Abstract
In this paper, the operation of the stimulated emission in Cerenkov freeelectron laser (CFEL) is studied on the basis of the modulations of electron velocity and density by the electromagnetic (EM) field. The influence of the electron relaxation, due to mutual electrons collisions, on the electron dynamics is taken into account. We investigate the growth characteristics of Cerenkov laser operating in the smallsignal and saturation regimes. In the saturation regime, the effect of velocity reduction of the electron beam on the gain dynamics is demonstrated. We also show that our results match with those of other wellknown treatments in the smallsignal gain limit.
I. INTRODUCTION
II. CFEL MODELING
III. STIMULATED EMISSION AND AMPLIFICATION
A. Dynamic motion of electrons and gain coefficients
B. Numerical examples and discussions
IV. SPATIALLY AVERAGED GAIN COEFFICIENT
V. CONCLUSIONS
Key Topics
 Electron beams
 36.0
 Relaxation times
 14.0
 Electric fields
 12.0
 Current density
 10.0
 Stimulated emission
 9.0
Figures
Geometry of the electron beamdielectric guide interaction in a CFEL as an amplifier. If two mirrors are added at both ends, the CFEL device will work as an oscillator.
Geometry of the electron beamdielectric guide interaction in a CFEL as an amplifier. If two mirrors are added at both ends, the CFEL device will work as an oscillator.
Variations of the gain coefficient with the normalized distance for different values of in the smallsignal approximation. The interaction regions induced by the stimulated emission can be divided into transition and steady states. In the transition state, the gain coefficient increases almost linearly with the spatial variation. In the steady state, when the passing distance reaches several times of the distance , the gain coefficient saturates at certain values.
Variations of the gain coefficient with the normalized distance for different values of in the smallsignal approximation. The interaction regions induced by the stimulated emission can be divided into transition and steady states. In the transition state, the gain coefficient increases almost linearly with the spatial variation. In the steady state, when the passing distance reaches several times of the distance , the gain coefficient saturates at certain values.
Numerical examples of the saturated gains and the relative angular frequency with the normalized distance . (a) Variations of the gain coefficients and . A high input power of is supposed to clarify the saturation effect. increases along the electron beam and reaches a maximum value and after that it will gradually decrease due to the shifting of the averaged velocity of the electron beam from the synchronism condition. The gain coefficient is proportional to the power of the EM wave; thus, it have the same behavior as for the gain coefficient . (b) The attenuation of the wave frequency as seen by traversing electrons vs. the normalized distance .
Numerical examples of the saturated gains and the relative angular frequency with the normalized distance . (a) Variations of the gain coefficients and . A high input power of is supposed to clarify the saturation effect. increases along the electron beam and reaches a maximum value and after that it will gradually decrease due to the shifting of the averaged velocity of the electron beam from the synchronism condition. The gain coefficient is proportional to the power of the EM wave; thus, it have the same behavior as for the gain coefficient . (b) The attenuation of the wave frequency as seen by traversing electrons vs. the normalized distance .
Variations of the gain coefficient with for different values of in the saturation regime. Due to the attenuation of the averaged velocity of electrons , the gain cannot reach to the steady state region observed in the smallsignal analysis and its maximum values occur at larger distances for larger values of .
Variations of the gain coefficient with for different values of in the saturation regime. Due to the attenuation of the averaged velocity of electrons , the gain cannot reach to the steady state region observed in the smallsignal analysis and its maximum values occur at larger distances for larger values of .
Comparison between the gain coefficient in the smallsignal gain and saturation limits. The smallsignal case is represented by dotted line. At saturation, numerical solutions to the gain coefficient given by Eq. (27) is shown by solid line and by dashed line when the term of is neglected in the denominator of Eq. (27).
Comparison between the gain coefficient in the smallsignal gain and saturation limits. The smallsignal case is represented by dotted line. At saturation, numerical solutions to the gain coefficient given by Eq. (27) is shown by solid line and by dashed line when the term of is neglected in the denominator of Eq. (27).
Spatial variation of the power amplification . The smallsignal gain is depicted by the dotted line, whereas the power amplification increases in the form of the exponential function. In the case of the saturation regime, the power amplification increases almost linearly with the normalized interaction length and decreases after reaching a maximum value as shown by the dashed line. In the saturation regime, if the averaged electron velocity is not significantly reduced, the amplification power would simultaneously vary linearly with the interaction length as shown by the solid line.
Spatial variation of the power amplification . The smallsignal gain is depicted by the dotted line, whereas the power amplification increases in the form of the exponential function. In the case of the saturation regime, the power amplification increases almost linearly with the normalized interaction length and decreases after reaching a maximum value as shown by the dashed line. In the saturation regime, if the averaged electron velocity is not significantly reduced, the amplification power would simultaneously vary linearly with the interaction length as shown by the solid line.
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