Page 111 - High Power Laser Handbook

80 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 81

The gain is provided over a fractional bandwidth given by 1/2N;
as opposed to more conventional lasers, all the electron beam power
can, in principle, be extracted from a narrow line within this band-
width. If the input electron beam’s energy spread is greater than or of
the same order as this value, then the gain will be reduced; electrons
whose energy falls outside this range will not significantly partici-
pate in the interaction.
Because the gain is limited to the 1/2N bandwidth, it is clear that
as electrons give up energy, they eventually fall out of the resonance
condition, as defined in Eq. (4.1). This is where the process stops unless
something is done, such as changing the wiggler parameters as a
function of distance along the wiggler, “tapering” the field strength
to lower values to keep the (now-lower) energy electrons in resonance
with the same wavelength. This was the approach initially investi-
gated during the Strategic Defense Initiative (SDI) era for increasing
3,4
the performance of high-power FELs. The physics of this approach
has been well demonstrated (although the product of the gain and
efficiency for a given FEL system is constant, so that at some point,
the gain is so low that optical losses prevent extraction of any more
power). From a practical systems point of view, such an approach
may not be advantageous, because the exhaust electron beam’s
energy spread also increases, which may render impractical the abil-
ity to recover the electron beam energy (see below).
Typically 50 or more wiggler periods are required to get sufficient
gain such that extraction of 1 percent of the electron beam power is a
reasonable expectation (1/2N ~ 0.01). The 99 percent of beam power
that remains leaves the system at nearly the speed of light; because
the lasing medium is in a vacuum, little distortion of the optical mode
can occur. Optical mode distortion due to thermal effects in the lasing
medium is a bane of conventional high-power, solid-state lasers, but
it does not occur in FELs. However, uncompensated thermal distor-
tion on FEL oscillator mirrors can lead to mode degradation, loss of
gain, and so on. In very high-gain systems, the needle-thin electron
beam only provides gain on axis, effectively providing a mode filter
to keep the output at high-beam quality.
Not all of the electrons give up their energy equally; some are
left out of the extraction process by virtue of having started at the
wrong optical phase relative to the ponderomotive wave. As a con-
sequence, these electrons remain at the initial energy or may even
be slightly accelerated. As the process of energy extraction proceeds
down the wiggler, the electron energy spread gradually increases.
Experimentally it is observed that extrema electrons may have a
total energy spread up to six times the average energy loss. For this
5
reason, once having lased, the electron bunch beam quality is usu-
ally unsuitable to permit reacceleration and reinsertion into the FEL
a second time.