Abstract
Linear and nonlinear behaviors of gyrotronbackward wave oscillators (gyroBWO) were investigated by both analytical theories and direct numerical calculations. Employing twoscalelength expansion, an analytical linear dispersion relation corresponding to absolute instabilities in a finitelength system has been derived. Detuning from the beamwave resonance condition due to the finite amplitude radiation fields, meanwhile, was found to play the crucial roles in the nonlinear physics. Near the start oscillation of the gyroBWO, the radiation field amplitude saturates when the resonance broadening is comparable to the linear growth rate. Far beyond the start oscillation threshold, the beamwave resonance detuning effectively shortens the interaction length toward that corresponding to the critical oscillation length for the given beam current. The theoretically predicted scaling laws for the linear stability properties and nonlinear stationary states of the gyroBWO are in good agreement with numerical results.
The work was supported by National Science Council under the Grant NSC 982112 M008006MY3. The authors would like to acknowledge the National Center for HighPerformance Computing in providing resources under the national project, “Taiwan Knowledge Innovation National Grid.” L.C. acknowledges support of US DOE and NSF grants, and Lee KuoTing Chair Professorship awarded by National Central University.
I. INTRODUCTION
II. LINEAR STABILITY PROPERTIES: ABSOLUTE INSTABILITIES IN A FINITELENGTH SYSTEM
III. LINEAR AND NONLINEAR FIELD PROFILES
IV. STATIONARY NONLINEAR PHYSICS: FIELD CONTRACTION AND BEAMWAVE RESONANCE DETUNING
V. SUMMARY AND DISCUSSION
Key Topics
 Electron beams
 11.0
 Backward wave oscillators
 7.0
 Dispersion relations
 7.0
 Number theory
 7.0
 Gyrotrons
 6.0
Figures
Figures plot (a) the start oscillation current versus the system size L and (b) the absolute growth rate versus for a cold electron beam with the beam voltage , the transversetolongitudinal velocity ratio , and the guiding center radius . The start oscillation current in (b) is corresponding to the interaction length . The externally applied magnetic field is and the uniform waveguide radius is .
Figures plot (a) the start oscillation current versus the system size L and (b) the absolute growth rate versus for a cold electron beam with the beam voltage , the transversetolongitudinal velocity ratio , and the guiding center radius . The start oscillation current in (b) is corresponding to the interaction length . The externally applied magnetic field is and the uniform waveguide radius is .
Figures plot the EM field profiles for at (a) and (b) (the solid line), respectively. The EM field profile for and (the dashed line) is plot in (b) for demonstrating that the effective length of the contracted field profile can be determined by the start oscillation length at the same beam current. Other operating parameters are the same as shown in Fig. 1.
Figures plot the EM field profiles for at (a) and (b) (the solid line), respectively. The EM field profile for and (the dashed line) is plot in (b) for demonstrating that the effective length of the contracted field profile can be determined by the start oscillation length at the same beam current. Other operating parameters are the same as shown in Fig. 1.
Figures plot (a) the spatial variation of particle trajectories in the phase space and (b) the resonance detuning (averaged over all electrons) versus z, respectively, for . Other operating parameters are the same as shown in Fig. 2(b).
Figures plot (a) the spatial variation of particle trajectories in the phase space and (b) the resonance detuning (averaged over all electrons) versus z, respectively, for . Other operating parameters are the same as shown in Fig. 2(b).
Figures plot (a) the maximum resonance detuning versus the maximum field amplitude (the corresponding beam current ) and (b) the effective length versus the maximum field amplitude (the corresponding beam current ), respectively. The complementary scalings of the resonance detuning and the effective length with the maximum field amplitude illustrate that the nonlinear field contraction is induced by the detuning of the resonance condition. Other operating parameters are the same as shown in Fig. 2(b).
Figures plot (a) the maximum resonance detuning versus the maximum field amplitude (the corresponding beam current ) and (b) the effective length versus the maximum field amplitude (the corresponding beam current ), respectively. The complementary scalings of the resonance detuning and the effective length with the maximum field amplitude illustrate that the nonlinear field contraction is induced by the detuning of the resonance condition. Other operating parameters are the same as shown in Fig. 2(b).
Figures plot the output power of the gyroBWO versus (a) at and (b) at , respectively. The start oscillation current in is corresponding to the interaction length . The corresponding power scaling laws are also shown in the figures. Other operating parameters are the same as shown in Fig. 2(b).
Figures plot the output power of the gyroBWO versus (a) at and (b) at , respectively. The start oscillation current in is corresponding to the interaction length . The corresponding power scaling laws are also shown in the figures. Other operating parameters are the same as shown in Fig. 2(b).
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