Exceptional Point of Degeneracy in Linear-Beam Tubes for High Power Backward-Wave Oscillators

Abstract An exceptional point of degeneracy (EPD) is induced in a system made of an electron beam interacting with an electromagnetic (EM) guided mode. This enables a degenerate synchronous regime in backward wave oscillators (BWOs) where the electron beams provides distributed gain to the EM mode with distributed power extraction. Current particle-in-cell simulation results demonstrate that BWOs operating at an EPD have a starting-oscillation current that scales quadratically to a non-vanishing value for long interaction lengths and therefore have higher power conversion efficiency at arbitrarily higher level of power generation compared to standard BWOs

Exceptional Point of Degeneracy in Backward-Wave Oscillator with Distributed Power Extraction

We show how an exceptional point of degeneracy (EPD) is formed in a system composed of an electron beam interacting with an electromagnetic mode guided in a slow wave structure (SWS) with distributed power extraction from the interaction zone. Based on this kind of EPD, a new regime of operation is devised for backward wave oscillators (BWOs) as a synchronous and degenerate regime between a backward electromagnetic mode and the charge wave modulating the electron beam. Degenerate synchronization under this EPD condition means that two complex modes of the interactive system do not share just the wavenumber, but they rather coalesce in both their wavenumbers and eigenvectors (polarization states). In principle this new condition guarantees full synchronization between the electromagnetic wave and the beam's charge wave for any amount of output power extracted from the beam, setting the threshold of this EPD-BWO to any arbitrary, desired, value. Indeed, we show that the presence of distributed radiation in the SWS results in having high-threshold electron-beam current to start oscillations which implies higher power generation. These findings have the potential to lead to highly efficient BWOs with very high output power and excellent spectral purity

General Conditions to Realize Exceptional Points of Degeneracy in Two Uniform Coupled Transmission Lines

We present the general conditions to realize a fourth order exceptional point of degeneracy (EPD) in two uniform (i.e., invariant along z) lossless and gainless coupled transmission lines (CTLs), namely, a degenerate band edge (DBE). Until now the DBE has been shown only in periodic structures. In contrast, the CTLs considered here are uniform and subdivided into four cases where the two TLs support combinations of forward propagation, backward propagation and evanescent modes (when neglecting the mutual coupling). We demonstrate for the first time that a DBE is supported in uniform CTLs when there is proper coupling between: (i) propagating modes and evanescent modes, (ii) forward and backward propagating modes, or (iii) four evanescent modes (two in each direction). We also show that the loaded quality factor of uniform CTLs exhibiting a fourth order EPD at k=0 is robust to series losses due to the fact that the degenerate modes do not advance in phase. We also provide a microstrip possible implementation of a uniform CTL exhibiting a DBE using periodic series capacitors with very sub-wavelength unit-cell length. Finally, we show an experimental verification of the existence DBE for a microstrip implementation of a CTL supporting coupled propagating and evanescent modes

Reduced Plasma Frequency Calculation Based on Particle-In-Cell Simulations

We propose a scheme to calculate the reduced plasma frequency of a cylindrical-shaped electron beam flowing inside of a cylindrical tunnel, based on results obtained from Particle-in-cell (PIC) simulations. In PIC simulations, we modulate the electron beam using two parallel, non-intercepting, closely-spaced grids which are electrically connected together by a single-tone sinusoidal voltage source. The electron energy and the beam current distributions along the length of the tunnel are monitored after the system is operating at steady-state. We build a system matrix describing the beam's dynamics, estimated by fitting a 2x2 matrix that best agrees with the first order differential equations that govern the physics-based system. Results are compared with the theoretical Branch and Mihran model, which is typically used to compute the plasma frequency reduction factor in such systems. Our method shows excellent agreement with the theoretical model, however, it is also general. Our method can be potentially utilized to determine the reduced plasma frequencies of electron beams propagating in differently-shaped beam tunnels, where no theoretical model yet exists, such as the case of a cylindrical or elliptical electron beam propagating inside of a metallic beam tunnel of cylindrical, square, or elliptical cross-section. It can be applied also to electron beams composed of multiple streams

Analytical Solution for Space-Charge Waves in a Two-Stream Cylindrical Electron Beam

We present an analytical method to compute the wavenumbers and electric fields of the space-charge-wave eigenmodes supported by a two-stream electron beam, consisting of a solid inner cylindrical stream and a coaxial outer annular stream, both contained within a cylindrical metallic tunnel.We extend the analytical model developed by Ramo to the case of two streams. The method accounts for the interaction between the two streams with the presence of the beam-tunnel wall; it can be used to model the complex wavenumbers associated with the two-stream instability and the plasma frequency reduction effects in vacuum electronic amplifiers and other vacuum electronic devices.Comment: 11 pages, 9 figure

Third Order Modal Exceptional Degeneracy in Waveguides with Glide-Time Symmetry

The dispersion of a three-way waveguide is engineered to exhibit exceptional modal characteristics. Two coupled waveguides with Parity-Time (PT) symmetry have been previously demonstrated to exhibit second order exceptional points of degeneracy (EPDs). In this work, we introduce and investigate a particular class of EPDs, applicable from radio frequency to optical wavelengths, whereby three coupled waveguides satisfy Glide-Time (GT) symmetry to exhibit a third order modal degeneracy with a real-valued wavenumber. GT symmetry involves glide symmetry of lossless/gainless components of the waveguide in addition to changing the sign of passive/active elements while applying a glide symmetry operation. This GT-symmetry condition allows three Floquet-Bloch eigenmodes of the structure to coalesce to a real-valued wavenumber at a single frequency, in addition of having one branch of the dispersion diagram with a purely real wavenumber. The proposed scheme may have applications including but not limited to distributed amplifiers, radiating arrays, and sensors, from radio frequency to optics

Parametric Modeling of Serpentine Waveguide Traveling Wave Tubes

A simple and fast model for numerically calculating small-signal gain in serpentine waveguide traveling-wave tubes (TWTs) is described. In the framework of the Pierce model, we consider one-dimensional electron flow along a dispersive single-mode slow-wave structure (SWS), accounting for the space-charge effect. The analytical model accounts for the frequency-dependent phase velocity and characteristic impedance obtained using various equivalent circuit models from the literature, validated by comparison with full-wave eigenmode simulation. The model includes a relation between the modal characteristic impedance and the interaction (Pierce) impedance of the SWS, including also an extra correction factor that accounts for the variation of the electric field distribution and hence of the interaction impedance over the beam cross section. By applying boundary conditions to our generalized Pierce model, we compute both the theoretical gain of a TWT and all the complex-valued wavenumbers of the hot modes versus frequency and compare our results with numerically intensive particle-in-cell (PIC) simulations; the good agreement in the comparison demonstrates the accuracy and simplicity of our generalized model. For various examples where we vary the average electron beam (e-beam) phase velocity, average e-beam current, number of unit cells, and input radio frequency (RF) power, we demonstrate that our model is robust in the small-signal regime.Comment: 16 pages, 14 figure