Free Electron Laser (IFEL)
An inverse free electron laser (IFEL) - operates by sending
an electron beam (e-beam) and laser beam simultaneously through
a device called an undulator or wiggler. This is illustrated in Fig. 1. The undulator consists of two arrays of permanent
magnets facing each other with the magnet poles alternating as depicted
in Fig. 1. This creates
an alternating magnetic field within the gap separating the magnet
arrays. A relativistic electron traveling through the
gap follows a sinusoidal trajectory, i.e., wiggles. The laser beam electric field (i.e., polarization)
is in the plane of the electron wiggle and transverse to the electron
mean trajectory. Thus, as
the electron moves at an angle with respect to its mean trajectory,
a component of the electric field will exert a force on the electron. This force can either accelerate or decelerate
the electron depending on the direction of the electric field with
respect to the electron trajectory.
1. Basic geometry for inverse free electron
achieve net energy exchange between the laser field and the electrons,
a resonance condition must be satisfied so that the electron wiggle
matches the period of the laser oscillation.
This resonance condition is given by,
g is the Lorentz factor,
is the undulator period, ll is the laser wavelength, and K
is the so-called wiggler parameter equal to eB0lw/2pmc,
(e is the electron charge, B0 is the peak
magnetic field, m is the mass of an electron, and c
is the speed of light).
2 shows one of the magnet arrays used in the STELLA undulator. It consists of NdFeB magnets sandwiched between
iron poles. The undulator
period is 3.3 cm and the total length of the undulator is 33 cm.
2. Photograph of one of the magnet arrays used
in the STELLA undulator
important modification of the undulator design is to taper the gap
 such that the gap separation decreases linearly from the entrance
to the exit of the device. In STELLA the gap is 11% smaller at the exit
end than at the entrance. This
increases the magnet field strength gradually along the undulator
in order to maintain the resonance condition as the electrons continuously
gain energy traveling through the device.
In fact, the amount of energy gain is now determined primarily
by the amount of energy taper rather than the amount of laser intensity. For the STELLA undulators, the 11% gap taper corresponds to an energy
taper of 12%. Put another
way, there is a minimum laser intensity needed to drive a tapered
undulator. Once this minimum has been reached, then the
amount of energy gain remains relatively fixed as the laser intensity
is possible to obtain energy gains higher than the taper by controlling
the amount of synchrotron oscillations occurring while the electrons
are trapped within the laser field ponderomotive potential well
inside the undulator. This is illustrated in Fig. 3, which shows
the electron energy-phase distribution exiting the accelerator undulator
for a case where the laser intensity is near threshold. Here the chicane field has been adjusted to place the bunched electrons
within the range of phases that experience trapping and acceleration
by the tapered-undulator IFEL.
The fish-shaped region outlined in red schematically represents
the initial position of the laser field accelerating ponderomotive
potential well (“bucket”). The IFEL interaction causes this bucket to
sweep upward in phase space as indicated by the arrows. The fish-shaped
region in blue indicates the final position of the bucket at the
end of the tapered undulator.
3. Example of energy-phase distribution at output
of accelerator IFEL, which shows schematically how electrons
can gain more energy than the amount of energy taper.
electrons start their process of acceleration by entering the undulator
at an initial energy near the bottom of the bucket (see “Start”
in Fig. 3). They then sweep
up one-half a synchrotron oscillation as they travel through the
undulator so that they end up near the top of the fish-shaped region
when they reach the exit of the undulator (see “End” in Fig. 3).
This process permits the electrons to gain even more energy
than the amount of energy taper.
For STELLA this resulted in a peak energy gain of 20% for
a 12% energy taper.
R. B. Palmer, J. Appl. Phys. 43, 3014 (1972).
 E. D. Courant, C. Pellegrini, and W.
Zakowicz, Phys. Rev. A 32, 2813 (1985).
N. M. Kroll, P. L. Morton, and M. Rosenbluth, IEEE J. Quant.
Elect., QE-17, 1436 (1981).