Quasi-linear analysis of Smith-Purcell free-electron amplifier
Calculations are presented of the scattering of an electromagnetic wave from a periodic structure above which flows an electron beam. The reflected fields are computed and found to comprise two separate contributions: 1) the reflection in the homogeneous case (without the beam) and 2) the contribution of the beam. Both are shown to depend upon the structure by means of its reflection properties, as expressed by a reflection matrix. Moreover, the beam contribution is shown to be exponentially dependent on the longitudinal position. It also includes the exponential decay, which depends upon the distance between the beam and the structure and is a characteristic of Smith-Purcell devices. Expressions for the local and global gains are obtained. The local gain is found to be proportional to the first velocity derivative of the electron distribution function. Considerations of nonlinear effects introduce spatial dependence to the expression of the local gain. This dependence is determined by a nonlinear diffusion equation. Moreover, the gain in the nonlinear regime is found to depend not only on the first velocity derivative of the distribution function but also on the second velocity derivative.
- Research Organization:
- Dept. of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000 (IL)
- OSTI ID:
- 6989160
- Journal Information:
- IEEE Trans. Plasma Sci.; (United States), Vol. 16:2
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
42 ENGINEERING
ELECTROMAGNETIC PULSES
SCATTERING
ELECTRON BEAMS
AMPLIFIERS
COMPUTER CALCULATIONS
DIFFUSION
GAIN
MATRICES
NONLINEAR PROBLEMS
PHASE VELOCITY
QUASILINEAR PROBLEMS
AMPLIFICATION
BEAMS
ELECTROMAGNETIC RADIATION
ELECTRONIC EQUIPMENT
EQUIPMENT
LEPTON BEAMS
PARTICLE BEAMS
PULSES
RADIATIONS
VELOCITY
656003* - Condensed Matter Physics- Interactions between Beams & Condensed Matter- (1987-)
420800 - Engineering- Electronic Circuits & Devices- (-1989)