Coupled-cavity traveling wave tube (CCTWT) is a high power microwave (HPM) vacuum electronic device used to amplify radio-frequency (RF) signals. CCTWTS have numerous applications, including radar, radio navigation, space communication, television, radio repeaters, and charged particle accelerators. The microwave-generating interactions in CCTWTs take place mostly in coupled resonant cavities positioned periodically along the electron beam axis. Operational features of a CCTWT particularly the amplification mechanism are similar to those of a multicavity klystron (MCK). We advance here a Lagrangian field theory of CCTWTs with the space being represented by one-dimensional continuum. The theory integrates into it the space-charge effects including the so-called debunching (electron-to-electron repulsion). The corresponding Euler-Lagrange equations are ODEs with coefficients varying periodically in the space. Utilizing the system periodicity we develop the instrumental features of the Floquet theory including the monodromy matrix and its Floquet multipliers. We use them to derive closed form expressions for a number of physically significant quantities. Those include in particular the dispersion relations and the frequency dependent gain foundational to the RF signal amplification. Serpentine (folded, corrugated) traveling wave tubes are very similar to CCTWTs and our theory applies to them also.

Analytic theory of coupled-cavity 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.

pdf/parametric-modeling-of-serpentine-waveguide-traveling-wave-z6v1f4n7ss.pdf

Parametric Modeling of Serpentine Waveguide Traveling Wave Tubes

Coupled-cavity traveling wave tube (CCTWT) is a high power microwave vacuum electronic device used to amplify radio frequency signals. CCTWTs have numerous applications, including radar, radio navigation, space communication, television, radio repeaters, and charged particle accelerators. Microwave-generating interactions in CCTWTs take place mostly in coupled resonant cavities positioned periodically along the electron beam axis. Operational features of a CCTWT, particularly the amplification mechanism, are similar to those of a multicavity klystron. We advance here a Lagrangian field theory of CCTWTs with the space being represented by one-dimensional continuum. The theory integrates into it the space-charge effects, including the so-called debunching (electron-to-electron repulsion). The corresponding Euler–Lagrange field equations are ordinary differential equations with coefficients varying periodically in the space. Utilizing the system periodicity, we develop instrumental features of the Floquet theory, including the monodromy matrix and its Floquet multipliers. We use them to derive closed form expressions for a number of physically significant quantities. Those include, in particular, dispersion relations and the frequency dependent gain foundational to the RF signal amplification. Serpentine (folded, corrugated) traveling wave tubes are very similar to CCTWTs, and our theory applies to them also. 

This paper introduces a high-power broadband X-band klystron amplifier that achieves an output power of 157 MW and a 3 dB operating bandwidth of 6.7%. The amplifier employs an explosive emission diode with high impedance, which balances the requirements of high power and broadband. The multi-gap input and output cavities are designed to operate at two different longitudinal modes within the operating frequency band, resulting in a flat absorption rate and output efficiency. Moreover, an eight-stage stagger-tuned bunching section is implemented to achieve a uniform fundamental harmonic current modulation depth across the frequency band. Simulation results indicate that when the diode voltage is 550 kV and the beam current is 550 A, the amplifier can achieve a maximum power of 157 MW with an efficiency of 51.9% at the central frequency of 9.8 GHz. Furthermore, within the 3 dB operating bandwidth of 6.7% (670 MHz), the power output remains higher than 80 MW. This novel klystron amplifier structure exhibits exceptional performance in terms of bandwidth, power, and efficiency, thus validating the effectiveness of the design in enhancing bandwidth and providing a solid foundation for the broadband design of high-power microwave sources. 

Research on a broad-band X-band high power relativistic klystron amplifier

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. 

Multicavity Klystron (MCK) is a high power microwave (HPM) vacuum electronic device used to amplify radio-frequency (RF) signals with numerous applications, including radar, radio navigation, space communication, television, radio repeaters, and charged particle accelerators. The microwave-generating interactions in klystrons take place in resonant cavities at discrete locations along the beam. Importantly, there is no electromagnetic coupling between cavities, they are coupled only by the bunched electron beam, which drifts from one cavity to the next. We advance here an analytic theory of MCKs operating in voltage amplification mode associated with the maximal gain. This theory features in particular exact formulas for the MCK instability frequencies, its dispersion relations and optimal values of the MCK parameters providing for maximal gain. 

/pdf/analytic-theory-of-multicavity-klystrons-1x09kewt.pdf

Analytic theory of multicavity klystrons

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Analytic theory of multicavity klystrons

Analytic theory of coupled-cavity traveling wave tubes

Analytic theory of coupled-cavity traveling wave tubes