# Advanced Scheme to Generate MHz, Fully Coherent FEL Pulses at nm Wavelength
## 1 Introduction  
Free-electron lasers (FELs) have been making enormous improvements during the past decades, delivering high-brightness radiation to users all over the world at wavelengths from mm to hard x-rays, covering a wide range of experiments. At the same time, many experiments, for instance, those that depend on spectroscopic techniques to resolve electronic structure, require full coherence and high statistics, which can only be fulfilled with fully coherent radiation at high repetition rate. These two requirements are becoming important for scientific applications and are driving new FEL developments. Currently, superconducting accelerators are capable of providing thousands of bunches per second at MHz repetition rate. This potential is currently exploited in self-amplified spontaneous emission (SASE) mode [1]. However, in this case, the FEL process starts from random fluctuations of the electron beam charge density distribution [2] leading to a limited temporal coherence, which impacts the peak brightness. The longitudinal coherence can be improved by self-seeding [3, 4] and single-mode [5, 6] lasing schemes which are based on the SASE process. As a consequence, the stochastic nature of SASE is imprinted on the final FEL pulse as intensity fluctuations even though improved longitudinal coherence is achieved. At wavelengths in the nanometer range and longer, alternatives to generate fully coherent radiation are based on external seeding. In this case, a seed laser of typicallyseveral tens MW of power is used to prepare an initial signal for a final FEL amplifier, usually tuned at a harmonic of its wavelength, thus imprinting its coherence properties upon the output FEL pulse. Many interesting experiments and methods are allowed due to the unique properties of seed radiation [7; 8; 9; 10]. Two chief examples of external seeding schemes are the high-gain harmonic generation (HGHG) [11; 12] and the echo-enabled harmonic generation (EEHG) [13; 14; 15]. As the harmonic conversion of seeding schemes is limited, it is advantageous to use short wavelength seed lasers. Currently, ultraviolet (UV) seed lasers are the most suitable candidates for such setups [14; 15; 16]. However, the requirements put on these laser systems in terms of peak power limit their repetition rate, which is usually in the kHz regime. As seeded radiation pulses can be generated at a maximum repetition rate defined by the seed laser repetition rate, not all electron bunches generated in superconducting accelerators can be seeded. This leads to high peak brightness FEL pulses, but limited average flux, in contrast to the number of electron bunches available. In order to address this limitation, alternatives have been recently studied to increase the repetition rate of seeding schemes by reducing the seed laser power requirements [17; 18], and in this paper, we propose an oscillator-amplifier setup. Here, we review and further discuss a scheme which can generate FEL pulses of both high peak brightness, compared to SASE, and of high average flux compared to standard seeding schemes, by generating high repetition rate seeded radiation pulses [19; 20; 21; 22]. In this scheme, an FEL oscillator is employed and acts as a feedback system which recirculates a seed pulse, and seeds the electron bunches at high repetition rate. In this case, one may either use a low repetition rate seed laser, or start from shot noise. Starting from shot noise lets us be independent of seed laser systems both in terms of repetition rate and wavelength. Oscillator FELs are a well-studied topic, and their technology has been established for a long time. There is a wide range of oscillator FELs that were operated during the past decades, and detailed simulation studies were performed almost two decades ago [23; 24; 25]. These studies led, more recently, to the development of other ideas such as XFELOs [26] and Regenerative Amplifier Free-Electron Lasers (RAFELs) [27; 28; 29; 30] (high-gain oscillators).