Page 112 - High Power Laser Handbook

82 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 83

The electrons have one other potentially limiting physical param-
eter that is analogous to optical beam quality of photon beams and is
called emittance. The emittance is defined as the product of the beam
width and the divergence. The normalized emittance—that is, the
emittance times g—is a conserved quantity. In other words, after ini-
tial acceleration, the normalized emittance may only degrade or, at
best, remain the same unless acted on by nonconservative forces. If
the electron trajectories point outside the optical mode, then it is obvi-
ous that little gain could occur. The normalized emittance e must lie
n
within l /4p for gain to remain undegraded. Another way of looking
s
at this is to realize that Liouville’s theorem (and the second law of
thermodynamics) says that it is not possible to make a brighter opti-
cal beam than the electron beam from which it is being made. The
power out of the FEL is simply the electron beam power (voltage
E times current <I>) times the FEL extraction efficiency.

4.2.4 Practical Considerations
Having described the FEL interaction, it should be recognized that
the implementation of such a system can be either as an oscillator or
as an amplifier, with each having attendant features and drawbacks.
An oscillator has the following advantages: it does not require a seed
laser, the required wigglers are short, and the peak currents required
are modest. The oscillator’s tunability is limited primarily by the mir-
rors and coatings used. High-power mirrors typically have 10 percent
bandwidth due to their quarter-wave stack of dielectric reflection
coatings. One mirror can be made partially transmissive to outcouple
the light. Typically the gain at saturation is kept low (~20 percent),
because for a given FEL, the product of the gain and efficiency is a
constant. The small signal gain needs to be at least three times the
gain at saturation for efficient energy extraction.
The price one pays for such advantages is dealing with the issue
6
of thermal loading on the mirrors. In addition, the alignment and
figure tolerances of such an optical cavity are quite tight. Because the
optical mode must match the electron beam in order to achieve high
gain and energy extraction, the optical cavity, especially for high-
power operation, tends to be long with a tight central core. The FEL
interaction naturally produces harmonics at a power approximately
–H
10 of the fundamental, where H is the harmonic number. If low-
7
order harmonics lie in the ultraviolet (UV) range, then care must be
taken that the mirror coatings can live under the UV fluence.
Although an amplifier configuration does away with having to
deal with high flux on mirrors (except the output mirror), it does
necessitate a seed laser and significantly longer wigglers. In wave-
length regimes where mirrors do not exist, operating in this manner is
the only option. Typically such an FEL would provide a gain of 100 or
more, and the electron beam–wiggler combination must provide for