The Physics and Properties of Free-Electron Lasers

We present an introduction to the operating principles of free-electron lasers, discussing the amplification process, and the requirements on the electron beam necessary to achieve desired performance. INTRODUCTION In the storage rings of synchrotron radiation facilities, the electrons are radiating incoherently [1,2]. Since there is no multi-particle coherence, the radiated intensity is linearly proportional to the number of electrons Ne. If the electrons in a beam are spatially bunched on the scale of the radiation wavelength [3,4], coherent radiation with intensity proportional to Ne will be emitted. Since Ne can be very large, coherent emission offers the potential of greatly enhancing the intensity. The technical challenge is to produce the required bunching on the scale of the radiation wavelength. A task that increases in difficulty as the wavelength is decreased. To obtain coherent emission at short wavelengths, one must develop methods to bunch the electron beam utilizing the radiation. One approach that has already been successfully applied down to the vacuum ultraviolet is the free electron laser (FEL). The FEL [5] is based on a resonant interaction between an electromagnetic wave and an electron beam traveling along the axis of an undulator magnet. The periodic undulator magnetic field produces a transverse component of the electron velocity that couples the energy of the electron to that of the wave. Under general conditions this coupling will merely result in a shifting of energy back and forth between the electron beam and the radiation. However, in resonance, there can be sustained energy transfer from the electrons to the wave. FELs are reviewed in refs. [6-8]. In designing an FEL, one must decide on the type of electron accelerator to be used: e.g. storage ring [9], room temperature linac [10], or superconducting linac [11]. Storage rings provide very high stability and continuous operation; however, the FEL action perturbs the electron beam, thus limiting performance. The development of photocathode RF electron guns [12,13] has made linacs attractive as drivers for FELs. They can produce high peak current and small normalized emittance. The microbunch pulse length in photoinjectors is typically on the order of 10 ps, and bunch compression can be used to reduce the pulse length down to the vicinity of 100 fs. The macropulse structure in room temperature linacs consists of pulse trains separated FIGURE 1. FEL configurations: oscillator; self-amplified spontaneous-emission; high-gain harmonic generation. by dead time. Superconducting linacs can provide continuous-wave beams and very high stability. A fundamental consideration in FEL design is whether to use a high-Q optical cavity, or to operate the FEL as a high-gain single-pass amplifier (see Fig. 1). An optical cavity has many advantages: it requires less gain per pass, simplifying the undulator, and it facilitates the production of narrow bandwidth output radiation. However, it is difficult to utilize optical cavities at short wavelengths because one requires high quality mirrors resistant to radiation damage. For this reason, present effort in the design of short wavelength FELs, from the VUV down to hard x-rays, is predominantly focused on using single pass FEL amplifiers employing long undulators [10]. UNDULATOR RADIATION Let us begin our discussion by considering an electron traversing an undulator magnet [1,2,14]. For the purposes of illustrating the basic principles, it is convenient for us to consider the undulator to be helical, resulting in a constant longitudinal velocity (along the undulator axis, z-direction)       + − = 2 2 * 2 1 1 γ K c v . (1) The transverse velocity is O S C I L L A T O R S I N G L E P A S S F E L