[Paper Review] Relativistic Split-Cavity Oscillator

V.G. Baryshevsky|arXiv (Cornell University)|Feb 14, 2014

Gyrotron and Vacuum Electronics Research11 references3 citations

TL;DR

This paper applies small-signal analysis to relativistic split-cavity oscillators (SCO) to evaluate their potential for high-power microwave (HPM) generation. It demonstrates that beam self-modulation is most effective at relativistic electron beam energies below 300–400 keV, with enhanced modulation possible at higher energies when beam current increases, enabling efficient HPM generation without external magnetic fields.

ABSTRACT

Using the method of small signal analysis, we study the application potential of relativistic electron beams in split-cavity oscillators (SCO's). A beam-energy change in the SCO as a function of the initial energy of a relativistic beam is considered. It is shown that the small-signal analysis method enables adequate evaluation of SCO parameters needed for effective modulation of a relativistic beam in a split cavity and for HPM generation using SCO's. The range of energies is found for which the effect of self-modulation of the beam density in SCO structures is most pronounced. It is also shown that for beam currents at which the space charge has little effect on the motion of electrons in a beam, the beam in a split-cavity oscillator is effectively self-modulated at beam energies less than ~300-400 keV. The self-modulation drops sharply in the range of energies from 250 to 400 keV, but as the beam current is increased, the effective beam self-modulation becomes appreciable in this range too, as well as even in a higher energy range.

Motivation & Objective

• To assess the feasibility of using relativistic electron beams in split-cavity oscillators (SCO) for high-power microwave (HPM) generation.
• To extend small-signal analysis—previously applied to nonrelativistic beams—to relativistic beam conditions in SCO structures.
• To identify the energy and current regimes where beam self-modulation is most pronounced for effective HPM generation.
• To determine the conditions under which space-charge effects are minimal yet beam modulation remains effective in SCO configurations.

Proposed method

• Adapted small-signal analysis from nonrelativistic to relativistic electron beams in a split-cavity oscillator geometry.
• Modelled the relativistic electron beam's longitudinal motion under a time-varying RF electric field in a pillbox cavity with a central screen.
• Used the Lorentz factor and relativistic momentum equations to derive particle trajectory and transit time through the cavity.
• Expanded the transit-time equation in powers of a small parameter ε = eE₀/(mγ₀v₀ω) to linear order for analytical tractability.
• Derived expressions for beam energy change and phase shift as functions of initial beam energy and RF field parameters.
• Evaluated coherent transition radiation power from modulated beams using spectral-angular distribution and beam modulation depth.

Experimental results

Research questions

• RQ1 At what beam energy range is self-modulation of the relativistic electron beam most effective in a split-cavity oscillator?
• RQ2 How does increasing beam current affect the effectiveness of beam self-modulation in the 250–400 keV energy range?
• RQ3 Can small-signal analysis accurately predict SCO parameters for effective HPM generation with relativistic beams?
• RQ4 What is the role of beam current and energy in enabling effective self-modulation when space-charge effects are negligible?

Key findings

• Beam self-modulation is most pronounced for relativistic electron beam energies below approximately 300–400 keV.
• Self-modulation drops sharply in the 250–400 keV range when beam current is low, but becomes appreciable again as current increases.
• At beam currents where space-charge effects are negligible, effective self-modulation occurs at energies below 300–400 keV.
• With increased beam current, effective self-modulation extends into the 250–400 keV range and even into higher energy regimes.
• Coherent transition radiation power can reach several hundred megawatts for beam currents of 4–6 kA and energies of 400–500 keV with modulation depth μ ≥ 0.5.
• The SCO structure enables efficient HPM generation without requiring an external magnetic field, similar to photonic crystal-based volume free electron lasers.