made in optics, both in the FEL program and in other (especially chemical) laser programs. Unfortunately, when the SDI program ended in the early 1990s, much of the progress in optics for FELs was lost. Industrial experience with high-power coatings atrophied, and understanding of relevant optical architecture was lost. On the positive side, injector development continued for other FEL programs, and substantial progress has been made in superconducting accelerators, so that these are now the preferred technology. Thus the Navy proposal to construct a high-power FEL is based on a long history of progress. This history includes both significant successes, such as the 14 kW continuous-wave (cw) FEL at the Thomas Jefferson National Accelerator Facility, known as the Jefferson Laboratory, or JLab, and enduring challenges in injectors and optics.

Table 2.1 lists demonstrated relativistic FELs in 2008. A location or institution, followed by the FEL’s name in parentheses, identifies each FEL. (In the location/name column, KAERI is the Korea Atomic Energy Research Institute, Nihon refers to Nihon University in Japan, RIKEN is a natural sciences research institute in Japan, and DESY is the German Electron-Synchrotron Research Center.) The first column following the FEL name lists the operating wavelength, λ, or the wavelength range. The longer wavelengths are listed at the top with short x-ray wavelength FELs at the bottom of the table. The large range of operating wavelengths, seven orders of magnitude, indicates the flexible design characteristics of the FEL mechanism. In the next column, σz is the electron pulse length divided by the speed of light, c, and ranges from 25 ns to short subpicosecond pulse timescales. The expected optical pulse length in an FEL oscillator can be three to five times shorter or longer than the electron pulse depending on the optical cavity Q, the FEL desynchronism, and the FEL gain. The optical pulse can be up to 10 times shorter in the high-gain FEL amplifier. Also, if the FEL is in an electron storage ring, the optical pulse is typically much shorter than the electron pulse. Most FEL oscillators produce an optical spectrum that is Fourier transform limited by the optical pulse length.

The electron beam energy, E, and peak current, I, are listed in the third and fourth columns, respectively. The next three columns list the number of undulator periods, N, the undulator wavelength, λ0, and the root mean square (rms) undulator parameter, K = eBλ0/2πmc2 (cgs units), where e is the electron charge magnitude, B is the rms undulator field strength, and m is the electron mass. For an FEL klystron undulator, there are two undulator sections as listed in the N column; for example, 2 × 33. The FEL klystron configuration uses two undulators separated by a drift space or dispersive section in order to increase the FEL gain in weak optical fields, but at the expense of extraction in strong optical fields. Some undulators used for harmonic generation have multiple sections with varying N, λ0, and K values as shown. Most undulators are configured to have linear polarization. Some FELs operate at a range of wavelengths by varying the undulator magnetic field, as indicated in the table by a range of values for K. The FEL resonance condition, λ = λ0(1 + K2)/2γ2, provides a relationship that can be used to relate the fundamental wavelength, λ, to K, λ0, and E = (γ − 1)mc2, where γ is the relativistic Lorentz factor. Some FELs achieve shorter wavelengths by using harmonics. The last column in Table 2.1 lists the accelerator types and FEL types, using the abbreviations defined at the bottom of the table.

For the conventional oscillator, the peak optical power can be estimated by the fraction of the electron beam peak power that spans the undulator spectral bandwidth, 1/(2N), or P ≈ EI/(8eN). For the FEL using a storage ring, the optical power causing saturation is substantially less than this estimate and depends on ring properties. For the high-gain FEL amplifier, the optical power at saturation can be substantially greater than 1/(2N). The average FEL power is determined by the duty cycle, or spacing between the electron micropulses, and is typically many orders of magnitude lower than the peak power. The infrared FEL at the Jefferson Laboratory has now reached an average power of 14 kW with the recovery of the electron beam energy in superconducting accelerator cavities.

In the FEL oscillator, the optical mode that best couples to the electron beam in an undulator of length L = Nλ0 has a Rayleigh length z0 ≈ L/121/2 and a mode waist radius of w0 ≈ N1/2γλ/π. The FEL optical mode typically has more than 90 percent of the power in the fundamental mode described by these parameters.

In 2008, the DESY FLASH FEL reached the shortest wavelength ever for an FEL, λ ≈ 6.5 nm. There was one other new lasing at Kyoto (KU-FEL) at λ ≈ 11-14 μm.

Countries worldwide participate in FEL development as a tool for scientific research. More than 10 countries from Europe, North America, and Asia are represented, with more than half of the FELs located in the United States and Japan.



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