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Title: Analysis of Smith-Purcell free-electron lasers


No abstract prepared.

Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States). Advanced Photon Source (APS)
Sponsoring Org.:
OSTI Identifier:
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print); Journal Volume: 73; Journal Issue: 2; Related Information: Feb. 2006
Country of Publication:
United States

Citation Formats

Kumar, Vinit, and Kim, Kwang-Je. Analysis of Smith-Purcell free-electron lasers. United States: N. p., 2006. Web. doi:10.1103/PhysRevE.73.026501.
Kumar, Vinit, & Kim, Kwang-Je. Analysis of Smith-Purcell free-electron lasers. United States. doi:10.1103/PhysRevE.73.026501.
Kumar, Vinit, and Kim, Kwang-Je. Wed . "Analysis of Smith-Purcell free-electron lasers". United States. doi:10.1103/PhysRevE.73.026501.
title = {Analysis of Smith-Purcell free-electron lasers},
author = {Kumar, Vinit and Kim, Kwang-Je},
abstractNote = {No abstract prepared.},
doi = {10.1103/PhysRevE.73.026501},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},
number = 2,
volume = 73,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2006},
month = {Wed Feb 01 00:00:00 EST 2006}
  • We present an analysis of the beam dynamics in a Smith-Purcell free-electron laser (FEL). In this system, an electron beam interacts resonantly with a copropagating surface electromagnetic mode near the grating surface. The surface mode arises as a singularity in the frequency dependence of the reflection matrix. Since the surface mode is confined very close to the grating surface, the interaction is significant only if the electrons are moving very close to the grating surface. The group velocity of the surface mode resonantly interacting with a low-energy electron beam is in the direction opposite to the electron beam. The Smith-Purcellmore » FEL is therefore a backward wave oscillator in which, if the beam current exceeds a certain threshold known as start current, the optical intensity grows to saturation even if no mirrors are employed for feedback. We derive the coupled Maxwell-Lorentz equations for describing the interaction between the surface mode and the electron beam, starting from the slowly varying approximation and the singularity in the reflection matrix. In the linear regime, we derive an analytic expression for the start current and calculate the growth rate of optical power in time. The analysis is extended to the nonlinear regime by performing a one-dimensional time-dependent numerical simulation. Results of our numerical calculation compare well with the analytic calculation in the linear regime and show saturation behavior in the nonlinear regime. We find that a significant amount of power grows in the surface mode due to this interaction. Several ways to outcouple this power to freely propagating modes are discussed.« less
  • Coupled-mode approach and electron Bloch equations are combined to calculate the gain of free-electron lasers using the Smith-Purcell effect in the gain quantum model. The possibility of increasing gain by changing the spatial frequency of the grating is studied.
  • The theory of linear and stimulated free-electron lasers using the Smith-Purcell effect is presented. These lasers depend upon the resonant interaction of an electron beam with the longitudinal field of a surface-harmonic wave on a diffraction grating. Detailed design criteria for the linear Smith-Purcell-effect laser are determined. Numerical estimates show that infrared lasers are feasible at beam currents smaller than 1 A and that single-mode operation may be achieved. Saturation estimates determine the power output in the range 10/sup 2/ W. An expression for the gain of the stimulated Smith-Purcell laser is derived. The frequency up-conversion factor for the stimulatedmore » interaction may be very large. Its possible use as a soft x-ray laser is limited by the available intensity of the pump wave.« less
  • This letter reports a theory to calculate the growth rate and start current of a Smith-Purcell free-electron laser, which is a promising radiation source in the terahertz domain. A two-dimensional model was used to investigate the interaction between a sheet electron beam and the surface wave above a lamellar grating. After deriving the growth rate from the dispersion equation, the start current was carefully estimated by considering the power flow above the grating. The agreement between the predictions of our theory and the results from the particle-in-cell simulations is acceptable.
  • 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 structuremore » 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.« less