossed fields

A general theory of multipactor in orthogonal electric and magnetic fields is given. The model consists of two parallel plates of known secondary emission properties, across which a time varying voltage is applied, and between which a constant magnetic field is applied. Expressions are derived for the resonant phases at which the RF‐driven cascades occur; these reduce to previously derived expressions in the limit of the vanishing magnetic field. In addition, this work obtains the conditions governing the stability of the motion about those phases, as well as a dynamic constraint from imposing the restriction that each impact on a plate is the first impact that is allowed by the equations of motion. Chaotic effects from the random ejection velocities of the secondaries are addressed for the first time. It is proven that the phase focusing effect from the radio frequency (RF) interaction will overcome the dispersive effect from the random emission, provided that the mean square emission velocity is suffici...

A review of the ac space‐charge effect in electron–circuit interactions

This paper provides a critical examination of traditional theoretical treatments of alternating current (ac) space‐charge effects in vacuum electronic devices. By treating several simple examples, it is found that the commonly made decomposition of the first‐order field into a ‘‘circuit part’’ and a ‘‘space‐charge part’’ is ambiguous and misleading. In at least one case, this terminology has led to a formulation that double counts the effect of space charge in the beam–circuit interaction. In other cases, the ‘‘space‐charge term’’ in the dispersion relation−equivalently Pierce’s space‐charge parameter (QC)−has been improperly or incompletely evaluated. The implications for gyrotrons, peniotrons, free‐electron lasers, Smith–Purcell‐type generators, and crossed‐field devices are addressed. The space‐charge effects are briefly discussed in nonlinear theories and in particle simulations. For the models examined, it is found that the most useful and convenient representation for the ac fields is one based on an eigenfunction expansion of the ac magnetic field, even when that field is not itself important to the electron dynamics.

Large-Signal Multifrequency Simulation of Coupled-Cavity TWTs

We describe a steady-state large-signal model of coupled-cavity traveling-wave tubes in which the input and output signals are periodic functions of time that may be represented by Fourier series of finite length. The model includes both linear and nonlinear effects including circuit dispersion, reflections, intermodulation, and harmonic generation. The model uses a lumped element representation of the circuit and a 1-D disk model of the beam. Several favorable comparisons of model predictions with experimental measurements, including gain versus frequency and power transfer characteristics, are illustrated. The inclusion of nonlinear effects in this multifrequency model enables predictions of intermodulation products, as functions of the input power. An example of the computation of C3IM is illustrated.

A Computationally Efficient Two-Dimensional Model of the Beam–Wave Interaction in a Coupled-Cavity TWT

A new computationally efficient 2-D model of the beam-wave interaction in coupled-cavity traveling-wave tubes (CC-TWTs) has been developed. The model provides self-consistent time-dependent solutions of Maxwells equations together with a fully relativistic solution of the electron equations of motion. The model is based on different treatments of the RF fields in the region occupied by an electron beam and in the region of the coupled-cavity structure. The RF fields inside the beam tunnel are represented as a sum of eigenmodes of the local cross section of the beam tunnel. The fields outside the beam tunnel are represented as a superposition of modes of an equivalent circuit with lumped capacitors, inductors, and resistors. The model has been implemented in the TESLA-CC code. The results of the code predictions agree well with measured data for a wideband CC-TWT operating in the Ka-band. The code also shows good agreement with predictions of the 1-D code CHRISTINE-CC in regimes in which a 1-D approximation is applicable. A numerical study of CC-TWT operation shows that, in the small-signal regime, the code is able to predict a gain enhancement due to transverse motion at focusing magnetic fields comparable with Brillouin equilibrium values, which is the major 2-D effect. In the large-signal regime, the code is also capable of treating cases in which the transverse displacement of electrons becomes large and of determining the dependence of the spent beam energy distribution on radial position.

A simulation study of beam loading on a cavity

Beam loading exerts a strong influence on the operation of high-power and medium-power microwave sources. This paper reports a simulation study of beam loading on a cavity using the two-dimensional particle-in-cell code, MAGIC. We vary the beam voltage, the beam current, the degree of current modulation on the dc beam before the beam enters the cavity, and the degree of charge neutralization on the beam. We deduce the beam-loaded quality factor Q and the beam-loaded resonant frequency from a Lorentzian fit of the numerical data on the gap voltage response as a function of the driving frequency. The MAGIC simulations have revealed several unanticipated results. The beam loading is observed to be a function of perveance. Constant perveance beams, of varying voltage and current, exercise about the same degree of beam loading on the model klystron cavity (except, of course, for the cases with very small beam current). The inclusion of an ac component on the dc beam current has no effect on the degree of beam loading; neither does the neutralization of the electron beam. Many of these simulation results cannot be explained by existing theories that ignore ac space charge effects.

Resistive destabilization of cycloidal electron flow and universality of (near‐) Brillouin flow in a crossed‐field gap

It is shown that a small amount of dissipation, caused by current flow in a lossy external circuit, can produce a disruption of steady‐state cycloidal electron flow in a crossed‐field gap, leading to the establishment of a turbulent steady state that is close to, but not exactly, Brillouin flow. This disruption, which has nothing to do with a diocotron or cyclotron instability, is fundamentally caused by the failure of a subset of the emitted electrons to return to the cathode surface as a result of resistive dissipation. This mechanism was revealed in particle simulations, and was confirmed by an analytic theory. These near‐Brillouin states differ in several interesting respects from classic Brillouin flow, the most important of which is the presence of a microsheath and a time‐varying potential minimum very close to the cathode surface. They are essentially identical to that produced when (i) injected current exceeds a certain critical value [P. J. Christenson and Y. Y. Lau, Phys. Plasmas 1, 3725 (1994)...