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Inverse Free Electron Laser (IFEL)

An inverse free electron laser (IFEL) [1]-[2] 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.

 Figure 1.  Basic geometry for inverse free electron laser interaction.

To 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,

,

where g is the Lorentz factor, lw 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).

Figure 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.

 Figure 2.  Photograph of one of the magnet arrays used in the STELLA undulator

An important modification of the undulator design is to taper the gap [3] 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 increases.

It 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.

 Figure 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.

The 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.

References:

[1]     R. B. Palmer, J. Appl. Phys. 43, 3014 (1972).

[2]     E. D. Courant, C. Pellegrini, and W. Zakowicz, Phys. Rev. A 32, 2813 (1985).

[3]     N. M. Kroll, P. L. Morton, and M. Rosenbluth, IEEE J. Quant. Elect., QE-17, 1436 (1981).