Page 108 - High Power Laser Handbook

78 G a s , C h e m i c a l , a n d F r e e - E l e c t r o n L a s e r s High-Power Fr ee-Electr on Lasers 79

Output
mirror
Wiggler magnet
array
Electron
dump
y
Electron
accelerator x z

λ w
Total
reflector
λ r ∝ λ w 1 Lorentz transform
2γ 2 x 1 Doppler shift
Figure 4.1 The free-electron laser interaction.

rest mass of 0.511 mega-electronvolts (MeV) (Fig. 4.1). In response to
this transverse acceleration, the electrons radiate in a dipole pattern.
Transformed back into the rest frame, this becomes Doppler shifted
by another factor of g and folded into a forward-directed 1/g cone of
radiation. This dipole radiation becomes the initial spontaneous emis-
sion from the laser.
Because the electrons are uniformly (at optical wavelength scales)
distributed within the bunch, the initial light is relatively broadband
and incoherent for wavelengths shorter than the bunch length. As the
process continues, however, something remarkable happens. The
electric field of the emitted photons when crossed with the wiggler
field causes the electron density to be modulated at the optical wave-
length. The once-smooth distribution of electrons becomes a set of
microbunches radiating together in phase, thus establishing coher-
ence in the emitted optical field. The bandwidth of the optical radia-
tion narrows, the optical mode becomes well defined, and significant
gain and energy extraction from the electrons can occur. 1,2
4.2.2 Wavelength
The longitudinal bunching of electron motion can easily be derived
from the equations of motion and the combined electromagnetic fields.
However, it is more important to understand the physical principles at
work; with that in mind, realize that the photon field constitutes a travel-
ing wave of ponderomotive force. Electrons can fall down into this mov-
ing potential well and give up energy to the electromagnetic wave.