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Description
This work presents the design and analytical optimization of a high-power, high-efficiency S-band multi-beam klystron (MBK) intended as an RF power source for large-scale scientific facilities. Existing accelerator klystrons demonstrate $50-80 MW$-class peak power near $2.856 GHz$, whereas established MBKs and recent high-efficiency developments operate in the $60-70\%$ electronic-efficiency range. The present design therefore targets $2.856 GHz$, $50 MW$ peak RF output, $62\% $electronic efficiency, at least $50 dB$ saturated gain, $3-4 μs$ RF pulses at $50-60 Hz$, and at least $99\%$ beam transmission. The design covers the multi-beam electron gun, magnetic focusing system, RF interaction structure, output coupling and window, and collector. The extracted RF power is written as $P_{out}≈ ½I_1 M V_g cos ψ$, giving the electronic efficiency $η_e = P_{out}/(V_0 I_{tot} ) ≈ ½(I_1/I_{tot} )((M V_g)/V_0 ) cos ψ$. This relation identifies the fundamental current ratio, transit-time factor, normalized output-gap voltage, and decelerating phase as the principal interaction parameters. The per-beam microperveance is $K_{(μ,b)} = 10⁶I_{tot}/(N V_0^{3/2} )$, which can be combined with the power balance to obtain $K_{(μ,b)}= 10⁶P_{out}/(N η_e V_0^{5/2} )$. The measured-tube trend $η_{fit} = 100/(1 + 0.79008K_μ )$ is used as a first-pass screen, so beam number and operating voltage are co-optimized to maintain low per-beam perveance without prescribing particular voltage or current values. The RF interaction structure combines staged fundamental bunching, harmonic correction, penultimate bunch shaping, and loaded output extraction. Drift lengths and detuning are adjusted to compress the phase distribution and maximize the fundamental beam-current component at the output gap. The gap geometry follows $M = (sin(θ/2))/(θ/2),θ = ωg/v_0$ , with a target $M ≥ 0.95$. Output loading and magnetic focusing are subsequently matched to the bunched beam, and the design is accepted only when the power, efficiency, gain, and transmission targets are achieved without excessive returning electrons, RF breakdown, or thermal loading. This approach converts demonstrated large-klystron performance into a self-consistent S-band MBK design route for subsequent multi-code simulation and experimental validation.*
