X-Ray Free-Electron Lasers and Self-Amplified Spontaneous Emission (SASE)

Early experiments on Raman free-electron masers were often based upon self-amplified spontaneous emission (SASE) where the electromagnetic field grew from shot noise in a single pass through the wiggler; however, the term often used for this configuration at the time was super-radiant amplifier. These experiments often made use of pulse line accelerators, modulators, or induction linacs that produced relatively long-pulse (10 nsec through 1 μsec), intense (1–10 kA) electron beams with relatively low energies (less than about 1–2 MeV), and operated at frequencies below about 100 GHz; hence, these experiments operated at millimeter wavelengths and longer. While these electron sources were typically low repetition rate accelerators, they were capable of producing bunch charges exceeding 300 μC; hence, the electromagnetic field could grow from noise to saturation in wigglers of 1–2 m in length. At the present time, SASE free-electron lasers are commonly used to generate short wavelengths where either lasers that can provide a seed pulse do not exist or where there are no high-reflectivity mirrors to create an optical resonator. In particular, x-ray free-electron lasers based on SASE configurations are becoming common. These free-electron lasers are driven by radio frequency (rf) linacs that produce high energy/short pulse electron beams. An intermediate SASE free-electron laser, which illuminated the principal characteristics of SASE, namely, large fluctuations in the pulse energy and spectrum from shot to shot, was conducted at the Massachusetts Institute of Technology. This experiment was discussed in Chap. 5 and operated at wavelengths in the neighborhood of 500–600 μm, so that the wavelengths excited in this experiment were much shorter than the transverse extent of the drift tube. Hence, the electromagnetic fields that were generated were transitional between the guided modes that existed in the long wavelength Raman free-electron masers and the optical modes that arise in the more recent shot wavelength rf linac-based SASE free-electron lasers. The development of laser-driven photocathodes and their application in free-electron lasers for use in either rf or dc electron guns to produce high brightness electron bunches combined with rf linacs to accelerate the electrons to high energies has permitted free-electron lasers to operate at wavelengths from the infrared through x-rays. This development has been crucial to the application of SASE free-electron lasers to the short wavelength range of the spectrum where high-reflectivity mirrors or seed lasers do not exist; in particular, to the development of UV and x-ray free-electron lasers. In this chapter, we discuss a number of issues related to the theory and simulation of x-ray free-electron lasers. We begin with a presentation of the parameterization of the interaction first presented by Ming Xie, which includes formulae for the equivalent noise power generated by incoherent synchrotron radiation, the gain (or exponentiation) length of the interaction in the undulators, and the saturation length and efficiency. These formulae have been largely validated by comparison with experiments and simulations and are in widespread use in the community. Based upon the presentation of the incoherent undulator radiation in Chap. 2 , we derive the Ming Xie’s formula for the equivalent noise power. This is followed by a discussion of electron bunch compression, which is often necessary to achieve the high peak currents required for the operation of x-ray free-electron lasers. Since most current x-ray free-electron lasers rely upon SASE, we next present a comparison between SASE and the MOPA interaction. We next discuss the phase match between the optical field and the electrons over the course of the long undulator lines in x-ray free-electron lasers. Since x-ray free-electron lasers are based upon a long line of relatively short undulators separated by drift spaces, which contain quadrupoles to provide strong focusing of the electron beam, it is important to understand and optimize the phase match between the optical field and the electron through these drift spaces. With these fundamental concepts in hand, we then describe simulations of the Linac Coherent Light Source (LCLS) at the Stanford Linear Accelerator Center and the Sorgente Pulsata ed. Amplificata di Radiazione Coerente (SPARC) conducted at the ENEA Frascati laboratory. This is followed by a treatment of enhanced harmonic generation in x-ray free-electron lasers. The frontiers of x-ray free-electron laser continue to advance, and interest is growing in the generation of terawatt power levels. In this chapter, we discuss several approaches to the generation of TW x-ray pulses and show that the production of electron beams with extremely high current densities is a necessary precondition to TW generation. Finally, since intense electron beams are necessary for x-ray free-electron lasers, we present a discussion of the effect of resistive wall wakefields on the free-electron laser interaction.