Coherent radiation in an undulator
This paper is concerned with the synchrotron radiation from an undulating electron beam in a rectangular waveguide. The analysis is based on the dyadic Green's function approach to solve Maxwell's equations in terms of the vector potential. It is shown analytically and numerically that the radiated energy spectrum may differ significantly from the free space results when the undulator length divided by the Lorentz factor of the electron beam is larger than the transverse size of the waveguide. Then, the appearance of the spectrum is changed into a small number of sharp peaks, each corresponding to an excited waveguide mode. The undulator radiation is identified with the wake field in beam instabilities. The concepts of wake function and impedance are introduced to formulate the present problem in the same manner as the beam instability problem, so that the accumulated techniques of the latter can be applied. It is shown that the obtained impedances satisfy the Panofsky-Wenzel theorem and other properties inevitable for wake fields. 4 refs., 2 figs.
- Research Organization:
- Lawrence Berkeley Lab., CA (USA)
- Sponsoring Organization:
- DOE/ER
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 6256926
- Report Number(s):
- LBL-29981; CONF-9009292-4; ON: DE91007744; TRN: 91-004676
- Resource Relation:
- Conference: 4. ICFA beam dynamics workshop, Tokyo (Japan), 22-29 Sep 1990
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ONDULATOR RADIATION
MAXWELL EQUATIONS
ANALYTICAL SOLUTION
COHERENT RADIATION
ELECTRIC IMPEDANCE
ELECTRON BEAMS
ENERGY SPECTRA
GREEN FUNCTION
NUMERICAL SOLUTION
POYNTING THEOREM
WAVE EQUATIONS
WAVEGUIDES
WIGGLER MAGNETS
BEAMS
BREMSSTRAHLUNG
DIFFERENTIAL EQUATIONS
ELECTRICAL EQUIPMENT
ELECTROMAGNETIC RADIATION
ELECTROMAGNETS
EQUATIONS
EQUIPMENT
FUNCTIONS
IMPEDANCE
LEPTON BEAMS
MAGNETS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE BEAMS
RADIATIONS
SPECTRA
430200* - Particle Accelerators- Beam Dynamics
Field Calculations
& Ion Optics