for high-gain FELs. It consists of a 20 MeV integrated photoinjector capable of 5 nC bunch charge at a repetition rate of 108 MHz, or 0.5 ampere average current over 10 μs.

At Argonne National Laboratory, the Argonne Wakefield Accelerator with an L-band high-Q injector has demonstrated the world’s highest charge per bunch. In single bunch operation, the system has demonstrated a micropulse charge that is tunable between 1 nC and 100 nC, a current of 10 kA, an energy of 15 MeV (using one 30 MW klystron), and an energy of 30 MeV (by adding a second 30 MW klystron). In bunch train operation, the system has demonstrated four bunches × 50 nC and 64 bunches × 50 nC, 50 ns long (needs a cesium telluride cathode), and a beam power of 1.5 GW.

It is important to achieve the 2 to 3 percent extraction mentioned above; otherwise the recirculating beam current will have to be increased further beyond the already impressive 1 A. FEL simulation and experiments indicate that more than 2 percent is possible with sufficiently good electron beam quality. This extraction would require something around a ~20-period undulator for the oscillator design and a ~200-period undulator for the amplifier design. Both the oscillator and the amplifier undulators can be tapered to increase extraction.1,2,3 In fact, the amplifier must be tapered to reach the 2 percent required extraction. The untapered amplifier will only achieve about 0.5 percent extraction (both simulation and experiment show this) and would therefore require substantially more average beam current to reach the same laser power levels.

The motivation for tapering to increase extraction can be seen in the resonance condition, which has already been described. As the average electron beam energy decreases, reducing the Lorentz factor in the denominator of the resonance condition, electrons go out of resonance, beginning the saturation process in strong optical fields. A “trick” to extend resonance is to increase the undulator gap, reducing the undulator magnetic field and hence the value of the undulator parameter, K, in the numerator of the resonance condition. The tapering trick has been demonstrated in a number of experiments and many simulations. Often, the tapering does not start until about halfway down the undulator, thereby allowing the FEL to reach strong optical fields near saturation in the first half.

While tapering can be used in the amplifier to increase the extraction to the 2-3 percent level, there is also an induced energy spread, as in the untapered case. This induced energy spread cannot be excessive and is considered to be limited to about 10-15 percent because of two important processes in the recirculating FEL. First, bending an electron beam around a 180-degree arc is difficult with a beam containing a large range of energies, and hence bending angles in the dipole magnetic field. The second process is the deceleration of an electron beam with a large energy spread. A fractional momentum spread of 10 percent in the 100 MeV beam becomes roughly 200 percent when the beam is decelerated to the injection energy, typically 5 MeV. Such a large momentum spread can exceed the acceptance of the downstream beam line, causing particle loss. Further, the large energy spread on the decelerating beam causes the longitudinal phase space to be curved, as the particles in the beam occupy a large range of the RF phases of the cavity fields. Beyond a certain limit of the energy spread, these nonlinear distortions of the phase space can cause some of the low-energy particles to get lost in the last RF cavities and not arrive at the exit of the linac. Experience at the Jefferson Laboratory FELs has shown that, for proper energy recovery, the nonlinear distortions must be corrected. So in the Jefferson Laboratory FEL, the optics of the recirculator are set up to impart not only a linear position-energy correlation, but also a quadratic dependence of the fractional momentum spread on the longitudinal position upstream from the linac, which compensates the RF-induced curvature. At the Jefferson Laboratory FEL, these corrections are done with sextupole magnets. The details of the process are too lengthy to include in this report, but are described in Piot et al.4

Optical sidebands can be generated in high-peak-power FELs. The sideband power can be significant and is a second laser line about ~1/N, or ~1 percent away from the fundamental frequency on the long-wavelength side. It is caused by the mixing of the oscillation frequency of electrons trapped in strong optical fields with the fundamental frequency of the FEL. This sideband generation has been observed in experiments and simulations and is the result of strong optical fields at saturations in each micropulse, not high average power.

Both the FEL oscillator and the amplifier may experience sideband generation for the parameters considered in this report. Their presence in the laser beam could be seriously detrimental to propagation through the atmosphere, since windows of low absorption tend to be narrow. If the fundamental FEL wavelength was in such a window, the sideband would experience significant absorption, leading to thermal blooming. Fortunately, the sideband instability can be controlled in a few ways. First, tapering the amplifier, or even the oscillator, in FEL configurations tends

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