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Derivation of nonlinear Schrödinger equation for electrostatic and electromagnetic waves in fully relativistic twofluid plasmas by the reductive perturbation method Phys. Plasmas 19, 082303 (2012) Parametric decays in relativistic magnetized electron-positron plasmas with relativistic temperatures A klystron-like relativistic backward wave oscillator with a ratio of transverse dimension to freespace wavelength being about four is presented. In the beam-wave interaction region, the electron beam interacts with surface wave and volume wave simultaneously. The cathode holder plays an important role in the reflection of backward waves. A guard electrode, an electron collector ring, and a reflection ring are used to optimize the beam-wave interaction. The particle in cell simulation results reveal that microwaves with a power of 2 GW and a frequency of 12.3 GHz are generated with an efficiency of 42% when the diode voltage is 400 kV, the beam current 12 kA, and the magnetic field 0.48 T.

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A high efficiency relativistic backward wave oscillator working at a low guiding magnetic field is designed and simulated. A trapezoidal resonant reflector is used to reduce the modulation field in the resonant reflector to avoid overmodulation of the electron beam which will lead to a large momentum spread and then low conversion efficiency. The envelope of the inner radius of the slow wave structure (SWS) increases stepwise to keep conformal to the trajectory of the electron beam which will alleviate the bombardment of the electron on the surface of the SWS. The length of period of the SWS is reduced gradually to make a better match between phase velocity and electron beam, which decelerates continually and improves the RF current distribution. Meanwhile the modulation field is reduced by the introduction of nonuniform SWS also. The particle in cell simulation results reveal that a microwave with a power of 1.8 GW and a frequency of 14.7 GHz is generated with an efficiency of 47% when the diode voltage is 620 kV, the beam current 6.1 kA, and the guiding magnetic field 0.95 T.