Normal Doppler effect in experiments on the interaction of relativistic electron beams with plasma: Plasma relativistic
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MA ELECTRONICS
Normal Doppler Effect in Experiments on the Interaction of Relativistic Electron Beams with Plasma: Plasma Relativistic Microwave Amplifier P. S. Strelkov, A. V. Ponomarev, and I. L. Bogdankevich Prokhorov Institute of General Physics, Russian Academy of Sciences, ul. Vavilova 38, Moscow, 119991 Russia Received June 22, 2006
Abstract—The Cherenkov interaction of a high-current relativistic electron beam with a spatially bounded plasma was studied experimentally. In the generation of electromagnetic radiation, an important role is played by the counterpropagating plasma wave produced due to the reflection from the end of the plasma column. It is shown that, at the resonant value of the magnetic field, the normal Doppler effect occurs and the amplitude of the counterpropagating wave decreases. This effect was used to design and create a plasma relativistic microwave amplifier in which 10% of the beam energy is converted into radiation. The radiation frequency is 9.1 GHz, and the radiation spectrum width (±0.17%) is determined by the microwave-pulse duration. The maximum radiation power is 100 MW, the gain factor being 32 dB. PACS numbers: 52.35.Qz DOI: 10.1134/S1063780X07040083
of the beam electrons, kz is the longitudinal wavenumber, u is the beam velocity, and γ is the relativistic factor. Figure 1 illustrates the dispersion curves of the coand counterpropagating plasma waves and the beam space-charge wave in the limit of low beam currents, ∞, the plasma-wave frequency ωb /γ3/2 ω. As kz approaches the plasma frequency ωp. The intersection point of the dispersion curves of the beam wave ω = kzu and the copropagating plasma wave (kz > 0) corresponds to the beam instability at the frequency ω* and wavenumber k z* . For a wave reflected from the end of the plasma waveguide (kz < 0), we have ω* = – k z* (–u). In an electron beam, a fast cyclotron wave with the frequency ω = kzu + ωH /γ (where ωH is the electron cyclo-
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ω
ω*
=
+
/γ ωH
zc
ω
k zu
=k
ωp ωH/γ
ω
1. INTRODUCTION Beam instability in plasma was first predicted theoretically in [1, 2] and then observed experimentally in [3, 4]. When an electron beam propagates in a waveguide, it generates a slow copropagating plasma wave via the Cherenkov mechanism. This wave is then reflected from the end of the plasma waveguide and propagates backward, providing a positive feedback wave and leading to microwave generation. The possibility of creating microwave sources based on the interaction of relativistic electron beams (REBs) with a plasma was first demonstrated in [5]. It was shown that the frequency of the plasma microwave oscillator can be tuned by varying the plasma density. Measurements of the frequency as a function of the plasma density show that, in this case, the E01 mode of the slow plasma wave is excited in a plasma waveguide [6, 7]. In order for the high-power microwave amplifier not to pass into the generation mode, the feedback factor should be made small enough. In vacuum microwave electronics, this problem is usually resolve
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